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Recent discovery of orbital currents in several material platforms including light element metals has opened new possibilities for exploring novel transport phenomena and applications to spin-orbitronic devices. These orbital currents, similar to spin currents, have the ability to generate torque on adjacent magnetic layers, opening a new avenue for efficient spintronic devices. However, separating spin and orbital currents has been one of the major challenges. Here, we show evidence for large conventional as well as unconventional spin and orbital currents in IrO$_2$ and disentangle them by crystal symmetry. We study the anisotropic spin and orbital Hall effects in IrO$_2$ (001), (100), and (111) orientations and find unconventional z-polarized orbital torques using angular spin torque ferromagnetic resonance of IrO$_2$/Ni heterostructures, which are in agreement regarding the relative signs with theoretical calculations of spin and orbital Hall conductivity. This work provides a promising route towards highly efficient low power spintronic and orbitronic devices in oxide heterostructures.

Lecture notes used as part of a graduate-level Introduction to Solid State Physics course at Cornell University. I attempt to unify and update the discussion of magnetism and superconductivity relative to standard textbook treatments, and include connections to recent research. A few related homework problems are attached at the end., Comment: 89 pages. includes homework problems

Unconventional spin-orbit torques arising from electric-field-generated spin currents in anisotropic materials have promising potential for spintronic applications, including for perpendicular magnetic switching in high-density memory applications. Here we determine all the independent elements of the spin torque conductivity tensor allowed by bulk crystal symmetries for the tetragonal conductor IrO2, via measurements of conventional (in plane) antidamping torques for IrO2 thin films in the high-symmetry (001) and (100) orientations. We then test that rotational transformations of this same tensor can predict both the conventional and unconventional anti-damping torques for IrO2 thin films in the lower-symmetry (101), (110), and (111) orientations, finding good agreement. The results confirm that spin-orbit torques from all these orientations are consistent with the bulk symmetries of IrO2, and show how simple measurements of conventional torques from high-symmetry orientations of anisotropic thin films can provide an accurate prediction of the unconventional torques from lower-symmetry orientations., Comment: Main text: 14 pages, 3 figures. Supporting Information: 19 pages, 10 figures, and 1 table

Antiferromagnetic spintronics offers the potential for higher-frequency operations compared to ferromagnetic spintronics and improved insensitivity to magnetic fields. However, previous electrical techniques to detect antiferromagnetic dynamics have required millimeter-scale samples to achieve measurable signals. Here we demonstrate direct electrical detection of antiferromagnetic resonance in devices 1000 times smaller using spin-filter tunneling in micron-scale PtTe$_2$/bilayer CrSBr/graphite junctions in which the tunnel barrier is the van der Waals antiferromaget CrSBr. This sample geometry allows not only efficient detection, but also electrical control of the antiferromagnetic resonance through spin-orbit torque from the PtTe$_2$ electrode. The ability to efficiently detect and control antiferromagnetic resonance provides the means to make detailed studies of the physics governing these high-frequency dynamics and to pursue applications including radiation sources, modulators, and detectors.

Magnons, bosonic quasiparticles carrying angular momentum, can flow through insulators for information transmission with minimal power dissipation. However, it remains challenging to develop a magnon-based logic due to the lack of efficient electrical manipulation of magnon transport. Here we present a magnon logic-in-memory device in a spin-source/multiferroic/ferromagnet structure, where multiferroic magnon modes can be electrically excited and controlled. In this device, magnon information is encoded to ferromagnetic bits by the magnon-mediated spin torque. We show that the ferroelectric polarization can electrically modulate the magnon spin-torque by controlling the non-collinear antiferromagnetic structure in multiferroic bismuth ferrite thin films with coupled antiferromagnetic and ferroelectric orders. By manipulating the two coupled non-volatile state variables (ferroelectric polarization and magnetization), we further demonstrate reconfigurable logic-in-memory operations in a single device. Our findings highlight the potential of multiferroics for controlling magnon information transport and offer a pathway towards room-temperature voltage-controlled, low-power, scalable magnonics for in-memory computing.

