POWER SPINTRONICS DEVICES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. provisional patent application number 16/225,071 that was filed December 19, 2018, the entire contents of which are incorporated herein by reference.

REFERENCE TO GOVERNMENT RIGHTS

[0002] This invention was made with government support under 1629270 awarded by the National Science Foundation and W91 l-NF-17-1-0462 awarded by the ARMY/ARO. The government has certain rights in the invention.

BACKGROUND

[0003] In the classical picture of current-induced magnetization dynamics, charge currents flowing along the in-plane direction (x direction) generate out-of-plane spin currents (z direction) that have spin polarization s, required by symmetry to be along the y direction. This particular spin current gives rise to an anti-damping spin torque in the adjacent ferromagnet, which has magnetization vector m, of the form of m x ( m x y ). This anti damping torque is responsible for efficient magnetization manipulation, but as it is restricted to lie along an in-plane direction, it is efficient only for the in-plane magnetization manipulation. To efficiently and deterministically drive perpendicularly magnetized devices preferred for high-density memories, out-of-plane anti-damping torque is required.

SUMMARY

[0004] Spintronic devices based on metallic antiferromagnets having a non-collinear spin structure are provided. Also provided are methods for operating the devices.

[0005] One embodiment of a spintronic device includes: a ferromagnetic layer comprising a ferromagnetic material having perpendicular magnetization; a spin-torque layer comprising a metallic antiferromagnetic material having a non-collinear spin structure adjoining the ferromagnetic layer at an interface; and a current source configured to pass an in-plane charge current through the spin torque layer. In some embodiments of the devices, the metallic antiferromagnetic material having a non-collinear spin structure comprises a nitride having the formula MmAN, where A is gallium, zinc, copper, or nickel.

[0006] One embodiment of a method of modulating the magnetization in a spintronic device of the type described herein includes passing an in-plane charge current through the spin-torque layer, whereby spin currents having out-of-plane spin polarizations are generated in the spin-torque layer giving rise to a spin torque in the ferromagnetic layer that modulates the magnetization of the ferromagnetic material.

[0007] The spintronic devices include three-terminal magnetic tunnel junction devices that include a magnetic tunnel junction comprising: a free magnetic layer comprising a ferromagnetic material; a pinned layer comprising a ferromagnetic material having a fixed direction of magnetization; and a barrier layer comprising an electrically insulating material separating the ferromagnetic layer from the pinned layer. The three-terminal devices further include: a spin torque layer comprising a metallic antiferromagnetic material having a having a non-collinear spin structure adjoining the free magnetic layer; a write current source configured to pass an in-plane charge current through the spin torque layer; a read current source configured to pass a charge current through the magnetic tunnel junction; and a voltage source configured to apply a bias voltage between the pinned layer and the spin- torque layer.

[0008] The three-terminal devices can be operated by passing an in-plane write current through the spin torque layer, whereby spin currents having out-of-plane spin polarizations are generated in the spin-torque layer, giving rise to a spin torque in the free magnetic layer that switches the magnetization of the free magnetic layer; and passing a read current through the magnetic tunnel junction and measuring the resistance of the magnetic tunnel junction.

[0009] Other principal features and advantages of the invention will become apparent to those skilled in the art upon review of the following drawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements. [0011] FIG. 1A - FIG. IF depict the concept of the unconventional spin-Hall effect in MmGaN. FIG. 1 A depicts the crystallographic unit cell of antiperovskite MmGaN with the antiferromagnetic 5g spin structure where Mn spins (arrows) formed a Kagome-type lattice in the (111) plane. The x, y, and z correspond to the cubic [100], [010], and [001] axis, respectively. FIG. IB depicts the spin structure of MmGaN in the (001) plane. The dashed line corresponds to the (110) mirror plane. FIG. 1C depicts schematic illustrations of the Py/MmGaN bilayer and the allowed spin-Hall spin polarization in the low-symmetry state (a). This indicates non-zero spin-Hall conductivities and sx _c, which correspond to spin polarizations along y, x and z direction, respectively (with the charge current along x and spin current along z). FIG. ID depicts calculated spin-Hall conductivities s^ _c , s _c and sx _c for MmGaN in the antiferromagnetic phase as a function of Fermi energy. FIG. IE depicts the crystal structure of MmGaN without non-collinear spin structure (i.e. above the antiferromagnetic transition temperature TN) in the (001) plane, which gave rise to a high- symmetry state. FIG. IF depicts the allowed spin polarization in the high-symmetry state, where only the conventional spin-Hall conductivity s _cc was non-zero. FIG. 1G. Spin structure of MmGaN in the (111) plane.

