Topological Control of Magnetic Textures.

A micromagnetic study is carried out on the role of using topology to stabilize different magnetic textures, such as a vortex or an anti-vortex state, in a magnetic heterostructure consisting of a Permalloy disk coupled to a set of nanomagnetic bars. The topological boundary condition is set by the stray field contributions of the nanomagnet bars and thus by their magnetization configuration, and can be described by a discretized winding number that will be matched by the winding number of the topological state set in the disk. The lowest number of nanomagnets that defines a suitable boundary is four, and we identify a critical internanomagnet angle of 225° between two nanomagnets, at which the boundary fails because the winding number of the nanomagnet configuration no longer controls that of the disk magnetization. The boundary also fails when the disk-nanomagnets separation is > 50 nm and for disk diameters > 480 nm. Finally, we provide preliminary experimental evidence from magnetic force microscopy studies in which we demonstrate that an energetically unstable, anti-vortex-like structure can indeed be stabilized in a Permalloy disk, provided that the appropriate topological conditions are set.

Neuromorphic Spintronics.

Neuromorphic computing uses basic principles inspired by the brain to design circuits that perform artificial intelligence tasks with superior energy efficiency. Traditional approaches have been limited by the energy area of artificial neurons and synapses realized with conventional electronic devices. In recent years, multiple groups have demonstrated that spintronic nanodevices, which exploit the magnetic as well as electrical properties of electrons, can increase the energy efficiency and decrease the area of these circuits. Among the variety of spintronic devices that have been used, magnetic tunnel junctions play a prominent role because of their established compatibility with standard integrated circuits and their multifunctionality. Magnetic tunnel junctions can serve as synapses, storing connection weights, functioning as local, nonvolatile digital memory or as continuously varying resistances. As nano-oscillators, they can serve as neurons, emulating the oscillatory behavior of sets of biological neurons. As superparamagnets, they can do so by emulating the random spiking of biological neurons. Magnetic textures like domain walls or skyrmions can be configured to function as neurons through their non-linear dynamics. Several implementations of neuromorphic computing with spintronic devices demonstrate their promise in this context. Used as variable resistance synapses, magnetic tunnel junctions perform pattern recognition in an associative memory. As oscillators, they perform spoken digit recognition in reservoir computing and when coupled together, classification of signals. As superparamagnets, they perform population coding and probabilistic computing. Simulations demonstrate that arrays of nanomagnets and films of skyrmions can operate as components of neuromorphic computers. While these examples show the unique promise of spintronics in this field, there are several challenges to scaling up, including the efficiency of coupling between devices and the relatively low ratio of maximum to minimum resistances in the individual devices.

Interfacial spin-orbit torques.

Spin-orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin-orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin-orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin-orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimentally. To facilitate progress, we review interfacial spin-orbit torques from a semiclassical viewpoint and relate these contributions to recent experimental results. Within the same model, we show the relationship between different interface transport parameters. For charges and spins flowing perpendicular to the interface, interfacial spin-orbit coupling both modifies the mixing conductance of magnetoelectronic circuit theory and gives rise to spin memory loss. For in-plane electric fields, interfacial spin-orbit coupling gives rise to torques described by spin-orbit filtering, spin swapping and precession. In addition, these same interfacial processes generate spin currents that flow into the non-magnetic layer. For in-plane electric fields in trilayer structures, the spin currents generated at the interface between one ferromagnetic layer and the non-magnetic spacer layer can propagate through the non-magnetic layer to produce novel torques on the other ferromagnetic layer.

Temporal pattern recognition with delayed feedback spin-torque nano-oscillators.

The recent demonstration of neuromorphic computing with spin-torque nano-oscillators has opened a path to energy efficient data processing. The success of this demonstration hinged on the intrinsic short-term memory of the oscillators. In this study, we extend the memory of the spin-torque nano-oscillators through time-delayed feedback. We leverage this extrinsic memory to increase the efficiency of solving pattern recognition tasks that require memory to discriminate different inputs. The large tunability of these non-linear oscillators allows us to control and optimize the delayed feedback memory using different operating conditions of applied current and magnetic field.

Interface-Generated Spin Currents.

Transport calculations based on ab initio band structures reveal large interface-generated spin currents at Co/Pt, Co/Cu, and Pt/Cu interfaces. These spin currents are driven by in-plane electric fields but flow out of plane and can have similar strengths to spin currents generated by the spin Hall effect in bulk Pt. Each interface generates spin currents with polarization along z[over ^]×E, where z[over ^] is the interface normal and E denotes the electric field. The Co/Cu and Co/Pt interfaces additionally generate spin currents with polarization along m[over ^]×(z[over ^]×E), where m[over ^] gives the magnetization direction of Co. The latter spin polarization is controlled by-but not aligned with-the magnetization, providing a novel mechanism for generating spin torques in magnetic trilayers.

