Ferromagnetic materials with skyrmions and process for their preparation

Abstract

The invention relates to a method for the formation of skyrmions or Néel-type spin textures in a ferromagnetic material, preferably in a ferromagnetic alloy, comprising the steps of (i) providing an underlayer material, (ii) depositing a film of a ferromagnetic material thereon in a manner that (iii) the film obtained shows a vertical strain gradient (∇tε = ∂εt / ∂t), where εt is the strain along the normal to the plane of the deposited film, and further to the materials so prepared and to their use in spintronics technology.

Description

[0001] The present invention relates to a method for the formation of skyrmions in ferromagnetic materials over a wide temperature range, in particular above room temperature. Furthermore, the invention relates to materials so prepared and their use in so-called spintronics technology, namely as materials for high-performance data storage and for improved computer architecture; Chem. Rev. 121, 2857 - 2897 (2020) and Nat. Nanotechnol. 8, 899 (2013).

[0002] A wide variety of chiral non-collinear spin textures have been discovered and have unique properties that make them highly interesting for technological applications. However, many of these are found in complex materials and only in a narrow window of temperature.

[0003] At the nanoscale, the magnetic interactions between the magnetic moments can form special chiral vortices from atomic magnetic moments, so-called skyrmions. Skyrmions have so-called topological spin textures that are thereby more stable (they have "topological protection") than non-topological spin textures. Skyrmions typically require the presence of a nearest neighbor vector Dzyaloshinskii-Moriya interaction (DMI) which is found in bulk materials whose structure is without a center of symmetry and typically, which have high spin-orbit coupling (SOC).

[0004] Modern computer technology expects skyrmions to be an extremely space-saving and ultra-fast way of storing data. It would be advantageous to use different skyrmions to represent the states 0 and 1. However, such skyrmions (non-collinear chiral spin textures) have so far mostly only been found in complex materials and only occur there in a narrow temperature range that is unsuitable for practical applications; Nat. Nanotechnol. 8, 152 (2013) and Science 320, 190 - 194 (2008).

[0005] Therefore, the present invention is based on the task of providing a method for the formation of such skyrmions in a material that is as easily accessible as possible and in a temperature range that is as wide as possible and above room temperature. The stabilization of skyrmions in thin films above ambient temperature is one of the biggest challenges.

[0006] This task here is solved by providing a thin ferromagnetic material deposited as a thin film on a special substrate, whose crystal symmetry in the direction perpendicular to the surface of the substrate is lowered by the formation of a strain gradient in this direction.Brief Description of the Figures

[0007] Fig. 1 shows strain gradient analysis and structural properties. Fig. lA: Schematic illustration of the epitaxial relationship between a strained ferromagnetic film (SF) on an IrAl(001) underlayer. Fig. 1B: Schematic of the XRD derived strain profile of a Co 2.3 Al film on IrAl(001). A constantly strained layer (∇ t ε = 0) is located between the IrAl layer and the SF which is characterized by a linear positive strain gradient. Fig. 1C - 1E: Experimental (circles) and calculated (solid line) x-ray diffraction profiles on a log scale in the vicinity of the L=2 reflection along the [00L] direction in reciprocal space. Profiles of 30 nm (∇ t ε=6.8×10 -4< Å / uc), 50 nm (∇ t ε = 5.8×10 -4< Å / uc) Co 2.3 Al and 27 nm thick Co 2.58 Ni 0.26 Al films (∇ t ε= 3.0×10 -3< Å / uc) exhibit a pronounced asymmetry directly indicating a large strain gradient. Fig. 1F: Cross-sectional, bright field, high-resolution transmission electronic microscopy (HR-TEM) image of an IrAl |Co 2.3 Al bilayer. Corresponding Fourier transform (FT) of two different regions (I, and II) showing the epitaxial relationship of the IrAl and Co 2.3 Al layer. Fig. 2 shows Lorentz transmission electron microscopy (LTEM) images at 300 K. Fig.2A: Schematic illustration of specimen tilting inside the electron microscope. Zero tilt corresponds to the incident electron beam being oriented along the surface normal

[001] of the lamella. Fig. 2B - F: LTEM images recorded for a 4.3 nm IrAl|30 nm Co 2.3 Al bilayer in the presence of a 0.15 T magnetic field applied along the TEM column.

[0008] (B) LTEM image at zero tilt that shows no magnetic contrast. (C to F) LTEM images recorded upon sample tilting about the x axis (C and D) α = ±30°, and the y axis (E and F)β = ±30°.

[0009] The insets in C to F show magnified images of the highlighted (blue or green circle) nano-object that corresponds to a Néel skyrmion. All images are taken at a defocus value of -1.5 mm. The scale bar for

[0010] (B) to (F) is 200 nm and the scale bar inset (C-F) is 100 nm.

[0011] (G and H) LTEM images of bilayer of 4.3 nm IrAl|27 nm Co 2.58 Ni 0.26 Al in the presence of a 0.28 T magnetic field applied along the TEM column at 300 K. Defocus was set to -0.6 mm, tilt angle (β) to +20° and -21°, the scale bar for G and H is 500 nm.Detailed Description of the Invention

[0012] In conventional scenarios, thin films deposited on various substrates tend to maintain a constant strain throughout their structure. The approach according to the invention diverges from this usual behavior by the introduction of a vertical strain gradient (∇ t ε = ∂ε t / ∂t) as shown in Fig. 1A and B, where ε t is the strain along the normal to the plane of a thin film.

[0013] The formation of many of these spin textures is only possible in bulk compounds without crystal inversion symmetry or at interfaces. So, the lowering of crystal symmetry in centrosymmetric magnetic systems is a key aspect and key feature of the present invention.

