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Field-free spin-orbit torque switching assisted by in-plane unconventional spin torque in ultrathin [Pt/Co] N
Electrical manipulation of magnetization without an external magnetic field is critical for the development of advanced non-volatile magnetic-memory technology that can achieve high memory density and low energy consumption. Several recent studies have revealed efficient out-of-plane spin-orbit torques (SOTs) in a variety of materials for field-free type-z SOT switching. Here, we report on the corresponding type-x configuration, showing significant in-plane unconventional spin polarizations from sputtered ultrathin [Pt/Co] N , which are either highly textured on single crystalline MgO substrates or randomly textured on SiO 2 coated Si substrates. The unconventional spin currents generated in the low-dimensional Co films result from the strong orbital magnetic moment, which has been observed by X-ray magnetic circular dichroism (XMCD) measurement. The x-polarized spin torque efficiency reaches up to −0.083 and favors complete field-free switching of CoFeB magnetized along the in-plane charge current direction. Micromagnetic simulations additionally demonstrate its lower switching current than type-y switching, especially in narrow current pulses. Our work provides additional pathways for electrical manipulation of spintronic devices in the pursuit of high-speed, high-density, and low-energy non-volatile memory.
Quantum Sensing and Imaging of Spin–Orbit-Torque-Driven Spin Dynamics in the Non-Collinear Antiferromagnet Mn 3 Sn
Novel non-collinear antiferromagnets with spontaneous time-reversal symmetry breaking, non-trivial band topology, and unconventional transport properties have received immense research interest over the past decade due to their rich physics and enormous promise in technological applications. One of the central focuses in this emerging field is exploring the relationship between the microscopic magnetic structure and exotic material properties. Nanoscale imaging of both spin–orbit-torque-induced deterministic magnetic switching and chiral spin rotation in non-collinear antiferromagnet Mn 3 Sn films using nitrogen-vacancy (NV) centers are reported. Direct evidence of the off-resonance dipole–dipole coupling between the spin dynamics in Mn 3 Sn and proximate NV centers is also demonstrated by NV relaxometry measurements. These results demonstrate the unique capabilities of NV centers in accessing the local information of the magnetic order and dynamics in these emergent quantum materials and suggest new opportunities for investigating the interplay between topology and magnetism in a broad range of topological magnets.
Imaging of a van der Waals spin-orbit torque system using spin ensembles in hBN
Recently, optically active spin defects embedded in two-dimensional (2D) van der Waals (vdW) crystals have emerged as a transformative quantum sensing platform to explore cutting-edge materials science. Taking advantage of excellent solid-state integrability, this new class of spin defects can be readily arranged in nanoscale proximity to target materials, showing great promise for realizing in-situ quantum sensing of microscopic spin and charge behaviors in vdW heterostructures. Here we report hexagonal boron nitride-based quantum imaging of field-free deterministic magnetic switching and electric current distributions in an all-vdW spin-orbit torque (SOT) system. By visualizing variations of nanoscale magnetic stray field profile of room-temperature 2D magnet Fe 3 GaTe 2 under different SOT conditions, we show how the magnetic switching evolves from deterministic to stochastic behavior due to the interplay between spin orientations, anisotropy and Joule heating. Micromagnetic simulations rationalize our results well, revealing the role of field-like SOT in inhibiting thermal fluctuation driven stochastic switching and chaotic multi-domain competition. This understanding, which is otherwise difficult to access by conventional transport measurements, offers valuable insights into material design, testing, and performance evaluation of next-generation vdW spintronic devices.