Heterostructures of two-dimensional (2D) van der Waals (vdW) magnets and topological insulators (TI) are of substantial interest as candidate materials for efficient spin-torque switching, quantum anomalous Hall effect, and chiral spin textures. However, since many of the vdW magnets have Curie temperatures below room temperature, we want to understand how materials can be modified to stabilize their magnetic ordering to higher temperatures. In this work, we utilize molecular beam epitaxy to systematically tune the Curie temperature ($T_C$) in thin film Fe$_3$GeTe$_2$/Bi$_2$Te$_3$ from bulk-like values ($\sim$220 K) to above room temperature by increasing the growth temperature from 300 $^\circ$C to 375 $^\circ$C. For samples grown at 375 $^\circ$C, cross-sectional scanning transmission electron microscopy (STEM) reveals the spontaneous formation of different Fe$_m$Ge$_n$Te$_2$ compositions (e.g. Fe$_5$Ge$_2$Te$_2$ and Fe$_7$Ge$_6$Te$_2$) as well as intercalation in the vdW gaps, which are possible origins of the enhanced Curie temperature. This observation paves the way for developing various Fe$_m$Ge$_n$Te$_2$/TI heterostructures with novel properties., Comment: 8 pages, 4 figures

Sagnac interferometry can provide a significant improvement in signal-to-noise ratio compared to conventional magnetic imaging based on the magneto-optical Kerr effect (MOKE). We show that this improvement is sufficient to allow quantitative measurements of current-induced magnetic deflections due to spin-orbit torque even in thin-film magnetic samples with perpendicular magnetic anisotropy for which the Kerr rotation is second-order in the magnetic deflection. Sagnac interfermometry can also be applied beneficially for samples with in-plane anisotropy, for which the Kerr rotation is first order in the deflection angle. Optical measurements based on Sagnac interferometry can therefore provide a cross-check on electrical techniques for measuring spin-orbit torque. Different electrical techniques commonly give quantitatively inconsistent results, so that Sagnac interferometry can help to identify which techniques are affected by unidentified artifacts.

A collective excitation of the spin structure in a magnetic insulator can transmit spin-angular momentum with negligible dissipation. This quantum of a spin wave, introduced more than nine decades ago, has always been manipulated through magnetic dipoles, (i.e., timereversal symmetry). Here, we report the experimental observation of chiral-spin transport in multiferroic BiFeO3, where the spin transport is controlled by reversing the ferroelectric polarization (i.e., spatial inversion symmetry). The ferroelectrically controlled magnons produce an unprecedented ratio of up to 18% rectification at room temperature. The spin torque that the magnons in BiFeO3 carry can be used to efficiently switch the magnetization of adja-cent magnets, with a spin-torque efficiency being comparable to the spin Hall effect in heavy metals. Utilizing such a controllable magnon generation and transmission in BiFeO3, an alloxide, energy-scalable logic is demonstrated composed of spin-orbit injection, detection, and magnetoelectric control. This observation opens a new chapter of multiferroic magnons and paves an alternative pathway towards low-dissipation nanoelectronics.

Magnetic van der Waals heterostructures provide a unique platform to study magnetism and spintronics device concepts in the two-dimensional limit. Here, we report studies of exchange bias from the van der Waals antiferromagnet CrSBr acting on the van der Waals ferromagnet Fe3GeTe2 (FGT). The orientation of the exchange bias is along the in-plane easy axis of CrSBr, perpendicular to the out-of-plane anisotropy of the FGT, inducing a strongly tilted magnetic configuration in the FGT. Furthermore, the in-plane exchange bias provides sufficient symmetry breaking to allow deterministic spin-orbit torque switching of the FGT in CrSBr/FGT/Pt samples at zero applied magnetic field. A minimum thickness of the CrSBr greater than 10 nm is needed to provide a non-zero exchange bias at 30 K.

Spin-orbit torques (SOTs) have been widely understood as an interfacial transfer of spin that is independent of the bulk properties of the magnetic layer. Here, we report that SOTs acting on ferrimagnetic FexTb1-x layers decrease and vanish upon approaching the magnetic compensation point because the rate of spin transfer to the magnetization becomes slower than the rate of spin relaxation into the crystal lattice due to spin-orbit scattering. These results indicate that the relative rates of competing spin relaxation processes within magnetic layers play a critical role in determining the strength of SOTs, which provides a unified understanding for the diverse and even seemingly puzzling SOT phenomena in ferromagnetic and compensated systems. Our work indicates that spin-orbit scattering within the magnet should be minimized for efficient SOT devices. We also find that the interfacial spin-mixing conductance of interfaces of ferrimagnetic alloys (such as FexTb1-x) is as large as that of 3d ferromagnets and insensitive to the degree of magnetic compensation.