Synthetic Antiferromagnetic Spintronics.

Spintronic and nanomagnetic devices often derive their functionality from layers of different materials and the interfaces between them. This is especially true for synthetic antiferromagnets - two or more ferromagnetic layers that are separated by metallic spacers or tunnel barriers and which have antiparallel magnetizations. Here, we discuss the new opportunities that arise from synthetic antiferromagnets, as compared to crystal antiferromagnets or ferromagnets.

Spin currents and spin-orbit torques in ferromagnetic trilayers.

Magnetic torques generated through spin-orbit coupling1-8 promise energy-efficient spintronic devices. For applications, it is important that these torques switch films with perpendicular magnetizations without an external magnetic field9-14. One suggested approach 15 to enable such switching uses magnetic trilayers in which the torque on the top magnetic layer can be manipulated by changing the magnetization of the bottom layer. Spin currents generated in the bottom magnetic layer or its interfaces transit the spacer layer and exert a torque on the top magnetization. Here we demonstrate field-free switching in such structures and show that its dependence on the bottom-layer magnetization is not consistent with the anticipated bulk effects 15 . We describe a mechanism for spin-current generation16,17 at the interface between the bottom layer and the spacer layer, which gives torques that are consistent with the measured magnetization dependence. This other-layer-generated spin-orbit torque is relevant to energy-efficient control of spintronic devices.

Simultaneous control of the Dzyaloshinskii-Moriya interaction and magnetic anisotropy in nanomagnetic trilayers.

Magneto-optical Kerr effect (MOKE) microscopy measurements of magnetic bubble domains demonstrate that Ar^{+} irradiation around 100 eV can tune the Dzyaloshinskii-Moriya interaction (DMI) in Pt/Co/Pt trilayers. Varying the irradiation energy and dose changes the DMI sign and magnitude separately from the magnetic anisotropy, allowing tuning of the DMI while holding the coercive field constant. This simultaneous control emphasizes the different physical origins of these effects. To accurately measure the DMI, we propose and apply a physical model for a poorly understood peak in domain wall velocity at zero in-plane field. The ability to tune the DMI with the spatial resolution of the Ar^{+} irradiation enables new fundamental investigations and technological applications of chiral nanomagnetics.

Theory of Kondo suppression of spin polarization in nonlocal spin valves.

We theoretically analyze contributions from the Kondo effect to the spin polarization and spin diffusion length in all-metal nonlocal spin valves. Interdiffusion of ferromagnetic atoms into the normal metal layer creates a region in which Kondo physics plays a significant role, giving discrepancies between experiment and existing theory. We start from a simple model and construct a modified spin drift-diffusion equation which clearly demonstrates how the Kondo physics not only suppresses the electrical conductivity but even more strongly reduces the spin diffusion length. We also present an explicit expression for the suppression of spin polarization due to Kondo physics in an illustrative regime. We compare this theory to previous experimental data to extract an estimate of the Elliot-Yafet probability for Kondo spin flip scattering of 0.7 ± 0.4, in good agreement with the value of 2/3 derived in the original theory of Kondo.

Neuromorphic Computing through Time-Multiplexing with a Spin-Torque Nano-Oscillator.

Fabricating powerful neuromorphic chips the size of a thumb requires miniaturizing their basic units: synapses and neurons. The challenge for neurons is to scale them down to submicrometer diameters while maintaining the properties that allow for reliable information processing: high signal to noise ratio, endurance, stability, reproducibility. In this work, we show that compact spin-torque nano-oscillators can naturally implement such neurons, and quantify their ability to realize an actual cognitive task. In particular, we show that they can naturally implement reservoir computing with high performance and detail the recipes for this capability.

Spin-orbit torques from interfacial spin-orbit coupling for various interfaces.

We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.

k-asymmetric spin-splitting at the interface between transition metal ferromagnets and heavy metals.

