Patent Description:
The present application claims priority to <CIT>.

Current-induced spin-torque originating from spin-orbit effects offers an energy-efficient scheme for the electrical manipulation of magnetic devices. A large spin-orbit torque ratio, the figure of merit of spin-orbit torque generation, is highly-desirable for enabling broad applications in spintronics. Great effort has been focused on semiconductors, heavy metals, oxides and, more recently, topological insulators with a spin-momentum locked surface state.

The following prior art references are acknowledged:.

A spin-orbit torque magnetic switching device is provided in accordance with claim <NUM>. Also provided is a method of switching the magnetic moment of a layer of ferromagnetic material in a spin-orbit torque magnetic switching device in accordance with claim <NUM>.

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. The scope of protection of the present invention is defined by appended claims <NUM>-<NUM>.

Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements.

Magnetic switching devices, including magnetic memory devices, are provided. The devices use single-crystalline films of epitaxially grown 4d or 5d transition metal perovskites having a strong spin-orbit coupling (SOC) to produce spin-orbit torque in adjacent ferromagnetic materials via the spin-Hall effect. In embodiments of the devices, the spin-orbit torque can be generated with a high efficiency, even at or near room temperature (e.g., ~ <NUM>).

One embodiment of a magnetic switching device includes a substrate, a layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite on the substrate, and a layer of ferromagnetic material on the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite. In the switching device, the magnetic moment of the ferromagnetic material can be switched by passing a charge current through the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite, whereby a perpendicular spin polarized current is generated in the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite and directed into the layer of ferromagnetic material. This produces a spin-orbit torque in the ferromagnetic material, which switches the spins of electrons in the ferromagnetic material.

4d or 5d transition metal perovskites are oxides having the formula ABO<NUM>, where A is a first metal cation, such as an alkaline earth metal cation, and B is a 4d or 5d transition metal cation. The crystal structures of the perovskites are characterized by BO<NUM> octahedra having shared corners in a three-dimensional arrangement, with the A cations occupying sites between the octahedra. The 4d or 5d transition metal perovskites used in the present devices and methods are characterized by an octahedral connectivity in which BO<NUM> octahedral building blocks in the crystal structure are tilted with respect to an ideal cubic structure.

The octahedral tilt in the 4d or 5d transition metal perovskite can be achieved or enhanced by growing the perovskites epitaxially on a growth substrate that induces a compressive strain or a tensile strain on the perovskite film as a result of a lattice mismatch between the growth substrate and the growing perovskite. As a result, the BOe octahedra in the crystal structure become tilted. As illustrated in the Examples, these tilted octahedra can provide an enhanced spin-Hall effect in the film.

In some embodiments of the 4d or 5d transition metal perovskites, A is an alkaline earth metal, such as Sr or Ba. Examples include SrIrO<NUM> and SrRuO<NUM>.

The 4d or 5d transition metal perovskites can be grown epitaxially as high-quality, single-crystalline films. Epitaxial single-crystalline films are characterized in that the single-crystal grows with a particular orientation determined by the single-crystal growth substrate upon which it is grown. The epitaxial films can form atomically sharp interfaces with their growth substrate and with an epitaxial ferromagnetic layer subsequently grown on the 4d or 5d transition metal perovskite. As used herein, the phrase single-crystalline film refers to films having perfect crystallinity and also to nearly perfect single-crystalline films having a small concentration of defects, such as dislocations, where the number of defects is low enough that the performance of a device incorporating the film is not significantly degraded. The atomically sharp interfaces provide for efficient spin current transmission and spin-orbit torque generation.

A variety of device configurations of the 4d or 5d transition metal perovskite films can be patterned along different in-plane crystallographic directions, using, for example, photolithography. By way of illustration, UV exposure and subsequent ion-milling can be used to provide a 4d transition metal perovskite film or a <NUM>d transition metal perovskite film having a [<NUM>] in-plane crystallographic orientation (where [<NUM>] refers to the cubic substrate crystallographic direction). As illustrated in Example <NUM>, this can give rise to a spin-orbit torque in an adjacent ferromagnetic material that is higher than the spin-orbit torques generated by different crystallographic directions, such as [<NUM>].

A variety of substrates can be used for epitaxial growth, provided they allow for the epitaxial growth of a perovskite layer up to a useful critical thickness. In some embodiments of the devices, a 4d or 5d transition metal perovskite film is grown to a thickness in the range from <NUM> to <NUM>. However, film thicknesses outside of this range can be used, since a high-quality film can be maintained for thicker films (> <NUM>). However, for a given amount of current flow (i.e., same amount of Joule heating), the current density in thicker films may be lower than the current density in thinner films. In other words, given the same efficiency (spin-Hall angle), devices based on thicker films consume more energy. For this reason, thinner films may be desirable for applications in which low energy consumption is important. Ultrathin perovskite films can be used. However, the film should not be so thin that it becomes insulating, which would suppress the spin-Hall effect in the material.

The growth substrate can be selected such that it has a small lattice mismatch with the 4d or 5d transition metal perovskite and, as a result, imparts a lattice-mismatch induced strain to the perovskite, which distorts the unit cell in the crystal structure of the perovskite. Perovskites, including oxide perovskites having the ABO<NUM> crystal structure, can be used as epitaxial growth substrates for other perovskites. One illustrative example of a growth substrate for a 4d or 5d transition metal perovskite, such as SrIrO<NUM>, is the cubic perovskite SrTiO<NUM> (<NUM>). Other examples include DyScO<NUM>, GdScO<NUM>, NdScOs, LSAT ([LaAlO<NUM>]<NUM>[Sr<NUM>AlTa0<NUM>]<NUM>), LaAlO<NUM>, and NdGaO<NUM> substrates. The epitaxial growth substrate may be a multilayered substrate comprised of a growth layer formed on an underlying base layer. For example, in some embodiments the substrate includes a growth layer that is grown or deposited onto an underlying silicon wafer.

The ferromagnetic material can be, for example, a metal, a metal alloy, including a Heusler alloy, or a metal oxide. Suitable transition metals and transition metal alloys include: Ni, Fe, Co and alloys thereof (for example, Ni-Fe alloys, Fe-Co alloys, Ni-Co alloys, Fe-Co-B alloys, Fe-Ga alloys, Co-Pd alloys, Fe-Pt alloys, and Fe-Pd alloys). Heusler alloys include Co<NUM>MnSi, Co<NUM>FeSi, Co<NUM>FeAl, Co<NUM>MnAl, Co<NUM>MnGa, and Co<NUM>FeGe. Metal oxides include Y<NUM>Fe<NUM>O<NUM>, Fe<NUM>O<NUM>, ZnFe<NUM>O<NUM>, MgFe<NUM>O<NUM> MnFe<NUM>O<NUM>, CoFe<NUM>O, NiFe<NUM>O<NUM>, LaSrMnC<NUM>, LaMnO<NUM>, LaCaMnO<NUM>, LaBaMnO<NUM>, Sr<NUM>FeMoO<NUM>, Sr<NUM>CrMoO<NUM>.

