Superconducting resonator for high-resolution detection of magnetic materials and its design method

Abstract

The present invention provides a superconducting resonator for high-resolution detection of magnetic materials and a design method thereof. The method comprises: determining a magnetic material layer to be measured; determining a resonant frequency of a resonator according to the magnetic material layer to be measured; constructing a simulation model, wherein the simulation model includes a substrate; a resonator formed on the substrate, wherein microwave lines located on the substrate surface are formed at both ends of the resonator, the microwave lines forming a coplanar waveguide, and the resonator is coupled to the microwave lines; grounding layers located on the substrate surface are provided on both sides of the resonator; an initial air gap, an initial coupling length, and a length of the resonator are determined according to the resonant frequency and the material of the substrate; performing simulation using the initial air gap, initial coupling length, and length of the resonator according to the simulation model to obtain a quality factor of the resonator; adjusting the initial air gap and initial coupling length according to the quality factor until the quality factor of the resonator meets the requirement, and determining the air gap and coupling length of the resonator.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic material detection, and in particular relates to a superconducting resonator for high-resolution detection of magnetic materials and a design method thereof. Background Art

[0002] The study of the spin dynamics of magnetic materials has important scientific value and application prospects in the fields of condensed matter physics and advanced information technology. Spin dynamics is directly related to the material's magnetic relaxation, spin transport properties, and the regulation mechanism of the magnetic order state, providing a key physical basis for the development of a new generation of spintronic devices, high-density magnetic storage media, and quantum information processing systems. This research direction can not only promote an order of magnitude increase in the sensitivity of magnetic sensors, but also achieve nanosecond-level spin state manipulation, laying a theoretical foundation for low-power non-volatile memory and topological spin structure devices. With breakthroughs in the study of spin-orbit coupling effects and ultrafast magnetodynamics, precise detection of spin dynamics will accelerate the practical application of disruptive technologies such as quantum bit coupling and magnon integrated circuits, and give rise to innovative application paradigms in fields such as quantum computing, microwave photonics, and biomedical testing.

[0003] While current microwave-based detection technologies (such as ferromagnetic resonance spectroscopy and microwave magneto-optical detection) can characterize macroscopic spin dynamics, they still face significant limitations in key performance dimensions. Conventional cavity detection relies on copper resonators with limited quality factors, and its frequency resolution and sensitivity are insufficient for quantitative analysis of nanoscale magnetic structures. Time-domain measurement techniques using coplanar waveguides, while capable of achieving picosecond temporal resolution, are limited by signal attenuation caused by impedance mismatch and struggle to maintain stable coupling in low-temperature, high-magnetic-field environments. Existing methods generally face a conflict between the spatial uniformity of the microwave field and localized detection sensitivity: expanding the detection area reduces the ability to detect individual magnetic domains, while focused probes struggle to avoid signal crosstalk caused by fringe field interference. Furthermore, the thermal noise floor of conventional microwave circuits limits the efficiency of extracting weak magnetic signals, making the detection of ultrafast spin fluctuations in ferrimagnets and antiferromagnets a technical bottleneck. These limitations severely restrict the study of multi-degree-of-freedom coupling mechanisms in complex magnetic systems and hinder the advancement of spintronic devices towards three-dimensional integration. Summary of the Invention

[0004] To address the above technical issues, the present invention provides a superconducting resonator for high-resolution detection of magnetic materials and its design method. By employing a coplanar waveguide structure and optimizing the resonator's materials and parameters, a high-quality resonator is achieved. Compared to conventional copper resonators, this superconducting resonator reduces surface current losses by three orders of magnitude. Furthermore, the superconducting resonator can measure magnon frequencies with an accuracy of up to 1 MHz, a two-order-of-magnetic improvement compared to conventional ferromagnetic resonance spectrometers.