[0012] FIG. 2A - FIG. 2F depict polar MOKE measurements. FIG. 2A depicts a schematic of the MOKE experiments geometry, where the charge current was applied along x, and the magnetic moment of Py was parallel to the current direction. The laser was scanned perpendicular to the current flow direction across the device. FIG. 2B depicts a scanning transmission electron microscope image of Py/MmGaN heterostructure on (001) LSAT substrate with the top Py/MmGaN interface (left), and the bottom MmGaN/LSAT interface (right). FIG. 2C and FIG. 2D depict the sum (FIG. 2C) and difference (FIG. 2D) of the MOKE signal across the device bar of 10 nm Py/20 nm MmGaN. The solid horizontal line in FIG. 2C represents the offset of the sum trace. FIG. 2E depicts the spin-torque ratio with the spin polarization along y axis 6 _y as a function of temperature. The dashed line denotes the Neel temperature 7N of -345 K determined from various measurements. FIG. 2F depicts the out-of-plane lattice parameter of a 30 nm MmGaN/LSAT sample as a function of

temperature.

[0013] FIG. 3A - FIG. 3C depict spin-torque ferromagnetic resonance (ST-FMR) measurements. FIG. 3A depicts a schematic of the ST-FMR geometry for the Py/MmGaN. T _|| and T _± denotes the in-plane and out-of-plane torque components which consisted of different torque terms. FIG. 3B and FIG. 3C depict a ST-FMR spectral for the 10 nm Py/2nm Cu/20 nm MmGaN device bar (50 pm ^c 100 pm) at 300 K (antiferromagnetic phase, FIG.

3B) and 360 K (paramagnetic phase, FIG. 3C) with the Py magnetization oriented at 40 ^° and 220 ^° relative to the current axis. The solid lines show the fit to a Lorentzian function. The microwave current was applied along axis. The applied microwave frequency and power were 7 GHz and 12 dBm, respectively.

[0014] FIG. 4A - FIG. 4D depict angular dependence of ST-FMR. FIG. 4A depicts symmetric and FIG 4B depicts antisymmetric ST-FMR components for the 10 nm Py/2nm Cu/20 nm MmGaN device as a function of the in-plane magnetic field angle at 300 K

(antiferromagnetic phase, AFM) and 360 K (paramagnetic phase, PM). The charge current direction is fixed at the x axis. The applied microwave frequency and power are 7 GHz and 12 dBm, respectively. FIG. 4C depicts a summary of T _{v AD} values extracted from FIG. 4A that are proportional to the amplitude of anti-damping torque terms in AFM and PM phases. The insert schematic on the top panel shows the geometry of the spin-Hall effect with different spin polarizations. FIG. 4D depicts a summary of T _{v FL} values extracted from FIG. 4B that are proportional to the amplitude of field-like torque terms in AFM and PM phases.

[0015] FIG. 5A depicts that the wide angle Q-2Q spectrum only shows the (001) reflections of LSAT substrate and MmGaN film, demonstrating the film is (OOl)-oriented and single phase. Inset shows registered RHEED pattern of the specular diffraction spot after growth. FIG. 5B depicts that the short range Q-2Q scan around the (002) diffraction peak of the MmGaN film showed Kiessig fringes, indicating pristine interfaces and high crystalline quality of the film. FIG. 5C depicts the rocking curve of the (002) MmGaN peak. FIG. 5D depicts 360° f-scans around the MmGaN and LSAT (022) peaks, which demonstrates cube- on-cube epitaxial relationship. FIG. 5E depicts RSM around the LSAT (-113) reciprocal lattice point, which shows the MmGaN is strain relaxed.

[0016] FIG. 6A is a schematic diagram showing a perspective view of a spin-Hall torque device, including the out-of-plane polarizations in the antiferromagnetic layer. FIG. 6B is a cross-sectional view of the device. FIG. 6C is a circuit diagram showing the reading and writing functions of the device. DETAILED DESCRIPTION

[0017] Spintronic devices based on metallic antiferromagnets having a non-collinear spin structure are provided. Also provided are methods for operating the devices. Applications in which the spintronic devices can be used include non-volatile memory applications and logic function applications.

[0018] The spintronic devices are based on a bilayer structure that includes a spin torque layer of a metallic antiferromagnetic material having a non-collinear triangular spin structure adjoining a layer of ferromagnetic material. When coupled to its crystal lattice, the non- collinear spin structure of the antiferromagnet, reduces the symmetry of the system, allowing for the generation of spin currents with different spin polarization directions, including spin currents that are polarized along the out-of-plane direction.

[0019] The unconventional spin structure of the ferromagnets is illustrated in FIG. 1 A and FIG. IB, which show a crystallographic unit cell of a crystalline antiferromagnetic material having a non-collinear spin structure, using MmGaN as an example. As shown in these figures, the spins, which are represented by the arrows, are non-collinear because they are not arranged in a parallel, oppositely facing configuration. In the non-collinear spin structure, the spins adopt a triangular spin texture, which can be seen in FIG. 1G, which shows spin structure of the antiferromagnet in the (111) plane. This low symmetry spin state facilitates the generation of an unconventional spin-torque via the spin-Hall effect, which can be used to control the magnetization in an adjoining ferromagnet. As used herein, the term adjoining means in sufficiently close proximity that the spin-torque generated in the antiferromagetic layer can modulate the magnetization in the ferromagnetic layer. Thus, an antiferromagnetic layer adjoining a ferromagnetic layer may in direct contact with the ferromagnetic layer, or may be spaced apart from the ferromagnetic layer by a thin layer of an intervening material, such as a metal (e.g., Cu or Al), that allows for spin current transmission between the two layers.

