Magnetometry method and apparatus

Abstract

Discloses is a magnetometer and a method of carrying out magnetometry. A sensor element comprising a sheet of a 2D layered material having a photon-emitting spin-active defect is provided. The defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field. An optically detected magnetic resonance measurement is conducted on the sensor element by subjecting the sensor element to optical excitation and photoluminescence detection whilst a variable frequency microwave signal is applied, the microwave signal causing transitions between the spin triplet state spin sublevels. The photoluminescence detection comprises: detecting a change in photoluminescence signal when the microwave signal is resonant with a transition between the spin triplet state spin sublevels; and determining a characteristic of a magnetic field based on the detected photoluminescence signals.

Description

[0001] MAGNETOMETRY METHOD AND APPARATUS

[0002] Related Application

[0003] The present case claims priority to, and the benefit of, GB 2409550.7 filed on 2 July 2024 (02.07.2024), the contents of which are incorporated by reference in their entirety.

[0004] The project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 884745).

[0005] Field of the Invention

[0006] The present invention relates to a method for performing magnetometry, a device and apparatus for performing magnetometry and a method for manufacturing a device for performing magnetometry. The invention relates particularly, although not necessarily exclusively, to using transitions of a spin active defect in a sheet of 2D layered material between spin sublevels of a spin triplet state to determine a characteristic of a magnetic field.

[0007] Background

[0008] To date, nanoscale quantum sensing of magnetic fields has been largely based on diamond having nitrogen vacancy (NV) defects, which possess a S-1 (spin triplet) ground state in the electronic structure To measure a magnetic field using this system, optically detected magnetic resonance is used. More particularly, the NV defect is first optically ‘initialised’ into one of the three spin sublevels making up the spin triplet state. Subsequently, a varying microwave field is applied, which will cause transitions of the defect between a first spin sublevel into which the defect was initialised, and a second spin sub-level whose separation from the first spin sublevel matches the frequency of the varying microwave field. By detecting changes in the photoluminescence of the NV defects in the diamond (generated via a process of laser excitation and relaxation of the defects) as a function of the microwave frequency, the magnetic field may be determined.

[0009] However, while NV magnetometry is well established in the few-mT regime, the NV electronic structure restricts the operational range of the system, both in terms of the magnitude of the magnetic field that is detectable and the target field directional sensitivity. This arises from the fact that, for systems with axial rotational symmetry like NV defects, a large off-axis magnetic field mixes the spin states and degrades the spin-initialization mechanism, leading to the loss of contrast of optically detected spin resonance signatures.

[0010] There therefore exists a need for quantum sensors with improved dynamic range and / or vectorial sensitivity. This would open the door to exploring new materials and regimes, including ferromagnetic nanostructures where the magnetization-induced field typically exceed tens of mT. The present invention has been devised in light of the above considerations.

[0011] Summary of the Invention

[0012] The present invention relates to a method and a device for performing magnetometry, and associated device and manufacturing methods.

[0013] In a first aspect of the invention, there is provided a method of carrying out magnetometry, comprising the steps: providing a sensor element comprising a sheet of a 2D layered material having a photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field; conducting an optically detected magnetic resonance measurement on the sensor element by subjecting the sensor element to optical excitation and photoluminescence detection whilst a variable frequency microwave signal is applied, the microwave signal causing transitions between the spin triplet state spin sublevels, wherein the photoluminescence detection comprises detecting a change in photoluminescence signal when the microwave signal is resonant with a transition between the spin triplet state spin sublevels; and determining a characteristic of a magnetic field based on the detected photoluminescence signals.

[0014] By using a sensor element comprising a sheet of a 2D layered material having a defect that introduces a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field to perform ODMR, the present inventors have found that it is possible to increase the sensitivity, dynamic range and / or accuracy of magnetic measurements.

[0015] Optionally, the defect may be a single photon-emitting spin-active defect. However, the present disclosure is not necessarily limited in this way. For example, the 2D layered material may alternatively have a plurality of photon-emitting spin-active defects, in which only a single defect of the plurality of defects is used to perform magnetometry. More particularly, an optically detected magnetic resonant measurement may be conducted only on a single defect of the plurality of defects.

[0016] The variable frequency microwave signal may cause transitions between the spin triplet state spin sublevels when it matches a resonant frequency of one or more of the transitions between the spin triplet state spin sublevels. A resonant frequency may match only a single transition between the spin triplet spin sublevels (e.g., when the spin levels are unequally spaced), or may correspond to two transitions (e.g., when the spin sublevels are evenly spaced).

[0017] When there is a population (ie. probability of the defect being in a particular spin triplet sublevel) imbalance between said triplet sublevels and a resonant frequency is applied that matches the splitting between said spin triplet spin sublevels, a transition of population between the sublevels may occur.

[0018] A population of the defect may be initialised into the spin triplet state. Optionally, the initialisation may be into a single spin triplet spin sublevel (e.g., in the absence of an applied magnetic field). However, the present disclosure is not limited in this way, and an initialised population of the spin triplet state may be split across two or three of the spin triplet spin sublevels. The initialised population distribution may change in the presence of an applied magnetic field.

[0019] The spin triplet spin sublevels may represent a ground state of the system. This advantageously improves the initialisation mechanism, as the defect naturally relaxes into the spin triplet state. However, the present disclosure is not necessarily limited in this way. For example, the spin triplet spin sublevels may instead represent a metastable state of the system.

[0020] The defect may further possess a spin singlet state between the ground and excited states.

[0021] The defect may possess a spin singlet in the ground and excited states and a spin triplet between ground and excited states.

[0022] The method may further comprise the step of determining a secondary characteristic based on one or more determined characteristics of the magnetic field. Said secondary characteristic may relate to the generation of the magnetic field whose characteristic is determined, and / or may be an electrical current, a temperature, or a (crystallographic) stress or strain.

[0023] The method may be used in nanoscale magnetometry. This may refer to the spatial resolution, and / or the magnetic field sensitivity.

[0024] The method may achieve a sensitivity of sub-3 pT / V / fz, sub-2 pT / V / fz, sub-1 pT / V / fz, or sub-500 n l Hz. This sensitivity may be achieved along a particular axial direction, or for any general measurement (e.g., a measurement in any direction).

[0025] Optionally, the characteristic of the magnetic field may be determined based on a single transition between a first and a second spin triplet spin sublevel of the three spin triplet spin sublevels. This may advantageously simplify the process of measuring the magnetic characteristic, as only a single photoluminescent signature (e.g., a change in the photoluminescent signal resulting from transitions of the defect between spin triplet spin sublevels) corresponding to one of the three possible transitions (these being between the three possible pair combinations of spin triplet spin sublevels) need be measured.

[0026] Alternatively, a plurality (e.g., two or more) of the transitions between pair combinations of the spin triplet spin sublevels may be used to determine the magnetic characteristic. In particular, each one of the plurality of transitions can be measured individually, and then used in combination to determine the characteristic magnetic field.

[0027] In some examples, each transition of the lattice defect between each pair combination of the spin triplet state spin sublevels is used to determine the characteristic of the magnetic field.

[0028] The use of a plurality of energy levels may advantageously increase the accuracy of the method at determining the characteristic of the magnetic field. Each of the plurality of transitions may be used in combination to determine the characteristic of the magnetic field to a higher accuracy than any transition could be used to do individually. Alternatively, one or more of the plurality of transitions may be selected from the plurality of transitions for a particular magnetic field characteristic determination as a result of having a higher accuracy than one or more of the other transitions in a particular set of circumstances. For example, one or more of the transitions may be particularly sensitive to magnetic fields aligned along a particular axis compared to one or more of the other transitions, and so may be used preferentially in determining the magnitude of a magnetic field so aligned.

[0029] Optionally, different transitions between the pair combinations of spin triplet spin sublevels are usable to determine different axial components of the magnetic field. Advantageously, this allows the magnetic field to be determined more accurately, as each axial component can be detected by the transition that returns the most accurate result for said axial component.

[0030] In some examples, a first transition between a pair of the spin triplet state spin sublevels is used to determine a first component of the magnetic field along a first axis, and a second transition between a pair of spin triplet state spin sublevels different from the first transition is used to determine a component of the magnetic field along a second axis different from the first axis.

[0031] Optionally, the first and second axes are perpendicular to one another, but the present disclosure is not limited in this way. Instead, the axes may be angled relative to one another at a non-perpendicular angle.

[0032] In some examples, a third transition between a pair of spin triplet state spin sublevels is further used to determine a third component of the magnetic field along a third axis different from the first and second axes. In this way, a 3D vectorial image of the magnetic field may be determined using the components sensed by the three respective transitions.

[0033] This third axis may be perpendicular to the first and second axes, but is not limited in this way.

[0034] In some examples, the defect has low symmetry. The low symmetry of a spin-triplet system (e.g., the defect) can be defined as a spin-triplet system that shows three distinct, non-degenerate electronic spin transitions in the absence of a magnetic field. In such cases the spin triplet spin sublevels are unequally spaced, which ensures that none of the resonant frequencies causing the photoluminescent signatures of each transition are the same (e.g., are non-degenerate). This is advantageous in that it allows the photoluminescent signatures to be distinguished from one another. Optionally, the low symmetry may result in three spin triplet sublevels that couple differently to the spin singlet state. This causes each of the three spin triplet sublevels to differ in their degree of optical spin initialisation, leading to different ODMR contrast. This leads to the three transitions, under some bias field configurations, being associated with different axes of the defect. The low-symmetry structure thus also gives rise to a multi-axis magnetic field sensor that may retain sensitivity to arbitrarily oriented fields exceeding 100 mT.

[0035] Optionally, the method may comprise the step of manipulating the transitions between the spin triplet spin sublevels (e.g., prior to conducting an optically detected magnetic resonance measurement on the sensor element). One advantage of this being the ability to distinguish between positive and negative orientations of a magnetic field the method is being used to determine.

[0036] In some examples, the method further comprises the step of applying a bias magnetic field across the sensor element. Said bias field being usable to manipulate one or more of the transitions between the spin triplet spin sublevels. The bias magnetic field represents a different magnetic field to the magnetic field whose characteristic(s) is (are) to be determined.

[0037] In some examples, the sensitivity of at least one of the transitions of the lattice defect between pair combinations of the three spin sublevels in the spin triplet state is controllable using the bias magnetic field.

[0038] The sensitivity of the at least one transition may be to a magnetic field whose characteristic is to be determined.

[0039] The bias magnetic field may be usable to affect the sensitivity of one, two or all three of the transitions.

[0040] Control of the sensitivities of the one or more transitions by the bias field may be usable to control the sensitivity of one or more of the transitions along one or more particular planes, or even one or more particular axial directions, defined relative to the sheet of 2D layered material.

[0041] For example, the bias field may be usable to increase the sensitivity of one transition between the spin triplet spin sublevels so that said transition is most sensitive to axial components lying within a particular plane, or along a particular axial direction. The bias field may further be usable to increase the sensitivity of one or both of the other transitions between the spin triplet spin sublevels within the same plane, or along the same direction, as the first sublevel. Alternatively, the bias field may increase the sensitivity of the one or more other transitions in a different plane or direction to the first transition.

[0042] Advantageously, manipulation of the transitions using the bias fields allows particular axial components of a magnetic field to be measured more accurately.

[0043] Optionally, the bias field may be a fixed strength magnetic field. For example, the strength of the bias field applied may be < 1 mT, < 5 mT, < 10 mT, < 20 mT, < 30 mT, < 40 mT, or < 50 mT. In other embodiments, the strength of the bias field applied may be > 1 mT, > 5 mT, > 10 mT, > 20 mT, > 30 mT, > 40 mT, or > 50 mT. Different end points of these ranges may be combined to provide suitable further ranges for the bias field.

[0044] The bias field may point in a fixed direction (e.g., along an X, Y or Z axis defined relative to the sheet of 2D layered material).