[0005] In one aspect, the present invention provides a method for designing a superconducting resonator for high-resolution detection of magnetic materials, comprising:

[0006] Determine the magnetic material layer to be tested;

[0007] Determining the resonant frequency of the resonator according to the magnetic material layer to be measured;

[0008] Constructing a simulation model, the simulation model including a substrate; a resonator formed on the substrate, microwave lines formed at both ends of the resonator and located on the surface of the substrate, the microwave lines forming a coplanar waveguide, the resonator coupled to the microwave lines; and ground layers located on the surface of the substrate on both sides of the resonator;

[0009] Determine an initial air gap of the resonator, an initial coupling length of the resonator, and a length of the resonator according to the resonant frequency and the material of the substrate; the initial air gap is the distance between the resonator and the ground layer;

[0010] According to the simulation model, the initial air gap of the resonator, the initial coupling length of the resonator, and the length of the resonator are used for simulation to obtain the quality factor of the resonator;

[0011] The initial air gap and the initial coupling length of the resonator are adjusted according to the quality factor of the resonator until the quality factor of the resonator meets the requirements, and the air gap and the coupling length of the resonator are determined.

[0012] Optionally, the substrate is a LAO substrate.

[0013] Optionally, the resonator is a half-wavelength resonator.

[0014] Optionally, the microwave line is formed of YBCO material.

[0015] Optionally, the resonator is formed of YBCO material.

[0016] Optionally, the resonator is a centrosymmetric structure.

[0017] Optionally, the resonator is a centrosymmetrical S-shaped structure.

[0018] Optionally, the length of the resonator is determined as follows:

[0019]

[0020]

[0021] Where, is the length of the resonator, is the wavelength of the electromagnetic wave at the resonant frequency of the resonator, It represents the transmission speed of electromagnetic waves in the coplanar waveguide. represents the resonant frequency of the resonator, represents the speed of light, represents the relative dielectric constant of the substrate.

[0022] Optionally, the initial air gap of the resonator and the initial width of the resonator are determined as follows:

[0023] According to the formula 、 、 、 Determining characteristic impedance Where, represents the input impedance of the resonator, represents the characteristic impedance of the resonator, Represents the resonator input impedance The corresponding capacitance, Represents the resonator input impedance The corresponding inductance and the resonator input impedance The corresponding resistance is set to 0, represents the attenuation constant of the transmission line, represents an imaginary number, is the difference between the resonator input frequency and the resonant frequency, represents the input frequency of the resonator, represents the resonant frequency of the resonator;

[0024] According to the characteristic impedance of the resonator And the formula 、 、 Sure Where, represents the inductance corresponding to the characteristic impedance of the resonator, represents the capacitance corresponding to the characteristic impedance of the resonator, represents the dielectric constant of vacuum, represents the elliptic integral of the first kind, represents the dependent variable obtained according to the initial coupling length of the signal line and the initial air gap of the signal line, represents the relative dielectric constant of the substrate;

[0025] According to the determined and formula , determines the initial coupling length of the resonator and the initial air gap of the resonator .

[0026] On the other hand, a superconducting resonator for high-resolution detection of magnetic materials is provided. The superconducting resonator for high-resolution detection of magnetic materials is designed using any of the methods described above.

[0027] The technical solution provided by the present invention has the following beneficial effects:

[0028] This invention provides a design method for a superconducting resonator for high-resolution detection of magnetic materials. By adjusting the coupling length and air gap of the resonator, precise impedance matching of 50-75Ω is achieved, facilitating integration with other microwave or quantum circuits. Compared to coaxial resonators, the device size can be significantly reduced, improving integration. The coplanar waveguide structure has excellent impedance matching characteristics, and the characteristic impedance can be precisely controlled by adjusting the air gap and coupling length of the resonator. The resonant frequency and mode can be controlled through different geometric designs. By optimizing the parameters of the superconducting resonator, a superconducting resonator with a high quality factor can be obtained while ensuring the resonant frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0030] Figure 1 A flow chart of a design method for a superconducting resonator for high-resolution detection of magnetic materials provided by the present invention;

[0031] Figure 2 A schematic structural diagram of a superconducting resonator for high-resolution detection of magnetic materials provided by the present invention;

[0032] Figure 3 A schematic structural diagram of another superconducting resonator for high-resolution detection of magnetic materials provided by the present invention;

[0033] Figure 4 A schematic diagram of experimental results of an S11 parameter provided by the present invention;

[0034] Figure 5 A magnetic field distribution diagram of a superconducting resonator provided by the present invention in the X direction;

[0035] Figure 6 A magnetic field distribution diagram of a superconducting resonator provided by the present invention in the Y direction;

[0036] Figure 7 An optical display of a superconducting resonator provided by the present invention;

[0037] Figure 8 A schematic diagram of a test system provided by the present invention;