In some embodiments of the switching devices, the ferromagnetic material is grown epitaxially on the 4d or 5d transition metal perovskite layer. This is advantageous because it produces a high-quality, single-crystalline film with a sharp interface between the 4d or 5d transition metal perovskite and the ferromagnetic material, which allows for very efficient spin current transmission. However, the ferromagnetic material can also be formed by other means. For example, metal layers and metal alloy layers, can be deposited via sputter deposition as polycrystalline layers comprising randomly oriented grains. In some devices, the ferromagnetic material is provided as one layer in a multilayered structure, such as a magnetic tunnel junction (MTJ). In an MTJ, the layer of ferromagnetic material that forms an interface with the 4d or 5d transition metal perovskite film provides a first ferromagnetic layer (a free layer) that is separated from a second, generally thicker, ferromagnetic layer (a fixed layer) by a thin layer of a non-magnetic material (a spacer layer), as described in greater detail with respect to <FIG>, below. A capping layer can be provided over any exposed surfaces of the ferromagnetic materials to prevent or reduce the oxidation of those materials. Metal oxides, such an Al<NUM>O<NUM>, can be used as a capping layer.

The magnetic switching devices can be used for a variety of spin-orbit torque-based switching applications, including logic and memory devices. In a basic embodiment of a magnetic memory device a pair of electrodes is configured to pass a charge current through the 4d or 5d transition metal perovskite layer. This generates a spin current in the 4d or 5d transition metal perovskite, which is passed into the adjacent layer of ferromagnetic material. As a result, a spin-orbit torque is produced and the spins of electrons in the material are flipped. This spin-orbit torque can be very high. For example, in some embodiments of the devices, the spin-orbit torque is at least <NUM>, as measured by spin-torque ferromagnetic resonance (ST-FMR). Methods for measuring spin-orbit torque via ST-FMR are described in the Examples.

<FIG> is a schematic diagram of a top view of a spin-torque magnetoresistance random access memory (ST-MRAM) cell. A side view is provided in the inset. <FIG> shows a circuit configuration for the STT-MRAM cell. This embodiment of a three terminal STT-MRAM cell includes a magnetic tunnel junction (MTJ) <NUM> on the layer of 4d or 5d transition metal perovskite <NUM>, such as SrIrO<NUM>, which provides a spin-Hall layer. A first electrode <NUM> and a second electrode <NUM> are positioned in electrical communication (direct or indirect) with layer of 4d or 5d transition metal perovskite <NUM>, such that they are configured to pass an in-plane charge current through that layer, as illustrated in <FIG>. The electrodes may be a metal, such as gold or copper. The MTJ includes a lower ferromagnetic layer (the free layer) <NUM> interfaced with layer of 4d or 5d transition metal perovskite <NUM>, a thicker, upper ferromagnetic layer (the fixed layer) <NUM>, and a dielectric spacer layer <NUM> that serves as a tunnel barrier between lower and upper ferromagnetic layers <NUM>, <NUM>. A variety of ferromagnetic materials and non-magnetic materials can be used for the layers of ferromagnetic material and the spacer layer, respectively. By way of illustration, the upper and lower ferromagnetic layers can be LaSrMnO<NUM> layers and the spacer layer can be an oxide, such as SrTiO<NUM>. The structure can be grown epitaxially on top of a growth substrate, which, in this embodiment, includes a base layer <NUM> and a growth layer <NUM>. These may be, for example, a silicon base layer and a SrTiO<NUM> growth layer. In order to achieve a high current density, layer of 4d or 5d transition metal perovskite <NUM> can be made with a low width and the MTJ can be fabricated with a small diameter. For example, in some embodiments of memory cells, the layer of 4d or 5d transition metal perovskite has a width of no greater than <NUM>, including embodiments in which the layer of 4d or 5d transition metal perovskite has a width of no greater than <NUM>. In some embodiments of the memory cells, the MTJ has a diameter of no greater than <NUM>, including embodiments in which the MTJ has a diameter of no greater than <NUM>.

When the memory cell carries out a write operation, the in-plane charge current flow through the layer of 4d or 5d transition metal perovskite gives rise to a perpendicular spin current in the free layer of the MTJ via the spin-Hall effect. This switches the magnetic moment of the free layer and modulates the resistance of the MTJ. Generally, the MTJ will be in a low resistance state when the magnetization of the free layer is aligned with the magnetization of the fixed layer. The memory cell can be read by measuring the resistance of the MTJ using a resistance measuring device. This can be done by, for example, sending a small sensing current to the tunnel junction to generate a sensing voltage, which can be detected (e.g., by a voltmeter) and used to measure the resistance, as illustrated in <FIG>.

A magnetic memory device can be constructed by connecting a plurality of the magnetic memory cells in an array. One embodiment of such an array is shown schematically in <FIG> (3D view) and <FIG> (2D view). In the array, the MTJ cells and their respective 4d or 5d transition metal perovskite layers (spin-Hall layers) serve as memory elements, which are connected by a grid of source lines, bit lines and word lines, with electrodes connecting the source lines to the spin-Hall layers. The various lines and electrodes are made of electrically conductive materials, such as metals (e.g., Au, Cu, and the like). The array operates as follows: to write a target bit, transistors <NUM> and <NUM> on the bit's source line and bit line, respectively, are turned on to create a charge current flow into the target spin-Hall 4d or 5d transition metal perovskite. The source line sources a large charge current (which can be several milliamps, depending on the critical current for magnetization switching). The charge current generates a transverse spin current in the MTJ cell and switches the magnetization of the free layer in the MTJ cell. To read a target bit, transistors <NUM> and <NUM> on the bit's bit line and word line, respectively, are turned on. The word line sources a small current for detecting the resistance of MTJ cell.

Example <NUM>: In this example, it is theoretically predicted that large spin-Hall effect is present in the SrIrO<NUM> (<FIG>) 3D bulk semi-metallic electronic band structure arising from the intrinsic Berry curvature (see <FIG> and <FIG>). An unexpectedly large spin-Hall conductivity (SHC) is obtained from a linear response theory for the bulk system. Such a large response originates from the characteristic structure of nearly degenerate energy bands (shaded in <FIG>) occurring as a combined effect of spin-orbit coupling and oxygen octahedral tilting in the bulk system. Surprisingly, an even larger SHC was found from experiments on SrIrO<NUM> films than predicted by theory, in which the observed SHC was comparable to the topological insulators at room temperature.