[0045] However, the present disclosure is not limited in these ways, and the bias magnetic field may instead be variable in one or both of its strength and direction.

[0046] In some examples, the characteristic of the magnetic field is determined by first measuring the photoluminescent signal whilst a first bias field is applied along a first axis, and subsequently measuring the photoluminescent signal whilst a second bias field is applied along a second axis angled relative to the first axis.

[0047] For example, a first bias field having a first strength may be pointed along a first direction whilst a first series of ODMR measurements are taken (used to determine one or more transitions between the spin triplet spin sublevels in the presence of the first bias field and a magnetic field to be measured), and a second bias field having either the first strength or a second strength different to the first strength may be pointed in a second direction different to the first direction whilst a second series of ODMR measurements are taken (used to determine one or more transitions of the spin triplet spin sublevels in the presence of the second bias field and the magnetic field to be measured). In this way, one or more of the transitions between the spin triplet spin sublevels may be altered in such a way that allows a determination of a first set of axial components during the first series of ODMR measurements, and a determination of a second set of axial components during the second series of ODMR measurements. The first and second sets of axial components may then advantageously be combined to determine a 2D or 3D vectorial picture of the magnetic field.

[0048] The first and second directions of the bias fields may be perpendicular to one another. For example, the first direction in the above may be in an XZ plane defined relative to the sheet of 2D layered material, and the second direction may be in the XY plane defined relative to the sheet of 2D layered material. However, the disclosure is not limited in this way.

[0049] During the application of the first and second bias fields, the same transitions between the spin triplet spin sublevels may be measured. Alternatively, different transitions may be measured in each case.

[0050] Optionally, each bias field applied has a magnetic strength of below 100 mT, below 90 mT, below 80 mT, below 70 mT, below 60 mT, or below 50 mT.

[0051] The sheet of 2D layered material has anisotropic binding forces. More particularly, intra-layer binding forces in the sheet of 2D material are high relative to the inter-layer binding forces.

[0052] In some examples, the sheet of 2D layered material has a thickness (e.g., a thickness defined along a direction parallel to the surface normal of the layers of the sheet of 2D layered material) that is less than 200 nm, or less than 100 nm, less than 90 nm, less than 80 nm, less than 70 nm, less than 60 nm, less than 50 nm, less than 40 nm, less than 30 nm, less than 20 nm, or less than 10 nm. Alternatively, or additionally, the sheet of 2D layered material may have less than a set number of layers. For example, the sheet of 2D layered material may have less than 300, less than 200, less than 100, less than 90, less than 80, less than 70, less than 60, less than 50, less than 40, less than 30, less than 25, less than 20, less than 15, less than 10, or less than 5 layers. Advantageously, a thinner sheet of 2D layered material means that the defect will be more sensitive to the magnetic field to be detected and can give higher spatial resolution. For example, because the defect can be closer in proximity to the target it is sensing. However, the present disclosure is not limited in this way, and the sheet of 2D layered material may have a greater thickness and / or number of layers.

[0053] Each layer of the sheet of 2D layered material is one unit cell thick.

[0054] The sheet of 2D layered material preferably comprises a single defect. However, the present disclosure is not limited in this way, and the sheet of 2D layered material may instead contain a plurality of defects.

[0055] The plurality of defects may optionally be arranged in a periodic arrangement. However, typically the defects are arranged in an aperiodic or random arrangement. In some examples, the defect is individually addressable. For example, the defect may be optically addressable.

[0056] More particularly, the defect may be individually excited into an excited state without also exciting other surrounding structures (e.g., other defects) into excited states. Additionally or alternatively, the photoluminescent signal generated from the defects relaxation into the spin triplet state may be detected in isolation from other (e.g., photoluminescent) signals generated by the sheet of 2D layered material). This is advantageous in that sheets of 2D layered material containing more than one defect may still be used to obtain high contrast photoluminescent signature measurements, and thus high accuracy magnetic field characteristic determinations.

[0057] The defect is preferably positioned in a surface layer of the sheet of 2D layered material, or in a layer close to the surface of the sheet of 2D layered material. For example, the defect may be within the top 20 (or within the top 15, the top 10, the top 9, the top 8, the top 7, the top 6, or the top 5) layers of the surface of the sheet of 2D layered material. However, the sensor element is not limited in this way, and the defect may be located anywhere within the sheet of 2D layered material.

[0058] Optionally the 2D layered material is a semiconductor, and more particularly a wide band gap semiconductor. This advantageously provides sufficient space for the defect introduced spin states (e.g., spin triplet and spin singlet states).

[0059] The band gap may preferably be greater than 4 eV, or more preferably may be 5-6 eV.

[0060] In some examples, the sheet of 2D layered material comprises hexagonal boron nitride. This material advantageously hosts optically addressable spin defects (e.g., at room temperature), which are usable in ODMR measurements. The layered nature of the material also provides a suitable environment for low symmetry defect formation, which is useful for achieving advantageously high contrasts in ODMR measurements.

[0061] In some examples, the defect is a carbon-related defect. For example, the defect may comprise one or more carbon atoms. These defects may also include additional structures, such as other atoms not native to the sheet of 2D layered material, and / or vacancies within the 2D layered material structure.

[0062] The combination of a sheet of 2D layered material comprising hexagonal boron nitride and a carbon- related defect may be particularly preferable, as these features synergistically combine to produce advantageously high contrast measurements of the photoluminescent signatures produced when the defect transitions between two of the spin triplet spin sublevels at a resonant frequency matching a transition between said spin triplet spin sublevels.

[0063] The characteristic of the magnetic field optionally refers to an absolute magnitude of the magnetic field. This may be a general magnitude of the magnetic field, or a magnitude of the magnetic field along a particular direction, e.g., along an X, Y, or Z axis defined relative to the sheet of 2D layered material. The method may for example be suitable for measuring magnetic fields > 140 mT, or for example > 150 mT, > 160 mT, > 170 mT, > 180 mT, > 190 mT, > 200 mT, > 250 mT, > 300 mT, > 350 mT, > 400 mT, > 450 mT, or > 500 mT.

[0064] Additionally, or alternatively, the characteristic of the magnetic field determined may be the vectorial direction of the magnetic field.

[0065] In some examples, the method determines a magnetic field vector of the magnetic field based on the photoluminescence signals. The vector may be in two dimensions (e.g., determined using first and second transitions between a first and second pairs of spin triplet state spin sublevels), or components in three dimensions (e.g., determined using all three transitions of the defect amongst the spin triplet state spin sublevels).

[0066] A two-dimensional vectorial determination may be in an XY plane, an XZ plane, or a YZ plane relative to the sheet of 2D layered material, and / or may be in a plane of the one or more layers of the sheet of 2D layered material.

[0067] In some examples, the method may determine a plurality of characteristics of a magnetic field. For example, the method may determine a direction of the magnetic field and a magnitude of the magnetic field in that direction.

[0068] According to a second aspect of the present invention, there is provided a magnetometer for carrying out magnetometry via optically detected magnetic resonance, the magnetometer comprising: a sensor element comprising a sheet of 2D layered material having a photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field; a microwave signal generator configurable to cause transitions of the lattice defect between pairs of the spin triplet state sublevels, an optical source for exciting the lattice defect; and a photodetector for detecting a change in photoluminescence signal emitted from the sheet of 2D layered material generated when the microwave signal is resonant with a transition between the spin triplet state sublevels, the magnetometer being configured to determine a characteristic of a magnetic field based on the detected photoluminescence signals.

[0069] The optical source and / or photodetector may be free space or fibre-coupled.

[0070] The photodetector and the optical source may be jointly provided in a confocal microscope, reducing the complexity of the system.

[0071] Said confocal microscope may preferably comprise additional components, such as one or more mirrors for redirecting optical signals, and / or a lens for focusing the optical signals.

[0072] Optionally, the optical source may comprise a laser.

[0073] In some examples, the optical source and / or the photodetector can be manipulated to individually address one or more particular defects.

[0074] Optionally, the microwave signal generator is arranged in close proximity to the sensor element. In some examples, the microwave signal generator comprises a coil of wire. This is a particularly advantageous shape for delivering microwave energy to the sensor element. However, the present disclosure is not limited in this way. For example, the microwave signal generator may instead be an antenna or a waveguide.

[0075] According to a third aspect of the present invention, there is provided a sensor for use in the method of the first aspect of the present invention, and / or the magnetometer of the second aspect of the present invention, the sensor element comprising a sheet of 2D layered material in the form of a layer having a photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field, the sensor element further comprising a support on which the sheet of 2D layered material is supported.

[0076] In some examples, the sensor element, sheet of 2D layered material and / or support are configured to enable optical interrogation of the defect. This advantageously increases the contrast of ODMR measurements of the photoluminescent signatures corresponding to resonant frequencies of the transitions between the spin triplet spin sublevels.

[0077] In some examples, the defect may be arranged to align with specific regions of the underlying support. For example, the defect may overlie with optical / electronic / structural features of the support.

[0078] Advantageously, this may increase the individual addressability of the defect (e.g., in terms of the excitability of the defect, its susceptibility to microwave signal transitions, or in the detectability of generated photoluminescent signals), such that the contrast of photoluminescent signals generated by the defect is increased.

[0079] Optionally, where there is a plurality of defects in the sheet of 2D layered material, one or more particular defects may be arranged to align with specific regions of the underlying support, so as to isolate said defects from the plurality of defects. This advantageously allows greater spatial resolution and / or greater contrast in ODMR measurements and / or of the photoluminescent signatures.

[0080] Optionally, the support is a semiconductor or an insulating material. For example, the support may comprise silicon, silicon nitride, and / or silicon dioxide.

[0081] In some examples, the support includes a tip region, the sheet of 2D layered material being located over at least part of the tip region. The inclusion of the tip region advantageously allows the sensor element to be better manipulated relative to the magnetic field being sensed by the sensor element. Moreover, the tip region allows the defect to be brought into closer contact with the surface of samples generating a magnetic field to be sensed.

[0082] Optionally, the tip region includes a tapering position ending in a pointed tip.

[0083] In some examples, the support forms a cantilever shape. The cantilever shape makes it advantageously easy to scan the sensor element across the surface of a material, so as to build up a 2D surface picture of the magnetic field. A tip region on said cantilever shape may comprise a pointed shape which extends along a direction parallel to a surface normal of the cantilever. The pointed shape may taper along said surface normal direction to form a pointed tip at an end distal to a cantilever surface from which the pointed shape protrudes.

[0084] Alternatively, the support may form a pillar shape having a tip region in which the pillar tapers along its longitudinal axis to form a pointed tip.

[0085] In some examples, the defect is located substantially in register with the tip region. Preferably, the defect is located substantially in register with an apex of the tip region (e.g., a pointed tip of the tip region). In this way, the defect may be brought into closer proximity to object surfaces to be sensed. Additionally, the defect is isolated from other defects (if any) and from the majority of the sheet of 2D layered material, increasing its optical addressability.

[0086] However, the present disclosure is not limited to examples in which a tip region is included, and the support may instead form a planar surface onto which the sheet of 2D layered material is applied.

[0087] According to a fourth aspect of the present invention, there is provided a method of manufacturing a sensor element according to the third aspect of the present invention, wherein the sheet of 2D layered material is grown on a first substrate and the sheet of 2D layered material is transferred from the first substrate onto the support.

[0088] In some examples, growth of the substrate is via chemical vapour deposition (CVD), wherein (e.g., carbon-related) defects are introduced into the sheet of 2D layered material by controlling the composition of the CVD precursors. The use of CVD advantageously allows a great degree of control over the growing process.

[0089] Optionally, the growth substrate is sapphire.

[0090] In some examples, the sheet of 2D layered material is separated from the first substrate via immersion in a liquid.

[0091] Optionally, the liquid is de-ionised water, but the present disclosure is not limited in this way.