[0014] It is found here that the high symmetry of a thin ferromagnetic material is lowered by introducing a vertical strain gradient along the normal to the plane of the thin film.

[0015] Typically, thin films grown on underlayers or substrates exhibit a uniform strain until the thickness exceeds a critical value at which the strain is released, typically by the formation of e.g. dislocations. However, here we show that certain materials, i.e. certain alloys, display a significant strain gradient when deposited on certain underlayers. Such a strain gradient allows for the formation of Néel-type skyrmions in an otherwise centrosymmetric, for example tetragonal, system or crystal structure. Due to the very high magnetic ordering temperature of these alloys, skyrmions can be observed at temperatures as high as 500°C.

[0016] In the following, the present invention will be explained in sufficient detail using the examples of a Co / Al-alloy and of a Co / Ni / Al-alloy (Co 2.3 Al and Co 2.58 Ni 0.26 Al).

[0017] It has been found that thin films of the tetragonal Co 2.3 Al and Co 2.58 Ni 0.26 Al ferromagnets display a significant strain gradient when deposited on a suitable underlayer, especially when their thickness lies within a certain range (preferably 30-50 nm).

[0018] To achieve large strain gradients an optimized underlayer formed from an alloy of the formula M 1-x Al x with M = Ir, Pd or Ru, preferably Ir where x is preferably in the range from x=0.30 to x= 0.60 and most preferably in the range from x=0.35 to x=0.55 was introduced. These cubic alloys were chosen because at ambient temperature they grow as flat films with a highly chemically ordered L1 0 structure and are characterized by a larger lattice parameter than the ferromagnetic layer. The largest strain gradient (∇ t ε=3×10 -3< Å / unit cell (uc)) was found for a ferromagnetic layer of Co 2.58 Ni 0.26 Al on an IrAl underlayer. For strain gradients larger than approximately 5~ 6×10 -4< Å / uc, Néel skyrmions are observed by Lorentz Transmission Electron Microscopy (LTEM) in both Co 2.3 Al and Co 2.58 Ni 0.26 Al in good agreement with ab-initio calculations of the strain gradient and the resulting DMI that will be discussed below. For the case of Co 2.3 Al high temperature studies show clear evidence for skyrmions up to very high temperatures of ~ 770 K.

[0019] The strain-gradient in the epitaxial films was determined by fitting the x-ray diffraction (XRD) reflection profiles collected by line scans along the q z direction in the vicinity of the (002) reflection in reciprocal space. The simulation of the reflection profiles was carried out by employing the recursive matrix formalism in the kinematic scattering approximation. The film is sub-divided into thin slices, each having a different strain (ε) along the surface normal

[001] as schematically shown in Fig. IB. Here and in the following reference will be made to the c-lattice parameter of the cubic IrAl underlayer (2.985 Å). Additional fitting parameters include the film thickness t and the root-mean squared (rms) surface roughness (σ) modelled by a Debye-Waller-type approach. The finite instrumental resolution along q z was taken into account by using a pseudo-Voigt function. Its full width at half maximum (Δq z ) was derived from a scan across the Si(202) reflection (Δq z was found to be « 2.2×10 -3< Å -1< which corresponds to 6.5×10 -3< reciprocal lattice units). A least squares fit of the simulated curve to the experimental data was carried out using a standard χ 2< minimization procedure. Results for 30 and 50 nm thick Co 2.3 Al and 27 nm thick Co 2.58 Ni 0.26 Al layers grown on top of IrAl are compared in Fig. 1 C-E. The experimental (00L) reflection profiles (symbols) are shown together with the corresponding calculated ones (solid line) on a logarithmic intensity scale. The analysis indicates that these films exhibit a significant positive strain gradient which ranges from approximately 6.8×10 -4< Å / uc (Fig. 1C and D) up to 3×10 -3< Å / uc (Fig. 1E). As an example, Fig.lB shows the details of the refined strain profile within the 50 nm thick Co 2.3 Al film. Next to the IrAl layer we find an approximately 9 nm thick Co 2.3 Al layer which is constantly strained by about -8.0% (c = 2.74 Å) relative to the lattice parameter of IrAl of 2.985Å. This layer is followed by an approximately 30 nm thick Co 2.3 Al layer in which the strain linearly diminishes from -8.0% at the bottom to -5.7% (2.81 Å) at the top corresponding to a strain gradient of 6.8×10 -4< Å / uc. There is also a 10~ 20% discrepancy between the nominal film thickness and that derived by XRD. It appears that this can be attributed to the lack of well-defined long-range order in some part of the film structure. Similar results are found for all films in this thickness regime. Our findings explain why for films in the thickness regime well outside the 30~ 50 nm regime exhibit much smaller strain gradients (« 2×10 -4< Å / uc) and correspondingly no Néel type skyrmions. Either the majority of the film volume is in a constantly strained state (t < 20 nm) or strain relaxation sets in for t > 50 nm.

[0020] The high quality of the epitaxially grown Co 2.3 Al films on IrAl was directly proved by cross-sectional high-resolution transmission electron microscopy (HRTEM). A typical image is shown in Fig. IF together with its Fourier transforms (FT) showing bright well-contrasted spots.

[0021] Figure 2A shows a schematic of the LTEM configuration in which a thin lamella, that has been prepared from a bilayer film, is oriented so that its surface normal is parallel to the electron beam. This situation corresponds to the tilt angles α=β=0 where these angles correspond to rotations about two mutually orthogonal rotation axes lying in the lamella plane (the sample holder allows maximum tilt angles of α = ±36° about the x-axis and β = ±31° about the y-axis). The lamella is prepared by initially mechanically polishing the backside of the MgO substrate followed by argon ion milling until the 200keV electron beam used in the LTEM experiments can penetrate the lamella.