High-quality single-crystal SrIrO<NUM> thin films were synthesized on SrTiO<NUM> (<NUM>) substrates by pulsed laser deposition. Ferromagnetic Permalloy Ni<NUM>Fe<NUM>(Py) thin films were then sputtered on SrIrO<NUM> in the same chamber without breaking the vacuum. This in situ synthesis preserves the interface transparency for the spin-current transmission and the efficiency of SOT generation. The bilayers were then capped with ~<NUM> Al<NUM>O<NUM> to prevent oxidation of Py. A reference control sample with a non-perfect Py/SrIrO<NUM> interface created by breaking the vacuum before Py deposition showed a much smaller SOT generation. Atomic force microscopy images of the <NUM> Al<NUM>O<NUM>/<NUM> Py/ <NUM> (<NUM> unit cell, uc) SrIrO<NUM> surface revealed an atomically-smooth surface preserving the substrate step-terrace. In <FIG>, the cross-sectional filtered STEM-HAADF image of a <NUM> uc SrIrO<NUM> film on (<NUM>) SrTiO<NUM> capped with <NUM> Py is shown. Here, the contrast of the image is approximately proportional to the atomic number Z where brighter colors represent heavier elements (heaviest atom in this case being Ir). From the image, it was determined that the SrIrO<NUM> shares the same pseudocubic epitaxial arrangement as the SrTiO<NUM> substrate, with sharp interfaces between both the SrTiO<NUM>/SrIrO<NUM> interface and the SrIrO<NUM>/Py interface. The SrTiO<NUM> substrates were treated to ensure that they were TiO<NUM> surface terminated, which means IrC<NUM>-termination for the SrIrO<NUM> films is expected, which is observed in the image (<FIG>).

The spin-Hall effect in SrIrO<NUM> was probed by measuring the spin-orbit torques in the adjacent Py layer by using the spin-torque ferromagnetic resonance (ST-FMR) technique, as illustrated in the schematic of the Py/SrIrO<NUM> bilayer system (<FIG>). (See, <NPL>); <NPL>); <NPL>). ) When an alternating charge current flowed in SrIrO<NUM>, due to the spin-Hall effect, spin accumulated at the interfaces and induced a spin current that flows into Py. This spin current exerted torque on the Py and excited the magnetic moment into precession, generating an alternating change of the resistance due to the anisotropic magnetoresistance (AMR) in Py. A dc voltage signal Vmix was measured across the device bar that arose from the mixing between the alternating current and changes in the device resistance. The resonance spectrum was obtained at a fixed microwave frequency, and with an in-plane external magnetic field swept through the ferromagnetic resonance condition in Py.

<FIG> shows a typical ST-FMR spectrum for a <NUM> Py/<NUM> (<NUM> uc) SrIrO<NUM> sample (<NUM> × <NUM>) with a microwave current applied along the substrate [<NUM>]c axis (subscript c for pseudocubic notation). The in-plane magnetic field is swept at an angle ϕ = -<NUM>° with respect to the current axis. The resonance line shape is well fitted to a sum of symmetric and antisymmetric Lorentzian components (dark and light dashed curves), where the anti-damping (in-plane, τ∥) and field torque (out-of-plane, τ⊥) components are proportional to the amplitudes of the symmetric and antisymmetric line shape, respectively. As shown in <FIG>, the symmetric and antisymmetric components both depend on ϕ according to the form sin(<NUM>ϕ)cosϕ, which can be interpreted as the product of the contributions from AMR in Py [dR/dϕ ∝ sin(<NUM>ϕ)] and the current-induced torque (τ ∝ cosϕ). (See, <NPL>);<NPL>). ) From the symmetric and antisymmetric amplitudes, it was found that the in-plane σ∥ and out-of-plane torque conductivity σ⊥ (torque per unit electric field) was (<NUM>±<NUM>)×<NUM><NUM> ℏ/2e Ω-<NUM>m-<NUM> and (<NUM>±<NUM>)×<NUM><NUM> ℏ/2e Ω-<NUM>m-<NUM>, respectively, by averaging different measurement frequencies (<NUM> to <NUM>). The sign for σ∥ was consistent with the first-principle calculations for bulk SrIrO<NUM> and that of the heavy metal Pt. The magnitude of σ∥ was comparable to that of Pt which has a much larger charge conductivity σ than SrIrO<NUM>. This indicated a large value for the spin-torque ratio <MAT>, figure of merit (generation of anti-damping torque per unit charge current density), for SrIrO<NUM> of <NUM>±<NUM>, which is about one order of magnitude higher than that reported for Pt thin films. (See, <NPL>). ) From the sign of σ⊥, the out-of-plane field-like torque was oriented in the same direction as the torque from the Oersted field that comes from the current in SrIrO<NUM>. However, the value for σ⊥ was larger than the expected Oersted field σoe=<NUM>×<NUM><NUM> ℏ/2e Ω-<NUM>m-<NUM> estimated by Ampere's law. Besides the strong spin-Hall effect from SrIrO<NUM>, the Rashba-Edelsein effect at the Py/SrIrO<NUM> interface could also contribute to the observed field-like torque.

The crystal orientation dependence of the spin-torque ratio as shown in <FIG> was also investigated. The ST-FMR measurements were performed on devices patterned along various in-plane crystal orientations from the [<NUM>]c axis or [-<NUM>]o (subscript o for orthorhombic notation) to [<NUM>]c or [<NUM>]o while keeping the magnetic field angle at ϕ = <NUM>°. The crystal orientation dependent Δθ∥ could be fitted to sin(ψ - ψ<NUM>), where ψ is the angle between the [<NUM>]c and the current axis, and ψ<NUM> accounts for the misalignment between the device pattern and the crystal orientation. Note that the higher θ∥ axis along the [<NUM>]c coincided with the lower resistivity axis of the SrIrO<NUM> thin.