[0092] According to a fifth aspect of the present invention, there is provided a sensor device comprising a sheet of 2D layered material mounted onto a cantilever probe, wherein the sheet of layered material comprises a photon-emitting spin-active defect which is positioned at a tip region of the cantilever probe, wherein the sensor device is configured to perform magnetometry via optically detected magnetic resonance, in which the sensor device is subjected to photoluminescence detection whilst a variable frequency microwave signal is applied, and a characteristic of a magnetic field is determined based on the detected photoluminescence signals.

[0093] By positioning the defect of the sheet of 2D layered material at a tip region of the cantilever probe, the defect can be easily scanned over, and in close proximity to, the surface of an object whose magnetic field is to be detected, increasing the contrast of the detected photoluminescent signatures.

[0094] Optionally, the sensor device is usable for nanoscale magnetometry. In some examples, the tip region includes a pointed shape that extends outward normally from a surface of the cantilever probe. Said pointed shape may taper to form a pointed tip at a point distal from the cantilever surface from which the pointed shape protrudes.

[0095] In some embodiments of the fifth aspect, the sensor device is according to the third aspect, but the fifth aspect is not necessarily limited to this.

[0096] The invention includes the combination of any two or more of the aspects and / or optional features described except where such a combination is clearly impermissible or expressly avoided.

[0097] Summary of the Figures

[0098] Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures, in which:

[0099] Figs. 1A-B are an apparatus and measurement sequence for performing magnetometry using continuous wave optically detected magnetic resonance (cwODMR) according to a first example of the present invention.

[0100] Fig. 2 is a schematic illustration of a sheet of 2D layered material forming part of the apparatus of Fig. 1 A.

[0101] Figs. 3A-B are an energy level diagram and example photoluminescence spectrum of a defect in the sheet of 2D layered material forming part of the apparatus of Fig. 1A.

[0102] Figs 4A-B are further example apparatuses for performing magnetometry using cwODMR.

[0103] Fig. 5 is an example set of cwODMR spectra performed using the apparatus of Fig. 1 A.

[0104] Fig. 6 is a model of the electronic structure of the sheet of 2D layered material.

[0105] Figs. 7A-C are experimental results performed on the sheet of 2D layered material of Fig. 1A.

[0106] Fig. 8 shows graphical representations of the contrast achieved with varying spin-selective direct (kEz .so) and reverse (kso .GZ) intersystem crossing rates.

[0107] Fig. 9 is a series of graphical representations of the variations in the spin triplet sublevels shown in Figs. 3A and 6 under varying magnetic fields.

[0108] Figs. 10A-C are graphical representations of the variations in resonant frequency and contrast of transitions between the spin triplet sublevels of Figs. 3A and 6 in the presence of a changing magnetic field.

[0109] Figs. 11A-C are diagrammatic representations of simulated sensitivities of the transitions between the spin triplet sublevels of Figs. 3A and 6 to different magnetic field directions, for one example defect.

[0110] Fig. 12 is a diagrammatic representation of the magnetic field direction that each transition between the spin triplet sublevels of Figs. 3A and 6 is most sensitive to under the influence of an applied bias magnetic field, for one example defect. Fig. 13 sets out a flow diagram for a method of performing magnetometry using cwODMR according to an example of the present invention.

[0111] Figs 14A-B are optical images of an example sensor element according to an example of the present invention.

[0112] Fig. 15 sets out a flow diagram for an exemplary method of forming the sensor element of Figs. 14A-B.

[0113] Fig. 16 provides further detail for the method of forming a sensor element.

[0114] Detailed Description of the Invention

[0115] Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference.

[0116] The present invention builds on the realisation that single solid-state spin defects offer atomic-scale magnetometers that can probe magnetic phenomena with nanoscale resolution [1 , 2]. To date, nanoscale magnetometry has primarily relied on the nitrogen-vacancy (NV) centre in diamond [3] where a S-1 ground state and spin-related optical contrast has enabled detailed studies of both condensed matter [4, 5] and biological systems [6, 7]. While NV magnetometry is well established in the few-mT regime, the NV electronic structure restricts the operational range of the system, both in terms of bias field orientation and target field directional sensitivity. This arises from the fact that, for system with axial rotational symmetry like the NV, large off-axis magnetic field mixes the spin states and degrades the spin-initialization mechanism, leading to the loss of contrast of optically detected spin resonance signatures [5, 8]. A nanoscale magnetometer with improved dynamic range and vectorial sensitivity would open the door to exploring new materials and regimes, including ferromagnetic nanostructures where the magnetization- induced field typically exceed tens of mT [9-11].

[0117] Figs. 1A and 1 B show an apparatus 100 and measurement protocol 200 for performing magnetometry using continuous wave optically detected magnetic resonance (cwODMR) according to an example of the present invention.

[0118] Fig. 1A shows a schematic depiction of the apparatus 100 for performing magnetometry, which includes a sensor element 120, a microwave signal generator 140, and a confocal microscope 150.

[0119] The sensor element 120 comprises a sheet of 2D layered material 130 having a single photon-emitting spin-active defect (referred to going forward as the ‘defect’). For avoidance of doubt, a layered material is one that has anisotropic bonding forces. More particularly, the material forms into 2D sheets with strong chemical bonding within the layers. Two or more such layers are then grown or stacked on top of one another, with adjacent layers being weakly bonded to one another (e.g., via van der Waals forces). A schematic example sheet of 2D layered material is shown in Fig. 2, which comprises layers 131 -134 (though the sheet of 2D layered material may optionally comprise either more or less layers than depicted in Fig. 2). The defect may be formed in any layer, but is preferably formed in either a surface layer 131 or a layer close to the surface layer (e.g., one of the layers 132, 133), as this advantageously increases the sensitivity of the defect to applied magnetic fields. Optionally, a sheet of 2D layered material may be used which has a plurality of defects.

[0120] In the present example, the sheet of 2D layered material 130 is made of hexagonal boron nitride (hBN), and the defect is a visible wavelength emitting defect. The material may for example be carbon-doped CVD-grown hBN. This arrangement has particularly advantageous material properties, including, but not limited to, advantageous optical relaxation times and transition coefficients representing the probabilities of transitioning between select energy levels of the defect.

[0121] More particularly, hBN is a wide-bandgap layered material hosting room temperature optically addressable spin defects [12-14]. Among these, the boron vacancy defect (Vg_) with a S-1 ground state has been recently applied for magnetometry of two-dimensional ferro-magnets, highlighting the appeal of a quantum sensor embedded in a van der Waals host [15-17]. However, the low intrinsic brightness of the Vg limits its application to ensemble-based wide-field magnetometry with diffraction-limited spatial resolution. On the other hand, the low-symmetry individually addressable carbon-related defect in hBN with a coherent S-1 ground state and room-temperature ODMR contrast of > 50% represents a new candidate for nanoscale magnetometry with the potential for close sample-target proximity, increased spatial resolution, and scalable device fabrication

[0014] .

[0122] The defect causes localised changes to the energy levels of the sheet of 2D layered material 130 around the defect, which are shown in the energy level diagram depicted in Fig. 3A. More particularly, the Fig. 3A energy level diagram shows a ground state G and a metastable state M, one or both of which are introduced by the defect. As shown in Fig. 3A, the defect introduces a spin triplet state comprising spin triplet spin sublevels X, Y and Z, wherein said triplet state may either represent the ground state G of the defect / system or the metastable state M of the defect / system. The defect may further introduce a spin singlet state S into the system, which may also represent either the ground state G (e.g., when the spin triplet state represents the metastable state M) or the metastable state M (e.g., when the spin triplet state represents the ground state G).

[0123] For clarity, an example is taken in the following in which the spin triplet state is taken to be the ground state G, having spin triplet sublevels Gz, Gyand Gx, and there is further assumed to be a spin singlet state that represents the metastable state M, having the spin singlet level S. The above example being characterised by photoluminescence at ~2.1 eV (Fig. 3B), a spin-1 ground state with non-degenerate spin sublevels at zero field (Fig. 3A) and spin-dependent intersystem crossing leading to optical spin initialization (see below). Having the spin triplet state G as the ground state advantageously makes optical initialisation (described in more detail below) easier as the defect naturally relaxes into this state. However, as noted above the present disclosure is not limited in this way, and it is also possible for the triplet state to be an excited metastable state.

[0124] Also shown in Fig. 3A is an exited state E, which is positioned at a higher energy value than both the spin triplet G and spin singlet S states. As mentioned, the spin triplet state G is subdivided into three spin sublevels Gz, Gyand Gx. Each of the three sublevels has a different energy eigenvalue, arranged as Gz, Gyand Gx in order of ascending energy, in the absence of an externally applied magnetic field. In other words, the three sublevels are non-degenerate. This is at least partly due to the defect having low symmetry (e.g., low rotational symmetry) within the layered material, which results in zero-field splitting of the spin triplet sublevels. In ascending order of energy, the separation between the spin triplet sublevels Gx and Gyis represented by the label LA, the separation between Gyand Gzis LB, and the separation between Gx and Gzis Lc. The spin-dependent photoluminescence (PL) observed for these emitters (e.g., the defects emitting photoluminescence provides access to spin-state readout through off-resonance optical excitation.

[0125] The electronic structure of the present example sheet of 2D layered material 130 is described in more detail below. More particularly, in the following, it is shown that this defect in hBN displays multiple ground-state ODMR resonances with high contrast across a broad magnetic field range, retaining the optical readout of spin signatures at applied off-axis field above 100 mT (Fig. 5 and 10C). Photonemission correlation spectroscopy and pulsed ODMR experiments are combined with microscopic modelling of the optical cycle to show the dynamics responsible for contrast retention at high magnetic field (Figs. 6-8). Based on angle-resolved magnetic field dependence of each ODMR resonance, it is shown that the reduced spatial symmetry of this defect gives rise to a system with robust optical readout of the spin state at arbitrary external field orientations (Figs. 9-10). Finally, the magnetic-field sensitivity of the three possible S-1 spin resonances is predicted and the fact that this system is capable of achieving sensitivity as low as sub-pT / VHz, even in the presence of bias fields above 50 mT, is shown (Figs. 11- 12). Said bias field being chooseable to provide dual-axis readout of the target field, with full vectorial identification possible based on two independent measurements.

[0126] Returning for now to Fig. 1 A, the microwave signal generator 140 is positioned in close proximity to the sensor element 120, and is configured to deliver a varying frequency microwave signal to the sensor element 120, and more particularly to the sheet of 2D layered material 130. In the present example, the microwave generator 140 is a coil of wire in the vicinity of the device. However, the present disclosure is not limited in this way, and the microwave generator may instead be an antenna, or a waveguide.

[0127] At select frequencies, the microwave signal will match the resonant frequency corresponding to the energy difference between one or more of the spin triplet spin sublevel separations LA, LB, or Lc. This matching microwave signal will cause a change in the populations (e.g., the percentage chance of defect occupation) between the two relevant spin triplet spin sublevels, providing that there is an initial population imbalance between the two. This difference in population may, for example, occur when initially the population of one of the two spin triplet spin sublevels (e.g., one of the two spin triplet spin sublevels on either side of the transition which the microwave signal is currently matched to) is zero, whilst the population of the other of the two spin triplet spin sublevels is non-zero. Alternatively, it may be that there is a population in both spin triplet spin sublevels, but that these populations are unbalanced.

[0128] The frequency of the microwave signal generated by the microwave signal generator 140 is ranged so as to encompass each of LA, LB, and Lc at zero applied magnetic field, and further to frequencies that will match the resonant frequencies of higher and lower energy transitions should the spin triplet sublevels Gz, Gyand Gx move further apart or closer together (e.g., in the presence of an external magnetic field). The microwave signal generator 140 is configured to (e.g., continuously) cycle through this frequency range.