[0020] FIG. 1C illustrates the use of the unconventional spin-torque to modulate the magnetization of an adjoining ferromagnetic material. When an in-plane charge current (j _c ) is passed through a layer of the metallic antiferromagnetic material, which is referred to as the spin torque layer and illustrated using MmGaN in this example, a transverse spin current (j _s ) having spin currents polarized in both in-plane and out-of-plane directions via the spin-Hall effect is generated. Such spin currents have not been observed in any other spin-Hall source materials. For comparison, the spin polarization directions for the spin current generated in a conventional antiferromagnet having collinear spins (FIG. ID) is shown if FIG. IF. As shown in that figure, the in-plane charge current generates transverse spin currents with spin polarizations that are required by symmetry to be orthogonal to both charge current (j _c ) and spin current (j _s ). These spin polarizations generate a spin-Hall torque in the ferromagnetic layer (illustrated using NiFe in this example), which can be used to manipulate the magnetization of the ferromagnet. A substantial disadvantage of the conventional antiferromagnet is that the in plane polarized spin currents strongly favor only the manipulation of the magnetization of ferromagnets with in-plane magnetic anisotropy. In contrast, the unconventional spin structure of ferromagnets having a non-collinear spin structure allows for the manipulation of the magnetization of perpendicularly magnetized ferromagnets, which are used for high-density memory and logic devices.

[0021] In some embodiments of the spintronic devices, the magnetization in the ferromagnet is switched, but the magnetization state can be modulated (i.e., changed) in different ways as well. For example, a high frequency oscillation of the magnetization can be induced, which can be used for microwave and terahertz signal sources.

[0022] As shown in the FIG. 1C, an in-plane charge current is one that passes parallel to the interface between the spin-torque layer and the ferromagnetic layer and is defined along the x-axis in FIG. 1C. Although not shown in the figure, an in-plane charge current can be passed between a first electrical terminal and a second electrical terminal on opposite ends of the spin torque layer using a current source configured to pass a current between the terminals.

[0023] The spintronic devices can be operated at low temperatures, for example room temperature (~23 °C). They also can be operated at elevated temperatures, provided that they remain below the antiferromagnetic-to-paramagnetic transition temperature (Neel

temperature) of the antiferromagnet.

[0024] The metallic antiferromagnetic materials can be incorporated as the spin-Hall source in a three-terminal spin-Hall torque device. One embodiment of a spin-Hall torque device is shown in FIG. 6A - 6C. FIG. 6A is a schematic diagram showing a perspective view of the spin-Hall torque device, including the out-of-plane polarizations in the antiferromagnetic layer. FIG. 6B is a cross-sectional view of the device and FIG. 6C is a circuit diagram showing the reading and writing functions of the device.

[0025] The device includes an MTJ 602 having a free magnetic layer 604, a pinned magnetic layer 606, and a barrier layer 608 separating the free and pinned magnetic layers. The free magnetic layer is composed of a metallic ferromagnetic material and is characterized in that it has a magnetization that can be switched or otherwise changed. The pinned magnetic layer is composed of a ferromagnetic layer, but is characterized in that it has a fixed direction of magnetization. The barrier layer is composed of an electrically insulating material that is sufficiently thin to allow for electron tunneling when a bias voltage is applied across the junction. The electrical resistance across the MTJ is controlled by the relative magnetizations of the free and pinned magnetic layers. By switching the magnetization direction of the free magnetic layer between two stable orientations, the resistance across (or impedance of) the MTJ can be switched between two values. These values represent two binary data states (1 and 0) for binary storage or logic applications. Thus, switching the direction of magnetization of the free magnetic layer provides the device’s write cycle and measuring the resistance (or impedance) of the MTJ, typically with a very low voltage across the MTJ, provides the device’s read cycle.

[0026] In the spin-Hall MTJ devices, the spin-Hall source 610 is provided by a layer of a non-collinear, antiferromagnetic material, as described herein, adjoining to the free magnetic layer. The device includes a first electrical terminal 612 and a second electrical terminal 614 on opposite ends of the spin-Hall source layer 610 and a current source 616 (i.e., a circuit that delivers an electric current) configured to pass a current (e.g., a“write” current through spin- Hall source 610 between the first and second electrical terminals. The device further includes a third electrical terminal 618 in electrical communication with pinned magnetic layer 606 and first electrical terminal 612 and a current source 620 configured to pass a current (e.g., a “read” current) through MTJ 602 between the first and third electrical terminals. A voltage source 622 is configured to apply a bias voltage across MTJ 602. During a write operation an in-plane current is passed through antiferromagnetic spin-Hall source 610 to induce magnetization switching by generating currents having out-of-plane spin polarizations in the spin-torque layer, giving rise to a spin torque in the free magnetic layer that switches its magnetization. During a read operation, a charge current is passed through MTJ 602 and the resistance of the MTJ is measured, where measuring the resistance can be directly measuring resistance or can be done indirectly by measuring the impedance.

