No Arabic abstract
We present theoretical studies of the intrinsic spin orbit torque (SOT) in a single domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the non-equilibrium Greens function formalism for a model Hamiltonian. We find that, to the first order in SOC, the intrinsic SOT has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material related parameters of the electronic structure, such as band filling, band width, exchange splitting, as well as the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results show that the different sign of SOT in identical ferromagnetic layers with different supporting layers, e.g. Co/Pt and Co/Ta, could be attributed to electrostatic doping of the ferromagnetic layer by the support.
We present a complete theory of the spin torque phenomena in a ultrasmall nanomagnet coupled to non-collinear ferromagnetic electrodes through tunnelling junctions. This model system can be described by a simple microscopic model which captures many physical effects characteristic of spintronics: tunneling magneto resistance, intrinsic and transport induced magnetic relaxation, current induced magnetization reversal and spin accumulation. Treating on the same footing the magnetic and transport degrees of freedom, we arrive at a closed equation for the time evolution of the magnetization. This equation is very close to the Landau-Lifshitz-Gilbert equation used in spin valves structures. We discuss how the presence of the Coulomb blockade phenomena and the discretization of the one-body spectrum gives some additional features to the current induced spin torque. Depending on the regime, the dynamic induced by the coupling to electrode can be viewed either as a spin torque or as a relaxation process. In addition to the possibility of stabilizing uniform spin precession states, we find that the system is highly hysteretic: up to three different magnetic states can be simultaneously stable in one region of the parameter space (magnetic field and bias voltage).We also discuss how the magneto-resistance can be used to provide additional information on the non-equilibrium peaks present in the nanomagnet spectroscopy experiments.
Spin torque and spin Hall effect nanooscillators generate high intensity spin wave auto oscillations on the nanoscale enabling novel microwave applications in spintronics, magnonics, and neuromorphic computing. For their operation, these devices require externally generated spin currents either from an additional ferromagnetic layer or a material with a high spin Hall angle. Here we demonstrate highly coherent field and current tunable microwave signals from nanoconstrictions in single 15 and 20 nm thick permalloy layers. Using a combination of spin torque ferromagnetic resonance measurements, scanning microBrillouin light scattering microscopy, and micromagnetic simulations, we identify the autooscillations as emanating from a localized edge mode of the nanoconstriction driven by spin orbit torques. Our results pave the way for greatly simplified designs of auto oscillating nanomagnetic systems only requiring a single ferromagnetic layer.
Spin-dependent transport phenomena due to relativistic spin-orbit coupling and broken space-inversion symmetry are often difficult to interpret microscopically, in particular when occurring at surfaces or interfaces. Here we present a theoretical and experimental study of spin-orbit torque and unidirectional magnetoresistance in a model room-temperature ferromagnet NiMnSb with inversion asymmetry in the bulk of this half-heusler crystal. Besides the angular dependence on magnetization, the competition of Rashba and Dresselhaus-like spin-orbit couplings results in the dependence of these effects on the crystal direction of the applied electric field. The phenomenology that we observe highlights potential inapplicability of commonly considered approaches for interpreting experiments. We point out that, in general, there is no direct link between the current-induced non-equilibrium spin polarization inferred from the measured spin-orbit torque and the unidirectional magnetiresistance. We also emphasize that the unidirectional magnetoresistance has not only longitudinal but also transverse components in the electric field -- current indices which complicates its separation from the thermoelectric contributions to the detected signals in common experimental techniques. We use the theoretical results to analyze our measurements of the on-resonance and off-resonance mixing signals in microbar devices fabricated from an epitaxial NiMnSb film along different crystal directions. Based on the analysis we extract an experimental estimate of the unidirectional magnetoresistance in NiMnSb.
We present an {it ab initio}-based theoretical framework which elucidates the origin of the spin-orbit torque (SOT) in Normal-Metal(NM)/Ferromagnet(FM) heterostructures. The SOT is decomposed into two contributions, namely, {it spin-Hall} and the {it spin-orbital} components. We find that {it (i)} the Field-Like (FL) SOT is dominated by the spin-orbital component and {it (ii)} both components contribute to the damping-like torque with comparable magnitude in the limit of thick Pt film. The contribution of the spin-orbital component to the DL-SOT is present only for NMs with strong SOC coupling strength. We demonstrate that the FL-SOT can be expressed in terms of the non-equilibrium spin-resolved orbital moment accumulation. The calculations reveal that the experimentally reported oxygen-induced sign-reversal of the FL-SOT in Pt/Co bilayers is due to the significant reduction of the majority-spin orbital moment accumulation on the interfacial NM atoms.
Spin currents can modify the magnetic state of ferromagnetic ultrathin films through spin-orbit torque. They may be generated by means of spin-orbit interaction by either bulk or interfacial phenomena. Electrical transport measurements reveal a six-fold increase of the spin-orbit torque accompanied by a drastic reduction of the spin Hall magnetoresistance upon the introduction of a Cu interlayer in a Pt/Cu/Co/Pt structure with perpendicular magnetic anisotropy. We analyze the dependence of the spin Hall magnetoresistance with the thickness of the interlayer in the frame of a drift diffusion model that provides information on the expected spin currents and spin accumulations in the system. The results demonstrate that the major responsible of both effects is spin memory loss at the interface. The enhancement of the spin-orbit torque when introducing an interlayer opens the possibility to design more effient spintronic devices based on materials that are cheap and abundant such as copper.