[0129] The confocal microscope 150 includes an optical source which is configured to direct an optical signal at the sheet of 2D layered material 130, so as to cause excitations of the population in the ground state G (e.g., in any one of the spin triplet sublevels Gz, Gyand Gx) up into the excited state E. The optical signal generated by the optical source is therefore configured to surpass the energy gap between the spin triplet state G and the excited state E. The defect may relax back into the spin triplet state G either radiatively (e.g., through photon-emission via a direct transition between the excited state and the spin triplet state G), or non-radiatively (e.g., through a sequence of direct and reverse intersystem crossing events, such as when the defect first relaxes into the spin singlet state S, before subsequently relaxing into the spin triplet state G). When the defect relaxes into the spin triplet state G radiatively, the sheet of 2D layered material 130 will generate a photon (e.g., a photoluminescent signal). In cases where the triplet state is a metastable excited state, the optical signal will match the energy gap between the spin singlet ground and excited states.

[0130] In the present example, the optical source is a laser, which generates an optical signal substantially comprising one frequency or a very narrow spectrum of frequencies. This advantageously increases the probability of exciting the defect into particular excited energy levels, and so allows a greater degree of control over the relaxation (and thus generated luminescence) of the sheet of 2D layered material 130. However, the optical source is not limited in this way, and may instead be any other type of photo generation device, such as one that generates an optical signal comprising a broad spectrum of frequencies.

[0131] The confocal microscope 150 further includes a photodetector, which is used to detect the photoluminescent signal generated by the sheet of 2D layered material 130.

[0132] The above-described components of the apparatus 100 can be used to perform cwODMR in the following general manner. First, the optical source is used to generate an optical signal that will optically initialise the sheet of 2D layered material 130 (and more particularly the defect) into one (or more) of the three spin triplet sublevels X, Y, Z The optical initialisation works on the basis that the defect, when excited into the excited state E, will at least occasionally relax back into the spin triplet state G via the spin singlet state S. From the spin triplet S state, the defect may relax into any one of the three spin triplet spin sublevels Gz, Gyand Gx, but the probability of each of the transitions S to Gz, S to Gyand S to Gx occurring will be different. In other words, the defect will have a higher probability of relaxing into one of the spin triplet sublevels Gz, Gyand Gx over the other two. By cycling the defect through a number of excitations and relaxations using the optical signal, the population of the preferred spin triplet sublevel (i.e. , the spin triplet sublevel into which the defect has the highest chance of relaxing from the singlet state S) will increase over time, initialising the system into that sublevel. The same holds if the triplet sublevels (x,y,z) are in a metastable state and the ground and excited states are singlet. In the present example, the defect is initialised into the Gysublevel, however the present disclosure is not limited to this case, and optical initialisations of other embodiments falling within the scope of the present disclosure may be into another one of the spin triplet sublevels Gz, Gyand Gx. Further, the present embodiment allows for the population to be initialised into more than one of the spin triplet sublevels Gz, Gyand Gx under an applied magnetic field, such that transitions may be detectable between all three sublevel pairs (e.g., between Gzand Gy, between Gzand Gx, and between Gx and Gy). This is discussed in more detail below, and particularly in relation to Fig. 6.

[0133] After optical initialisation, the microwave signal generator 140 is used to supply the varying frequency microwave signal to the sheet of 2D layered material 130, which, as described above, will cause transitions between spin triplet sublevels Gz, Gyand Gx having unbalanced populations when the applied microwave signal matches a resonant frequency corresponding to one or more of the transitions LA, LB, or Lc. The presence of the transitions causes changes in the photoluminescence signal generated by the sheet of 2D layered material 130 (for the reasons described below), such that when the photoluminescent signal is plotted against the varying frequency microwave signal, photoluminescent signatures appear at the resonant frequencies causing population transitions between the spin triplet sublevels Gz, Gyand Gx. Since the spin triplet sublevel transitions LA, LB, or Lc are sensitive to changes in an external magnetic field, detection of the position of the photoluminescent signatures is usable to detect characteristics of said external magnetic field.

[0134] The above process may be carried out using a measurement sequence 200, an example of which is shown in Fig. 1 B. The measurement sequence 200 is for detecting the cwODMR contrast, defined as the relative change in PL induced by the presence of microwaves. More particularly, the contrast is measured using the formula: 100 where PLsigis the photoluminescence signal measured in the presence of the varying frequency microwave signal, and PLrefis the photoluminescence signal measured in the absence of the varying frequency microwave signal.

[0135] In particular, the measurement sequence 200 shows a sequence where a laser beam (e.g., from the confocal microscope 150) is constantly applied. Meanwhile, a MW pulse (e.g., from the microwave signal generator 140) is modulated between ‘off and ‘on’ states with equal duration. When the MW is off, this is defined as ‘ref’, when the MW is on, this is defined as ‘signal’. Note also that photons are always being collected, and are defined as photons collected during ‘ref and during ‘signal’.

[0136] The brackets enclosing the second row of the measurement sequence 200 indicate that the MW sequence is repeated many times. In the present example, the MW sequence is repeated 10 times per frequency, though the present disclosure is not limited in this way.

[0137] The apparatus 100 of Fig. 1A further includes a bias field generator 180, which is configurable to supply a bias magnetic field across the sensor element 120, and more particularly the sheet of 2D layered material 130. The bias field is usable to manipulate one or more of the spin triplet spin sublevels Gz, Gyand Gx prior to measuring, or during measurement of, an external magnetic field, the utility of which is described in more detail below (particularly in relation to Fig. 9). However, the present disclosure is not limited to embodiments including said bias field generator 180, and examples are envisaged in which the bias field generator 180 is not present.

[0138] FIGS. 4A-B show further example apparatuses 300 400 for performing magnetometry using cwODMR. These are similar to the apparatus 100 of Fig. 1 , and like features are given like reference numerals incremented to have lead digits of 3xx and 4xx, respectively. Further, the apparatuses 300, 400 operate in a similar manner to the apparatus 100, which is described above. But the apparatuses 300, 400 do differ both from each other and the apparatus 100 in several ways. These differences are discussed below.

[0139] Fig. 4A shows an apparatus 300 including a sensor element 320, an optical source 340, and a photodetector 390, as well as a sample 398 (e.g., a magnetic material) which is to subject to characterisation by the apparatus 300. The apparatus 300 further includes a microwave generator, and may optionally also include a bias field generator. However, neither of these components are shown in Fig. 4A (or Fig. 4B).

[0140] As in the apparatus 100 of Fig. 1A, the optical source 360 generates an optical signal which is directed toward the sensor element 320, with the resulting luminescence generated by the sensor element 320 being detected by the photodetector 390. In Fig. 4A, the optical signal and resulting photoluminescence are directed along the correct path via mirrors 362, 364, and are focused using the focusing element 366 (e.g., a lens). Each of at least the optical source 360, mirrors 362 364, focusing element 366, and photodetector 390 optionally form part of a confocal microscope.

[0141] The sensor element 320 of Fig. 4A includes a support 322 and a sheet of 2D layered material 330 supported on a tip region 325 of the support 322, wherein a single photon-emitting spin-active defect of the sheet of 2D layered material 330 is in register with the tip region 325 (e.g., a pointed end of the tip region 325). The inclusion of the tip region 325 advantageously allows the body of material 330 to be more accurately manipulated relative to the sample 398. Moreover, aligning the defect of the sheet of 2D layered material 330 in register with the tip region 325 allows the defect to be brought into closer proximity to the sample 398, allowing for measurements with higher spatial resolution of the sample 398 magnetic field.

[0142] Fig. 4B shows an apparatus 400 that is similar to the apparatus 300 of Fig. 4A, once again including a sensing element 420, an optical source 460, mirrors 462 454, a focusing element 466, and a photodetector 490, all of which are used to perform magnetometry on a sample 498. However, the apparatus 400 differs from the apparatus 300 in the arrangement of the sensing element 420.

[0143] More particularly, the sensor element 420 comprises only a sheet of 2D layered material 430 applied directly to the sample 498, as shown in Fig. 4B. Optionally, the sheet of 2D layered material 430 is grown onto the sample 498, but the present disclosure is not limited in this way. For example, the sheet of 2D layered material 430 may instead simply be placed onto the sample 498.

[0144] Several of the remaining features are as discussed in relation to Fig. 1A. However, it is emphasized that similar results would be expected using either of the apparatuses 300, 400 in place of the apparatus 100, as each uses the sheet of 2D layered material to generate photoluminescence for the cwODMR measurements.

[0145] Fig. 5 shows an example set of cwODMR spectra performed at 0 mT and 50 mT respectively using the apparatus 100 of Fig. 1A, in which the circle data points are measured mean values, with grey error bars indicating standard error of mean, and the shaded regions are fits to the data using a Gaussian peak shape. For a spin-1 system such as the apparatus 100, the energies of the three spin sublevels GO, G- and G+ is described by Hamiltonian of the type where D and E are the zero-field splitting (ZFS) parameters that define the defect’s X, Y, Z principal axes, S is the spin-1 operator, and B is the applied magnetic field.

[0146] The lower panel of Fig. 5 shows an exemplar first cwODMR spectra taken using the apparatus 100 in the absence of an external magnetic field, and an upper panel of Fig. 5 shows a second cwODMR spectra taken using the apparatus 100 in the presence of a 50 mT magnetic field. The inset in the 50 mT spectra (upper panel) shows the direction of the magnetic field. It is noted that the spectra shown in Fig. 5 are only one example of ODMR spectra produced by a defect according to the present disclosure. Other defects, and defect types, falling within the scope of the present disclosure will show different spectra under the same conditions.

[0147] The first (lower) spectra show a photoluminescent signature corresponding to an LA transition on the left hand side of the panel, and a photoluminescent signature corresponding to an LB transition on the right- hand-side of the panel. Both the LA and LB photoluminescent signatures have strong contrast, at approximate values of 22(5)% and 30(2)% respectively. However, no photoluminescent signature is detected for Lc, as there is no substantial population difference in either the Tz, or Tx sublevels following the optical initialisation into the Tylevel discussed above (see Fig. 6) meaning that no transition is detected at the Lc resonant frequency.

[0148] On the other hand, the second (upper) spectra, measured in the presence of a 50 mT magnetic field, shows photoluminescent signatures for each of LA, LB, and Lc. More particularly, there is an LA photoluminescent signature with a measured contrast of 1 .8(2)%, an LB photoluminescent signature with a measured contrast of 12.9(5)%, and an Lc photoluminescent signature with a measured contrast of 2.7(3)%. The appearance of all three possible photoluminescent signatures (LA, LB, and Lc) results from a spin initialisation mechanism which results in population differences across all three spin triplet sublevels. This gives rise to three detectable ODMR transitions at resonant frequencies corresponding to each of LA, LB, and Lc. The field-dependent spectra in Fig. 5 allow the orientation of the magnetic field with respect to the principal axes of the defect to be extracted. In this case, the field is applied parallel to the XZ plane (which coincides with the plane of the hBN layers), at 50(1) degrees from the z-axis. The retention of cwODMR contrast under magnetic field at an arbitrary direction shown in Fig. 5 is unlike what is seen for the NV centre in diamond, for example, where a few-degree misalignment with respect to the defect’s quantization axis causes a degradation of the spin initialisation mechanism that is enough to quench the cwODMR contrast. In other words, even small levels of spin initialisation degradation of the NV centres in diamond leads to undetectable photoluminescent signatures. Thus, NV centres in diamond cannot generally be used to measure the orientation and magnitude of arbitrarily oriented magnetic fields.

[0149] The characteristics of the sheet of 2D layered material 130 (e.g., the hexagonal boron nitride having a carbon-related defect) used in the apparatus of Fig. 1 A are now discussed in more detail in relation to Figs. 6-8. More particularly, to understand the retention of ODMR contrast with off-axis field and the defect-to-defect variability of the hBN system, time-resolved spectroscopy is combined with a rateequation model providing insight into the optical initialization cycle.