The exceptionally large spin-torque ratio in SrIrO<NUM> was further confirmed by measuring the dc current-induced transformation of the ST-FMR resonance. (See, <NPL>); <NPL>). ) The injection of the dc current exerted an additional dc spin-torque on the adjacent Py. The dc in-plane torque component modified the relaxation of the Py magnetization precession, modulating its resonance linewidth, as this torque component was parallel or antiparallel to the Gilbert damping torque depending on the relative orientation between the current and magnetic field. ST-FMR measurements were performed on the Py/SrIrO<NUM> bilayer device patterned along [<NUM>]c axis (<NUM> × <NUM>) with applied dc current by using a lock-in amplifier. A quantitative analysis of the θ∥ is shown in <FIG>, where resonance linewidth W scales linearly with the applied dc current. The magnitude of the in-plane torque was proportional to the change of the effective Gilbert damping αeff over the current density jc in SrIrO<NUM>. It was found that the sign and magnitude of θ∥(=<NUM>±<NUM>, averaged by different frequencies and devices) measured by the dc biased ST-FMR was in good agreement with the ST-FMR line shape analysis. To investigate the importance of SOC on the spin-orbit torques, a control experiment was also performed on a <NUM> Py/<NUM> SrRuO<NUM> bilayer. While SrRuO<NUM> assumes a similar crystal structure as SrIrO<NUM>, the Ru atom hosts <NUM>d electrons with relatively weak spin-orbit coupling compared to the Ir in SrIrO<NUM>. It was shown that the ruthenate control sample yields a much smaller current-induced change in αeff, which corresponds to a θ∥ of <NUM>±<NUM> (<FIG>). <FIG> shows the in-plane magnetic field angle ϕ dependent current-induced change in the effective damping Δαeff/jc (slope of the linear fit in <FIG> and <FIG>), which can be well-fitted to sinϕ. This is consistent with the symmetry of the current-induced torque, again suggesting that the large spin-torque ratio in SrIrO<NUM> was free from any spurious microwave rectification or thermoelectric effects.

Having established a large spin-torque efficiency in the <NUM> uc SrIrO<NUM> films, the effect of structural variation on the spin-torque efficiency was next investigated. A study was performed on a series of SrIrO<NUM>/Py bilayers where the SrIrO<NUM> thickness was varied from <NUM> uc to <NUM> uc (with the Py thickness fixed), combining the dc-biased ST-FMR results with x-ray measurements at the synchrotron to determine the SrIrO<NUM> symmetry at each thickness. It was found that a structural change from tetragonal to orthorhombic symmetry indeed occurred. As shown in <FIG>, σ∥ increased sharply and saturated at the thickness tSIO of <NUM> uc from a nearly constant value when tSIO ≤ <NUM> uc. This abrupt change cannot be explained simply by standard spin-diffusion theory, as the SrIrO<NUM> shows a short spin-diffusion length of ~<NUM> determined from its resonance linewidth broadening. However, the suppression of σ∥ can be closely related to the global SrIrO<NUM> lattice symmetry transition (from orthorhombic to tetragonal) with the decreasing tSIO as shown in <FIG>, where the orthorhombicity a/b is the ratio between the SrIrO<NUM> orthorhombic lattice parameters whose components line along the in-plane [<NUM>]c and out-of-plane [<NUM>]c substrate directions. Such orthorhombic distortions (a/b><NUM>) originate from the IrO<NUM> octahedral tilt, which is suppressed below a critical thickness of ~<NUM> uc likely due to the structural imprint of the underlying cubic SrTiO<NUM> substrate that does not exhibit TiO<NUM> tilt. This yields a strained tetragonal SrIrO<NUM> structure (<FIG>). It should be noted here that the RHEED and synchrotron work show that small domains with orthorhombic distortion persisted even in the thinnest sample. Nonetheless, the global crystal structure of the SrIrO<NUM> films trended towards an undistorted tetragonal. Since the degree of rotation and distortion of the octahedra in perovskites can dramatically change the band structure of the material, it was expected that this structural transition explains the observation of suppressed spin-torque efficiency. This strong dependency of σ∥ on lattice symmetry points out a direct connection between the SrIrO<NUM> crystal structure and its spin-torque efficiency. By tuning the crystal structure of epitaxial SrIrO<NUM> through strain, it was demonstrated that the SrIrO<NUM> SHC produced characteristic signatures of an intrinsic spin-Hall effect.

To get an insight about the intrinsic origin of the observed spin-Hall effect, the SHC was theoretically investigated based on the Berry curvature mechanism. (See, <NPL>); <NPL>). ) It is important to note that the intrinsic effects encoded in the electron bands were generated by the interplay of spin-orbit coupling and tilted oxygen octahedra. For the electron band structure of SrIrO<NUM>, an effective tight-binding model constructed for the bulk orthorhombic perovskite structure was employed (see <FIG> and <FIG> for the band structure). (See, <NPL>); <NPL>). ) (The model incorporates various spin-dependent hopping channels for Ir electrons generated by oxygen octahedron tilting in the bulk structure. Using the Kubo formula for the intrinsic spin-Hall effect (Methods), the SHC <MAT> was calculated, where a charge current applied along the υ direction generates a spin current along the µ direction with the spin polarization along ρs. The SHC is a sum of the Berry curvatures of occupied electron states below the Fermi level ∈F. The SHC computed for the bulk system had significantly large values as shown in <FIG>. Specifically, <MAT> (where the spin current flows along the bulk c axis, circles curve) shows large and positive SHC over an extended region except around the zero energy. Nonzero SHCs were even observed in the configurations, in which v, µ, ρs were not orthogonal to each other: <MAT> (triangles) and <MAT> (squares) peak around the zero energy with an opposite sign.

Such large spin-Hall effects mainly originated from the nearly degenerate energy bands marked by gray in <FIG> as revealed by the momentum-resolved SHC <MAT> <MAT> in <FIG>. In particular, <FIG> demonstrate how the distribution of <MAT> changed within the Brillouin zone as the Fermi level increased. High intensity of <MAT> appeared around the k points where the Fermi level crossed the nearly degenerate bands (<FIG>). Remarkably, the high intensity points occurred with the same sign in the form of loops extended over zone boundaries. Such cooperative contributions from many k points were also observed in <MAT> and <MAT>. These patterns contrast SrIrO<NUM> with Pt where SHC is dominated by a few high symmetry points. (See, <NPL>).

The experimental geometry used is shown in <FIG>, where the charge current is passed along either orthogonal in-plane surface direction and the spin current is normal to surface. The bulk calculation that is closest to this setup is the <MAT> (circles) configuration. The bulk calculation predicted a large intrinsic SHC, but one order of magnitude smaller compared to the experimental results on the thin films. From this theoretical investigation, an unusually large SHC for the bulk system was found that is qualitatively consistent with the experimental results and also illustrates the intrinsic origin of the large spin-Hall effect in SrIrO<NUM>.