[0038] Figure 9 A schematic diagram of experimental results of an S21 parameter provided by the present invention;

[0039] Figure 10 A schematic diagram of another dispersion relation of resonant frequency with static magnetic field provided by the present invention;

[0040] Figure 11 A schematic diagram of experimental results of an S21 parameter provided by the present invention;

[0041] Figure 12 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 38K provided by the present invention;

[0042] Figure 13 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.9K provided by the present invention;

[0043] Figure 14 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.8K provided by the present invention;

[0044] Figure 15 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.7K provided by the present invention;

[0045] Figure 16 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.6K provided by the present invention;

[0046] Figure 17 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.5K provided by the present invention;

[0047] Figure 18 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.4K provided by the present invention;

[0048] Figure 19 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.3K provided by the present invention;

[0049] Figure 20 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.2K provided by the present invention;

[0050] Figure 21 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37.1K provided by the present invention;

[0051] Figure 22 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 37K provided by the present invention;

[0052] Figure 23 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.9K provided by the present invention;

[0053] Figure 24 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.8K provided by the present invention;

[0054] Figure 25 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.7K provided by the present invention;

[0055] Figure 26 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.6K provided by the present invention;

[0056] Figure 27 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.5K provided by the present invention;

[0057] Figure 28 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.4K provided by the present invention;

[0058] Figure 29 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.3K provided by the present invention;

[0059] Figure 30 A schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field at a temperature of 36.2K provided by the present invention;

[0060] Figure 31 This is a schematic diagram of the dispersion relationship between the resonant frequency and the static magnetic field under the temperature condition of 36.1K provided by the present invention.

[0061] The reference numerals are as follows:

[0062] 11: substrate; 12: resonator; 121: first bend; 122: second bend; 123: first coupling portion; 124: second coupling portion; 13: microwave line; 14: magnetic material layer to be measured; 15: ground layer

[0063] 21: Vector network analyzer; 22: Physical property measurement system; 221: First temperature region; 222: Second temperature region; 223: Third temperature region. DETAILED DESCRIPTION

[0064] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0065] Figure 1 This is a flow chart of the design method of a superconducting resonator for high-resolution detection of magnetic materials provided by the present invention. Figure 1 , the method steps include:

[0066] S101. Determine a magnetic material layer to be tested.

[0067] S102 : Determine the resonant frequency of the resonator according to the magnetic material layer to be measured.

[0068] Taking the CrPS4 layer as an example, the process of determining the resonant frequency of the resonator is as follows:

[0069] Based on the relationship curve between the frequency of the excited magnetic oscillators and the external magnetic field in the ferromagnetic resonance mode of the magnetic material layer to be measured, the frequency of the magnetic oscillators under the target external magnetic field is then selected as the resonant frequency of the resonator.

[0070] For example, based on the uniaxial anisotropy of CrPS4, the temperature is determined to be 36.5K-38K and the easy axis is the in-plane b-axis. At the same time, based on the ferromagnetic resonance (FMR) resonance field and resonance frequency of CrPS4 in this temperature range, the resonance frequency of 11.3GHz at 38K when the static magnetic field (i.e., the external magnetic field) increases by 4000oe is selected as the resonant frequency of the resonator.

[0071] S103. Construct a simulation model, the simulation model including a substrate; a resonator formed on the substrate, microwave lines formed at both ends of the resonator and located on the surface of the substrate, the microwave lines forming a coplanar waveguide, the resonator and the microwave lines being coupled; and a ground layer located on the surface of the substrate on both sides of the resonator.

[0072] Figure 2 This is a schematic diagram of the structure of a superconducting resonator for high-resolution detection of magnetic materials provided by the present invention, which is also a schematic diagram of a simulation model. Specifically, it shows:

[0073] A substrate 11; a resonator 12 formed on the substrate 11, with microwave lines 13 formed at both ends of the resonator 12 and located on the surface of the substrate 11, the microwave lines 13 forming a coplanar waveguide, and the resonator 12 coupled to the microwave lines 13; a magnetic material layer 14 to be measured is provided on the surface of the resonator, and ground layers 15 located on the surface of the substrate 11 are provided on both sides of the resonator 12.

[0074] In this embodiment, substrate 11 is a LAO substrate. LAO refers to a lanthanum aluminum oxide (LaAlO3) substrate. LAO is a substrate that better matches the YBCO lattice and has a lower loss tangent, helping to reduce microwave losses.