[0150] Fig. 6 shows a model of the electronic structure of the sheet of 2D layered material 130 at the defect site. This model is similar to the example taken above in relation to the energy level diagram of Fig. 3A, which also represents the electronic structure of the sheet of 2D layered material 130 at the defect site. In particular, like the example taken above in relation to Fig. 3A, the spin triplet model of Fig. 6 also includes the spin triplet state G (referred to going forward as the spin triplet ground state, or more simply as the ground state) comprising spin sublevels Tz, Tyand Tx (in ascending order of energy in the absence of an external magnetic field), the excited state E, and the spin singlet state S arranged in between the ground state G and the excited state E. But unlike Fig. 3A, Fig. 6 further breaks down the excited state into specific excited sublevels Ez, Eyand Ex (arranged in ascending order of energy in the absence of an external magnetic field). Each respective excited sublevel Ez, Eyand Ex represents an excited state of a respective spin triplet spin sublevel Tz, Tyand Tx. More particularly, Ezrepresents the excited state of Tz, Eyrepresents the excited state of Tyand Ex represents the excited state of Tx.

[0151] Fig. 6 further includes several arrows representing transitions of the defect between different levels in the model, said arrows being labelled with transmission coefficients representing the probability of the indicated transition. Three arrows, labelled by the transmission coefficient FG .E, point from the spin triplet state G to the excited state E, with each of the three going between a specific ground state sublevel GzGyGx and the corresponding excited sublevel EzEyEx (for example, one arrow goes from Gzto Ez). A further three arrows, labelled by the coefficient FE .G, point in the reverse direction between the excited state E and the ground state G, once again between matched pairs of ground state G and excited state E sublevels.

[0152] In addition to these, arrows are also included to represent transitions from the excited state E to the spin singlet state S, and from the spin singlet state S to the ground state G. In each case, there are three arrows representing transitions between each of the sublevels in the excited / ground state and the singlet state. The arrows marking the transitions from the excited state E to the spin singlet state S are labelled KEZ .SO, KEY .SO, and KEX .so, (i.e. , transmission coefficients / rates between the respective exited state sublevels Ez, Eyand Ex and the spin singlet state S) and the arrows marking the transitions from the spin singlet state S to the ground state G are KSO .GZ, KSO- .Gy, and KSO+ .GX (i.e., transmission coefficients / rates between the spin singlet state S and the respective ground state sublevels Gz, Gyand Gx).

[0153] It is the differences in transmission coefficients KEZ .so, KE^SO, and KEX .so which cause the photoluminescent signatures (i.e., changes in the photoluminescent signal) detected at the resonant frequencies of LA, LB and Lc. In particular, higher values in any one of KEZ .so, KE^SO, and KEX .so correspond to a higher probability of the defect in the relevant excited state relaxing into the ground state via the spin singlet state S. In other words, there is a higher probability of the defect relaxing non- radiatively via an intersystem transition (i.e., excited state to spin singlet state, then spin singlet state to ground state), meaning a lower photoluminescent signal. Differences between these transmission coefficients therefore mean that the generated photoluminescent signal will be different depending on which spin triplet sublevel Gz, Gyand Gx has the greatest population, since the population would be excited into a particular excited sublevel Ez, Eyor Ex from which there will be either a greater or lesser chance of relaxing non-radiatively. The differences also mean that there will be a detectable photoluminescent signature at resonant frequencies when a population that was located in a particular spin triplet level is being caused to transition between two sublevels by the microwave signal, since the probabilities of the defect being excited into each respective excited state, and thus the probability of the defect relaxing non-radiatively, will have changed.

[0154] The model of Fig. 6 further includes a double-ended arrow labelled yTi, which represents the probability of transitions between the ground state spin sublevels Gz, Gyand Gx in the absence of any applied signals (e.g., the microwave signal). In other words, yTi represents the transitions LA, LB and Lc occurring naturally.

[0155] The above transfer rates are used to build a set of rate equations describing the transfer of population between the different energy levels, and determine the values of the relevant rates by performing global fits of the predictions of the model to the experimental data presented in Figs. 7A-C which show experimental results performed on the sheet of 2D layered material 130 of Fig. 1A. In each of Figs. 7A-C, the experimental results are the scattered dots (in Figs. 7B-7C, for example, these dots represent the mean value of the contrast measured for various delay times Tr, with the error bars indicating standard error of mean), whilst the lines are global fittings of the experimental results used to determine the transmission coefficient parameters.

[0156] The top panel of Fig. 7A shows background-corrected second-order autocorrelation measurements g(2)(t), whilst the bottom panel shows the residuals of the fit of the model to the data (see below discussion). The time axis is presented in linear scale between -30 and 30 ns, where a characteristic antibunching dip at t = 0 can be observed. For |t| > 30 ns, the time axis is presented in log scale. These emitters show significant bunching behaviour, which only subsides after ~100 ps. Similar trends have been found in various types of hBN emitters [12, 21 -24], where careful analysis of the different timescales present in g(2)(t) experiments has helped determine their electronic structures. It is noted that fitting the g(2)(t) results to a microscopic model involves multiple unrestrained parameters, such that the analysis indicates that different microscopic models and a wide variety of combinations of individual rates can give rise to coinciding g(2)(t) behaviour.

[0157] To clarify this ambiguity, time-resolved pulsed-microwave experiments are performed at 0 mT and the rates that allow for a global fit of the g(2)(t) traces as well as the results of these pulsed-microwave experiments are identified, with pulse sequences illustrated in the insets of Figs. 7B-C and microwave pulses on resonance with LB. Fig. 7B shows the results of an experiment tracking the spin-dependent photoluminescent decay, whilst Fig. 7C presents results of an experiment tracking the spin-relaxation dynamics of the same defect. In both Fig. 7B and Fig. 7C, there is included an inset which presents the pulse protocol used during the respective experiments, in which the optical signal applied is represented by the top row of the inset, applied microwave drive pulses are represented on the third row down of the inset, the readout times are represented on the second row down of the inset, and the reference signal measurement is represented on the bottom row of the inset. For Fig. 7C, the signal corresponds to the integrated PL when two microwave pi pulses are applied, each before and after delay time T between the two optical pulses, and the reference corresponds to a single microwave pi pulse at the end of T.

[0158] As mentioned above, the transmission coefficient parameters of the Fig. 6 model were determined by performing global fits (i.e., the black curves in Figs. 7A-C) of the predictions of the model to the experimental data presented in Figs. 7A-C. Optical excitation and radiative recombination processes are assumed to be spin conserving at zero magnetic field. Further, to match the data shown in Fig. 5, which shows the photoluminescence signatures corresponding to LA and LB respectively having similar zerofield cwODMR contrasts, it was further assumed that KEZ^S0= KEZ^S0= KEy^S0, and KS0^GX= KS0^GZ=Kso^cy This follows naturally in the case of low symmetry systems

[0020] , in contrast to what’s observed in high-symmetry systems like NV centre in diamond and the Vg in hBN.

[0159] Table 1 presents the transmission coefficients extracted from this global fitting procedure for the defect in the absence of an applied magnetic field. The table shows the defect having comparable radiative and non-radiative decay rates from the optically excited state, and strongly spin-selective direct and reverse intersystem crossing paths. This co-occurrence of fast optical relaxation and strongly spin-selective intersystem crossing is responsible for the favourable combination of large contrast and brightness generally observed for the sheet of 2D layered material 130 in the apparatus of Fig. 1A.

[0160] Table 1

[0161] It is noted that a model with singlet ground and optically excited states and a triplet metastable state was also considered, but it was found that it fails to capture the observed behaviour, therefore confirming the assignment of a spin triplet ground state G.

[0162] It is further noted that whilst a defect having the above parameters of table 1 may be used in one example of the present invention, the present disclosure is not limited in this way. For example, defects having other parameter combinations possessing the general attributes of fast optical relaxation and strongly spin-selective intersystem crossing, which the inventors have identified as being a cause of the favourable combination of large contrast and brightness in the present invention, also fall within the present scope. Fig. 8, which is discussed below, helps illustrate this point, and provides a variety of other parameter combinations that suitably fall within the present disclosure.

[0163] After repeating the procedure for N different emitters, it has been found that the maximum value of contrast observed varies significantly between defects and is associated with a change in the internal rates of the system. The results in Fig. 8 present the magnitude of cwODMR contrast in LB measured for each emitter (size of the circles) as a function of internal rates obtained from fits to defect -specific time- resolved experiments. More specifically, the circles represent data measured for different defects, with the position indicating relative rates extracted from photon emission correlation spectroscopy (PECS) and pulsed ODMR experiments, and size corresponding to measured cwODMR contrast. These data are overlaid on a 2D map presenting the simulated cwODMR contrast of LB, where the rates indicated in the axes are varied and all remaining rates are kept constant at the values presented in Table 1 . The colour (e.g., shading) represents the amplitude of cwODMR contrast predicted by the model, with red (blue) regions indicating positive (negative) contrast.

[0164] In the top panel of Fig. 8, the dependence between cwODMR contrast and the spin-selectivity of the direct (kEy .so, vertical axis) and reverse (kso .Gy, horizontal axis) intersystem crossing rates is studied. These results indicate that this class of hBN emitters is characterized by strong spin-selectivity in both direct and reverse intersystem crossing directions, leading to the retention of cwODMR contrast with large off-axis field. In contrast, in the case of the NV centre in diamond and Vg in hBN, only the direct intersystem crossing pathway from the optically excited state to the metastable singlet is spin-selective. This leads to a situation where magnetic-field-induced mixing of the excited-state eigenbasis degrades the spin-selectivity of the intersystem crossing process, fully suppressing optical spin initialization at large off-axis applied field.

[0165] Further, the effect of radiative and non-radiative relaxation pathways from the optically excited state on the cwODMR contrast is explored. The bottom panel of Fig. 8 presents the dependence between measured and calculated cwODMR contrast of LB on non-radiative (vertical axis) and radiative (horizontal axis) relaxation rates from the optically excited state, showing that contrast increases when ke .so is comparable to or larger than FE .G. For the N individual defects studied here, radiative relaxation rates varying between 130 and 280 MHz and intersystem crossing rate varying between 350 and 850 MHz are extracted, indicating that defects that show the same ground-state zero field splitting (ZFS) can display highly variable optical rates in the excited state. This gives rise to variable degree of initialization of the ground-state spin and therefore variable saturated cwODMR contrast. In organic molecular systems, intersystem crossing rates depend exponentially on the energetic alignment between singlet and triplet states, as well as the degree of spin-orbit coupling [25, 26]. For a low-symmetry system as the one here, it is likely that inhomogeneity in local strain experienced by each emitter strongly influences their intersystem crossing rate. Despite being a source of inhomogeneous behaviour, this feature could be harnessed as a pathway to enhance contrast of individual emitters through external fields capable of tuning the energetic alignment between singlet and triplet states, like strain or electric field .

[0166] Attention is now turned to the spin triplet electronic structure in the presence of an external magnetic field.

[0167] Fig. 9 presents the evolution of the ground-state spin eigenstates under applied magnetic field in the x, y, z direction (top to bottom panels), and the simulated optically initialized population, represented by the size of the purple circles. The effect of magnetic field in the model is included by adjusting the spindependent intersystem crossing rates based on a statistical average of the zero-field rates, such that similar to the approach taken by Epstein et al and Tetienne et al for the NV in diamond [8, 27].

[0168] Here, k°qare the zero-field direct and reverse spin-dependent intersystem crossing rates; the coeffcients aipcan be obtained by comparing the zero-field eigenstates (|p(0)» to the eigenstates of the Hamiltonian at a field (|i(B)», such that |i(B)> = Sparp IPC°)>- In the zero-field limit, the system is initialized into the |Gy> state, a direct consequence of the low symmetry observed in this system

[0020] . Magnetic field along the defect y axis (middle panel) mixes |GZ) and |Gx), preserving the zero-field character of |Gy) and retaining overall contrast. Conversely, applied field along x (z) mixes |Gy) and |GZ) (|Gx», redistributing the zero-field initialized population and modifying the saturated cwODMR contrast of each resonance with respect to their zero-field values.