In summary, a new material candidate has been discovered for spin-orbit torque applications in a transition metal perovskite with spin-orbit coupled <NUM>d electrons in which SOC and the crystal structure combine to produce the largest spin-torque efficiency in a bulk system to date. From the application point of view, less current was shunted through the adjacent metallic ferromagnets (due to the semimetallic nature of SrIrO<NUM>) compared to the surface driven mechanisms which show a comparable efficiency. This material also acted as an ideal building block for oxide spintronics, since a broad range of ferromagnetic perovskites could be easily integrated in an epitaxial heterostructure with atomically sharp interfaces for efficient spin current transmission. Furthermore, the extended nature of 5d orbitals allowed sensitive response of the electronic band structure to an externally manipulated lattice structure. This was, for example, manifested in the strong dependency of the SHC on the octahedral tilting and rotation. Such intricate coupling between the electronic and lattice degrees of freedom enable a new avenue to engineer spin-orbit torques by tailoring the lattice symmetry.

Sample growth, fabrication and characterization. SrIrO<NUM> films were epitaxially synthesized on (<NUM>) SrTiO<NUM> substrates using pulsed laser deposition (PLD). During the growth, layer-by-layer deposition was observed by in situ reflection high energy electron diffraction (RHEED). Before the growth, the SrTiO<NUM> (<NUM>) substrates were chemically etched and annealed to ensure TiO<NUM> surface termination. The substrates were first immersed in buffered hydrofluoric acid for <NUM> seconds before being annealed at <NUM> for <NUM> hours in an O<NUM>-rich environment. After annealing, the substrates were etched again in buffered hydrofluoric acid to remove any leftover SrO on the surface. The PLD growth was conducted at a substrate temperature of <NUM> and an oxygen partial pressure of <NUM> mTorr. The laser fluence at the SrIrO<NUM> target surface was ~<NUM> J/cm<NUM> and the pulse repetition was <NUM>. The working distance between target and substrate was ~<NUM>. After the SrIrO<NUM> growth, the sample was cooled down in an oxygen rich atmosphere. The chamber was re-evacuated at room temperature and Py was sputter deposited at an Ar pressure of <NUM> mTorr with a background pressure <<NUM> × <NUM>-<NUM> Torr, followed by a <NUM> Al passivation layer. The Py film is shown to be polycrystalline, which was confirmed by the observation of RHEED diffraction rings after deposition. The atomically flat Py surface on top of SrIrO<NUM> was verified using atomic force microscopy. The thickness, epitaxial arrangement, and coherence of the SrIrO<NUM> films was confirmed using x-ray reflectivity, x-ray diffraction, and reciprocal space mappings. The thickness of Py films was measured by using x-ray reflectivity. The actual Py ferromagnetic thickness excluding the magnetic dead layer was determined by measuring the saturation magnetization as a function of thickness. The Py thickness here refers to the actual ferromagnetic thickness.

The Py/SrIrO<NUM> sample was patterned by using photolithography followed by ion beam milling. Then <NUM> Pt/<NUM> Ti electrodes were sputter deposited and defined by a lift-off procedure. Devices for ST-FMR were patterned into microstrips (<NUM>-<NUM> wide and <NUM>-<NUM> long) with ground-signal-ground electrodes. Devices for electrical transport measurements were patterned into <NUM> wide and <NUM> long Hall bars.

STEM measurements. TEM specimens were prepared by a focused ion multibeam system (JIB-4610F, JEOL, Japan). To protect the Py/SrIrO<NUM> films, an amorphous carbon layer was deposited on the top surface before the ion beam milling. A Ga+ ion beam with an acceleration voltage of <NUM> kV was used to fabricate the thin TEM lamella. To minimize the surface damage induced by the Ga+ ion beam milling, the sample was further milled by an Ar+ ion beam (PIPS II, Gatan, USA) with an acceleration voltage of <NUM> meV for <NUM>. HAADF-STEM images were taken by using a scanning transmission electron microscope (JEM-2100F, JEOL, Japan) at <NUM> kV with a spherical aberration corrector (CEOS GmbH, Germany). The optimum size of the electron probe was ~<NUM>Å. The collection semi-angles of the HAADF detector were adjusted from <NUM> to <NUM> 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 background noise (HREM research Inc.

Synchrotron X-ray Thin Film diffraction. Synchrotron X-ray diffraction measurements were carried out to precisely characterize the structural and lattice symmetry evolution as a function of thickness of SrIrO<NUM> thin films epitaxially grown on a (<NUM>) SrTiO<NUM> substrate. The thin film diffraction measurements were performed on a five-circle diffractometer with χ-circle geometry, using an X-ray energy of <NUM> keV (wavelength λ = <NUM>Å) at sector <NUM>-ID-D of the Advanced Photon Source, Argonne National Laboratory. The X-ray beam at the beamline <NUM>-ID-D had a total flux of <NUM> × <NUM><NUM> photons/s and was vertically focused by beryllium compound refractive lenses down to a beam profile of ~ <NUM>. The L-scans along respective truncation rods {<NUM>} were obtained by subtracting the diffuse background contributions using the two-dimensional images acquired with a pixel 2D array area detector (Dectris PILATUS-<NUM> Si <NUM>). The separation of respective {<NUM>} film peak position in reciprocal space can be used to extract the out-of-plane tilt angle of the SrIrO<NUM> film with respect to a cubic perovskite lattice, so that the degree of orthorhombic distortion (a/b > <NUM>) can be obtained for each SrIrO<NUM> thin film as a function of thickness.

ST-FMR measurements. During ST-FMR measurements, a microwave current at a fixed frequency (<NUM> to <NUM>) was applied to the ac port of a bias-T and a RF ground-signal-ground probe tip. The microwave power output (<NUM> to <NUM> dBm) was also fixed. For the applied powers, the line shape of the ST-FMR spectrum was within the linear region of small-angle precession. The in-plane magnetic fields (±<NUM> T) were generated by a rotary electromagnet. For the line shape analysis, the rectified mixing voltage was detected by using a dc voltage meter through the dc port of the bias-T. For the dc-tuned analysis, the rf current amplitude was modulated and the mixing voltage signal was measured by using a lock-in amplifier. The jc was carefully calibrated by measuring the <NUM>-point-resistance for each layer with a parallel resistor model. For the crystalline orientation dependent measurement, devices were patterned on the same sample to minimize the possible variations on sample fabrication. The in-plane magnetic field angle was fixed at ϕ = <NUM>°, and the microwave frequency and power were <NUM> and <NUM> dBm, respectively.