[0075] In this embodiment, the resonator 12 is a half-wavelength resonator.

[0076] In this embodiment, the microwave line 13 is formed of YBCO material.

[0077] In this embodiment, the resonator 12 is formed of YBCO material, wherein the YBCO layer is a yttrium barium copper oxide (YBa2Cu3O7) high temperature superconductor.

[0078] In this embodiment, the resonator 12 is a centrosymmetrical structure, wherein the resonator is a centrosymmetrical smooth curve structure.

[0079] In this embodiment, the resonator 12 includes a first bent portion 121, a second bent portion 122, a first coupling portion 123 and a second coupling portion 124; wherein, one end of the first bent portion 121 is connected to one end of the second bent portion 122, the first coupling portion 123 is connected to the other end of the first bent portion 121, and the second coupling portion 124 is connected to the other end of the second bent portion 122; the first coupling portion 123 and the second coupling portion 124 are used to perform capacitive coupling with the microwave line 13.

[0080] After determining the resonant frequency of the resonator 12, it is also necessary to determine the shape of the resonator 12. In the present invention, setting up a centrally symmetrical resonator 12 has the following advantages: First, the resonator 12 provided in this application, which is similar to an "S"-shaped structure and is centrally symmetrical, has a uniform magnetic field distribution, and can excite a high-intensity magnetic field in both the X and Y directions, which is conducive to detecting magnetic materials with different excitation modes. For example, some magnetic materials can only be excited by the magnetic field in the X direction, and some magnetic materials can only be excited by the magnetic field in the Y direction. The magnetic material of this application can detect the performance of the above two magnetic materials. Second, the resonator 12 provided in this application, which is similar to an "S"-shaped structure and is centrally symmetrical, is conducive to reducing the size of the device, thereby improving the degree of integration.

[0081] It is worth noting that when the superconducting resonator provided in the present application is used to measure a magnetic material layer to be measured that is excited by an X-direction magnetic field, the magnetic material layer to be measured can be disposed on the first coupling portion 123 or the second coupling portion 124. When the superconducting resonator provided in the present application is used to measure a magnetic material layer to be measured that is excited by a Y-direction magnetic field, the magnetic material layer to be measured can be disposed at the connection point between the first curved portion 121 and the second curved portion 122.

[0082] Of course, the shape of the resonator 12 is an example provided in the present application and is not intended to limit the present invention. The shape of the resonator 12 can also be simply adjusted according to the required magnetic field.

[0083] In this embodiment, sonnet simulation software (an electromagnetic field simulation software) can be used to set the substrate 11 and the corresponding geometric structure for simulation to obtain the quality factor (Q value), resonant frequency and electromagnetic field distribution of the corresponding superconducting resonator.

[0084] Figure 3 The schematic diagram of the structure of another superconducting resonator for high-resolution detection of magnetic materials provided by the present invention is also provided along the Figure 2 The cross-sectional view of the virtual gate A-A', Figure 3 The width of the resonator 12 is specifically shown in FIG. (ie, coupling length), the air gap of the resonator 12 .

[0085] S104 , determining an initial air gap of the resonator 12 , an initial coupling length of the resonator 12 , and a length of the resonator according to the resonant frequency and the material of the substrate 11 ; the initial air gap is the distance between the resonator 12 and the ground layer 15 .

[0086] In this embodiment, the length of the resonator 12 is determined as follows:

[0087]

[0088]

[0089] Where, is the length of the resonator, is the wavelength of the electromagnetic wave at the resonant frequency of the resonator, It represents the transmission speed of electromagnetic waves in the coplanar waveguide. represents the resonant frequency of the resonator, represents the speed of light, represents the relative dielectric constant of the substrate.

[0090] In this embodiment, the initial air gap of the resonator and the initial width of the resonator are determined as follows:

[0091] The first step is to use the formula 、 、 、 Determining characteristic impedance Where, represents the input impedance of the resonator, represents the characteristic impedance of the resonator, Represents the resonator input impedance The corresponding capacitance, Represents the resonator input impedance The corresponding inductance and the resonator input impedance The corresponding resistance is set to 0, represents the attenuation constant of the transmission line, represents an imaginary number, is the difference between the resonator input frequency and the resonant frequency, represents the input frequency of the resonator, Indicates the resonant frequency of the resonator.