[0169] More particularly, the second (middle) graph shows the variations in the spin triplet sublevels Gz, Gyand Gx in the presence of a magnetic field pointed along the y-direction. As the magnetic field increases, the Gy(middle) sublevel remains the same, whilst the Gx (top) sublevel and Gz(bottom) sublevel curve away from each other. At 50 mT, the initialised population remains substantially completely within the Gysublevel, from which it follows that only LA and LB photoluminescent signatures would be detected should a cwODMR spectra be taken using the apparatus 100 of Fig. 1 A when a magnetic field is applied along the y-axis.

[0170] The first (top) graph shows the variations in the spin triplet sublevels Gz, Gyand Gx in the presence of a magnetic field pointed along the x-direction. In this case, increases in the magnetic field cause a cross over of the Gyand Gx levels, such that Gybecomes the highest energy sublevel, whilst the Gzlevel once again drops. Additionally, the magnetic field causes mixing between the Gyand Gzsublevels, resulting in a transfer of some of the initialised population from the former to the latter as shown in the Fig. In other words, the x-directed magnetic field causes one or more of the transmission coefficient values (e.g.,KSO^GX,Z and / or KS0^Cy) quoted in Table 1 to change, such that a portion of the initialised population moves from the G- sublevel to the Gzsublevel.

[0171] The result of this is a population imbalance between each pair combination of the spin sublevels Gz, Gyand Gx (e.g., population imbalances between each of the combinations Gzand Gy, Gx and Gx, and Gyand Gx), meaning that there is the potential that each of LA, LB and Lc would be detectable in the presence of a 50 mT magnetic field. Of the three, the LA photoluminescent signal would have the highest contrast, as a result of this pair combination of spin sublevels having the greatest population imbalance. The third (bottom) graph in Fig. 9 shows the variations in the spin triplet sublevels Gz, Gy and Gx in the presence of a magnetic field pointed along the Z-direction. As the magnetic field increases, the Gyand Gx layers move apart, whilst a portion of the Gyinitialised spin population is transferred to the Gx level. This suggests that once again photoluminescent signatures corresponding to each of LA, LB and Lc would be detectable. However, such would not be the case for the LA photoluminescent signature in the presence of the Z-directed 50 mT magnetic field, at which point the Gy and Gx spin initialised populations appear substantially equal (i.e., the populations of the two levels are balanced), resulting in no changes to the photoluminescence detected during LA transition.

[0172] These predictions are confirmed by studying the influence of magnetic field orientation and amplitude on the saturated cwODMR contrast of LA-C, for the defect modelled in Figs. 3A and 6. Figs 10A-B respectively show the dependence of cwODMR central frequencies (top panel) and normalized cwODMR contrast of LA-C (bottom panels), on the 50-mT magnetic field orientation in the yz and xy planes, compared to the predictions of the model (solid curves). More particularly, Fig. 10A and 10B both show a series of four graphs, in which a first (top) graph represents the variations in resonant frequency of the transitions LA, LB and Lc across a changing magnetic field direction, and the subsequent three graphs respectively represent variations in normalised contrast of the respective transitions LA, LB and Lc. The insets in these graphs represent the direction of rotation of the bias magnetic field. In Fig. 10A, the applied magnetic field follows a rotational path that begins along the z direction, before rotating to the y direction, and then finishing along the z direction again. Meanwhile, in Fig. 10B the applied magnetic field begins along the x direction, before rotating through the y direction and then back to the z direction. In both cases, experimental data is plotted as a series of circles, whilst overlaid curves represent the predictions of the spin triplet model of Fig. 6 using the transmission coefficients in Table 1 .

[0173] The cwODMR contrast is normalised by the zero-field cwODMR contrast of LB. Applied field along the defect y-axis preserves the zero-field contrast distribution. While the cwODMR contrast of LA (LB) is completely (partially) suppressed as the bias field is rotated towards the z axis, the cwODMR contrast of Lc increases (Fig. 10B). Rotating the bias field in the XY plane away from the y axis leads to a slower suppression of the cwODMR contrast of both LA and LB, with a correspondingly slower pick up of the cwODMR contrast of Lc.

[0174] In more detail, in Fig. 10A, the predicted normalised contrasts for the LA and LB transitions peak when the applied magnetic field is parallel to the y-axis, and fall off as the magnetic field moves toward the z-axis, with the LA contrast going down to 0%, and the LB transition going to approximately 40-50%, of the maximum measured contrast. On the other hand, the Lc contrast is expected to be substantially 0% with the applied magnetic field parallel to the y-axis, but rise to approximately 30-40% of the maximum measured contrast when the magnetic field is rotated to the z-axis. These expected trends are broadly born out in the experimental data, which follows similar trends.

[0175] The model-predicted contrasts in Fig. 10B are expected to follow a similar pattern to Fig. 10A. Once again, the normalised contrasts for both LA and LB are highest when the applied magnetic field is along the y direction, with expected drop off toward the now x-axis. Though it is now the LB contrast which goes to near zero when the magnetic field is applied along the x axis, whereas the LA transition contrast, after dipping to substantially zero at a midway point between the y and x axes, finishes at around 60-70% when the magnetic field fully rotates to run along the x axis. Additionally, the Lc transition once again rises from substantially zero when the magnetic field is along the y-axis to around 20-30% of the maximum measured contrast when the magnetic field is along the x-axis. In this case, the experimental data is in even greater agreement with the model than in Fig. 10A, following a very similar pattern to that predicted.

[0176] The results of Figs. 10A-B provide experimental evidence that photoluminescent signatures are detectable for at least two of the transitions regardless of magnetic field direction, and in some cases all three transitions are measurable.

[0177] Turning to Fig. 10C, this presents the cwODMR spectra as a function of By amplitude up to 140 mT. As shown, a substantial portion of the contrast is maintained even when the X-directed magnetic field is increased up to 140 mT, confirming that for this class of defects, contrast is maximally preserved for an applied field along the defect’s y-axis. These results show that, in a low-symmetry system, the preferred direction of applied field for maximal contrast retention may lie in an axis that does not coincide with the defect z-axis.

[0178] Typical nanoscale magnetometry requires the presence of a bias magnetic field that enables distinguishing between positive and negative orientations of target field [1 , 5, 9, 28]. Therefore, the results above are extended to show how the anisotropic cwODMR response of this system impacts its magnetic- field sensitivity at different bias-field configurations.

[0179] Figure 11 A-C present the calculated cwODMR sensitivity (r]DC) of each resonance LA-C as a function of bias-field orientation. More particularly, Fig. 11A represents the sensitivity of the LA transition to magnetic fields applied along varying directions, Fig. 11 B represents the sensitivity of the LB transition to magnetic fields applied along varying directions, and Fig. 11C represents the sensitivity of the Lc transition to magnetic fields applied along varying directions.

[0180] The relationship: where a is a prefactor associated with the cwODMR lineshape (^a = l -88ll —ogg22 / ffo°raGaussian lineshape),

[0181] 3Ei / 3B is the resonance frequency dependence on magnetic field amplitude, Av is the cwODMR resonance full width at half maximum, C is the contrast and PLo is the brightness of the defect in the absence of microwaves corrected by a factor 0.1 to account for collection losses is used. Further, Av ® 30 MHz is used, extracted from the cwODMR spectra f Fig. 1a, and 3Ei / 3B, C and PLO predicted by the above Hamiltonian and the model in Fig. 6, with rates from Table 1 . The calculated sensitivity is plotted as shading on a sphere (i.e., a darker square indicates that the magnitude of the magnetic field can be measured to a higher accuracy in that direction than a lighter square), where the position on the sphere corresponds to the 50-mT bias field orientation. Box, Bo,yand Bo,zaxes indicate bias field aligned to the X-, Y-, Z-axes of the defect, respectively.

[0182] In agreement with the results presented in Fig. 10, the system is predicted to show at least one of the three possible spin resonances at arbitrary 50-mT bias-field orientation, enabling sub-10 pT / VHz sensitivity in any direction. This is in stark contrast with what is seen in the case of the NV centre in diamond, for which the magnetic-field sensitivity decays sharply in the presence of off-axis bias field. These results demonstrate that the hBN defect studied here forms a sensor with large dynamic range, capable of detecting absolute magnetic-field differences four orders of magnitude smaller than the bias field acting on the sensor. Conservative predictions also show that the sensitivity of this system can reach < 500 n l Hz under optimally aligned bias field, indicating that this hBN defect performs competitively with state-of-the-art contenders for single-defect DC magnetometry [11 , 30]. Notably, the simultaneous presence of multiple resonances in certain bias-field configurations provides a route to vectorial mapping of target magnetic fields.

[0183] Building on the findings of Fig. 11 , Fig. 12 presents the calculated vectorial target-field sensitivity for arbitrary bias-field orientation. More particularly, Fig. 12 shows the outline of part of a spherical object, having a plurality of arrow sets distributed across its outer surface. Arrow sets referring to groups of arrows which all originate from a single point on the outer surface of the spherical object. Each arrow in an arrow set represents one of the transitions LA, LB and Lc. The direction of each arrow represents the direction of the maximal sensitivity, and the size of the arrows corresponds to their inverse absolute sensitivity. The point from which each set of arrows emerges from the outer surface of the spherical object represents the direction in which the bias magnetic field is applied. For example, the arrow set emerging from the outer surface point aligned with the Z-axis correspond to the sensitivities of the transitions when the bias magnetic field is applied along the Z-axis.

[0184] Two configurations indicated in the scheme by the black vectors 510, 520, which represent the bias magnetic field orientation. When the off-axis bias field is in the yz plane (i.e., black vector 510), LA 512, LB 514 and Lc 516 are all present with non-collinear sensitivity directions that lie in the yz plane. In this configuration, measurements performed on any two of the three possible resonances enable determining the y and z components of the target field. In this case, no resonance is sensitive to target field orthogonal to the yz plane, such that the x-component of the target field cannot be extracted. Conversely, the x component of the target field can be determined when the off-axis bias field is in the xy plane (i.e., the black vector 520). In this case, LA 522 and Lc 526 are present and sensitive to both the x and y components of the target field.

[0185] In this way, this system enables vectorial mapping of target magnetic field with two independent measurements at different bias field configurations. More particularly, using two non-parallel bias magnetic fields such as (but not limited to) the bias magnetic fields indicated by the bias field arrows 310 320, the magnetic vector of a measurable magnetic field can be determined. More particularly, the first bias magnetic field is first applied across the sheet of 2D layered material 130, and the photoluminescent signatures corresponding to one or more of the transitions LA, LB and Lc are measured in the presence of the measurable magnetic field. These photoluminescent signatures are then subsequently used to determine one or more axial components of the magnetic field. Subsequently, the second bias magnetic field is applied, and the photoluminescent signatures are again measured in the presence of the measurable magnetic field. Providing the bias magnetic fields have been chosen correctly, these second photoluminescent signals can then be used to determine the remaining components of the measurable magnetic field, so as to form a complete 3D vectorial picture of the measurable magnetic field.

[0186] The approach presented here differs from existing protocols for vectorial magnetic field sensing as it does not require an ensemble of differently oriented emitters

[0031] or physical rotation of the quantum sensor itself [32, 33],

[0187] Fig. 13 shows flow diagram illustrating steps of a method 600 of performing magnetometry using cwODMR according to an example of the present invention, comprising steps 602-608. The method may be performed using the apparatus 100 of Fig. 1A, but is not limited in this way.