Theoretical calculation. For the spin-Hall conductivity calculations, a jeff=<NUM>/<NUM> tight-binding model constructed for the orthorhombic perovskite bulk structure was employed. (See, <NPL>);<NPL>). ) The model Hamiltonian H consists of four doubly degenerate electron bands on account of four Ir sites in each unit cell. <MAT> Here, ψ = (ψ<NUM>↑, ψ<NUM>↑, ψ<NUM>↑, ψ<NUM>↑, ψ<NUM>↑, ψ<NUM>↓, ψ<NUM>↓, ψ<NUM>↓)T are electron operators with the subscripts meaning the sub-lattice (<NUM>,<NUM>,<NUM>,<NUM>) and jeff=<NUM>/<NUM> pseudo-spin (↑, ↓). The explicit form of Hk and the values of hopping parameters can be found in Refs. <NUM> and <NUM>. (See,<NPL>); <NPL>). ) Then, the SHC <MAT> is calculated by the Kubo formula: <MAT> where <MAT> (See, <NPL>); <NPL>).

Here, <MAT> is charge current, and <MAT> is spin current with the jeff=<NUM>/<NUM> spin represented by the Pauli matrix σρ. In the above expression, Vis the volume of the system, ∈F is the Fermi level, and |mk〉 represents a Bloch state of H with energy ∈mk. The momentum-resolved SHC represented by <MAT> enables the tracing of the electron states responsible for the large spin-Hall effect. In these calculations, the pseudocubic axes were taken for the three indices {ρ, µ, v} representing a measurement geometry, and a <NUM>×<NUM>×<NUM>-point mesh was used for the summation over momentum. (See, <NPL>); <NPL>).

In <FIG>, the RHEED intensity spectrum of a <NUM> uc (<NUM>) SrIrO<NUM> film on SrTiO<NUM> is plotted in which the intensity oscillations indicate layer-by-layer growth of the film. The RHEED pattern in the right inset indicates near preservation of the substrate RHEED pattern in the left inset. After deposition of Py onto the SrIrO<NUM> film, RHEED patterns of the Py surface showed faint rings, indicating a textured polycrystalline Py structure. After deposition of the in situ Al<NUM>O<NUM>/Py deposition, atomic force microscopy images were taken. As can be seen in <FIG>, the final surface of the Al<NUM>O<NUM>/Py/SrIrO<NUM>//SrTiO<NUM> (<NUM>) surface retained the step-terrace features of the chemically and thermally treated TiO<NUM>-terminated SrTiO<NUM> substrate in <FIG>.

In <FIG>, <FIG>, and <FIG>, the lab-source x-ray diffraction data of a <NUM> Al<NUM>O<NUM>/<NUM> Py/<NUM> SrIrO<NUM>/SrTiO<NUM> (<NUM>) heterostructure is presented. The 2θ-ω out-of-plan scan aligned to the (<NUM>) SrTiO<NUM> peak shows an epitaxial SrIrO<NUM> film without the presence of additional peaks that would indicate that different phases of SrIrO<NUM> exist. The SrIrO<NUM> films show distinct Kiessig fringes around the main (<NUM>) and (<NUM>) pseudocubic reflections, which indicates a smooth film surface and interfacial structure. The azimuthal ϕ-scan around the (<NUM>)pc pseudocubic reflection shows that the SrIrO<NUM> film shares the same pseudocubic arrangement with the underlying SrTiO<NUM> substrate. From the reciprocal space mapping around the (<NUM>) SrTiO<NUM> peak shown in <FIG>, it is shown that the SrIrO<NUM> films are fully coherent with the underlying SrTiO<NUM> substrate.

Synchrotron x-ray diffraction experiments were performed to determine the tilt and symmetry of a series of SrIrO<NUM> films on SrTiO<NUM> (<NUM>) capped with <NUM> of Py. Orthorhombic perovskites like SrIrO<NUM> with Pbnm space group symmetry orient themselves on cubic substrates with [<NUM>]o out of plane along [<NUM>]pc with [-<NUM>]o and [<NUM>]o in-plane along [<NUM>]pc and [<NUM>]pc, respectively. Such epitaxial arrangement produces a distortion of the orthorhombic unit cell due to the compressive/tensile strain along [-<NUM>]o, which causes the orthorhombic film to assume a slightly distorted monoclinic structure with α = β = <NUM>° ≠ γ. By examining the {<NUM>}pc reflection at <NUM>° increments, it is possible to determine the pseudocubic tilt of the orthorhombic films by comparing the peak position in L at each ϕ angle, as their film peak positions will show deviations in the surface-normal component of Qz, the surface normal component of the x-ray scattering vector. This will shift the peak position in L along <NUM> of the ϕ-angle peaks, whereas the other <NUM> alignments will have identical peak positions in L. The L-shifts will exist along the [<NUM>]pc and [-<NUM>]pc peaks since the in-plane direction of the strain that creates the distorted tilt lies along [<NUM>]pc. Therefore, the [<NUM>] and [<NUM>-<NUM>] reflections should exhibit the same film peak position in L, since no tilt exists along this direction. As can be seen in <FIG>, the splitting from [<NUM>] and [-<NUM>] was pronounced at <NUM> uc but was slowly suppressed as the film thickness decreased. At <NUM> uc, the {<NUM>}pc family showed no deviation in L, indicating that relatively no tilt from the strain existed, which means that a global tetragonal symmetry was established. From the position of these Z peaks, geometrical analysis was performed to calculate the a/b ratio presented in <FIG>. (See, <NPL>).

However, while such scans are effective for determining the tilt from epitaxial strain, they ignore tilting of the octahedral from small orientations of orthorhombic domains. Since lower symmetry perovskites like orthorhombic SrIrO<NUM> show tilts and rotation patterns in their octahedra along different pseudocubic directions, they will exhibit extra x-ray reflections between pseudocubic peaks that arise from doubling the unit cell along particular crystallographic directions. Therefore, based on the bulk tilt pattern of SrIrO<NUM>, scans to look for the (<NUM>)o reflection were performed to check if the films were completely tetragonal. This reflection corresponds to a half-order pseudocubic {<NUM>/<NUM><NUM>} family of reflections that do not exist in non-tilted perovskite system. Thus, any measured intensity from the (<NUM>) peak would indicate the presence of small orthorhombic domains in the films. <FIG> shows that intensity from the measured (<NUM>)o reflection in the SrIrO<NUM> films persisted even in the <NUM> uc film that showed no tilt from the {<NUM>} work. It should be noted however, that although the (<NUM>) orthorhombic peak was still observable in the thin <NUM> uc film, the intensity of this peak dropped much more quickly with decreasing thickness than the primary (<NUM>) peak from <NUM> to <NUM> uc. If this (<NUM>) intensity change were solely due to the progressively thinner SrIrO<NUM> films, the (<NUM>) should have decreased at the same rate, which was not the case, as shown in <FIG>. Thus, this signifies a global suppression of the orthorhombic tilt, and from there, the suppression of octahedral tilts and rotations. Thus, while the <NUM> uc film may have retained small orthorhombic domains (this was also verified from RHEED experiments along the (<NUM>,<NUM>) and (<NUM>,<NUM>) pseudocubic directions), these domains were greatly suppressed as the global structure clearly tends towards the tetragonal symmetry from <NUM> to <NUM> uc.