[0027] The spintronic devices described herein can be used individually or can be provided as an array of device cells. For example, in magnetic random-access memory (MRAM) device can include an array of electronically coupled spin-Hall MTJ devices.

[0028] In the Examples below, a spintronic device comprising an MmGaN

antiferromagnetic layer and a NiFe ferromagnetic layer is described in detail. However, it should be understood that this particular spintronic device is illustrative only and that other materials can be used. Other metallic, antiferromagnetic materials that have a non-collinear, triangular spin structure include other manganese nitrides having the formula MmAN, where A is a transition metal, such as zinc, copper, or nickel. Still other metallic non-collinear antiferromagnets include MmSn, MmGa, MmGe, Mmlr, and MmPt.

[0029] Suitable ferromagnetic materials for the ferromagnetic layers, including the free and pinned magnetic layers, in the devices include, but are not limited to, nickel (Ni), cobalt (Co), iron (Fe) and alloys thereof, including alloys of these elements with non-magnetic materials. Specific examples include, Nii- _x Fe _x alloys, Co _x Fe _y B _a-(x+y) , and Fei- _x Pt _x . Suitable dielectric materials that can be used as the barrier layer in an MTJ include oxides, such as magnesium oxide (MgO).

[0030] High quality, crystalline layer of the antiferromagnetic and ferromagnetic material can be grown epitaxially using, for example, reactive magnetron sputtering, on a growth substrate. However, the materials need not be single-crystalline. They can be polycrystalline or amorphous.

EXAMPLE 1

[0031] MmGaN is a metallic nitride with the antiperovskite crystal structure (identical to the perovskite structure, but with anion and cation positions interchanged) and a lattice parameter close to that of commonly used perovskite substrates. It exhibits antiferromagnetic ordering with a non-collinear ^5g Kagome-like structure (magnetic space group: R3m) stabilized by the magnetic frustration of the Mn atoms in the (111) plane (FIG. 1 A). (Bertaut, E. F. et ak, Solid State Commun. 6, 251-256 (1968) and Matsunami, D. et ah, Nat. Mater. 14, 73-78 (2015).) In the (001) plane of MmGaN (FIG. IB), the (110) plane was the only mirror plane. In this low-symmetry state, charge currents along x generated unconventional anti damping torque components in the form of t _c oc m x ( m x x ) and t _z oc m x ( m x z) in addition to the conventional T _y oc m x (m x y), which correspond to spin currents with s along , z and y, respectively (FIG. 1C). These spin polarized currents have corresponding spin-Hall conductivities s , s _z and s^ _c (in the form of aj _k, where ij and k denote the spin polarization, spin current and charge current directions). FIG ID shows that

calculated by using the bulk MmGaN band structure were large within a wide energy window around the charge neutrality point, reflecting the existence of a sizable spin-Hall current even in the presence of charge carrier doping by defects. Above the antiferromagnetic-to- paramagnetic transition temperature (Neel temperature 7N), disordered spins gave rise to a high-symmetry state (space group: Pm3m) having 4 mirror planes in the crystal lattice (FIG. IE), where only conventional spin-Hall conductivity s^ _c was non-zero.

[0032] Epitaxial MmGaN thin films were grown on (001) (Lao _.3 Sro _.7 )(Alo _.65 Tao _.35 )0 ₃ (LSAT) substrates by reactive magnetron sputtering with in-situ high-pressure RHEED (see Methods). The high crystalline quality of MmGaN and the cube-on-cube epitaxial relationship between the film and substrate were confirmed by x-ray diffraction.

Ferromagnetic permalloy NisiFew (Py) thin films were then in situ deposited on MmGaN to form the Py/MmGaN bilayer, and finally were patterned into device bars for spin-torque measurements (FIG. 2A). FIG. 2B shows the cross-sectional filtered STEM-HAADF image of the bilayer, which reveals sharp interfaces between both MmGaN/LSAT (left) and Py/MmGaN (right). The in-plane magnetization of Py was measured with a SQUID magnetometer. Atomic force microscope images of the 10 nm Py/20 nm MmGaN surface indicated an atomically-smooth surface with a surface roughness of -0.2 nm.

[0033] The conventional spin-torque in the Py/MmGaN was first characterized using the polar magneto-optic-Kerr-effect (MOKE) (Fan, X. et al. Nat. Commun. 5, 3042 (2014).) and its temperature dependence across the Neel temperature of MmGaN. FIG. 2 A shows the MOKE experimental geometry. The charge current and the Py magnetization lay along x, and the laser was normally incident onto a 20 mpi x 40 mpi device. Kerr rotation data was acquired while the laser’s focal point was scanned across the sample along y. As polar MOKE is sensitive to the out-of-plane magnetization, this technique measured the out-of- plane effective magnetic field oc m x y in Py that was produced by the conventional anti- damping torque m x (m x y). It also measured a spatially varying out-of-plane Oersted field generated by the charge current in MmGaN. The anti -damping torque induced effective magnetic field changes sign when m is reversed, so repeating the experiment twice with m along x and -x allowed the anti-damping and Oersted signals to be separated. FIG. 2C and FIG. 2D show the sum and difference of the two MOKE signals measured at room temperature for a 10 nm Py/20 nm MmGaN sample, which were proportional to the Oersted field and spin-torque induced effective magnetic field, respectively. The conventional spin- torque ratio Oy was determined to be 0.11±0.01, which describes the t _g generation by spin current polarized along y absorbed by the Py relative to the charge current density in