[0188] In step 602, a sensor element is provided, the sensor element comprising a sheet of 2D layered material having a photon-emitting spin-active defect. The defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field. Providing the sensor element may involve bringing the sensor element to a position from which it can detect the magnetic field to be measured (the ‘measurable magnetic field’). In the present example, it is intended that the sensor element be used to determine relatively small magnetic fields (e.g., on the order of sub mT-10’s mT) generated at object surfaces. In which case, providing the sensor element may involve bringing a portion of the sensor element into close proximity with the object surface (e.g., within 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm or 5 nm.).

[0189] In step 604, a bias magnetic field is applied across the sensor element. The bias magnetic field represents a distinct magnetic field to the magnetic field that is to be determined using the method 600. Rather, the bias magnetic field is applied to the sensor system at a known magnitude and in a known direction, and is usable in the method to control one or more characteristics of the sheet of 2D layered material in preparation for detection of the measurable magnetic field. For example, the applied bias magnetic field can be used to control the spacing of the transitions between the non-degenerate spin sublevels (see discussion in relation to Fig. 9). The skilled person would recognise this as being useful in determining the direction of a measurable magnetic field (e.g., whether the magnetic field is pointed in a +Z or -Z axial direction). Additionally, the applied bias magnetic field is usable to control the sensitivity of transitions between the non-degenerate levels to the measurable magnetic fields, either in general or along specific axial directions (see the discussion in relation to Fig. 12). In this way, sensitivities of sub pT / VHz are achievable.

[0190] In some examples, applying the bias magnetic field involves applying a bias magnetic field of a fixed strength (e.g., 10 mT, 20 mT, 30 mT, 40 mT, or 50 mT, 60 mT, 70 mT, 80 mT, 90 mT, or 100 mT) and direction. Alternatively, a bias magnetic field may be applied which varies in strength and / or direction throughout the method, either continuously or in discreet steps. For example, a first bias field of a first magnitude may be applied along a first direction whilst a first set of measurements are taken (e.g., whilst steps 606-608, discussed below, are performed to measure one or more photoluminescent signatures and thus determine one or more characteristics of the measurable magnetic field), before being replaced by a second bias magnetic field of a second magnitude that is applied along a second direction whilst a second set of measurements are taken. Using multiple bias fields in this way allows a full 3D vectorial picture of the measurable magnetic field to be determined, as discussed in relation to Fig. 12.

[0191] In steps 606 and 608, an ODMR measurement is conducted on the sensor, and a characteristic of a magnetic field is determined based on detected photoluminescence signals.

[0192] The ODMR measurement is performed by subjecting the sensor element to photoluminescence detection whilst a variable frequency microwave signal is applied, where the photoluminescence detection comprises exciting the defect out of the spin triplet state and into an excited state and detecting a photoluminescence signal when the defect relaxes into the spin triplet state. As discussed above, the photoluminescence signal changes dependent on transitions of the defect between the spin triplet state spin sublevels, resulting in photoluminescent signatures appearing at the resonant frequencies of the spin sublevel transitions. These photoluminescent signatures therefore allow detection of the spin sublevel transitions, which can be used to determine the measurable magnetic field.

[0193] Figs. 14A-B show optical images of an example sensor element 720. More particularly, Fig. 14A is a zoomed-out version of the sensor element 720, and Fig. 14B is a zoomed-in version of the sensor element 720. The sensor element 720 may be for use in the apparatus 100 of Fig. 1 A (e.g., the sensor element 720 may be used as the sensor element 120 of the apparatus 100), but is not limited to this function.

[0194] In Fig. 14A, the sensor element 720 comprises a support 722 which is shaped to form a cantilever 724. The support 722 is formed from a, substantially 2D, substrate made of an insulator or semiconductor material, wherein the cantilever 724 protrudes from a side of the substrate. A tip region 725, shown as a black triangle in Figs. 14A-B, is formed from a tapering end portion of the cantilever 724, and further protrudes outward from the surface of the cantilever 724 (e.g., out of the page in Figs. 14A-B) to form a pointed shape along the normal direction to the cantilever surface (not shown in Figs. 14A-B). Said pointed shape being the portion of the sensor element 720 that is brought into closest proximity to the object to be sensed during use of the sensor element 720. However, alternative embodiments of the support are also envisaged. For example, the support may instead form a tapered pillar ending with a pointed tip at a distal end.

[0195] In use, the sensor element 720, and more particularly the pointed shape of the tip region 725, is scanned over the surface of an object to be sensed, whilst measurements of the object to be sensed are simultaneously taken. During, or after, this process, the measurements can be combined into 2D image of the object showing changes in the sensed characteristic across the surface of the object to be sensed.

[0196] The sensor element 720 further comprises a sheet of 2D layered material 730, which is supported on the outer surface of the support. More particularly, the sheet of 2D layered material 730 is supported on the cantilever 724, and more particularly still on the tip region 725. Preferably, the sheet of 2D layered material 730 is a film having a thickness of no more than 10 nm, 20 nm, 30 nm, 40 nm, 50 nm 60 nm, 70 nm, 80 nm, 90 nm, or 100 nm. This advantageously makes it easier to manufacture (e.g., grow), as well as making it easier to apply over the surface of the support 722. However, the present disclosure is not limited in this way, and alternative examples may include sheets of 2D layered material 730 that have a higher thickness.

[0197] The sheet of 2D layered material 730 includes a single-photon-emitting spin-active defect, which can be used to sense one or more characteristics of the object to be sensed as described in relation to the previous Figs. The photon emitting defect is located in register with an apex of the pointed shape (e.g., the distal end of the pointed shape furthest from the surface of the cantilever 724). Further, the defect is preferably located at or substantially near the surface of the sheet of 2D layered material 730 (e.g., the surface of the sheet of 2D layered material 730 facing away from the cantilever 724). For example, the defect may be located in a surface layer of the sheet of 2D layered material 730, or may be located one or two layers below the surface layer. In this way, the defect is positioned as close to the object to be sensed as possible during measurement, which advantageously increases the sensitivity of the defect to the sensed characteristic (e.g., the magnetic field) of the object to be sensed.

[0198] Figs. 15 and 16 show a method 800 of forming a sensor element for use in the apparatus 100 of Fig. 1A, comprising the steps 802-806. More particularly, Fig. 15 shows a flowchart representation of the method 800, whilst Fig. 16 shows a pictorial representation of the method 800.

[0199] In step 802, the sheet of 2D layered material 830 is grown onto the growth substrate 810. The growth substrate 810 may be a sapphire substrate. Furthermore, the growth may be produced via chemical vapour deposition (CVD), using several precursor materials 812 to form the base 2D layered material as well as one or more spin-active defects. The sheet of 2D layered material 830 may be grown to a particular thickness that is less than 50 mm, 40 mm, 30 mm, 20 mm or 10 mm. Alternatively, the sheet of 2D layered material 830 may be grown to comprise fewer than a particular number of layers. E.g., 100 layers, 50 layers, 10 layers, 9 layers, 8 layers, 7 layers, 6 layers, or 5 layers. However, the present disclosure is not limited in these ways.

[0200] Between step 802 and step 804, the growth substrate 810 / sheet of 2D layered material 830 may be cleaved into multiple smaller pieces. These pieces may be on the scale of 10 mm by 10 mm, 9 mm by 9 mm, 8 mm by 8 mm, 7 mm by 7 mm, 6 mm by 6 mm, 5 mm by 5 mm, 4 mm by 4 mm, 3 mm by 3 mm, 2 mm by 2 mm, 1 mm by 1 mm or smaller.

[0201] In step 804, the sheet of 2D layered material 830 is separated from the growth substrate 810 via immersion in a liquid. For example, the growth substrate 810 and sheet of 2D layered material 830 combination may be placed into (e.g., submerged in) deionised water. The liquid causes a separation of the heavier growth substrate 810 and the lighter sheet of layered material 830, such that the sheet of 2D layered material 830 may be left floating on a surface of the liquid.

[0202] In step 806, the sheet of 2D layered material 830 is transferred to the support 822. As shown in Fig. 16, the transfer takes place within the liquid. The support 822 may be submerged in the liquid, and applied to a bottom side of the sheet of 2D layered material 830. However, the present disclosure is not limited in this way, and the sheet of 2D layered material 830 may instead be removed from the liquid first before being applied to the support 822. The sheet of 2D layered material 830 may be arranged on the support 822 to overlay with specific regions of the underlying structure. For example, the defect may be arranged to overlay a particular, structural electrical or optical feature on the underlying support 822. However, the present disclosure is not limited in this way.

[0203] Fig. 16 highlights three examples of sensor elements 820 falling within the scope of the present disclosure which may be formed by the method 800. A first sensor element 820-1 consists of a flat support 822-1 onto which the sheet of 2D layered material 830-1 is placed flatly. A second sensor element 820-2 consists of a support 822-2 that tapers at one end to form a tip region 825-2, onto which the sheet of 2D layered material 830 is applied. A third sensor element 820-3 resembles the sensor element 820, and includes a support 822-3 formed into a cantilever probe extending in a longitudinal direction with a tip region 825-3 at one longitudinal end. Said tip region 825-3 extends outward in a direction perpendicular to the longitudinal direction, and further tapers inward to form a pointed tip, onto which the sheet of 2D layered material 830-3 is applied. In both the sensor elements 820-2 and 820-3, the defect of the sheet of 2D layered material 830-2 830-3 is aligned with the tip region 825-2 825-3. The defect may be in register with the pointed end of the tip region 825-2 825-3, or may be within a certain distance of said pointed end.

[0204] The above method 800 may be conducted multiple times, with each resulting sensor element being tested to determine whether a spin-active defect is aligned with the apex of the pointed shape. In cases where it is determined that a defect is present in this position, the sensor element may then be used to perform magnetometry measurements. In cases where tit is determined that no defect is suitably located on the apex of the pointed shape of the tip, the sensor element may be discarded.

[0205] ***

[0206] The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

[0207] While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.

[0208] For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations. Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0209] Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

[0210] It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / - 10%.

[0211] References

[0212] A number of publications are cited above in order to more fully describe and disclose the invention and the state of the art to which the invention pertains. Full citations for these references are provided below. The entirety of each of these references is incorporated herein.

[0213] [1] G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, “Nanoscale imaging magnetometry with diamond spins under ambient conditions,” Nature 455, 648 (2008).

[0214] [2] J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature 455, 644 (2008).

[0215] [3] L. Rondin, J. P. Tetienne, T. Hingant, J. F. Roch, P. Maletinsky, and V. Jacques, “Magnetometry with nitrogen-vacancy defects in diamond,” Rep. Prog. Phys. 77, 056503 (2014).

[0216] [4] F. Casola, T. van der Sar, and A. Yacoby, “Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond,” Nat. Rev. Mater. 3, 17088 (2018).

[0217] [5] A. K. C. Tan, H. Jani, M. Hogen, L. Stefan, C. Castelnovo, D. Braund, A. Geim, A. Mechnich, M. S. G. Feuer, H. S. Knowles, A. Ariando, P. G. Radaelli, and M. Atature, “Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry,”

[0218] Nat. Mater., 20, 205 (2023). [6] D. Le Sage, K. Arai, D. R. Glenn, S. J. DeVience, L. M. Pham, L. Rahn-Lee, M. D. Lukin, A. Yacoby, A. Komeili, and R. L. Walsworth, “Optical magnetic imaging of living cells,” Nature 496, 486 (2013).

[0219] [7] Y. Wu, F. Jelezko, M. B. Plenio, and T. Weil, “Diamond quantum devices in biology,” Angew Chem. Int. Ed. Engl. 55, 6586 (2016).

[0220] [8] J. P. Tetienne, L. Rondin, P. Spinicelli, M. Chipaux, T. Debuisschert, J. F. Roch, and V. Jacques, “Magnetic-field-dependent photodynamics of single nv defects in diamond: An application to qualitative all-optical magnetic imaging,” New J. of Phys., 14, 103033, (2012).