[0092] The second step is to determine the characteristic impedance of the resonator And the formula 、 、 Sure Where, represents the inductance corresponding to the characteristic impedance of the resonator, represents the capacitance corresponding to the characteristic impedance of the resonator, represents the dielectric constant of vacuum, represents the elliptic integral of the first kind, represents the dependent variable obtained according to the initial coupling length of the signal line and the initial air gap of the signal line, represents the relative dielectric constant of the substrate.

[0093] The third step is to determine and formula , determines the initial coupling length of the resonator and the initial air gap of the resonator .

[0094] S105 , performing simulation according to the simulation model using the initial air gap of the resonator, the initial coupling length of the resonator, and the length of the resonator to obtain a quality factor of the resonator.

[0095] S106 , adjusting the initial air gap and the initial coupling length of the resonator according to the quality factor of the resonator until the quality factor of the resonator meets the requirement, and determining the air gap and the coupling length of the resonator.

[0096] When the quality factor is low, the coupling length can be increased (that is, the width of the resonator can be increased). ) to improve the quality factor.

[0097] The present invention also introduces magnetic materials into the designed resonator structure to conduct coupling tests:

[0098] Use klayout software to design the layout (the design has Figure 2 The layout of the superconducting resonator structure shown in the figure) is imported into the sonnet software based on impedance matching, and the parameters of the substrate 11 are set (the substrate is a LAO substrate), the relative dielectric constant of the substrate 11 is set to 22, the thickness of the substrate 11 is set to 500um, and the resonator 12 is set to an ideal conductor, ignoring the influence of the thickness of the resonator 12. Finally, the air layer above the resonator layer (not shown in the figure) is set to 5000um. And set the adaptive frequency scan to obtain the S parameter (S parameter is the scattering coefficient, which is a network parameter based on the relationship between the incident microwave and the reflected microwave. The ratio of the incident wave to the reflected wave can be used to calculate the input impedance, frequency response, isolation and other indicators. In addition, the vector network analyzer (VNA) can directly measure the S parameter) simulation results are shown as follows Figure 4 As shown ( Figure 4 The fit in the figure represents the curve of the fitted S11 parameters. The resonant frequency is 11.768 GHz, and the intrinsic quality factor of the Q value is 2764 using the Lorentz calculation. In addition, in order to verify the accuracy of the calculated frequency, the electromagnetic field distribution of the superconducting resonator is simulated, and the magnetic field distribution of the superconducting resonator along the X direction near the resonant frequency is obtained as follows: Figure 5 As shown, the magnetic field distribution of the superconducting resonator along the Y direction near the resonance frequency is obtained as follows Figure 6 As shown, energy is stored in the resonator 12 , and it can be determined that the corresponding calculated frequency is the resonant frequency of the resonator 12 .

[0099] See also Figure 7 , Figure 7 This is a physical picture of the superconducting resonator prepared by the present invention (also a light display picture of the superconducting resonator), in which the structure of the resonator 12 is specifically shown.

[0100] See also Figure 8 , Figure 8This is a schematic diagram of a test system provided by the present invention. The superconducting resonator test system primarily includes two parts: resonant frequency testing and Q-value fitting. The test system primarily uses a vector network analyzer (VNA) 21 and a physical property measurement system (PPMS) 22. The VNA 21 is used to excite microwaves and perform transmission spectrum detection, while the PPMS 22 provides a low-temperature environment and an external static magnetic field. The temperature environment provided by the PPMS 22 includes a first temperature region 221, a second temperature region 222, and a third temperature region 223. The temperature in the first temperature region 221 is above 200K, the temperature in the second temperature region 222 is between 40K and 200K, and the temperature in the third temperature region 223 is below 40K.

[0101] The test system obtains the transmission spectrum of the superconducting resonator's S parameters. Finally, the computer processes the S21 parameter (S21 represents frequency response) or the S11 parameter (S11 represents input impedance) to find the valley or peak value, thereby obtaining the resonant frequency. The Q value is then obtained using a Lorentz fitting method. Design adjustments are made based on the deviation between the measured frequency value and the designed value.