We complete measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents in the topological insulator Bi$_2$Se$_3$ by quantifying the efficiency with which thermal gradients can generate transverse spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnesistance for bilayers of Bi$_2$Se$_3$/CoFeB. We find that Bi$_2$Se$_3$ does generate substantial thermally-driven spin currents. A lower bound for the ratio of spin current to thermal gradient is $J_s/\nabla_x T$ = (4.9 $\pm$ 0.9) $\times$ 10$^{6}$ ($\hbar/2e$) A m$^{-2}$ / K $\mu$m$^{-1}$, and a lower bound for the magnitude of the spin Nernst ratio is $-$0.61 $\pm$ 0.11. The spin Nernst ratio for Bi$_2$Se$_3$ is the largest among all materials measured to date, 2-3 times larger compared to previous measurements for the heavy metals Pt and W.

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a 3-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe2 and the magnet Cr2Ge2Te6, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet., Comment: submitted version

We report measurements of antiferromagnetic resonances in the van der Waals easy-axis antiferromagnet CrSBr. The interlayer exchange field and magnetocrystalline anisotropy fields are comparable to laboratory magnetic fields, allowing a rich variety of gigahertz-frequency dynamical modes to be accessed. By mapping the resonance frequencies as a function of the magnitude and angle of applied magnetic field we identify the different regimes of antiferromagnetic dynamics. The spectra show good agreement with a Landau-Lifshitz model for two antiferromagnetically-coupled sublattices, accounting for inter-layer exchange and triaxial magnetic anisotropy. Fits allow us to quantify the parameters governing the magnetic dynamics: at 5 K, the interlayer exchange field is $\mu_0 H_E =$ 0.395(2) T, and the hard and intermediate-axis anisotropy parameters are $\mu_0 H_c =$ 1.30(2) T and $\mu_0 H_a =$ 0.383(7) T. The existence of within-plane anisotropy makes it possible to control the degree of hybridization between the antiferromagnetic resonances using an in-plane magnetic field., Comment: 50 pages 16 Figures

We present room-temperature measurements of magnon spin diffusion in epitaxial ferrimagnetic insulator MgAl$_{0.5}$Fe$_{1.5}$O$_{4}$ (MAFO) thin films near zero applied magnetic field where the sample forms a multi-domain state. Due to a weak uniaxial magnetic anisotropy, the domains are separated primarily by 180$^\circ$ domain walls. We find, surprisingly, that the presence of the domain walls has very little effect on the spin diffusion -- nonlocal spin transport signals in the multi-domain state retain at least 95% of the maximum signal strength measured for the spatially-uniform magnetic state, over distances at least five times the typical domain size. This result is in conflict with simple models of interactions between magnons and static domain walls, which predict that the spin polarization carried by the magnons reverses upon passage through a 180$^\circ$ domain wall.

Efficient manipulation of antiferromagnetically coupled materials that are integration-friendly and have strong perpendicular magnetic anisotropy (PMA) is of great interest for low-power, fast, dense magnetic storage and computing. Here, we report a distinct, giant bulk damping-like spin-orbit torque in strong-PMA ferrimagnetic Fe100-xTbx single layers that are integration-friendly (composition-uniform, amorphous, sputter-deposited). For sufficiently-thick layers, this bulk torque is constant in the efficiency per unit layer thickness, {\xi}_DL^j/t, with a record-high value of 0.036nm-1, and the dampinglike torque efficiency {\xi}_DL^j achieves very large values for thick layers, up to 300% for 90 nm layers. This giant bulk torque by itself switches tens of nm thick Fe100-xTbx layers that have very strong PMA and high coercivity at current densities as low as a few MA/cm2. Surprisingly, for a given layer thickness, {\xi}_DL^j shows strong composition dependence and becomes negative for composition where the total angular momentum is oriented parallel to the magnetization rather than antiparallel. Our findings of giant bulk spin torque efficiency and intriguing torque-compensation correlation will stimulate study of such unique spin-orbit phenomena in a variety of ferrimagnetic hosts. This work paves a promising avenue for developing ultralow-power, fast, dense ferrimagnetic storage and computing devices., Comment: To appear in Applied Physics Reviews

We compare thermal-gradient-driven transverse voltages in ferrimagnetic-insulator/heavy-metal bilayers (Tm3Fe5O12/W and Tm3Fe5O12/Pt) to corresponding electrically-driven transverse resistances at and above room temperature. We find for Tm3Fe5O12/W that the thermal and electrical effects can be explained by a common spin-current detection mechanism, the physics underlying spin Hall magnetoresistance (SMR). However, for Tm3Fe5O12/Pt the ratio of the electrically-driven transverse voltages (planar Hall signal/anomalous Hall signal) is much larger than the ratio of corresponding thermal-gradient signals, a result which is very different from expectations for a SMR-based mechanism alone. We ascribe this difference to a proximity-induced magnetic layer at the Tm3Fe5O12/Pt interface.