We systematically investigate the spin-orbit coupling-induced band splitting originating from inversion symmetry breaking at the interface between a Co monolayer and 4d (Tc, Ru, Rh, Pd, and Ag) or 5d (Re, Os, Ir, Pt, and Au) transition metals. In spite of the complex band structure of these systems, the odd-in-k spin splitting of the bands displays striking similarities with the much simpler Rashba spin-orbit coupling picture. While we do not find salient correlations between the interfacial magnetic anisotropy and the odd-in-k spin-splitting of the bands, we establish a clear connection between the overall strength of the band splitting and the charge transfer between the d-orbitals at the interface. Furthermore, we show that the spin splitting of the Fermi surface scales with the induced orbital moment, weighted by the spin-orbit coupling.

Spin-transfer torque in ferromagnetic bilayers generated by anomalous Hall effect and anisotropic magnetoresistance.

We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this contribution from measurements of the longitudinal resistivity as a function of the thickness can give the spin-transfer torque efficiency.

Perpendicular magnetic anisotropy of two-dimensional Rashba ferromagnets.

We compute the magnetocrystalline anisotropy energy within two-dimensional Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic anisotropy is exactly zero regardless of the strength of the Rashba coupling, unless only the lowest band is occupied. For this latter case, the model predicts in-plane anisotropy. For a more realistic Rashba model with finite band width, the magnetic anisotropy evolves from in-plane to perpendicular and back to in-plane as bands are progressively filled. This evolution agrees with first-principles calculations on the interfacial anisotropy, suggesting that the Rashba model captures energetics leading to anisotropy originating from the interface provided that the model takes account of the finite Brillouin zone. The results show that the electron density modulation by doping or an external voltage is more important for voltage-controlled magnetic anisotropy than the modulation of the Rashba parameter.

Probing electric field control of magnetism using ferromagnetic resonance.

Exchange coupled CoFe/BiFeO3 thin-film heterostructures show great promise for power-efficient electric field-induced 180° magnetization switching. However, the coupling mechanism and precise qualification of the exchange coupling in CoFe/BiFeO3 heterostructures have been elusive. Here we show direct evidence for electric field control of the magnetic state in exchange coupled CoFe/BiFeO3 through electric field-dependent ferromagnetic resonance spectroscopy and nanoscale spatially resolved magnetic imaging. Scanning electron microscopy with polarization analysis images reveal the coupling of the magnetization in the CoFe layer to the canted moment in the BiFeO3 layer. Electric field-dependent ferromagnetic resonance measurements quantify the exchange coupling strength and reveal that the CoFe magnetization is directly and reversibly modulated by the applied electric field through a ~180° switching of the canted moment in BiFeO3. This constitutes an important step towards robust repeatable and non-volatile voltage-induced 180° magnetization switching in thin-film multiferroic heterostructures and tunable RF/microwave devices.

Intrinsic spin torque without spin-orbit coupling.

We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxation mechanisms nor spin-orbit coupling. This intrinsic non-adiabatic spin torque is related by a chiral connection to the intrinsic spin-orbit torque that has been calculated from the Berry phase for Rashba systems.

Chirality from interfacial spin-orbit coupling effects in magnetic bilayers.

As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

Control of magnetic fluctuations by spin current.

We use microfocus Brillouin light scattering spectroscopy to study the interaction of spin current with magnetic fluctuations in a Permalloy microdisk located on top of a Pt strip carrying an electric current. We show that the fluctuations can be efficiently suppressed or enhanced by different directions of the electric current. Additionally, we find that the effect of spin current on magnetic fluctuations is strongly influenced by nonlinear magnon-magnon interactions. The observed phenomena can be used for controllable reduction of thermal noise in spintronic nanodevices.

Effects of disorder and internal dynamics on vortex wall propagation.

Experimental measurements of domain wall propagation are typically interpreted by comparison to reduced models that ignore both the effects of disorder and the internal dynamics of the domain wall structure. Using micromagnetic simulations, we study vortex wall propagation in magnetic nanowires induced by fields or currents in the presence of disorder. We show that the disorder leads to increases and decreases in the domain wall velocity depending on the conditions. These results can be understood in terms of an effective damping that increases as disorder increases. As a domain wall moves through disorder, internal degrees of freedom get excited, increasing the energy dissipation rate.

Current-induced torques in the presence of spin-orbit coupling.

In systems with strong spin-orbit coupling, the relationship between spin transfer torque and the divergence of the spin current is generalized to a relation between spin transfer torques, total angular momentum current, and mechanical torques. In ferromagnetic semiconductors, where the spin-orbit coupling is large, these considerations modify the behavior of the spin transfer torques. One example is a persistent spin transfer torque in a spin valve: the spin transfer torque does not decay away from the interface but approaches a constant value. A second example is a mechanical torque at a single ferromagnetic-nonmagnetic interface.