[0102] In this embodiment, the temperature of the third temperature region 223 is lowered to 4K by the physical property measurement system 22. At this time, the corresponding microwave frequency band is introduced, the frequency is swept, and the magnetic field is gradually increased. The shift of the absorption valley (peak) of the S parameter transmission spectrum is used to determine whether it is the resonant frequency of the resonator 12. The results are as follows: Figure 9 As shown in the figure (curves obtained when the external magnetic field is 0oe and 2000oe respectively), the dispersion relationship of the resonator 12 with the magnetic field is as follows Figure 10 Finally, the computer processes the S parameter transmission spectrum data to obtain the quality factor (Q value), as shown in Figure 11 As shown (in Figure 11 Where fit represents the curve of the fitted S21 parameters).

[0103] After verifying the performance of the resonator, the magnetic material to be tested is placed within the electromagnetic field of the resonator 12, and a microwave photon-magneton coupling experiment is conducted to characterize the spin dynamics behavior of the magnetic material to be tested. The specific steps are as follows: First, CrPS4 (the magnetic material to be tested) is placed on the resonator 12 using tape. Then, an aluminum wire is soldered to the microwave line 13 and the ground layer 15 using a wire bonding machine. The superconducting resonator is then placed in the physical property measurement system 22, and then connected to the vector network analyzer 21 using a microwave cable. The physical property measurement system 22 is cooled to 4K. At this time, the corresponding microwave frequency band is introduced, the frequency is swept, and the magnetic field is gradually increased. The transmission spectrum will show anti-splitting (see Figure 12 , the anti-splitting phenomenon occurs in Figure 12 The purple area is shown in Figure 12The purple area on the left and the purple area on the right are included. The coupling strength of the resonator can be calculated by the difference between the highest frequency corresponding to the purple area on the left and the lowest frequency corresponding to the purple part on the right). The coupling strength is characterized by the corresponding degree of anti-splitting. The coupling strength variation can reach megahertz. The phase transition temperature range of the material with temperature is as follows. Figures 12 to 31 As shown, after calculation, the coupling strength increases from 500 MHz at 38 K to 2.3 MHz at 36.1 K. Compared with the traditional ferromagnetic resonance detection, the resonator detection of the present invention not only has a local strong magnetic field, but also has a detection resolution of MHz level.

[0104] The superconducting resonator provided by the present invention reads microwave signals by utilizing the strong interaction between microwave photons and magnons, and characterizes the spin dynamics behavior of the magnetic material layer to be measured through the dispersion relation.

[0105] Experiments have revealed that the temperature-dependent changes in the magnetic phase of CrPS4 have been detected, and the temperature range over which the coupling strength characterizes the phase transition is as high as 0.1 K. Furthermore, this fabrication and testing scheme is compatible with CMOS processes, providing solutions and technical support for integrated detection.

[0106] Finally, it should be noted that the technical contributions made by the technical solution provided by the present invention are:

[0107] (1) Combining the coplanar waveguide structure and the half-wavelength resonator, the coplanar waveguide structure has better impedance matching characteristics, while the half-wavelength resonator has a better quality factor than the quarter-wavelength resonator. The coplanar waveguide structure and the half-wavelength resonator are coupled through capacitance, and the coupling length is the width of the half-wavelength resonator. By adjusting the width of the half-wavelength resonator, the coupling length can be controlled, thereby making it easier to adjust the quality factor of the resonator.

[0108] (2) The geometric structure of the half resonator is optimized. The half resonator adopts an S-shaped central symmetric structure. On the one hand, this structure can save space and reduce the size of the superconducting resonator, which is conducive to improving the integration level. On the other hand, the magnetic field excited by the centrally symmetric resonator is relatively uniform, and a high-intensity magnetic field can be excited in both the X and Y directions, which is conducive to detecting magnetic materials with different excitation modes. For example, some magnetic materials can only be excited by the magnetic field in the X direction, while some magnetic materials can only be excited by the magnetic field in the Y direction. The magnetic material of this application can detect the performance of the above two materials.

[0109] (3) The substrate of the superconducting resonator in this application is a LAO substrate, and the resonator is formed using YBCO material.

[0110] The use of LAO material to form the substrate of the superconducting resonator of this application has the following advantages:

[0111] First, lattice constant matching: The lattice constant of LAO (approximately 3.78 Å) is close to that of YBCO (001) (approximately 3.83 Å), with a lattice mismatch of only about 1.3%. This close lattice constant reduces interfacial stress during epitaxial growth and lowers defect density (such as dislocations and grain boundaries), resulting in higher-quality YBCO films.