[0022] Only type-II bubbles are found in Co 2.3 Al films grown without an underlayer, irrespective of thickness. Furthermore, when the composition (x) of Co x Al is modified to x = 2.0, 2.6, and 2.9, or when IrAl is replaced by PdAl or RuAl only labyrinth domains and type-II bubbles are found.

[0023] To explore the thermal stability of the Néel skyrmions, in-situ LTEM experiments were carried out up for temperatures as high as 773 K. A novel method was developed to make this experiment possible. A freestanding membrane formed from 12 nm MgO|4.3 nm IrAl|30 nm Co 2.3 Al was prepared by first growing this structure on a sacrificial layer of Sr 3 Al 2 O 6 that had been deposited by pulsed laser deposition on a SrTiO 3 (001) substrate. The Sr 3 Al 2 O 6 layer was subsequently dissolved in water from the edges of the substrate and the membrane floated off and subsequently transferred to a heating chip (DENS Solutions) (see Methods for more details). The chip was placed on a sample holder that allows for in-situ heating. The membrane was then heated in steps of 100 K to 773 K at a heating rate of 5 K / sec. From selected area electron diffraction (SAED) the structure of the membrane was found to be highly thermally stable. LTEM images were recorded at each temperature using the same protocol. The temperature was increased in zero field and zero tilt. After the temperature was stabilized the sample was tilted (to α=20°) and then the field was increased in steps of 25 mT and a LTEM image taken at each field until the sample was fully field polarized. A transition from a labyrinth domain state into a Neel skyrmion state with increasing magnetic field and finally a fully polarized state was found at all temperatures. Both the skyrmion diameter and the skyrmion density decrease with increasing temperature, which is presumably related to the decrease in saturation magnetization (M s ) with increasing temperature.

[0024] A linear strain gradient is considered by assuming an increase of the c-lattice parameter beginning with c 1 = 2.7 Å for the first unit cell (uc) at the Co 2.3 Al (Co 2.58 Ni 0.26 Al) interface with IrAl up to c n = 2.933 Å for the n-th unit cell at the top surface of the layer. The latter value corresponds to the limit where the topmost unit cell becomes cubic given the in-plane film lattice parameter of 2.933 Å. Thus, the lattice parameter c i of the i-th unit cell from the interface is given by c i = c 1 +∇ t ε×(i-1), where ∇ t ε denotes the strain gradient in Å / uc. For ∇ t ε = 0.024 Å / uc, 0.0116 Å / uc, 0.006 Å / uc, 0.005 Å / uc and 0.003 Å / uc the Co 2.3 Al and Co 2.58 Ni 0.26 Al films consist of 10, 20, 45, 60, and 80 uc's, respectively. The lowest strain gradient corresponds to the largest experimental value found in Co 2.58 Ni 0.26 Al.

[0025] In general, D / A is proportional to the strain gradient. While the spin stiffness A is almost constant, the DMI parameter D increases monotonically. In the case of Co 2.58 Ni 0.26 Al both A and D are smaller than in Co 2.3 Al, since the presence of Ni reduces the magnetic interaction in CoAl alloys. Nevertheless, the D / A ratio, which is mainly responsible for skyrmion formation, is calculated to be similar in both systems for similar strain gradients. Experimentally, a much larger strain gradient has been found for Co 2.58 Ni 0.26 Al compared to Co 2.3 Al and, correspondingly, as expected, a larger skyrmion diameter, as discussed above.

[0026] Real space images were simulated by micromagnetic simulations using the Mumax3 solver. Material parameters were partially taken from experiment (saturation magnetization, uniaxial anisotropy) and partially from calculations (A, D). In agreement with the LTEM images (see Fig. 2), the micromagnetic simulations show a labyrinth magnetic ground state in the absence of an external magnetic field. Applying a perpendicular magnetic field results in the formation of magnetic Néel skyrmions, which can be distinguished by determining their topological charge. Further increase of the external magnetic field results in a fully polarized state in agreement with experiment.

[0027] In summary, through a comprehensive analysis combining LTEM and XRD experiments with first principles calculations, the stabilization of chiral Néel-type spin textures within simple ferromagnetic alloys, even at elevated temperatures of up to 773 K, has been demonstrated. This stabilization arises from the presence of a sufficiently large strain gradient through the film thickness, achieved through the use of an appropriate underlayer. The strain gradient acts as a symmetry breaker across the film thickness, thereby enabling the appearance of a bulk DMI within the interior of the film. These findings significantly broaden the scope of potential magnetic materials capable of exhibiting complex chiral spin textures, which are highly relevant for numerous spintronic applications. Moreover, the approach to generating "hot" skyrmions can be extended to various other systems characterized by high magnetic ordering temperatures.

[0028] Using LTEM and XRD experiments provides clear evidence for the stabilization of chiral Néel-type spin textures in a nominally centrosymmetric ferromagnetic alloy up to very high temperatures (773 K). The stabilization is a result of a sufficiently large vertical strain gradient throughout the thickness of the film obtained by the use of a suitable underlayer. These findings dramatically widen the range of potential magnetic candidate materials that can exhibit complex chiral spin textures of interest for many spintronic technologies. This approach to the formation of "hot" skyrmions can be generalized to many other systems with high magnetic ordering temperatures.

[0029] Clear evidence of skyrmions are also found in layers of Ni 1-x Al x from LTEM studies. These layers are also prepared on IrAl underlayers. Thus, layers formed from alloys of Co, Ni and Al that are ferromagnetic and which display perpendicular magnetic anisotropy when prepared on suitable underlayers and which possess a sufficiently large strain gradient are suitable for the stabilization of skyrmions to high temperatures, well above room temperature.