We measure spin-orbit torque generated by exfoliated layers of the low-symmetry semi-metal ZrTe$_3$ using the spin-torque ferromagnetic resonance (ST-FMR) technique. When the ZrTe$_3$ has a thickness greater than about 10 nm, artifacts due to spin pumping and/or resonant heating can cause the standard ST-FMR analysis to overestimate the true magnitude of the torque efficiency by as much as a factor of 30, and to indicate incorrectly that the spin-orbit torque depends strongly on the ZrTe$_3$ layer thickness. Artifact-free measurements can still be achieved over a substantial thickness range by the method developed recently to detect ST-FMR signals in the Hall geometry as well as the longitudinal geometry. ZrTe$_3$/Permalloy samples generate a conventional in-plane anti-damping spin torque efficiency $\xi_{||}^{\text{DL}}$ = 0.014 $\pm$ 0.004, and an unconventional in-plane field-like torque efficiency $|\xi_{||}^{\text{FL}}|$ = 0.003 $\pm$ 0.001. The out-of-plane anti-damping torque is negligible. We suggest that artifacts similarly interfere with the standard ST-FMR analysis for other van der Waals samples thicker than about 10 nm.

We adapt Sagnac interferometry for magneto-optic Kerr effect measurements of spin-orbit-torque-induced magnetic tilting in thin-film magnetic samples. The high sensitivity of Sagnac interferometry permits for the first time optical quantification of spin-orbit torque from small-angle magnetic tilting of samples with perpendicular magnetic anisotropy (PMA). We find significant disagreement between Sagnac measurements and simultaneously-performed harmonic Hall (HH) measurements of spin-orbit torque on Pt/Co/MgO and Pd/Co/MgO samples with PMA. The Sagnac results for PMA samples are consistent with both HH and Sagnac measurements for the in-plane geometry, so we conclude that the conventional analysis framework for PMA HH measurements is flawed. We suggest that the explanation for this discrepancy is that although magnetic-field induced magnetic tilting in PMA samples can produce a strong planar Hall effect, when tilting is instead generated by spin-orbit torque it produces negligible change in the planar Hall signal. This very surprising result demonstrates an error in the most-popular method for measuring spin-orbit torques in PMA samples, and represents an unsolved puzzle in understanding the planar Hall effect in magnetic thin films.

We report measurements demonstrating that when the Neel vector of the collinear antiferromagnet RuO2 is appropriately canted relative to the sample plane, the antiferromagnet generates a substantial out of plane damping-like torque. The measurements are in good accord with predictions that when an electric field, E is applied to the spin split band structure of RuO2 it can cause a strong transverse spin current even in the absence of spin-orbit coupling. This produces characteristic changes in all three components of the E induced torque vector as a function of the angle of E relative to the crystal axes, corresponding to a spin current with a well defined tilted spin orientation s approximately (but not exactly) parallel to the Neel vector, flowing perpendicular to both E and S. This angular dependence is the signature of an antiferromagnetic spin Hall effect with symmetries that are distinct from other mechanisms of spin-current generation reported in antiferromagnetic or ferromagnetic materials.

Using a multilayer structure containing (cobalt detector layer)/(copper spacer)/(Permalloy source layer), we show experimentally how the non-reorientable spin-orbit torque generated by the Permalloy source layer (the component of spin-orbit torque that does not change when the Permalloy magnetization is rotated) can be measured using spin-torque ferromagnetic resonance (ST-FMR) with lineshape analysis. We find that dynamic spin pumping between the magnetic layers exerts torques on the magnetic layers as large or larger than the spin-orbit torques, so that if dynamic spin pumping is neglected the result would be a large overestimate of the spin-orbit torque. Nevertheless, the two effects can be separated by performing ST-FMR as a function of frequency. We measure a non-reorientable spin torque ratio $\xi_{\text{Py}} = 0.04 \pm 0.01$ for spin current flow from Permalloy through an 8 nm Cu spacer to the Co, and a strength of dynamic spin pumping that is consistent with previous measurements by conventional ferromagnetic resonance., Comment: 16 pages, 7 figures