[0112] Second, surface flatness: LAO has high surface flatness and low roughness (usually <0.5nm), providing an ideal template for the epitaxial growth of YBCO and reducing the negative impact of surface roughness on superconducting properties.

[0113] Third, thermal expansion coefficient matching: the thermal expansion coefficient of LAO (approx. ) and YBCO (approx. ) close to each other, reducing cracks or interface delamination caused by thermal stress during high-temperature annealing or cooling, ensuring the long-term stability of the film.

[0114] Fourth, dielectric properties:

[0115] Low dielectric loss: LAO is an insulator with low dielectric loss. It can be used as a dielectric in the resonator to reduce the loss of electromagnetic energy and improve the quality factor (Q value) of the resonator.

[0116] Moderate dielectric constant: The dielectric constant of LAO (about 20~25) helps to optimize the capacitance and inductance design of the resonator, thereby adjusting the resonant frequency.

[0117] Fifth, chemical stability

[0118] Anti-pollution and oxidation: LAO has high surface chemical stability and is not easily contaminated by oxygen or water molecules, thus avoiding adverse effects on the surface state of the superconducting film and ensuring that the superconducting properties of YBCO are not destroyed.

[0119] The superconducting resonator provided by this application using YBCO has the following advantages:

[0120] First, high-temperature superconductivity: The critical temperature (Tc) of YBCO is about 85K (liquid nitrogen temperature range), which is much higher than that of traditional low-temperature superconducting materials (such as Nb, Tc≈9K), reducing the refrigeration cost and making it suitable for practical devices.

[0121] Second, high critical current density (Jc): YBCO has an extremely high critical current density (up to 10 6 A / cm² or more), can carry large currents while maintaining a superconducting state, and is suitable for high-frequency and high-power applications.

[0122] Third, high frequency performance:

[0123] Low surface resistance (Rs): In the microwave frequency band (such as 5~10GHz), the surface resistance of YBCO is extremely low (less than 1μΩ), which significantly reduces the loss of the resonator and improves the Q value.

[0124] High cutoff frequency (fc): YBCO has high superconducting electron mobility and a cutoff frequency much higher than traditional superconducting materials, making it suitable for high-frequency and even millimeter-wave devices.

[0125] Fourth, mechanical and processing performance

[0126] Thin film processability: YBCO can be grown into thin layers (tens to hundreds of nanometers) on LAO substrates through methods such as pulsed laser deposition (PLD) and magnetron sputtering, which facilitates patterning into resonators or circuits.

[0127] The LAO substrate and YBCO resonator of this application have the following synergistic effects:

[0128] First, high-quality films and interface optimization

[0129] Low defect density: The lattice matching and surface flatness of LAO significantly reduce the lattice distortion and defects (such as dislocations and antiphase domain boundaries) of YBCO films, thereby improving the superconducting critical current density (Jc) and critical magnetic field (Hc2).

[0130] Interface transparency: The atomic-level flatness of the LAO / YBCO interface ensures coherent tunneling of superconducting electrons, reduces interface scattering, and further reduces surface resistance.

[0131] Second, high-performance resonator characteristics

[0132] High Q value and low loss: The low dielectric loss of LAO and the low surface resistance of YBCO work together to make the resonator's Q value reach 104~105 in the liquid nitrogen temperature range (77K), which is suitable for high-sensitivity detection or readout circuits in quantum computing.

[0133] Broadband and tunability: The combination of the dielectric constant of LAO and the superconducting properties of YBCO allows for flexible tuning of the resonant frequency (e.g., 5-20 GHz range) by adjusting the film thickness or structural design (e.g., resonator geometry).

[0134] Third, long-term stability and reliability

[0135] Thermodynamic stability: The thermal expansion matching of LAO and YBCO reduces mechanical stress during long-term use and avoids performance degradation due to thermal cycling.

[0136] Anti-environmental interference: The chemical stability of LAO protects the YBCO film from impurities or oxidation in the environment, extending the life of the device.