[0030] In the following, more details on materials and methods used in the context and for carrying out the present invention will be described:Materials and Methods Thin films growth, characterization

[0031] The films were deposited in an AJA 'Flagship Series' sputtering system in the presence of Ar gas on 10×10 mm MgO substrates with

[001] orientation. The base pressure before deposition was less than 10 -8< Torr and the pressure during deposition was 3 mTorr. The IrAl, PdAl, RuAl, Co x Al, and Co-Ni-Al alloy thin films were prepared by co-sputtering from individual heavy metal and Aluminum targets with 2-inch diameter and 0.25-inch thickness. The composition of thin films is calibrated by Rutherford Backscattering spectroscopy. The atomic ratio of IrAl, PdAl, and RuAl is 42:58, 35:65 and 46:54 respectively. The highly resistive TaN-capping layer was prepared by introducing 20% N 2 into the Ar gas flow. The magnetization hysteresis loops (Fig. ID) were measured with a superconducting quantum interference device vibrating sample magnetometer (SQUID-VSM).X-ray Analysis of the Strain Gradient in thin MAl (M= Ru, Pd and Ir)|Co x Al films

[0032] The magnitude of the strain gradient along the sample normal (c-axis) was analyzed by X-ray diffraction probing the reflection profiles collected by line scans in reciprocal space along the q z direction in the vicinity of the (002) reflection. The experiments were carried out in our home laboratory using a Ga-jet x-ray source (1=1.3414 Å) and a six circle diffractometer as well as at the beamline 25b of the European Synchrotron Radiation Source (ESRF) in Grenoble (France). In both cases, a two-dimensional pixel detector was used employing a region of interest to provide high resolution in k-space along the longitudinal scan direction (qz); J. Magn. Magn. Mater. 319, 13 - 55 (2007) and Acta Crystallographica Section A 25, 165 - 173 (1969).Magneto-transport measurements

[0033] By the Van-der-Pauw method, the conventional Hall resistivity is measured with 3×3 mm square samples cut from 10×10 mm blanket films and a set of direct current source (Keithley 6221), nanovoltmeter (Keithley 2182a) was used.Transmission Electron Microscopy

[0034] For the transmission electron microscopy (TEM) investigations, cross sectional lamellae from the thin films were prepared by Focused Ion Beam (FIB) Ga +< ion milling [TESCAN GAIA3 operating at 30 kV ion-beam energy] using standard lift-out procedures. For Lorentz TEM imaging several plane-view lamellae were prepared from the as-deposited films by Ar ion milling from the back-side of the MgO substrate. Structural imaging was performed using JEOL ARM300F2 TEM. Magnetic textures were investigated by TEM [FEI TITAN 80-300 and JEOL JEM-F200] in the Lorentz mode operated at an accelerating voltage of 300 kV and 200 kV respectively, using a GATAN double-tilt LN2 cooling holder (Model 636) which is capable of varying the temperature. A vertical magnetic field was applied to the lamella within the TEM column by passing currents through the coils of the objective lens and a Lorentz mini-lens was used for imaging; see Sci. Rep. 8, 5703 (2018) and Nat. Commun. 8, 14761 (2017).Free-standing thin film transfer procedure

[0035] For the LTEM investigation on this multilayer sample at different temperatures, a lift-off and transfer method was used. To protect the entire structure, a 100 nm thick PMMA layer was coated onto the as deposited sample that are prepared by combining deposition in a pulsed laser deposition and a sputtering chamber. Then, the multilayer structure was immersed in deionized water for -30 min to remove the Sr 3 Al 2 O 6 layer. The separated sheet together with water was then picked up and transferred onto heating chip. Before the LTEM measurement, the protective PMMA layer was removed by dropping acetone on the sample after drying in nitrogen for 6 hours.

[0036] The above examples, especially with regard to the CoAl-alloys and Co / Ni / Al-alloys employed, are just for showing a way to carry out the invention and are not meant to limit the scope of the invention in any respect. Each feature being employed in furtherance of the invention can be freely combined with other features to further promote and develop the invention.

Examples

Embodiment Construction

[0012]In conventional scenarios, thin films deposited on various substrates tend to maintain a constant strain throughout their structure. The approach according to the invention diverges from this usual behavior by the introduction of a vertical strain gradient (∇ t ε = ∂ε t / ∂t) as shown in Fig. 1A and B, where ε t is the strain along the normal to the plane of a thin film.

[0013]The formation of many of these spin textures is only possible in bulk compounds without crystal inversion symmetry or at interfaces. So, the lowering of crystal symmetry in centrosymmetric magnetic systems is a key aspect and key feature of the present invention.

[0014]It is found here that the high symmetry of a thin ferromagnetic material is lowered by introducing a vertical strain gradient along the normal to the plane of the thin film.

[0015]Typically, thin films grown on underlayers or substrates exhibit a uniform strain until the thickness exceeds a critical value at which the strain is released, typi...

[0001] The present invention relates to a method for the formation of skyrmions in ferromagnetic materials over a wide temperature range, in particular above room temperature. Furthermore, the invention relates to materials so prepared and their use in so-called spintronics technology, namely as materials for high-performance data storage and for improved computer architecture; Chem. Rev. 121, 2857 - 2897 (2020) and Nat. Nanotechnol. 8, 899 (2013).

[0002] A wide variety of chiral non-collinear spin textures have been discovered and have unique properties that make them highly interesting for technological applications. However, many of these are found in complex materials and only in a narrow window of temperature.

