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

Abstract

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.

13 pages, 8 figures

References in corpus (14)

• Microwave Oscillations of a Nanomagnet Driven by a Spin-Polarized Current
• Direct-Current Induced Dynamics in Co90Fe10/Ni80Fe20 Point Contacts
• Anatomy of Spin-Transfer Torque
• Magnetization dynamics with a spin-transfer torque
• Current-Driven Magnetic Excitations in Permalloy-Based Multilayer Nanopillars
• Boltzmann Test of Slonczewski's Theory of Spin Transfer Torque
• Field dependence of magnetization reversal by spin transfer
• First-principles scattering matrices for spin-transport
• Theory of Current-Induced Magnetization Precession
• Magnetization reversal by injection and transfer of spin: experiments and theory
• A selfconsistent theory of current-induced switching of magnetization
• Non-monotonic angular magnetoresistance in asymmetric spin valves
• Influence Of Current Leads On Critical Current For Spin Precession In Magnetic Multilayers
• Impurity scattering and quantum confinement in giant magnetoresistance systems

Cited by in corpus (15)

• Spin Transfer Torques
• Current induced torques and interfacial spin-orbit coupling: Semiclassical Modeling
• Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology
• Spin-Torque Driven Magnetization Dynamics: Micromagnetic Modelling
• Spin-transfer torque in magnetic tunnel junctions: Scattering theory
• Interfacial spin-orbit torques
• Spin-Torque Generation in Topological-Insulator-Based Heterostructures
• Particle-in-cell simulation of ultrafast hot-carrier transport in Fe/Au-heterostructures
• Observation of spin-orbit magnetoresistance in metallic thin films on magnetic insulators
• Microwave excitations associated with a wavy angular dependence of the spin transfer torque : model and experiments
• Multiscale approach to spin transport in magnetic multilayers
• Spin torque oscillator for microwave assisted magnetization reversal
• Ballistic vs Diffusive Transport in Current-Induced Magnetization Switching
• Adiabatic quantum pumping, magnification effects and quantum size effects of spin-torque in magnetic tunnel junctions
• Derivation of a linear collision operator for the spinorial Wigner equation and its semiclassical limit