Efficient generation of spin-orbit torques (SOTs) is central for the exciting field of spin-orbitronics. Platinum, the archetypal spin Hall material, has the potential to be an outstanding provider for spin-orbit torques due to its giant spin Hall conductivity, low resistivity, high stabilities, and the ability to be compatible with CMOS circuits. However, pure clean-limit Pt with low resistivity still provides a low damping-like spin-orbit torque efficiency, which limits its practical applications. The efficiency of spin-orbit torque in Pt-based magnetic heterostructures can be improved considerably by increasing the spin Hall ratio of Pt and spin transmissivity of the interfaces. Here we reviews recent advances in understanding the physics of spin current generation, interfacial spin transport, and the metrology of spin-orbit torques, and summarize progress towards the goal of Pt-based spin-orbit torque memories and logic that are fast, efficient, reliable, scalable, and non-volatile., Comment: Comments are welcome

Recent discovery of spin-orbit torques (SOTs) within magnetic single-layers has attracted attention in the field of spintronics. However, it has remained elusive as to how to understand and how to tune the SOTs. Here, utilizing the single layers of chemically disordered Fe$_x$Pt$_{1-x}$, we unveil the mechanism of the "unexpected" bulk SOTs by studying their dependence on the introduction of a controlled vertical composition gradient and on temperature. We find that the bulk damping like SOT arises from an imbalanced internal spin current that is transversely polarized and independent of the magnetization orientation. The torque can be strong only in the presence of a vertical composition gradient and the SOT efficiency per electric field is insensitive to temperature but changes sign upon reversal of the orientation of the composition gradient, which are in analogue to behaviors of the strain. From these characteristics we conclude that the imbalanced internal spin current originates from a bulk spin Hall effect and that the associated inversion asymmetry that allows for a non-zero net torque is most likely a strain non-uniformity induced by the composition gradient. The fieldlike SOT is a relatively small bulk effect compared to the dampinglike SOT. This work points to the possibility of developing low-power single-layer SOT devices by strain engineering., Comment: Advanced Functional Materials (in production)

We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite $\mathrm{MgAl_{0.5}Fe_{1.5}O_4}$ (MAFO), which has a substantial in-plane four-fold magnetic anisotropy. We observe spin diffusion lengths $> 0.8$ $\mathrm{\mu m}$ at room temperature in 6 nm films, with spin diffusion length 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these results.

When spin-orbit torques are measured using spin-torque ferromagnetic resonance (ST-FMR), two alternative ways of analyzing the results to extract the torque efficiencies -- lineshape analysis and analysis of the change in linewidth versus DC current -- often give inconsistent results. We identify a source for these inconsistencies. We show that fits of ST-FMR data to the standard analysis framework leave significant residuals that we identify as due to (i) current-induced excitations of a small volume of magnetic material with magnetic damping much larger than the bulk of the magnetic layer, that we speculate is associated with the heavy-metal/magnet interface and (ii) oscillations of the sample magnetization at the modulation frequency due to heating. The dependence of the residual signals on DC current can interfere with an accurate extraction of spin-torque efficiencies by the linewidth method. We show that the discrepancies between the two types of analysis can be largely eliminated by extrapolating the window of magnetic fields used in the linewidth fits to small values so as to minimize the influence of the residual signals., Comment: 8 pages, 7 figures

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T'-TaTe$_{2}$. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

Strong damping-like spin-orbit torque ({\tau}DL) has great potential for enabling ultrafast energy-efficient magnetic memories, oscillators, and logic. So far, the reported {\tau}DL exerted on a thin-film magnet must result from an externally generated spin current or from an internal non-equilibrium spin polarization in noncentrosymmetric GaMnAs single crystals. Here, we for the first time demonstrate a very strong, unexpected {\tau}DL from current flow within ferromagnetic single layers of chemically disordered, face-centered-cubic CoPt. We establish that the novel {\tau}DL is a bulk effect, with the strength per unit current density increasing monotonically with the CoPt thickness, and is insensitive to the presence or absence of spin sinks at the CoPt surfaces. This {\tau}DL most likely arises from a net transverse spin polarization associated with a strong spin Hall effect (SHE), while there is no detectable long-range asymmetry in the material. These results broaden the scope of spin-orbitronics and provide a novel avenue for developing single-layer-based spin-torque memory, oscillator, and logic technologies., Comment: This manuscript is a primary version, see Advanced Functional Materials for the updated manuscript and for the supporting information