[0003] At the nanoscale, the magnetic interactions between the magnetic moments can form special chiral vortices from atomic magnetic moments, so-called skyrmions. Skyrmions have so-called topological spin textures that are thereby more stable (they have "topological protection") than non-topological spin textures. Skyrmions typically require the presence of a nearest neighbor vector Dzyaloshinskii-Moriya interaction (DMI) which is found in bulk materials whose structure is without a center of symmetry and typically, which have high spin-orbit coupling (SOC).

[0004] Modern computer technology expects skyrmions to be an extremely space-saving and ultra-fast way of storing data. It would be advantageous to use different skyrmions to represent the states 0 and 1. However, such skyrmions (non-collinear chiral spin textures) have so far mostly only been found in complex materials and only occur there in a narrow temperature range that is unsuitable for practical applications; Nat. Nanotechnol. 8, 152 (2013) and Science 320, 190 - 194 (2008).

[0005] Therefore, the present invention is based on the task of providing a method for the formation of such skyrmions in a material that is as easily accessible as possible and in a temperature range that is as wide as possible and above room temperature. The stabilization of skyrmions in thin films above ambient temperature is one of the biggest challenges.

[0006] This task here is solved by providing a thin ferromagnetic material deposited as a thin film on a special substrate, whose crystal symmetry in the direction perpendicular to the surface of the substrate is lowered by the formation of a strain gradient in this direction.Brief Description of the Figures

[0007] Fig. 1 shows strain gradient analysis and structural properties. Fig. lA: Schematic illustration of the epitaxial relationship between a strained ferromagnetic film (SF) on an IrAl(001) underlayer. Fig. 1B: Schematic of the XRD derived strain profile of a Co 2.3 Al film on IrAl(001). A constantly strained layer (∇ t ε = 0) is located between the IrAl layer and the SF which is characterized by a linear positive strain gradient. Fig. 1C - 1E: Experimental (circles) and calculated (solid line) x-ray diffraction profiles on a log scale in the vicinity of the L=2 reflection along the [00L] direction in reciprocal space. Profiles of 30 nm (∇ t ε=6.8×10 -4< Å / uc), 50 nm (∇ t ε = 5.8×10 -4< Å / uc) Co 2.3 Al and 27 nm thick Co 2.58 Ni 0.26 Al films (∇ t ε= 3.0×10 -3< Å / uc) exhibit a pronounced asymmetry directly indicating a large strain gradient. Fig. 1F: Cross-sectional, bright field, high-resolution transmission electronic microscopy (HR-TEM) image of an IrAl |Co 2.3 Al bilayer. Corresponding Fourier transform (FT) of two different regions (I, and II) showing the epitaxial relationship of the IrAl and Co 2.3 Al layer. Fig. 2 shows Lorentz transmission electron microscopy (LTEM) images at 300 K. Fig.2A: Schematic illustration of specimen tilting inside the electron microscope. Zero tilt corresponds to the incident electron beam being oriented along the surface normal

[001] of the lamella. Fig. 2B - F: LTEM images recorded for a 4.3 nm IrAl|30 nm Co 2.3 Al bilayer in the presence of a 0.15 T magnetic field applied along the TEM column.

[0008] (B) LTEM image at zero tilt that shows no magnetic contrast. (C to F) LTEM images recorded upon sample tilting about the x axis (C and D) α = ±30°, and the y axis (E and F)β = ±30°.

[0009] The insets in C to F show magnified images of the highlighted (blue or green circle) nano-object that corresponds to a Néel skyrmion. All images are taken at a defocus value of -1.5 mm. The scale bar for

[0010] (B) to (F) is 200 nm and the scale bar inset (C-F) is 100 nm.

[0011] (G and H) LTEM images of bilayer of 4.3 nm IrAl|27 nm Co 2.58 Ni 0.26 Al in the presence of a 0.28 T magnetic field applied along the TEM column at 300 K. Defocus was set to -0.6 mm, tilt angle (β) to +20° and -21°, the scale bar for G and H is 500 nm.Detailed Description of the Invention

[0012] In conventional scenarios, thin films deposited on various substrates tend to maintain a constant strain throughout their structure. The approach according to the invention diverges from this usual behavior by the introduction of a vertical strain gradient (∇ t ε = ∂ε t / ∂t) as shown in Fig. 1A and B, where ε t is the strain along the normal to the plane of a thin film.

[0013] The formation of many of these spin textures is only possible in bulk compounds without crystal inversion symmetry or at interfaces. So, the lowering of crystal symmetry in centrosymmetric magnetic systems is a key aspect and key feature of the present invention.

[0014] It is found here that the high symmetry of a thin ferromagnetic material is lowered by introducing a vertical strain gradient along the normal to the plane of the thin film.

[0015] Typically, thin films grown on underlayers or substrates exhibit a uniform strain until the thickness exceeds a critical value at which the strain is released, typically by the formation of e.g. dislocations. However, here we show that certain materials, i.e. certain alloys, display a significant strain gradient when deposited on certain underlayers. Such a strain gradient allows for the formation of Néel-type skyrmions in an otherwise centrosymmetric, for example tetragonal, system or crystal structure. Due to the very high magnetic ordering temperature of these alloys, skyrmions can be observed at temperatures as high as 500°C.

[0016] In the following, the present invention will be explained in sufficient detail using the examples of a Co / Al-alloy and of a Co / Ni / Al-alloy (Co 2.3 Al and Co 2.58 Ni 0.26 Al).

[0017] It has been found that thin films of the tetragonal Co 2.3 Al and Co 2.58 Ni 0.26 Al ferromagnets display a significant strain gradient when deposited on a suitable underlayer, especially when their thickness lies within a certain range (preferably 30-50 nm).