Symmetry Control of Unconventional Spin–Orbit Torques in IrO 2
Abstract Spin–orbit torques generated by a spin current are key to magnetic switching in spintronic applications. The polarization of the spin current dictates the direction of switching required for energy‐efficient devices. Conventionally, the polarizations of these spin currents are restricted to be along a certain direction due to the symmetry of the material allowing only for efficient in‐plane magnetic switching. Unconventional spin–orbit torques arising from novel spin current polarizations, however, have the potential to switch other magnetization orientations such as perpendicular magnetic anisotropy, which is desired for higher density spintronic‐based memory devices. Here, it is demonstrated that low crystalline symmetry is not required for unconventional spin–orbit torques and can be generated in a nonmagnetic high symmetry material, iridium dioxide (IrO 2 ), using epitaxial design. It is shown that by reducing the relative crystalline symmetry with respect to the growth direction large unconventional spin currents can be generated and hence spin–orbit torques. Furthermore, the spin polarizations detected in (001), (110), and (111) oriented IrO 2 thin films are compared to show which crystal symmetries restrict unconventional spin transport. Understanding and tuning unconventional spin transport generation in high symmetry materials can provide a new route towards energy‐efficient magnetic switching in spintronic devices.
Collective spin dynamics under dissipative spin Hall torque
Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets but also more complex noncollinear spin systems. We develop a general Lagrangian–Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of the order and, in particular, on whether there is a net magnetic moment. The latter endows the system with a unipolar switching capability, while magnetically compensated materials tend to evolve toward limit cycles, at large torques, with chirality dependent on the torque sign. Apart from the ferromagnetic and antiferromagnetic cases, we discuss ferrimagnets, which display an intricate competition between switching and limit cycles. As a simple case for compensated noncollinear order, we consider isotropic spin glasses and a scenario of their coexistence with a collinear magnetic order.
Novel Spin?Orbit Torque Generation at Room Temperature in an All-Oxide Epitaxial La[subscript 0.7]Sr
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Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI 3
The recently discovered two-dimensional magnetic insulator CrI 3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI 3 /monolayer-TaSe 2 van der Waals (vdW) heterostructure will induce spin–orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI 3 in direct contact with TaSe 2 . By combining the calculated complex angular dependence of spin–orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI 3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI 3 carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe 2 , while concurrently acquiring strong spin–orbit coupling via such a proximity effect, whereas the second monolayer of CrI 3 remains insulating. Furthermore, the transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.
Unconventional Spin-Orbit Torques Due to Reduced Crystal Symmetries
Spin-orbit torques have emerged as a powerful mechanism for manipulating magnetic moments in spintronic devices, offering a pathway to more efficient and scalable memory and logic technologies. While conventional spin-orbit torques generated in heavy metals and topological insulators have been extensively studied, recent advancements in unconventional spin-orbit torques demonstrated out-of-plane spin polarizations that could effectively switch perpendicular magnetizations without the need for additional external in-plane magnetic fields, promising significant implications for the development of energy-efficient and compact spintronic devices. Unconventional spin-orbit torques are usually found in materials with low symmetries, such as transition metal dichalcogenides, topological insulators, and 2-D materials. Here, we provide a brief overview of unconventional spin-orbit torques and present two example material systems: CrPt 3 and MoTe 2 , both exhibiting strong spin-orbit coupling and phase-dependent spin-orbit torques, and focus on their unique origins and potential applications. We discuss the roles of magnetic and crystallographic orders in generating unconventional spin-orbit torques, highlighting how these factors contribute to the observed anisotropic and directional dependencies.
Effects of Anisotropic Strain on Spin–Orbit Torque Produced by the Dirac Nodal Line Semimetal IrO 2
We report spin-torque ferromagnetic resonance studies of the efficiency of the damping-like (ξ DL ) spin–orbit torque exerted on an adjacent ferromagnet film by current flowing in epitaxial (001) and (110) IrO 2 thin films. IrO 2 possesses Dirac nodal lines (DNLs) in the band structure that are gapped by spin–orbit coupling, which could enable a very high spin Hall conductivity, σ SH . We find that the (001) films do exhibit exceptionally high ξ DL ranging from 0.45 at 293 K to 0.65 at 30 K, which sets the lower bounds of σ SH to be 1.9 × 10 5 and 3.75 × 10 5 Ω –1 m –1 , respectively, 10 times higher and of opposite sign than the theoretical prediction. Furthermore, ξ DL and σ SH are substantially reduced in anisotropically strained (110) films. Here, we suggest that this high sensitivity to anisotropic strain is because of changes in contributions to σ SH near the DNLs.
