Dynamics of macrospin under periodic field and spin transfer torque

TL;DR

This paper investigates macrospin dynamics under periodic magnetic fields and spin transfer torque, revealing stable solutions, hysteresis behavior, and sensitivity to initial conditions depending on the external influences.

Contribution

It provides a comprehensive analysis of macrospin behavior under combined periodic fields and spin transfer torque, highlighting stability and sensitivity conditions.

Findings

Hysteresis loops are closed curves oscillating between stable points without spin transfer torque.

Stable solutions are reached regardless of initial conditions under constant field and spin transfer torque.

Periodic fields with spin transfer torque can lead to stable limit cycles or sensitive attractors.

Abstract

The dynamics of a macrospin model for a single magnetic domain is investigated in two cases: (i) under the action of a periodic magnetic field and (ii) under the external field plus a spin transfer torque from spin-polarized current or spin current. It has been proved that (i) without spin transfer torque, the trajectory of magnetization (hysteresis) is always a closed curve oscillating between two stable points and following the same path each time; (ii) under the action of a constant field (or with small periodic perturbation) and a constant spin transfer torque, the spin would always turn to the stable solution finally, which is independent of the parameters or initial conditions; (iii) considering a periodic oscillating field plus a spin transfer torque, the system can also have a stable solution around a limit circle, but on some special points on the attractor, the system may be sensitive to the initial conditions and have no limit circle.