[0018] To achieve large strain gradients an optimized underlayer formed from an alloy of the formula M 1-x Al x with M = Ir, Pd or Ru, preferably Ir where x is preferably in the range from x=0.30 to x= 0.60 and most preferably in the range from x=0.35 to x=0.55 was introduced. These cubic alloys were chosen because at ambient temperature they grow as flat films with a highly chemically ordered L1 0 structure and are characterized by a larger lattice parameter than the ferromagnetic layer. The largest strain gradient (∇ t ε=3×10 -3< Å / unit cell (uc)) was found for a ferromagnetic layer of Co 2.58 Ni 0.26 Al on an IrAl underlayer. For strain gradients larger than approximately 5~ 6×10 -4< Å / uc, Néel skyrmions are observed by Lorentz Transmission Electron Microscopy (LTEM) in both Co 2.3 Al and Co 2.58 Ni 0.26 Al in good agreement with ab-initio calculations of the strain gradient and the resulting DMI that will be discussed below. For the case of Co 2.3 Al high temperature studies show clear evidence for skyrmions up to very high temperatures of ~ 770 K.

[0019] The strain-gradient in the epitaxial films was determined by fitting the x-ray diffraction (XRD) reflection profiles collected by line scans along the q z direction in the vicinity of the (002) reflection in reciprocal space. The simulation of the reflection profiles was carried out by employing the recursive matrix formalism in the kinematic scattering approximation. The film is sub-divided into thin slices, each having a different strain (ε) along the surface normal

[001] as schematically shown in Fig. IB. Here and in the following reference will be made to the c-lattice parameter of the cubic IrAl underlayer (2.985 Å). Additional fitting parameters include the film thickness t and the root-mean squared (rms) surface roughness (σ) modelled by a Debye-Waller-type approach. The finite instrumental resolution along q z was taken into account by using a pseudo-Voigt function. Its full width at half maximum (Δq z ) was derived from a scan across the Si(202) reflection (Δq z was found to be « 2.2×10 -3< Å -1< which corresponds to 6.5×10 -3< reciprocal lattice units). A least squares fit of the simulated curve to the experimental data was carried out using a standard χ 2< minimization procedure. Results for 30 and 50 nm thick Co 2.3 Al and 27 nm thick Co 2.58 Ni 0.26 Al layers grown on top of IrAl are compared in Fig. 1 C-E. The experimental (00L) reflection profiles (symbols) are shown together with the corresponding calculated ones (solid line) on a logarithmic intensity scale. The analysis indicates that these films exhibit a significant positive strain gradient which ranges from approximately 6.8×10 -4< Å / uc (Fig. 1C and D) up to 3×10 -3< Å / uc (Fig. 1E). As an example, Fig.lB shows the details of the refined strain profile within the 50 nm thick Co 2.3 Al film. Next to the IrAl layer we find an approximately 9 nm thick Co 2.3 Al layer which is constantly strained by about -8.0% (c = 2.74 Å) relative to the lattice parameter of IrAl of 2.985Å. This layer is followed by an approximately 30 nm thick Co 2.3 Al layer in which the strain linearly diminishes from -8.0% at the bottom to -5.7% (2.81 Å) at the top corresponding to a strain gradient of 6.8×10 -4< Å / uc. There is also a 10~ 20% discrepancy between the nominal film thickness and that derived by XRD. It appears that this can be attributed to the lack of well-defined long-range order in some part of the film structure. Similar results are found for all films in this thickness regime. Our findings explain why for films in the thickness regime well outside the 30~ 50 nm regime exhibit much smaller strain gradients (« 2×10 -4< Å / uc) and correspondingly no Néel type skyrmions. Either the majority of the film volume is in a constantly strained state (t < 20 nm) or strain relaxation sets in for t > 50 nm.

[0020] The high quality of the epitaxially grown Co 2.3 Al films on IrAl was directly proved by cross-sectional high-resolution transmission electron microscopy (HRTEM). A typical image is shown in Fig. IF together with its Fourier transforms (FT) showing bright well-contrasted spots.

[0021] Figure 2A shows a schematic of the LTEM configuration in which a thin lamella, that has been prepared from a bilayer film, is oriented so that its surface normal is parallel to the electron beam. This situation corresponds to the tilt angles α=β=0 where these angles correspond to rotations about two mutually orthogonal rotation axes lying in the lamella plane (the sample holder allows maximum tilt angles of α = ±36° about the x-axis and β = ±31° about the y-axis). The lamella is prepared by initially mechanically polishing the backside of the MgO substrate followed by argon ion milling until the 200keV electron beam used in the LTEM experiments can penetrate the lamella.

[0022] Only type-II bubbles are found in Co 2.3 Al films grown without an underlayer, irrespective of thickness. Furthermore, when the composition (x) of Co x Al is modified to x = 2.0, 2.6, and 2.9, or when IrAl is replaced by PdAl or RuAl only labyrinth domains and type-II bubbles are found.

[0023] To explore the thermal stability of the Néel skyrmions, in-situ LTEM experiments were carried out up for temperatures as high as 773 K. A novel method was developed to make this experiment possible. A freestanding membrane formed from 12 nm MgO|4.3 nm IrAl|30 nm Co 2.3 Al was prepared by first growing this structure on a sacrificial layer of Sr 3 Al 2 O 6 that had been deposited by pulsed laser deposition on a SrTiO 3 (001) substrate. The Sr 3 Al 2 O 6 layer was subsequently dissolved in water from the edges of the substrate and the membrane floated off and subsequently transferred to a heating chip (DENS Solutions) (see Methods for more details). The chip was placed on a sample holder that allows for in-situ heating. The membrane was then heated in steps of 100 K to 773 K at a heating rate of 5 K / sec. From selected area electron diffraction (SAED) the structure of the membrane was found to be highly thermally stable. LTEM images were recorded at each temperature using the same protocol. The temperature was increased in zero field and zero tilt. After the temperature was stabilized the sample was tilted (to α=20°) and then the field was increased in steps of 25 mT and a LTEM image taken at each field until the sample was fully field polarized. A transition from a labyrinth domain state into a Neel skyrmion state with increasing magnetic field and finally a fully polarized state was found at all temperatures. Both the skyrmion diameter and the skyrmion density decrease with increasing temperature, which is presumably related to the decrease in saturation magnetization (M s ) with increasing temperature.