Enhancement of the spin–orbit torque efficiency in W/Cu/CoFeB heterostructures via interface engineering
Here, the spin-torque ferromagnetic resonance signal and the spin Hall magnetoresistance induced by the spin Hall effect of W/Cu/CoFeB heterostructures with different Cu layer thicknesses (t Cu ) have been systemically studied. The effective spin mixing conductance $g^{↑↓}_{eff}$, the interfacial spin transparency T, and the real spin–orbit torque efficiency ( J s J c ) real show a significant increase compared to the W/CoFeB heterostructure. ( J s J c ) real reaches its maximum of ~0.54, increased up to ~50% at the optimized tCu ~ 0.52 nm according to our theoretical prediction. More importantly, the intrinsic spin Hall angle of W, $θ^{int}_{SH}$ ~ 0.79 ± 0.20, has also been obtained after the correction of the inverse spin Hall effect and T. This suggests that the Cu insertion improves the interface quality and, therefore, assists the spin transport in the heterostructures, which potentially improves the performance of next-generation spintronic devices.
Direct and indirect spin current generation and spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers
Spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers are studied using a combination of symmetry analysis, circuit theory, semiclassical simulations, and first-principles calculations using the nonequilibrium Green's function method with supercell disorder averaging. Here, we focus on unconventional processes involving the interplay between the two ferromagnetic layers, which are classified into direct and indirect mechanisms. The direct mechanism involves spin current generation by one ferromagnetic layer and its subsequent absorption by the other. In the indirect mechanism, the in-plane spin-polarized current from one ferromagnetic layer “leaks” into the other layer, where it is converted into an out-of-plane spin current and reabsorbed by the original layer. The direct mechanism results in a predominantly dampinglike torque, which damps the magnetization towards a certain direction 𝐬 𝑑 . The indirect mechanism results in a predominantly fieldlike torque with respect to a generally different direction 𝐬 𝑓 . Similarly to the current-in-plane giant magnetoresistance, the indirect mechanism is only active if the thickness of the nonmagnetic spacer is smaller than or comparable to the mean free path. Numerical calculations for a semiclassical model based on the Boltzmann equation confirm the presence of both direct and indirect mechanisms of spin current generation. First-principles calculations reveal sizable unconventional spin-orbit torques in Co/Cu/Co, Py/Cu/Py, and Co/Pt/Co trilayers and provide strong evidence of indirect spin current generation.
First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers
A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Furthermore, errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.
Tunable multistate field-free switching and ratchet effect by spin-orbit torque in canted ferrimagnetic alloy
Spin-orbit torque is not only a useful probe to study manipulation of magnetic textures and magnetic states at the nanoscale but also it carries great potential for next-generation computing applications. Here we report the observation of rich spin-orbit torque switching phenomena such as field-free switching, multistate switching, memristor behavior and ratchet effect in a single shot, co-sputtered, rare earth-transition metal Gd x Co 100-x . Notably such effects have only been observed in antiferromagnet/ferromagnet bi-layer systems previously. We show that these effects can be traced to a large anistropic canting, that can be engineered into the Gd x Co 100-x system. Further, we show that the magnitude of these switching phenomena can be tuned by the canting angle and the in-plane external field. The complex spin-orbit torque switching observed in canted Gd x Co 100-x not only provides a platform for spintronics but also serves as a model system to study the underlying physics of complex magnetic textures and interactions.