Spin-torque ferromagnetic resonance (ST-FMR) is a common method used to measure spin-orbit torques (SOTs) in heavy metal/ferromagnet bilayer structures. In the course of a measurement, other resonant processes such as spin pumping (SP) and heating can cause spin current or heat flows between the layers, inducing additional resonant voltage signals via the inverse spin Hall effect (ISHE) and Nernst effects (NE). In the standard ST-FMR geometry, these extra artifacts exhibit a dependence on the angle of an in-plane magnetic field that is identical to the rectification signal from the SOTs. We show experimentally that the rectification and artifact voltages can be quantified separately by measuring the ST-FMR signal transverse to the applied current (i.e., in a Hall geometry) in addition to the usual longitudinal geometry. We find that in Pt (6 nm)/CoFeB samples the contribution from the artifacts is small compared to the SOT rectification signal for CoFeB layers thinner than 6 nm, but can be significant for thicker magnetic layers. We observe a sign change in the artifact voltage as a function of CoFeB thickness that we suggest may be due to a competition between a resonant heating effect and the SP/ISHE contribution.

The use of current-generated spin-orbit torques[1] to drive magnetization dynamics is under investigation to enable a new generation of non-volatile, low-power magnetic memory. Previous research has focused on spin-orbit torques generated by heavy metals[2-8], interfaces with strong Rashba interactions[9,10] and topological insulators [11-14]. These families of materials can all be well-described using models with noninteracting-electron bandstructures. Here, we show that electronic interactions within a strongly correlated heavy fermion material, the Kondo lattice system YbAl$_{3}$, can provide a large enhancement in spin-orbit torque. The spin-torque conductivity increases by approximately a factor of 4 as a function of decreasing temperature from room temperature to the coherence temperature of YbAl$_{3}$ ($T^* \approx 37$ K), with a saturation at lower temperatures, achieving a maximum value greater than any heavy metal element. This temperature dependence mimics the increase and saturation at $T^*$ of the density of states at the Fermi level arising from the ytterbium 4$f$-derived heavy bands in the Kondo regime, as measured by angle-resolved photoemission spectroscopy[15]. We therefore identify the many-body Kondo resonance as the source of the large enhancement of spin-orbit torque in YbAl$_{3}$. Our observation reveals new opportunities in spin-orbit torque manipulation of magnetic memories by engineering quantum many-body states., Comment: 7 pages, 3 figures

Lecture notes used in a graduate-level Introduction to Solid State Physics course at Cornell University, to serve as a supplement to textbooks at the level of Ashcroft & Mermin., Comment: 53 pages. Includes homework problems

Spin-orbit torque is a promising mechanism for writing magnetic memories, while field-effect transistors are the gold-standard device for logic operation. The spin-orbit torque field effect transistor (SOTFET) is a proposed device that couples a spin-orbit-torque-controlled ferromagnet to a semiconducting transistor channel via the transduction in a magnetoelectric multiferroic. This allows the SOTFET to operate as both a memory and a logic device, but its realization depends on the choice of appropriate materials. In this report, we discuss and parametrize the types of materials that can lead to a SOTFET heterostructure.

Scenario Analysis is a risk assessment tool that aims to evaluate the impact of a small number of distinct plausible future scenarios. In this paper, we provide an overview of important aspects of Scenario Analysis including when it is appropriate, the design of scenarios, uncertainty and encouraging creativity. Each of these issues is discussed in the context of climate, energy and legal scenarios.

Spin-based memories are attractive for their non-volatility and high durability but provide modest resistance changes, whereas semiconductor logic transistors are capable of large resistance changes, but lack memory function with high durability. The recent availability of multiferroic materials provides an opportunity to directly couple the change in spin states of a magnetic memory to a charge change in a semiconductor transistor. In this work, we propose and analyze the spin-orbit torque field-effect transistor (SOTFET), a device with the potential to significantly boost the energy efficiency of spin-based memories, and to simultaneously offer a palette of new functionalities.