MmGaN via spin-Hall effect. This value is comparable to the spin-torque ratio reported in heavy metal Pt. (Liu, L. et al., Phys. Rev. Lett. 106, 036601 (2011).) The spin-torque ratio for Py/MmGaN was found to be robust against a zero-field cooling process which nullifies the exchange bias field at the Py/MmGaN interface. The temperature dependence of the torque ratio Oy was further evaluated as shown in FIG. 2E. The torque ratio Oy in Py/MmGaN drastically reduced to 0.056±0.005 around the MmGaN Neel temperature. The Neel temperature was determined by tracking the temperature dependence of the MmGaN out-of- plane lattice parameter (FIG. 2F) because the negative thermal expansion of MmGaN was accompanied with the first-order transition from the antiferromagnetic to the paramagnetic phase. (Takenaka, K. et al., Appl. Phys. Lett. 87, 1-3 (2005).) The Neel temperature of MmGaN was also confirmed by the temperature dependence of the ordinary Hall coefficient and neutron diffraction. Such an abrupt change in Oy was consistent with the theory calculation, where the spin-Hall conductivity s _zc for MmGaN changed from

2.3 x 10 ⁴ h/2eCi ^~1 m ^~1 in the antiferromagnetic phase to 7 x 10 ³ ft/2en ^_1 m ^_1 in the paramagnetic phase. In the sum MOKE signal scan shown in FIG. 2C, there is a shift of the curve (different absolute value for positive and negative peaks), which indicates a uniformly distributed out-of-plane field produced by a field-like torque that was odd in in as, T _{z FL} OC m x z. While any field-like torque due to Oersted field and Rashba-Edelstein effect would have the form of m x y, the presence of an in-plane field-like torque T _{Z FL} in the Py/MmGaN indicates that the spin currents had polarization aligned away from y

[0034] To analyze the symmetry of the spin torque components in more detail, the ST-

FMR technique was used (FIG. 3 A). (MacNeill, D. et al, Nat. Phys. 1, (2016) and Liu, L. et al., Phys. Rev. Lett. 106, 036601 (2011).) It was performed at room temperature and above the MmGaN Neel temperature. During the ST-FMR measurement, a microwave current applied to MmGaN produced alternating torques on the Py, and excited the Py magnetic moment into precession, generating a corresponding alternating sinusoidal change of the resistance R due to the anisotropic magnetoresistance (AMR) of Py. A dc voltage signal Fmix was measured across the device bar that arose from the mixing between the alternating current and changes in the device resistance. The resonance in mix was obtained by sweeping the external in-plane magnetic field through the Py resonance condition (see Methods). Both in-plane and out-of-plane torque components were then determined individually, as the symmetric and antisymmetric part of the line shape were proportional to the amplitude of the in-plane t _N and out-of-plane t _± torque components, respectively. Considering only the conventional spin-Hall effect (or the Rashba-Edelstein effect and Oersted field), the in-plane and out-of-plane torque components would only have the form of m x ( m x y) and m x y, respectively. (Mellnik, A. R. et al., Nature 511, 449-451 (2014) and Garello, K. el at. , Nat. Nanotechnol. 8, 587-593 (2013).) When the sign of m was inverted by rotating the in-plane magnetic field angle f (with respect to ) by 180 ^° , the torque, and thus Fmix, also changed sign but retained the same amplitude, since V _mix (p) =—V _mix ( p + 180 ^° ). Any additional, unconventional torque component present would cause a difference in the resonance line shape between F _mi (<p) and -V _mix ( p + 180 ^° ).

[0035] FIG. 3B and FIG. 3C show the resonance spectral of the 10 nm Py/2 nm Cu/20 nm MmGaN sample with f equal to 40 ^° and 220 ^° , and measured at 300 K and 360 K, respectively. The Cu insertion layer broke the exchange coupling at the Py/MmGaN interface, but it allowed the transmission of the spin current since Cu has a long spin diffusion length. The and—V _mix (220 ) scans were notably different at 300 K (antiferromagnetic phase of MmGaN), indicating the presence of the unconventional torque components. (MacNeill, D. et al, Nat. Phys. 1, (2016).) While heating the sample up to 360 K, despite the reduced resonance amplitude, the two scans overlapped with each other, indicating the absence of the unconventional torque components. These observations suggested the direct link between the non-collinear spin structure and the existence of unconventional spin toque.