[0024] A linear strain gradient is considered by assuming an increase of the c-lattice parameter beginning with c 1 = 2.7 Å for the first unit cell (uc) at the Co 2.3 Al (Co 2.58 Ni 0.26 Al) interface with IrAl up to c n = 2.933 Å for the n-th unit cell at the top surface of the layer. The latter value corresponds to the limit where the topmost unit cell becomes cubic given the in-plane film lattice parameter of 2.933 Å. Thus, the lattice parameter c i of the i-th unit cell from the interface is given by c i = c 1 +∇ t ε×(i-1), where ∇ t ε denotes the strain gradient in Å / uc. For ∇ t ε = 0.024 Å / uc, 0.0116 Å / uc, 0.006 Å / uc, 0.005 Å / uc and 0.003 Å / uc the Co 2.3 Al and Co 2.58 Ni 0.26 Al films consist of 10, 20, 45, 60, and 80 uc's, respectively. The lowest strain gradient corresponds to the largest experimental value found in Co 2.58 Ni 0.26 Al.

[0025] In general, D / A is proportional to the strain gradient. While the spin stiffness A is almost constant, the DMI parameter D increases monotonically. In the case of Co 2.58 Ni 0.26 Al both A and D are smaller than in Co 2.3 Al, since the presence of Ni reduces the magnetic interaction in CoAl alloys. Nevertheless, the D / A ratio, which is mainly responsible for skyrmion formation, is calculated to be similar in both systems for similar strain gradients. Experimentally, a much larger strain gradient has been found for Co 2.58 Ni 0.26 Al compared to Co 2.3 Al and, correspondingly, as expected, a larger skyrmion diameter, as discussed above.

[0026] Real space images were simulated by micromagnetic simulations using the Mumax3 solver. Material parameters were partially taken from experiment (saturation magnetization, uniaxial anisotropy) and partially from calculations (A, D). In agreement with the LTEM images (see Fig. 2), the micromagnetic simulations show a labyrinth magnetic ground state in the absence of an external magnetic field. Applying a perpendicular magnetic field results in the formation of magnetic Néel skyrmions, which can be distinguished by determining their topological charge. Further increase of the external magnetic field results in a fully polarized state in agreement with experiment.

[0027] In summary, through a comprehensive analysis combining LTEM and XRD experiments with first principles calculations, the stabilization of chiral Néel-type spin textures within simple ferromagnetic alloys, even at elevated temperatures of up to 773 K, has been demonstrated. This stabilization arises from the presence of a sufficiently large strain gradient through the film thickness, achieved through the use of an appropriate underlayer. The strain gradient acts as a symmetry breaker across the film thickness, thereby enabling the appearance of a bulk DMI within the interior of the film. These findings significantly broaden the scope of potential magnetic materials capable of exhibiting complex chiral spin textures, which are highly relevant for numerous spintronic applications. Moreover, the approach to generating "hot" skyrmions can be extended to various other systems characterized by high magnetic ordering temperatures.

[0028] Using LTEM and XRD experiments provides clear evidence for the stabilization of chiral Néel-type spin textures in a nominally centrosymmetric ferromagnetic alloy up to very high temperatures (773 K). The stabilization is a result of a sufficiently large vertical strain gradient throughout the thickness of the film obtained by the use of a suitable underlayer. These findings dramatically widen the range of potential magnetic candidate materials that can exhibit complex chiral spin textures of interest for many spintronic technologies. This approach to the formation of "hot" skyrmions can be generalized to many other systems with high magnetic ordering temperatures.

[0029] Clear evidence of skyrmions are also found in layers of Ni 1-x Al x from LTEM studies. These layers are also prepared on IrAl underlayers. Thus, layers formed from alloys of Co, Ni and Al that are ferromagnetic and which display perpendicular magnetic anisotropy when prepared on suitable underlayers and which possess a sufficiently large strain gradient are suitable for the stabilization of skyrmions to high temperatures, well above room temperature.

[0030] In the following, more details on materials and methods used in the context and for carrying out the present invention will be described:Materials and Methods Thin films growth, characterization

[0031] The films were deposited in an AJA 'Flagship Series' sputtering system in the presence of Ar gas on 10×10 mm MgO substrates with

[001] orientation. The base pressure before deposition was less than 10 -8< Torr and the pressure during deposition was 3 mTorr. The IrAl, PdAl, RuAl, Co x Al, and Co-Ni-Al alloy thin films were prepared by co-sputtering from individual heavy metal and Aluminum targets with 2-inch diameter and 0.25-inch thickness. The composition of thin films is calibrated by Rutherford Backscattering spectroscopy. The atomic ratio of IrAl, PdAl, and RuAl is 42:58, 35:65 and 46:54 respectively. The highly resistive TaN-capping layer was prepared by introducing 20% N 2 into the Ar gas flow. The magnetization hysteresis loops (Fig. ID) were measured with a superconducting quantum interference device vibrating sample magnetometer (SQUID-VSM).X-ray Analysis of the Strain Gradient in thin MAl (M= Ru, Pd and Ir)|Co x Al films