Magnetic asymmetry induced anomalous spin-orbit torque in IrMn
We demonstrate an anomalous spin-orbit torque induced by the broken magnetic symmetry in the antiferromagnet IrMn. We study the magnetic structure of three phases of IrMn thin films using neutron diffraction technique. The magnetic mirror symmetry M ' is broken laterally in both L 1 0 - IrMn and L 1 2 - IrM n 3 but not γ - IrM n 3 . We observe an out-of-plane dampinglike spin-orbit torque in both L 1 0 - IrMn /permalloy and L 1 2 - IrM n 3 /permalloy bilayers but not in γ - IrM n 3 /permalloy. This is consistent with both the symmetry analysis on the effects of a broken M ' on spin-orbit torque and the theoretical predictions of the spin Hall effect and the Rashba-Edelstein effect. In addition, the measured spin-orbit torque efficiencies are 0.61 ± 0.01, 1.01 ± 0.03, and 0.80 ± 0.01 for the L 1 0 , L 1 2 , and γ phases, respectively. Our work highlights the critical roles of the magnetic asymmetry in spin-orbit torque generation.
Tuning Spin-Orbit Torques Across the Phase Transition in VO 2 /NiFe Heterostructure
The emergence of spin-orbit torques as a promising approach to energy-efficient magnetic switching has generated large interest in material systems with easily and fully tunable spin-orbit torques. We report current-induced spin-orbit torques in VO 2 /NiFe heterostructures are investigated using spin-torque ferromagnetic resonance, where the VO 2 layer undergoes a prominent insulator-metal transition. A roughly twofold increase in the Gilbert damping parameter, α, with temperature is attributed to the change in the VO 2 /NiFe interface spin absorption across the VO 2 phase transition. More remarkably, a large modulation (±100%) and a sign change of the current-induced spin-orbit torque across the VO 2 phase transition suggest two competing spin-orbit torque generating mechanisms. The bulk spin Hall effect in metallic VO 2 , corroborated by the first-principles calculation of the spin Hall conductivity σ SH ≈ -10 4 ($\frac{\hbar}{e}$) Ω -1 m -1 , is verified as the main source of the spin-orbit torque in the metallic phase. The self-induced/anomalous torque in NiFe, with opposite sign and a similar magnitude to the bulk spin Hall effect in metallic VO 2 , can be the other competing mechanism that dominates as temperature decreases. For applications, the strong tunability of the torque strength and direction opens a new route to tailor spin-orbit torques of materials that undergo phase transitions for new device functionalities.
Self-induced spin-orbit torques in metallic ferromagnets
Herein we present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a dissipative torque on the order parameter, giving rise to a current-dependent linewidth in the ferromagnetic resonance with a characteristic angular dependence. We compare our model to recent spin-torque ferromagnetic resonance measurements, illustrating how rich self-induced spin-torque phenomenology can arise even in simple magnetic structures.
Unconventional spin-orbit torques from sputtered MoTe 2 films
Materials with strong spin-orbit coupling and low crystalline symmetry are promising for generating large unconventional spin-orbit torques (SOTs), such as in-plane fieldlike (FL) torques and out-of-plane dampinglike (DL) torques, which can effectively manipulate and deterministically switch an out-of-plane magnetization without the need for additional external in-plane magnetic fields. Here, we report SOTs generated by magnetron-sputtered 1T' MoTe 2 /Permalloy (Py; Ni 80 Fe 20 )/MgO heterostructures using both spin-torque ferromagnetic resonance (ST-FMR) and second harmonic Hall measurements. We observed unconventional FL and DL torques in our samples due to spins polarized normal to the interface of MoTe 2 and Py layers, and studied the influence of crystallographic order and MoTe 2 layer thickness on the SOTs. By comparing the Raman spectra of 1T' MoTe 2 samples prepared in different ways, we found a tensile strain in sputtered MoTe 2 films, which might further enhance the generation of unconventional torques by reducing the symmetry of 1T' MoTe 2 .