[0036] To quantitatively examine the torque components, ST-FMR measurements were performed as a function of the in-plane magnetic field angle f. FIG. 4A and FIG. 4B show the angular dependence of symmetric _mix, s and antisymmetric V _mix,A part for the 10 nm Py/2 nm Cu/20 nm MmGaN sample, measured at 300 K and 360 K. Such angular dependence was understood as the product of the in-plane or out-of-plane torque components, and the AMR in Py, which has a dependence on f \άR/άf oc sin(2 p)], as V _{mix S} oc sin(2 p)T _|| and V _{mix A} oc sin(2<p)T _j _ The conventional anti-damping torque _{y AD} oc m x ( m x y) and fi eld-like torque T _{y FL} oc m x y have a cos (f) dependence, giving rise to an overall angular dependence of the form sin(2<p)cos (f) for both V _{mix S} and V _{mix A .} This conventional model well describes the angular dependence of the Py/MmGaN when the MmGaN was in the paramagnetic phase. However, the angular dependence of both V _{mix S} and V _{mix A} for the antiferromagnetic MmGaN clearly deviated from this simple picture, but can be fitted by adding additional, unconventional torque terms with the presence of spin currents with spin polarizations oriented away from y. The spin currents that are polarized along would generate torque [ T _{x AD} OC X ( m x x ) and T _{X FL} OC m x X] with a sin (f) dependence; and the torque with spin polarization along z [t _{z /1ΰ} oc m x ( m x z) and T _{Z FL} OC m x z], since m is oriented in the plane, are independent of f. Thus, V _{mix S} ((p) and V _{mix A} ((p) were fit to more general forms to take all possible torque terms into account:

where T _{v v} is a constant and proportional to the amplitude of t _{n u} (v=x, , or z; v =AD or FL). The T _{v v} values in both antiferromagnetic and paramagnetic phases are summarized in FIG. 4C and FIG. 4D, from which several key findings can be extracted.

In the paramagnetic phase, only conventional terms (T _{y AD} , T _{y FL} ) present. In the

antiferromagnetic phase, the non-zero anti-damping torque terms T _{x AD} T _{y AD} and T _{z AD} demonstrated the existence of unconventional torque terms T _{X AD} and T _{Z AD} in addition to the conventional torque term T _{y AD .} The out-of-plane anti-damping torque T _{Z AD} has been observed previously in a system with low crystalline symmetry, Py/WTe2. (MacNeill, D. et al, Nat. Phys. 1, (2016).) The new in-plane anti-damping torque term T _{x AD} that existed in Py/MmGaN had not been found in other lower-crystalline-symmetry systems, but was consistent with the symmetry allowed spin currents derived from the non-collinear antiferromagnetic MmGaN magnetic space group. The strength of individual torque terms was parameterized into the spin-torque ratios q _n (v=x, y, or z), where q _n denoted the efficiency of the T _vAD generation (see Method). For MmGaN in antiferromagnetic phase, 6k=0.023±0.003, 0 _y =O.12±O.OO3 and 6k=0.013±0.001 were found, where the conventional torque ratio (K agreed with that measured by MOKE (FIG. 3 A - FIG. 3B). To make a direct comparison with the theory calculation and experimental results, the experimental torque h

ratios were converted to the corresponding spin-Hall conductivity aj _k (=— s, where s is the conductivity of the MmGaN) with spin currents polarized along i, yielding^ =

9.3 x 10 ^s h/2e W ^_1 ?h ^_1 , af _x = 4.8 x 10 ⁴ h/2e W ^_1 ?h ^_1 , and sx _c = 5.3 x 10 ³ h/

2e n ^_1 m ^_1 , which were comparable with the calculated values (FIG. ID). This indicates the origin of the observed unconventional torques originated from the bulk spin-Hall effect. Methods

Sample growth, fabrication and characterization.

[0037] Epitaxial MmGaN thin films were grown on (OOl)-oriented LSAT substrates by DC reactive magnetron sputtering using a stoichiometric MmGa target in a vacuum chamber with a base pressure of 1 ^c 10 ⁸ Torn During the growth, MmGaN growth mode and surface crystalline structure was monitored by in situ reflection high energy electron diffraction (RHEED). The growth underwent a 3D to 2D growth mode transition. A streaky RHEED pattern after the deposition implied a smooth film surface. The growth was performed at a substrate temperature of 550 °C and an Ar (62 sccm)/N2 (8 seem) atmosphere of 10 mTorr. After the MmGaN growth, the sample was cooled down in vacuum. The Py was then subsequently sputter deposited at an Ar pressure of 3 mTorr. The atomically flat Py surface on top of MmGaN was verified using atomic force microscopy. The thickness, epitaxial arrangement, and coherence of the MmGaN films were confirmed using x-ray reflectivity, x- ray diffraction, and reciprocal space mappings. The thickness of Py films was measured by using x-ray reflectivity.

[0038] The Py/MmGaN sample was patterned by using photolithography followed by ion beam milling. Then 200 nm Pt/5 nm Ti electrodes were sputter deposited and defined by a lift-off procedure. Devices for ST-FMR and MOKE were patterned into microstrips (20-50 pm wide and 40-100 pm long) with ground-signal-ground electrodes. Devices for electrical transport measurements were patterned into 100 pm wide and 500 pm long Hall bars.