[0032] The magnitude of the strain gradient along the sample normal (c-axis) was analyzed by X-ray diffraction probing the reflection profiles collected by line scans in reciprocal space along the q z direction in the vicinity of the (002) reflection. The experiments were carried out in our home laboratory using a Ga-jet x-ray source (1=1.3414 Å) and a six circle diffractometer as well as at the beamline 25b of the European Synchrotron Radiation Source (ESRF) in Grenoble (France). In both cases, a two-dimensional pixel detector was used employing a region of interest to provide high resolution in k-space along the longitudinal scan direction (qz); J. Magn. Magn. Mater. 319, 13 - 55 (2007) and Acta Crystallographica Section A 25, 165 - 173 (1969).Magneto-transport measurements

[0033] By the Van-der-Pauw method, the conventional Hall resistivity is measured with 3×3 mm square samples cut from 10×10 mm blanket films and a set of direct current source (Keithley 6221), nanovoltmeter (Keithley 2182a) was used.Transmission Electron Microscopy

[0034] For the transmission electron microscopy (TEM) investigations, cross sectional lamellae from the thin films were prepared by Focused Ion Beam (FIB) Ga +< ion milling [TESCAN GAIA3 operating at 30 kV ion-beam energy] using standard lift-out procedures. For Lorentz TEM imaging several plane-view lamellae were prepared from the as-deposited films by Ar ion milling from the back-side of the MgO substrate. Structural imaging was performed using JEOL ARM300F2 TEM. Magnetic textures were investigated by TEM [FEI TITAN 80-300 and JEOL JEM-F200] in the Lorentz mode operated at an accelerating voltage of 300 kV and 200 kV respectively, using a GATAN double-tilt LN2 cooling holder (Model 636) which is capable of varying the temperature. A vertical magnetic field was applied to the lamella within the TEM column by passing currents through the coils of the objective lens and a Lorentz mini-lens was used for imaging; see Sci. Rep. 8, 5703 (2018) and Nat. Commun. 8, 14761 (2017).Free-standing thin film transfer procedure

[0035] For the LTEM investigation on this multilayer sample at different temperatures, a lift-off and transfer method was used. To protect the entire structure, a 100 nm thick PMMA layer was coated onto the as deposited sample that are prepared by combining deposition in a pulsed laser deposition and a sputtering chamber. Then, the multilayer structure was immersed in deionized water for -30 min to remove the Sr 3 Al 2 O 6 layer. The separated sheet together with water was then picked up and transferred onto heating chip. Before the LTEM measurement, the protective PMMA layer was removed by dropping acetone on the sample after drying in nitrogen for 6 hours.

[0036] The above examples, especially with regard to the CoAl-alloys and Co / Ni / Al-alloys employed, are just for showing a way to carry out the invention and are not meant to limit the scope of the invention in any respect. Each feature being employed in furtherance of the invention can be freely combined with other features to further promote and develop the invention.

Examples

Embodiment Construction

[0012]In conventional scenarios, thin films deposited on various substrates tend to maintain a constant strain throughout their structure. The approach according to the invention diverges from this usual behavior by the introduction of a vertical strain gradient (∇ t ε = ∂ε t / ∂t) as shown in Fig. 1A and B, where ε t is the strain along the normal to the plane of a thin film.

[0013]The formation of many of these spin textures is only possible in bulk compounds without crystal inversion symmetry or at interfaces. So, the lowering of crystal symmetry in centrosymmetric magnetic systems is a key aspect and key feature of the present invention.

[0014]It is found here that the high symmetry of a thin ferromagnetic material is lowered by introducing a vertical strain gradient along the normal to the plane of the thin film.

[0015]Typically, thin films grown on underlayers or substrates exhibit a uniform strain until the thickness exceeds a critical value at which the strain is released, typi...

Claims

1. A method for the formation of skyrmions or Néel-type spin textures in a ferromagnetic material, preferably in a ferromagnetic alloy, comprising the steps of (i) providing an underlayer material, (ii) depositing a film of a ferromagnetic material thereon in a manner that (iii) the film obtained shows a vertical strain gradient (∇tε = ∂εt / ∂t), where εt is the strain along the normal to the plane of the deposited film.

2. The method of claim 1, wherein LTEM and XRD measurements are used to confirm the formation of skyrmions or Néel-type spin textures.

3. The method of claim 1 or 2, wherein the ferromagnetic material has a centrosymmetric, preferably cubic, crystal structure in the absence of the underlayer.

4. The method of claim 1 or 2, wherein the film of the ferromagnetic material has a non-centrosymmetric crystal structure.

5. The method of claim 1 or 2, wherein the film of the ferromagnetic material has a magnetic ordering temperature above room temperature.

6. The method of claim 1 or 2, wherein the film of the ferromagnetic material has a magnetic ordering temperature above 350 °C preferably above 450 °C, most preferred above 500 °C.

7. The method of any of claims 1 to 6, wherein the underlayer material has a crystal structure with a larger lattice than the deposited ferromagnetic material.

8. The method of any of claims 1 to 6, wherein the underlayer is an alloy of the formula M1-xAlx with M = Ir, Pd or Ru, preferably Ir where x is preferably in the range from x=0.30 to x= 0.60 and most preferably in the range from x=0.35 to x=0.55.

9. A ferromagnetic material, preferably an alloy, prepared by the method as recited in any of claims 1 to 8.

10. The ferromagnetic material of claim 9 showing skyrmions or Néel-type spin textures.

11. The ferromagnetic material of claim 9 or 10 being a Co-Al-, a Co-Al-Ni- or a Ni-Al-alloy.

12. The ferromagnetic material of claim 11 being Co2.3Al or Co2.58Ni0.26Al.

13. The use of the ferromagnetic material of any of claims 9 to 12 in spintronics technology, preferably as a material for data storage and improved computer architecture.

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