The ST-FMR signal with the current-induced in-plane and out-of-plane torque components can be described by the Landau-Lifshitz-Gilbert-Slonczewski equation, <MAT> where γ is the gyromagnetic ratio, µ<NUM> is the permeability in vacuum, Heff is the effective magnetic field including the external magnetic field Hext and the demagnetization field, α is the Gilbert damping coefficient, and τ⊥ and τ∥ are the out-of-plane and in-plane torque components shown in <FIG>. (See, <NPL>). ) The ST-FMR mixing voltage can be then written in the form as: <MAT> where W is the half-width-at-half-maximum resonance linewidth, and HFMR is the resonance field. S and A are the symmetric and antisymmetric amplitude of the Lorentzian, and can be expressed as, <MAT> <MAT> where Irf is the microwave current, R(ϕ) is the device resistance as a function of in-plane magnetic field angle ϕ due to the anisotropic magnetoresistance of Py, and µ<NUM>Meff is the effective magnetization. The S and A amplitudes are proportional to the microwave power (<FIG>), which indicates that the measurement is within the linear regime to the driving field. In this study, the Vmix was directly measured by a dc voltmeter without any amplitude modulation of the microwave power. To calibrate dR/dϕ, the device resistance was measured as a function of magnetic field angle by rotating an in-plane magnetic field of <NUM> T produced by a rotary electromagnet (<FIG>). By fitting the ΔR to cos(<NUM>ϕ), dR/dϕ at a certain ϕ angle could be calculated. The microwave current Irf was calibrated by measuring the device resistance change due to Joule heating effect. (See, <NPL>);<NPL>). ) This same amount of heating can be obtained with an injection of dc current Idc by comparing the change of the device resistance. Therefore, the rf current can be determined as <MAT>, since Joule heating from ac and dc current are <MAT> and I<NUM>R. <FIG> shows a typical device resistance change curve due to de (circles) and rf (squares5. <NUM>) currents, in which they are fitted to a quadratic and a linear function, respectively. The rf current was estimated for different rf frequencies and powers.

Then the magnitude of torque components could be determined by extracting the symmetric and antisymmetric amplitude from Eq. S3 and Eq. S4. The two torque ratios could be calculated as <MAT>, where Ms and t are the saturation magnetization and the thickness of Py; l is the length of the device bar, ℏ is the reduced Planck's constant, e is the electron charge. The saturation magnetization Ms was measured by vibration sample magnetometry. The effective magnetization Meff was obtained by measuring the frequency dependent HFMR with a fit to Kittel equation, <MAT> where µ<NUM>HK is the in-plane magnetic anisotropy field. It was found that Meff ≈ Ms for all samples with <NUM> Py, indicating negligible perpendicular magnetic anisotropy. <FIG> shows the frequency dependent ST-FMR spectra for a <NUM> Py/ 20uc SrIrO<NUM> bilayer sample, in which the Py effective magnetization Meff (<FIG>) and Gilbert damping parameter α (<FIG>) were determined. The spin torque ratio θ∥ of a <NUM> uc SrIrO<NUM> sample was then calculated at various frequencies (<NUM>-<NUM>), since the spin torque ratio is expected to be independent of frequency. (See, <NPL>). ) <FIG> shows the frequency dependent spin torque ratio determined from both ST-FMR line shape (squares) and dc-tuned analysis (circles). Both methods yielded a small frequency variation.

Alternatively, the spin torque ratio was obtained by inserting a dc Idc current superimposed on the microwave current, which induced a subtle change in the ST-FMR line shape. (See,<NPL>);<NPL>); <NPL>); <NPL>). ) In particular, the θ∥ was quantified by linearly fitting the current dependent resonance linewidth or αeff as <MAT> where αeff is the effective magnetic damping of Py and can be related to W as αeff = <MAT>. To extract resonance linewidth with smaller deviation, the rf current amplitude was modulated and the mixing voltage signal was measured by using a lock-in amplifier. The dc current was restricted to below <NUM> mA to acquire a good fit curve and minimize Joule heating. The current density in SrIrO<NUM> layer was estimated by using a parallel resistance model.

<FIG>, <FIG> show the change of resonance linewidth as the functions of current density in SrIrO<NUM> for the Py/ SrIrO<NUM> bilayer, in which the Py thickness is fixed at <NUM> and the SrIrO<NUM> thickness varies from <NUM> uc to <NUM> uc (at ϕ=-<NUM>° only). The thickness dependent spin torque ratio and spin Hall conductivity of SrIrO<NUM> are summarized in <FIG>.

To estimate the spin diffusion length in the SrIrO<NUM> thin film, the Gilbert damping parameter α of Py in Py/SrIrO<NUM> bilayer was characterized with various SrIrO<NUM> thicknesses by using both ST-FMR (on patterned samples) and a broadband FMR (on <NUM> by <NUM> samples). The Gilbert damping parameter α was obtained from the frequency dependent measurement (<NUM>-<NUM> for ST-FMR, and <NUM>-<NUM> for FMR) of the resonance linewidth W. The enhancement of α was observed with the increasing SrIrO<NUM> thickness due to the spin pumping effect as shown in <FIG>. The data could be fitted to diffusive spin transport model as, <MAT> where gop is Lande g factor, α<NUM> is the Gilbert damping with zero SrIrO<NUM> thickness, G↑↓ is the interfacial spin mixing conductance per unit area, and λs is the spin diffusion length in SrIrO<NUM>. (See, <NPL>). ) A constant SrIrO<NUM> resistivity ρ was used in the fit, which gave a spin mixing conductance G↑↓ of <NUM> × <NUM><NUM> Ω-<NUM> m-<NUM> and a spin diffusion length of <NUM>. The large spin mixing conductance of SrIrO<NUM> enabled efficient spin transport at the Py/SrIrO<NUM> interface. The spin diffusion length in SrIrO<NUM> suggests that the spin accumulation in SrIrO<NUM> can take place in a very short thickness length scale. The measured changes in the SrIrO<NUM> SHC occurred at a thickness scale well above the SrIrO<NUM> spin diffusion length, allowing it to be concluded that the suppression of the SHC at the thin SrIrO<NUM> sample is due to the change of lattice symmetry rather than due to spin diffusion.