STEM measurements. [0039] The STEM sample was prepared through the mechanical flat polishing down to a thickness of ~10 pm by using the precise polishing system (EM TXP, Leica). The polished specimen was ion-milled using Ar ion beam having the voltage range of 1-3 keV (PIPS II, Gatan) to make the hole for the STEM observation. After that, the low energy milling was performed using 0.1 keV Ar beam to minimize the surface damage from the prior ion-milling process.

[0040] The atomic structures were observed using a STEM (JEM-ARM200F, JEOL) at 200 kV equipped with an aberration corrector (ASCOR, CEOS GmbH). The optimum size of the electron probe was ~ 0.8 A. The collection semi-angles of the HAADF detector were adjusted from 68 to 280 mrad in order to collect large-angle elastic scattering electrons for clear Z-sensitive images. The obtained raw images were processed with a band-pass Wiener filter with a local window to reduce a background noise (HREM research Inc.).

MOKE measurements.

[0041] Polar MOKE measurements allowed for the measurement of the small out-of- plane magnetizations induced by the Oersted field and _{y AD} present in Py/MmGaN bilayers. The Oersted field magnitude depended only on the sample current and physical dimensions of the pattern, known quantities, and could be used to self-calibrate the measurements. A spin current was excited with a 21.1 kHz AC charge current, creating Oersted and in-plane anti damping torques oscillating at this same frequency. The sample was mounted on a motion stage, affixed between the poles of an electromagnet, and aligned so that the current and applied magnetic field directions were parallel to . A 633nm HeNe was intensity stabilized, p-polarized (polarized along ) and focused to a ~3 pm spot on the sample. The focal spot was scanned along y (perpendicular to the current), and the Kerr rotation was recorded for both Py magnetization along v and -v To detect the Kerr rotation, the polarization of the beam reflected from the sample was rotated 45°, using a l/2 plate, and then split into s- and p-polarization components. A balanced differential photodetector subtracted the two components, producing a signal proportional to Kerr rotation. The differential signal was amplified with a lock-in referenced to the sample current source (21.1kHz). The sum of the lock-in outputs for v and -v magnetization was proportional to the Oersted field, and the difference to _{y AD .} [0042] To calculate the torque ratio (h further analysis of the sum and difference signals was conducted. The sum signal was fit to the known out-of-plane Oersted field functional form (easily computed from the Biot-Savart law) convolved with a gaussian (because the spatial distribution in optical intensity of the laser beam is gaussian). This fit yielded the sensitivity (in V/T) of the final lock-in output to the out-of-plane magnetic fields responsible for canting the Py moments. The difference signal was fit to the convolution of a“box” function (zero everywhere not on the sample, and constant across the width of the sample) and a gaussian. The height of this function, converted to units of field using the experimental sensitivity (V/T), was the magnitude of the out-of-plane effective field due to r _{y AD .} As non linear curve fitting with many parameters can be a hazardous endeavor, the torque ratios were cross-checked against another analysis method. The torque ratio could also be related directly to the ratio of the area under the absolute value of the differential signal to the area under the sum signal. (Fan, X. et al, Appl. Phys. Lett. 109, 122406 (2016).)

ST-FMR measurements.

[0043] During ST-FMR measurements, a microwave current at a fixed frequency (5 to 8 GHz) was applied through the ac port of a bias-T to a RF ground-signal -ground probe tip.

The microwave power was 13 dBm. The in-plane magnetic fields were generated by a rotary electromagnet which allowed for magnetic field angle dependence of ST-FMR

measurements. Magnetic fields were swept from 0-0.12 T for driving the Py through its resonance condition. The resonance line shape was fitted to a sum of symmetric Vs and antisymmetric FA Lorentzian components in the form as V _mix = the

half-width-at-half-maximum resonance linewidth, mo is the permeability in vacuum and H _FMR is the resonance field. The in-plane t _N and out-of-plane t _± components were proportional to V _{mix S} ^ar| d V _{fiix A} components, which can be expressed as,

where /r _f is the microwave current, R is the device resistance as a function of in-plane magnetic field angle f due to the AMR of Py, a is the Gilbert damping coefficient, and _eff is the effective magnetization. The AMR of Py was determined by measuring the device resistance as a function of magnetic field angle where the field was kept at 0.1 T. The microwave current /r _f was calibrated by measuring the microwave current induced device resistance change due to Joule heating effect. (Tshitoyan, V. et al. , Rhys. Rev. B 92, 214406 (2015) and Zhang, W. el al ., Rhys. Rev. B - Condens. Matter Mater. Phys. 92, 1-7 (2015).)

Electrical transport measurements ofMn GaN.

[0044] Electrical transport measurements of MmGaN films were performed directly on as-grown films wire-bonded in a four-comer van der Pauw geometry. Both sheet resistance and Hall resistance were measured with changing temperature and magnetic induction in a Quantum Design Physical Property Measurement System. Film resistivity was computed by solving the van der Pauw equation in conjunction with film thickness as measured with x-ray reflectivity, while Hall resistance was calculated by summing the two approximately orthogonal Hall configurations.

Temperature dependence of neutron diffraction.