[0137] (4) By optimizing the structure of the superconducting coplanar waveguide resonator and the λ / 2 resonant cavity, the synergistic enhancement of the quality factor (Q>105) and the localization of the mode field in the GHz frequency band was achieved. Compared with the traditional copper resonant cavity, the surface current loss of the superconducting resonator is reduced by three orders of magnitude. The superconducting resonator still maintains 50Ω impedance matching at a low temperature of 4K, effectively suppressing the signal distortion caused by microwave reflection. At the same time, its two-dimensional planar structure allows for sub-micron spacing capacitive coupling with the magnetic film to be measured, and the spatial resolution is improved to below 500nm. The spin precession of the magnetic material is coupled to the resonator microwave field through dipole interaction, and key parameters such as the Gilbert damping factor are extracted by computer. This end-to-end signal link avoids the information loss in conventional multi-stage conversion and is particularly suitable for the study of spin precession of magnetic materials. Experiments have confirmed that the device has an accuracy of 1MHz for measuring the frequency of magnetic oscillators, which is two orders of magnitude higher than that of traditional ferromagnetic resonance spectrometers, laying a technical foundation for the detection of two-dimensional spin dynamics and its application in magnetic storage and computing devices.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for designing a superconducting resonator for high-resolution detection of magnetic materials, characterized in that: include: Determine the magnetic material layer to be tested; Determining the resonant frequency of the resonator according to the magnetic material layer to be measured; Constructing a simulation model, the simulation model including a substrate; a resonator formed on the substrate, microwave lines formed at both ends of the resonator and located on the surface of the substrate, the microwave lines forming a coplanar waveguide, the resonator coupled to the microwave lines; and ground layers located on the surface of the substrate on both sides of the resonator; Determine the initial air gap of the resonator, the initial coupling length of the resonator, and the length of the resonator according to the resonant frequency and the material of the substrate; The initial air gap is the distance between the resonator and the ground layer; According to the simulation model, the initial air gap of the resonator, the initial coupling length of the resonator, and the length of the resonator are used for simulation to obtain the quality factor of the resonator; The initial air gap and the initial coupling length of the resonator are adjusted according to the quality factor of the resonator until the quality factor of the resonator meets the requirements, and the air gap and the coupling length of the resonator are determined.

2. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 1, characterized in that: The substrate is a LAO substrate.

3. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 1, characterized in that: The resonator is a half-wavelength resonator.

4. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 1, characterized in that: The microwave line is formed by using YBCO material.

5. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 1, characterized in that: The resonator is formed of YBCO material.

6. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 5, characterized in that: The resonator has a central symmetrical structure.

7. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 6, characterized in that: The resonator includes a first bent portion, a second bent portion, a first coupling portion, and a second coupling portion; wherein one end of the first bent portion is connected to one end of the second bent portion, the first coupling portion is connected to the other end of the first bent portion, and the second coupling portion is connected to the other end of the second bent portion; the first coupling portion and the second coupling portion are used to couple with the microwave line.

8. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to any one of claims 1 to 7, characterized in that: The length of the resonator is determined as follows: Where, is the length of the resonator, is the wavelength of the electromagnetic wave at the resonant frequency of the resonator, It represents the transmission speed of electromagnetic waves in the coplanar waveguide. represents the resonant frequency of the resonator, represents the speed of light, represents the relative dielectric constant of the substrate.

9. The method for designing a superconducting resonator for high-resolution detection of magnetic materials according to claim 8, characterized in that: The initial air gap of the resonator and the initial coupling length of the resonator are determined as follows: According to the formula 、 、 、 Determining characteristic impedance Where, represents the input impedance of the resonator, represents the characteristic impedance of the resonator, Represents the resonator input impedance The corresponding capacitance, Represents the resonator input impedance The corresponding inductance and the resonator input impedance The corresponding resistance is set to 0, represents the attenuation constant of the transmission line, represents an imaginary number, is the difference between the resonator input frequency and the resonant frequency, represents the input frequency of the resonator, represents the resonant frequency of the resonator; According to the characteristic impedance of the resonator And the formula 、 、 Sure Where, represents the inductance corresponding to the characteristic impedance of the resonator, represents the capacitance corresponding to the characteristic impedance of the resonator, represents the dielectric constant of vacuum, represents the elliptic integral of the first kind, represents the dependent variable obtained according to the initial coupling length of the signal line and the initial air gap of the signal line, represents the relative dielectric constant of the substrate; According to the determined and formula , determines the initial coupling length of the resonator and the initial air gap of the resonator .

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