Macrospin models of spin transfer dynamics

Abstract

The current-induced magnetization dynamics of a spin valve are studied using a macrospin (single domain) approximation and numerical solutions of a generalized Landau-Lifshitz-Gilbert equation. (2003)], we calculate the resistance and microwave power as a function of current and external field including the effects of anisotropies, damping, spin-transfer torque, thermal fluctuations, spin-pumping, and incomplete absorption of transverse spin current. While many features of experiment appear in the simulations, there are two significant discrepancies: the current dependence of the precession frequency and the presence/absence of a microwave quiet magnetic phase with a distinct magnetoresistance signature. Comparison is made with micromagnetic simulations designed to model the same experiment.

Numerical Simulations of Nano-Scale Magnetization Dynamics

“…The role of this fixed layer consists in aligning the magnetic moments of the passing carriers, so that the current injected into the second, much thinner analyzer layer, will be spin-polarized. The analyzer layer, on the contrary, can be easily influenced by the applied magnetic field, and it will manage to change its magnetization as a whole -thus representing a macrospin (Xiao, Zangwill & Stiles, 2005). The experimental studies of spin valves successfully confirmed the theoretical predictions made in the macrospin approximation, including precessional and ballistic magnetization reversal, two types of steady magnetization oscillations -in-plane and out-of-plane, as well as magnetization relaxation to an intermediate canted state.…”

“…One would expect the transition temperature to correspond to the Curie temperature, which for the model material (Co) is 1404K; the simulation plot shows that the loss of ferromagnetism occurs for temperatures about one order of magnitude higher. These unrealistic temperatures are a known problem with macrospin simulations (Xiao, Zangwill, & Stiles, 2005). They can be partially explained by the fixed length of the magnetization vector, while in real-life ferromagnetics the saturation magnetization decreases for increasing temperature.…”

Oscillation characteristics of zero-field spin transfer oscillators with field-like torque

“…Here, m xi is the value of m x at i-th time-step, m x,av is the average value of m x for a "waiting time" t using n time steps of length ∆t. 38 It is important to note that m x,rms = 0 corresponds to the static states regime; while m x,rms > 0 the steady precessional regime. 36…”

Multiscale approach to spin transport in magnetic multilayers

“…On the other hand it is becoming increasingly clear that the magnetization dynamics of real devices cannot be properly captured by simple (analytically tractable) models and that numerical simulations that treat the magnetic and transport degrees of freedom on an equal footing need to be developed. Several steps have already been taken in that direction [34][35][36][37][38] and should eventually lead to simulations of good predictive capabilities. Let us mention, as example, the recent experiments on spin torque induced ferromagnetic resonance in the nonlinear regime 39 which has been successfully compared to coupled simulations at the macrospin level for the magnetic part and onedimensional semi-classical level for spin transport.…”