ST-FMR measurements were also performed on an ex-situ grown Py/SrIrO<NUM> sample since the Py/SrIrO<NUM> interfacial transparency plays an important role in the spin current transmission and the spin torque generation. <FIG> shows the ST-FMR spectra for the ex-situ and in-situ grown Py/SrIrO<NUM> sample. For the ex-situ sample, Py was deposited after breaking the chamber vacuum for <NUM> minutes. Two samples have the same layered structure (<NUM> Py/<NUM> uc SrIrO<NUM>) and similar SrIrO<NUM> film quality characterized with XRD and AFM. At the same ST-FMR measurement condition (<NUM> dBm, <NUM>), the in-situ sample shows a much higher S and A amplitudes. Assuming both samples have the same microwave current flow during the measurements, the in-situ sample would exhibit much higher spin torque ratio. This suggests that the non-idea Py/SrIrO<NUM> interface decreases the spin mixing conductance.

To check any spurious effect from the non-uniform current distribution at microwave frequency, ST-FMR measurements were performed on the single layer Py sample. <FIG> shows the ST-FMR spectrum of a <NUM> Py//LSAT sample. The symmetric component of the Py sample was negligibly small and opposite to that of Py/SrIrO<NUM> samples. The observed small antisymmetric component could be attributed to the FMR rectification or non-uniform current distribution in Py.

ST-FMR measurement and dc-tuned analysis were also performed on a <NUM> Pt/ <NUM> Py// SrTiO<NUM> sample as shown in <FIG>, <FIG> and <FIG>. The resistivity of Pt is <NUM>µΩ cm, and its current fraction is <NUM>. In a <NUM> wide, <NUM> long device, <NUM> mA de current were injected, which modified the ST-FMR spectrum (<FIG>). By fitting the change of the resonance linewidth as a function of current density in SrIrO<NUM> to a linear function (<FIG>), the spin torque ratio was calculated based on Eq. S6. Averaging over various frequencies (<FIG>), it was found that the Pt spin torque ratio θ∥ = <NUM> ± <NUM> and SHC σ∥ = <NUM> × <NUM><NUM> ℏ/2e Ω-<NUM>m-<NUM>.

The bare SrIrO<NUM> thin film transport property was measured by using the van der Pauw technique in <NUM> by <NUM> SrIrO<NUM>//SrTiO<NUM> samples. The SrIrO<NUM> room temperature resistivity showed a slight sample-to-sample variation. To determine the anisotropy of the transport property of SrIrO<NUM>, the sheet resistance of the SrIrO<NUM> thin film was measured by using a <NUM>-point resistance technique on Hall bars patterned along [<NUM>]pc and [<NUM>]pc axes. Typical SrIrO<NUM> resistivity versus temperature curves are shown in <FIG> exhibiting metallic transport characteristics in both crystalline orientations.

The Py resistivity was measured by using the van der Pauw technique in Al<NUM>O<NUM>/Py//SrTiO<NUM> reference samples. The resistivity for the <NUM> Py in this work is <NUM>µΩ cm. To determine the current fraction of SrIrO<NUM> in each Py/SrIrO<NUM> bilayer samples, the Py and SrIrO<NUM> layers were treated as parallel resistors. The SrIrO<NUM> resistivity and its current fraction were estimated by assuming that the Py resistivity is constant among different samples. <FIG> shows the estimated SrIrO<NUM> resistivity and its current fraction as a function of SrIrO<NUM> thickness tsio in <NUM> Py/ tsio SrIrO<NUM>//SrTiO<NUM> samples.

The calculated bulk spin-Hall conductivity is shown in <FIG> for the three different measurement geometries in which the system exhibits the largest response. Around the zero Fermi energy (corresponding to charge-neutrality in the bulk system), different patterns of SHC were observed in the three cases. The origin of those patterns can be understood by resolving the SHC in the Brillouin zone as shown in <FIG>. Momentum-resolved SHC <MAT> was basically a net Berry curvature of the occupied electron levels at a given k point. The SHC around the zero-energy originated from two different regions of the zone: (i) around the U and T points at the zone boundaries and (ii) interior regions of the zone. Depending on the measurement geometry, these two distinct regions could have a same sign or different signs in the distribution of the net Berry curvature. In the case of <MAT>, the two regions had different signs for the net Berry curvature leading to highly suppressed SHC by cancellation. In the other cases <MAT> and <MAT>, the overall net Berry curvature had the same sign over the two regions, which resulted in large SHC. Note that the three cases showed very different responses even though they shared the same origin for spin-Hall effect.

Example <NUM>: A series of spin-torque studies were also performed for SrIrO<NUM> grown on a DyScO<NUM> substrate, a GdScO<NUM> substrate, and a NdScO<NUM> substrate. The SrIrO<NUM> layers were epitaxially stabilized on all of the substrates, as confirmed by x-ray diffraction. This allowed for a wide range of lattice mismatches between the SrIrO<NUM> and the substrates. The graph in <FIG> shows the lattice mismatch-dependent spin-orbit ratio for SrIrO<NUM> films grown to a thickness of <NUM> unit cells, with the <NUM> permalloy (Py) overlayer. The spin-orbit ratio (as characterized by the spin-torque ferromagnetic resonance) of SrIrO<NUM> on the NdScO<NUM> substrate was comparable to that of SrIrO<NUM> on SrTiO<NUM>, but higher than that of SrIrO<NUM> on the DyScO<NUM> and GdScO<NUM> substrates (the data points in the figure are fitted to a parabola function). This indicates that the spin-orbit ratio favors a large compressive/tensile strain. The strong dependency of the spin-orbit ratio on the strain opens a route to design an even higher spin Hall effect in a transition metal perovskite with <NUM>d electrons through band structure engineering.

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".

Claim 1:
A spin-orbit torque magnetic switching device comprising:
a substrate (<NUM>);
a layer (<NUM>) of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite on the substrate, wherein the substrate induces a compressive or tensile strain in the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite;
a layer (<NUM>) of ferromagnetic material on the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite;
a first electrode (<NUM>) in electrical communication with the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite; and
a second electrode (<NUM>) in electrical communication with the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite, wherein the first electrode and the second electrode are configured to pass a charge current through the layer of electrically conductive, epitaxial, single-crystalline 4d or 5d transition metal perovskite.