The ability to make controlled patterns of magnetic structures within a nonmagnetic background is essential for several types of existing and proposed technologies. Such patterns provide the foundation of magnetic memory and logic devices, allow the creation of artificial spin-ice lattices and enable the study of magnon propagation. Here, we report a novel approach for magnetic patterning that allows repeated creation and erasure of arbitrary shapes of thin-film ferromagnetic structures. This strategy is enabled by epitaxial Fe$_{0.52}$Rh$_{0.48}$ thin films designed so that both ferromagnetic and antiferromagnetic phases are bistable at room temperature. Starting with the film in a uniform antiferromagnetic state, we demonstrate the ability to write arbitrary patterns of the ferromagnetic phase by local heating with a focused laser. If desired, the results can then be erased by cooling with a thermoelectric cooler and the material repeatedly re-patterned., Comment: 3 figures, 5 pages

Uncompensated moments in antiferromagnets are responsible for exchange bias in antiferromagnet/ferromagnet heterostructures; however, they are difficult to directly detect because any signal they contribute is typically overwhelmed by the ferromagnetic layer. We use magneto-thermal microscopy to image uncompensated moments in thin films of FeRh, a room-temperature antiferromagnet that exhibits a 1st-order phase transition to a ferromagnetic state near 100~$^\circ$C. FeRh provides the unique opportunity to study both uncompensated moments in the antiferromagnetic phase and the interaction of uncompensated moments with emergent ferromagnetism within a relatively broad (10-15~$^\circ$C) temperature range near $T_C$. In the AF phase below $T_C$, we image both pinned UMs, which cause local vertical exchange bias, and unpinned UMs, which exhibit an enhanced coercive field that reflects exchange-coupling to the AF bulk. Near $T_C$, where AF and FM order coexist, we find that the emergent FM order is exchange-coupled to the bulk N\'eel order. This exchange coupling leads to the nucleation of unusual configurations in which different FM domains are pinned parallel, antiparallel, and perpendicular to the applied magnetic field before suddenly collapsing into a state uniformly parallel to the field., Comment: 29 pages and 16 figures with appendix

Single-crystal materials with sufficiently low crystal symmetry and strong spin-orbit interactions can be used to generate novel forms of spin-orbit torques on adjacent ferromagnets, such as the out-of-plane antidamping torque previously observed in WTe$_2$/ferromagnet heterostructures. Here, we present measurements of spin-orbit torques produced by the low-symmetry material $\beta$-MoTe$_2$, which unlike WTe$_2$ retains bulk inversion symmetry. We measure spin-orbit torques on $\beta$-MoTe$_2$/Permalloy heterostructures using spin-torque ferromagnetic resonance as a function of crystallographic alignment and MoTe$_2$ thickness down to the monolayer limit. We observe an out-of-plane antidamping torque with a spin torque conductivity as strong as 1/3 of that of WTe$_2$, demonstrating that the breaking of bulk inversion symmetry in the spin-generation material is not a necessary requirement for producing an out-of-plane antidamping torque. We also measure an unexpected dependence on the thickness of the $\beta$-MoTe$_2$ -- the out-of-plane antidamping torque is present in MoTe$_2$/Permalloy heterostructures when the $\beta$-MoTe$_2$ is a monolayer or trilayer thick, but goes to zero for devices with bilayer $\beta$-MoTe$_2$.

More than a decade after the first theoretical and experimental studies of the spin Hall conductivity (SHC) of Pt, both its dominant origin and amplitude remain in dispute. Resolving these questions is of fundamental importance for advancing understanding of very strong spin-orbit effects in conducting systems and for maximizing the spin Hall effect for energy-efficient spintronics applications. Here, we report the experimental determination of the rapid variation of the intrinsic SHC of Pt with the carrier lifetime ({\tau}) in the dirty-metal regime by incorporating finely dispersed MgO inter-site impurities into the Pt while maintaining the essential elements of its band structure (face-centered-cubic order). This findings conclusively validate the theoretical prediction that the SHC in Pt in the dirty-metal regime should be dominated by the intrinsic Berry curvature contribution and should decrease rapidly with shortening {\tau}. This also establishes the limit to which the spin Hall ratio {\theta}SH of pure Pt can be increased by shortening {\tau}. When the spin backflow at the Pt/ferromagnet interface due to the finite interfacial spin-mixing conductance is taken into account, the amplitude of the intrinsic SHC of Pt in the clean limit is found to be at least 1.6x10^6 (h_bar/2e) {\Omega}-1 m-1, more than 3.5 times greater than the available theoretical predictions. Our work also establishes a compelling spin Hall metal Pt0.6(MgO)0.4 that combines a giant {\theta}SH (0.73) with a moderate resistivity (74 {\mu}{\Omega} cm), a strong Dzyaloshinskii-Moriya interaction, easy growth, and good integration compatibility for spintronics technology.

