Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology

This paper presents the boundary conditions needed for drift-diffusion models to treat interfaces with spin-orbit coupling. Using these boundary conditions for heavy metal/ferromagnet bilayers, solutions of the drift-diffusion equations agree with solutions of the spin-dependent Boltzmann equation and allow for a much simpler interpretation of the results. A key feature of these boundary conditions is their ability to capture the role that in-plane electric fields have on the generation of spin currents that flow perpendicularly to the interface. The generation of these spin currents is a direct consequence of the effect of interfacial spin-orbit coupling on interfacial scattering. In heavy metal/ferromagnet bilayers, these spin currents provide an important mechanism for the creation of damping-like and field-like torques; they also lead to possible reinterpretations of experiments in which interfacial contributions to spin torques are thought to be suppressed.Comment: 16 pages, 4 figures; abstract revised, introduction extended, references added, results unchange

Ab initio studies of the spin-transfer torque in tunnel junctions

We calculate the spin-transfer torque in Fe/MgO/Fe tunnel junctions and compare the results to those for all-metallic junctions. We show that the spin-transfer torque is interfacial in the ferromagnetic layer to a greater degree than in all-metallic junctions. This result originates in the half metallic behavior of Fe for the $\Delta_1$ states at the Brillouin zone center; in contrast to all-metallic structures, dephasing does not play an important role. We further show that it is possible to get a component of the torque that is out of the plane of the magnetizations and that is linear in the bias. However, observation of such a torque requires highly ideal samples. In samples with typical interfacial roughness, the torque is similar to that in all-metallic multilayers, although for different reasons.Comment: 5 pages, 4 figure

Non-collinear spin transfer in Co/Cu/Co multilayers

This paper has two parts. The first part uses a single point of view to discuss the reflection and averaging mechanisms of spin-transfer between current-carrying electrons and the ferromagnetic layers of magnetic/non-magnetic heterostructures. The second part incorporates both effects into a matrix Boltzmann equation and reports numerical results for current polarization, spin accumulation, magnetoresistance, and spin-transfer torques for Co/Cu/Co multilayers. When possible, the results are compared quantitatively with relevant experiments.Comment: The following article has been submitted to J. Appl. Phys. After it is published, it will be found at http://ojps.aip.org/japo

A numerical method to solve the Boltzmann equation for a spin valve

We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for layers that are translationally invariant in plane so that properties only vary perpendicular to the planes. Physical quantities like spin density, spin current, and spin-transfer torque are calculated directly from the distribution function. We illustrate our solution method with a systematic study of the spin-transfer torque in a spin valve as a function of its geometry. The results agree with a hybrid circuit theory developed by Slonczewski for geometries typical of those measured experimentally.Comment: 13 pages, 8 figure

Overcoming device unreliability with continuous learning in a population coding based computing system

The brain, which uses redundancy and continuous learning to overcome the unreliability of its components, provides a promising path to building computing systems that are robust to the unreliability of their constituent nanodevices. In this work, we illustrate this path by a computing system based on population coding with magnetic tunnel junctions that implement both neurons and synaptic weights. We show that equipping such a system with continuous learning enables it to recover from the loss of neurons and makes it possible to use unreliable synaptic weights (i.e. low energy barrier magnetic memories). There is a tradeoff between power consumption and precision because low energy barrier memories consume less energy than high barrier ones. For a given precision, there is an optimal number of neurons and an optimal energy barrier for the weights that leads to minimum power consumption

Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations

The Landau-Lifshitz equation reliably describes magnetization dynamics using a phenomenological treatment of damping. This paper presents first-principles calculations of the damping parameters for Fe, Co, and Ni that quantitatively agree with existing ferromagnetic resonance measurements. This agreement establishes the dominant damping mechanism for these systems and takes a significant step toward predicting and tailoring the damping constants of new materials.Comment: 4 pages, 1 figur