[0045] Single crystal neutron diffraction measurements were performed on the WISH time-of-flight diffractometer at ISIS, the UK neutron and muon source. (Chapon, L. C. el al. , Neutron News (2011). doi: 10.1080/10448632.2011.569650) An approximately 205 nm thick (001) MmGaN thin film sample, with lateral dimensions 10 x 10 mm, was oriented for the measurement of nuclear and magnetic diffraction intensities in the (HHL) reciprocal lattice plane. Specifically, the sample was rotated such that the (001) diffraction peak could be measured with optimal resolution and incident flux. The sample was first mounted within a ⁴ He cryostat, and diffraction patterns were collected from a base temperature of 1.5 K up to 300 K, in 50 K steps. The sample was transferred to a medium-range furnace, and diffraction patterns were then collected at 350, 370, and 390 K.

Temperature dependence of X-ray diffraction.

[0046] The x-ray diffraction data was acquired at beamline 6-ID-B at the Advanced Photon Source with 12 keV incident x-ray energy. The sample temperature was controlled employing an ARS high temperature cryostat. Data was taken with 5 K steps, at each temperature sample position was realigned with respect to base temperature reciprocal space matrix. Sample was mounted on a standard PSI Huber diffractometer.

Theoretical calculations.

[0047] The electronic band structure of MmGaN was calculated by using the First- principles density functional theory (DFT) calculations with Quantum ESPRESSO with fully relativistic ultrasoft pseudopotentials. (Giannozzi, P. et al. , J. Phys. Condens. Matter 21, (2009) and Vanderbilt, D., Phys. Rev. B 41, 7892-7895 (1990).) The exchange and correlation effects were treated within the generalized gradient approximation (GGA).

(Perdew, J. P. et al., Phys. Rev. Lett. 77, 3865-3868 (1996).) The plane-wave cut-off energy of 57 Ry and a l6 x 16 x 16 &-point mesh in the irreducible Brillouin zone were used in the calculations. Spin-orbit coupling and noncollinear ^5g antiferromagnetism were included in all electronic structure calculations.

[0048] The spin-Hall effect is given by

the wth band, jf = {v , s _k } is the spin current operator with spin operator s _k , V _j = is the

velocity operator, and i,j, k = x,y, z. (Gradhand, M. et al, Journal of Physics Condensed Matter 24, (2012).) - _n,ij (k) is referred to as the spin Berry curvature in analogy to the ordinary Berry curvature. In order to calculate the spin-Hall conductivities, the tight-binding Hamiltonians were constructed using PAOFLOW code based on the projection of the pseudo-atomic orbitals (PAO) from the non-self-consistent calculations with a l6 x 16 16 &-point mesh.

(Buongiomo Nardelli, M. el at. , Comput. Mater. Sci. 143, 462-472 (2018); Agapito, L. A. et al., Phys. Rev. B - Condens. Matter Mater. Phys. 88, (2013); and Agapito, L. A. et al., Phys. Rev. B 93, (2016).) The spin-Hall conductivities were calculated using the tight-binding Hamiltonians with a 48 ^c 48 ^c 48 &-point mesh by the adaptive broadening method to get the converged values. EXAMPLE 2

[0049] This example describes the growth of high-quality epitaxial MmGaN films on (OOl)-oriented LSAT and SrTiCE single-crystal substrates as paradigms of AAAX/ri/iO, interfaces.

[0050] FIG. 5 A - FIG. 5E summarize the x-ray diffraction (XRD) structural

characterization for a 60 nm thick MmGaN film grown on a (001) LSAT substrate. The epitaxial growth and single-phase structure of the films was monitored using in-situ reflection high-energy electron diffraction (RHEED) and confirmed through symmetric Q-2Q XRD measurements by the observation of only the (00/) reflections (FIG. 5A). FIG. 5B shows a representative Q-2Q XRD scan taken around the (002) LSAT substrate peak. The presence of Kiessig fringes surrounding the MmGaN (002) peak indicates the high crystalline quality of the film and a pristine interface. The narrow 0.035° full-width at half-maximum (FWHM) value measured from the MmGaN (002) rocking curve demonstrates the high crystalline quality of the MmGaN film (FIG. 5C). Decreasing the thickness of the films resulted in an improvement of the crystallinity, reaching films with FWHM values as low as 0.023°. The in plane cube-on-cube epitaxial relationship between MmGaN film and substrate was confirmed by off-axis azimuthal f-scan around the (022) reflection (FIG. 5D). From x-ray reciprocal space mapping (RSM) measurements centered in the asymmetrical (-113) LSAT peak (FIG. 5B), the out-of-plane (a _± ) and in-plane (an) lattice constant was determined to be a _± = 3.90 ± 0.01 A and a\\ = 3.92 ± 0.01 A, which was in good agreement with the lattice constant value reported to bulk MmGaN, a = 3.898 A. (Bertaut, E. F. et ak, Solid State Commun. 1968, 6, 251-256.)

[0051] The word "illustrative" is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "illustrative" is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, "a" or "an" means "one or more.”

[0052] The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention.

The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.