The effective spin-mixing conductance (G_eff) of a heavy metal/ferromagnet (HM/FM) interface characterizes the efficiency of the interfacial spin transport.Accurately determining G_eff is critical to the quantitative understanding of measurements of direct and inverse spin Hall effects. G_eff is typically ascertained from the inverse dependence of magnetic damping on the FM thickness under the assumption that spin pumping is the dominant mechanism affecting this dependence.Here we report that, this assumption fails badly in many in-plane magnetized prototypical HM/FM systems in the nm-scale thickness regime. Instead, the majority of the damping is from two-magnon scattering at the FM interface, while spin-memory-loss scattering at the interface can also be significant.If these two effects are neglected, the results will be an unphysical "giant" apparent G_eff and hence considerable underestimation of both the spin Hall ratio and the spin Hall conductivity in inverse/direct spin Hall experiments.

We report that atomic-layer alloying (intermixing) at a Pt/Co interface can increase, by approximately 30%, rather than degrade the interfacial spin transparency, and thereby strengthen the efficiency of the dampinglike spin-orbit torque arising from the spin Hall effect in the Pt. At the same time, this interfacial alloying substantially reduces fieldlike spin-orbit torque. Insertion of an ultrathin magnetic alloy layer at heavy-metal/ferromagnet interfaces represents an effective approach for improving interfacial spin transparency that may enhance not only spin-orbit torques but also the spin detection efficiency in inverse spin Hall experiments.

Despite their great promise for providing a pathway for very efficient and fast manipulation of magnetization at the nanoscale, spin-orbit torque (SOT) operations are currently energy inefficient due to a low damping-like SOT efficiency per unit current bias, and/or the very high resistivity of the spin Hall materials. Here, we report an advantageous spin Hall material, Pd1-xPtx, which combines a low resistivity with a giant spin Hall effect as evidenced through the use of three independent SOT ferromagnetic detectors. The optimal Pd0.25Pt0.75 alloy has a giant internal spin Hall ratio of >0.47 (damping-like SOT efficiency of ~ 0.26 for all three ferromagnets) and a low resistivity of ~57.5 {\mu}{\Omega} cm at 4 nm thickness. Moreover, we find the Dzyaloshinskii-Moriya interaction (DMI), the key ingredient for the manipulation of chiral spin arrangements (e.g. magnetic skyrmions and chiral domain walls), is considerably strong at the Pd1-xPtx/Fe0.6Co0.2B0.2 interface when compared to that at Ta/Fe0.6Co0.2B0.2 or W/Fe0.6Co0.2B0.2 interfaces and can be tuned by a factor of 5 through control of the interfacial spin-orbital coupling via the heavy metal composition. This work establishes a very effective spin current generator that combines a notably high energy efficiency with a very strong and tunable DMI for advanced chiral spintronics and spin torque applications., Comment: Submitted to Advanced Functional Materials on Augest 21, 2018

We report measurements of current-induced torques in heterostructures of Permalloy (Py) with TaTe$_2$, a transition-metal dichalcogenide (TMD) material possessing low crystal symmetry, and observe a torque component with Dresselhaus symmetry. We suggest that the dominant mechanism for this Dresselhaus component is not a spin-orbit torque, but rather the Oersted field arising from a component of current that flows perpendicular to the applied voltage due to resistance anisotropy within the TaTe$_2$. This type of transverse current is not present in wires made from a single uniform layer of a material with resistance anisotropy, but will result whenever a material with resistance anisotropy is integrated into a heterostructure with materials having different resistivities, thereby producing a spatially non-uniform pattern of current flow. This effect will therefore influence measurements in a wide variety of heterostructures incorporating 2D TMD materials and other materials with low crystal symmetries.

As electrical control of N\'eel order opens the door to reliable antiferromagnetic spintronic devices, understanding the microscopic mechanisms of antiferromagnetic switching is crucial. Spatially-resolved studies are necessary to distinguish multiple nonuniform switching mechanisms; however, progress has been hindered by the lack of tabletop techniques to image the N\'eel order. We demonstrate spin Seebeck microscopy as a sensitive, table-top method for imaging antiferromagnetic order in thin films, and apply this technique to study spin-torque switching in NiO/Pt and Pt/NiO/Pt heterostructures. We establish the interfacial antiferromagnetic spin Seebeck effect in NiO as a probe of surface N\'eel order, resolving antiferromagnetic spin domains within crystalline twin domains. By imaging before and after applying current-induced spin torque, we resolve spin domain rotation and domain wall motion, acting simultaneously. We correlate the changes in spin Seebeck images with electrical measurements of the average N\'eel orientation through the spin Hall magnetoresistance, confirming that we image antiferromagnetic order., Comment: 26 pages including supporting information