[0221] [9] L. Rondin, J. P. Tetienne, P. Spinicelli, C. Dal Savio, K. Karrai, G. Dantelle, A. Thiaville, S. Rohart, J. F. Roch, and V. Jacques, “Nanoscale magnetic field mapping with a single spin scanning probe magnetometer,” Appl. Phys. Lett. 100,153118, (2012), 10.1063 / 1.3703128.

[0222]

[0010] P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Yacoby, “A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres,” Nat Nanotechnol 7, 320 (2012).

[0223]

[0011] Jared Rovny S. G. and Eugene Dernier Nathalie P. de Leon N.P. Ania C. Bleszynski Jayich and- Patrick Maletinsky, “New opportunities in condensed matter physics for nanoscale quantum sensors,” (2024), https: / / doi.Org / 10.48550 / arXiv.2403.13710.

[0224]

[0012] H. L. Stern, Q. Gu, J. Jarman, S. Eizagirre Barker, N. Mendelson, D. Chugh, S. Schott, H. H. Tan, H. Sirringhaus, I. Aharonovich, and M. Atature, “Room-temperature optically detected magnetic resonance of single defects in hexagonal boron nitride,” Nat. Commun. 13, 618 (2022).

[0225]

[0013] A. Gottscholl, M. Kianinia, V. Soltamov, S. Orlinskii, G. Mamin, C. Bradac, C. Kasper, K. Krambrock, A. Sperlich, M. Toth, I. Aharonovich, and V. Dyakonov, “Initialization and read-out of intrinsic spin defects in a van der waals crystal at room temperature,” Nat. Mater. 19, 540 (2020).

[0226]

[0014] H. S. Stern, C. M. Gilardoni, Gu Q., S. Eizagirre Barker, O. F. J. Powell, X. Deng, S. A. Fraser, L. Follet, C. Li, A. J. Ramsay, H. H. Tan, I. Aharonovich, and M. Atature, “A quantum coherent spin in hexagonal boron nitride at ambient conditions,” Nat. Mater. (2024).

[0227]

[0015] A. J. Healey, S. C. Scholten, T. Yang, J. A. Scott, G. J. Abrahams, I. O. Robertson, X. F. Hou, Y. F. Guo, S. Rahman, Y. Lu, M. Kianinia, I. Aharonovich, and J. P. Tetienne, “Quantum microscopy with van der waals heterostructures,” Nat. Phys., 19, 87 (2022), 10.1038 / s41567-022-01815-5.

[0016] M. Huang, J. Zhou, D. Chen, H. Lu, N. J. McLaughlin, S. Li, M. Alghamdi, D. Djugba, J. Shi, H.

[0228] Wang, and C. R. Du, “Wide field imaging of van der waals ferromagnet Fe(3)GeTe(2) by spin defects in hexagonal boron nitride,” Nat. Commun. 13, 5369 (2022).

[0229]

[0017] S. Vaidya, X. Gao, S. Dikshit, I. Aharonovich, and T. Li, “Quantum sensing and imaging with spin defects in hexagonal boron nitride,” Adv. in Phys.: X 8 (2023), 10.1080 / 23746149.2023.2206049.

[0230]

[0018] B. Whitefield, M. Toth, I. Aharonovich, J. P. Tetienne, and M. Kianinia, “Magnetic field sensitivity optimization of negatively charged boron vacancy defects in hBN,” Adv. Quantum Technol., 2300118 (2023).

[0231]

[0019] R. E. K. Fishman, R. N. Patel, D. A. Hopper, T.-Y. Huang, and L. C. Bassett, “Photon-emission- correlation spectroscopy as an analytical tool for solid-state quantum defects,” PRX Quantum 4, 010202 (2023).

[0232]

[0020] A. Mena, S. K. Mann, Cowley-Semple A., E. Bryan, Heutz S., McCamey D. R., Attwood M., and Sam L. Bayliss, “Room-temperature optically detected coherent control of molecular spins,” https: / / doi.org / 10.48550 / arXiv.2402.07572.

[0233]

[0021] R. N. Patel, D. A. Hopper, J. A. Gusdorff, M. E. Turiansky, T.-Y. Huang, R. E. K. Fishman, B. Porat, C. G. Van de Walle, and L. C. Bassett, “Probing the optical dynamics of quantum emitters in hexagonal boron nitride,” PRX Quantum 3, 030331 (2022)..

[0234]

[0022] Tzu-Yung Huang Jordan A. Gusdorff David A. Fehr David A. Hopper S. Alex Breitweiser Benjamin Porat Michael E. Flatte Lee C. Bassett Raj N. Patel, R. E. K. F., “Room temperature dynamics of an optically addressable single spin in hexagonal boron nitride,” Nano Lett. 24, 7623 (2024).

[0235]

[0023] Kristina Malinowski Benjamin E.C. Koltenbah Harry A. Atwater Hamidreza Akbari, P. K. J., “Photon statistics analysis of h-BN quantum emitters with pulsed and continuous-wave excitation,” https: / / doi.org / 10.48550 / arXiv.2403.12291.

[0236]

[0024] D. Zhong, S. Gao, M. Saccone, J. R. Greer, M. Bernardi, S. Nadj-Perge, and A. Faraon, “Carbon- related quantum emitter in hexagonal boron nitride with homogeneous energy and 3-fold polarization,” Nano Lett. 24, 1106 (2024).

[0237]

[0025] M. Attwood, X. Xu, M. Newns, Z. Meng, R. A. Ingle, H. Wu, X. Chen, W. Xu, W. Ng, T. T. Abiola, V. G. Stavros, and M. Oxborrow, “N-heteroacenes as an organic gain medium for room-temperature masers,” Chem. Mater. 35, 4498 (2023).

[0026] S. Bogatko, P. D. Haynes, J. Sathian, J. Wade, J.-S. Kim, K.-J. Tan, J. Breeze, E. Salvadori, A.

[0238] Horsfield, and M. Oxborrow, “Molecular design of a room-temperature maser,” The J. of Phys. Chemistry C 120, 8251 (2016).

[0239]

[0027] RJ Epstein, FM Mendoza, YK Kato, and DD Awschalom, “Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond,” Nat. Phys. 1 , 94 (2005).

[0240]

[0028] C. L. Degen, “Scanning magnetic field microscope with a diamond single-spin sensor,” Appl. Phys. Lett. 92, 243111 (2008).

[0241]

[0029] N. Oshnik, P. Rembold, T. Calarco, S. Montangero, E. Neu, and M. M. Muller, “Robust magnetometry with single nitrogen-vacancy centers via two-step optimization,” Phys. Rev. A 106, 013107 (2022).

[0242]

[0030] J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, “Sensitivity optimization for nv-diamond magnetometry,” Rev. of Mod. Phys. 92, 015004 (2020).

[0243]

[0031] B. Chen, X. Hou, F. Ge, X. Zhang, Y. Ji, H. Li, P. Qian, Y. Wang, N. Xu, and J. Du, “Calibration-free vector magnetometry using nitrogen-vacancy center in diamond integrated with optical vortex beam,” Nano Lett. 20, 8267 (2020).

[0244]

[0032] S.-Y. Lee, M. Niethammer, and J. Wrachtrup, “Vector magnetometry based on s=3 / 2 electronic spins,” Phys. Rev. B 92, 115201 (2015).

[0245]

[0033] M. Niethammer, M. Widmann, S.-Y. Lee, P. Stenberg, O. Kordina, T. Ohshima, N. T. Son, E. Janzen, and J. Wrachtrup, “Vector magnetometry using silicon vacancies in 4H-SiC under ambient conditions,” Phys. Rev. Appl. 6, 034001 (2016).

Claims

Claims:1 . A method of carrying out magnetometry, comprising the steps: providing a sensor element comprising a sheet of a 2D layered material having a photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field; conducting an optically detected magnetic resonance measurement on the sensor element by subjecting the sensor element to optical excitation and photoluminescence detection whilst a variable frequency microwave signal is applied, the microwave signal causing transitions between the spin triplet state spin sublevels, wherein the photoluminescence detection comprises detecting a change in photoluminescence signal when the microwave signal is resonant with a transition between the spin triplet state spin sublevels; and determining a characteristic of a magnetic field based on the detected photoluminescence signals.

2. The method of claim 1 , wherein each transition of the lattice defect between each pair combination of the spin triplet state spin sublevels is used to determine the characteristic of the magnetic field.

3. The method of claim 1 or claim 2, wherein a first transition between a pair of the spin triplet state spin sublevels is used to determine a first component of the magnetic field along a first axis, and a second transition between a pair of spin triplet state spin sublevels different from the first transition is used to determine a component of the magnetic field along a second axis different from the first axis.

4. The method of any one of the previous claims, wherein the defect has low symmetry.

5. The method of any one of the previous claims, further comprising the step of applying a bias magnetic field across the sensor element.

6. The method of claim 5, wherein the sensitivity of at least one of the transitions of the lattice defect between pair combinations of the three spin sublevels in the spin triplet state is controllable using the bias magnetic field.

7. The method of claim 5 or claim 6, wherein the characteristic of the magnetic field is determined by first measuring the photoluminescent signal whilst a first bias field is applied along a first axis, and subsequently measuring the photoluminescent signal whilst a second bias field is applied along a second axis that is non-parallel with the first axis.

8. The method of any one of the previous claims, wherein the defect is individually addressable.

9. The method of any one of the previous claims, wherein the sheet of 2D layered material comprises hexagonal boron nitride.

10. The method of any one of the previous claims, wherein the lattice spin defect is a carbon-related defect.11 . The method of any one of the previous claims, wherein the method determines a magnetic field vector of the magnetic field based on the photoluminescence signals.

12. A magnetometer for carrying out magnetometry via optically detected magnetic resonance, the magnetometer comprising: a sensor element comprising a sheet of 2D layered material having a photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field; a microwave signal generator configurable to cause transitions of the lattice defect between pairs of the spin triplet state sublevels, an optical source for exciting the lattice defect; and a photodetector for detecting a change in photoluminescence signal emitted from the sheet of 2D layered material generated when the microwave signal is resonant with a transition between the spin triplet state sublevels, the magnetometer being configured to determine a characteristic of a magnetic field based on the detected photoluminescence signals.

13. A sensor element for use in the method of any one of claims 1-11 , and / or in the magnetometer of claim 12, the sensor element comprising a sheet of 2D layered material in the form of a layer having a single photon-emitting spin-active defect, wherein the defect has a spin triplet state with first, second and third non-degenerate spin sublevels in the absence of applied magnetic field, the sensor element further comprising a support on which the sheet of 2D layered material is supported.

14. A sensor element according to claim 13 wherein the sensor element, sheet of 2D layered material and / or support are configured to enable optical interrogation of the defect.

15. A sensor element according to claim 13 or claim 14 wherein the support includes a tip region, the sheet of 2D layered material being located over at least part of the tip region.

16. A sensor element according to claim 15 wherein the defect is located substantially in register with an apex of the tip region.

17. A method of manufacturing a sensor element according to any one of claims 13-16, wherein the sheet of 2D layered material is grown on a first substrate and the sheet of 2D layered material is transferred from the first substrate onto the support.

18. The method of claim 17, wherein the sheet of 2D layered material is separated from the first substrate via immersion in a liquid.

19. A sensor device comprising a sheet of 2D layered material mounted onto a cantilever probe, wherein the sheet of layered material comprises a photon-emitting spin-active defect which is positioned at a tip region of the cantilever probe, wherein the sensor device is configured to perform magnetometry via optically detected magnetic resonance, in which the sensor device is subjected to photoluminescence detection whilst a variable frequency microwave signal is applied, and a characteristic of a magnetic field is determined based on the detected photoluminescence signals.

20. The sensor device of claim 19, wherein the tip region includes a pointed portion that extends outward normally from a surface of the cantilever probe.

Images