Spin-injection-generated shock waves and solitons in a ferromagnetic thin film: the spin piston problem

TL;DR

This paper models the nonlinear magnetization dynamics in a ferromagnetic thin film induced by spin injection, revealing complex wave phenomena like shocks and solitons using a dispersive hydrodynamic approach.

Contribution

It introduces a hydrodynamic framework for analyzing spin injection effects, classifies nonlinear wave solutions, and predicts novel spin wave structures in ferromagnetic channels.

Findings

Identification of spin shock and rarefaction waves as spin-based counterparts to classical waves.

Discovery of composite wave complexes with contact spin shocks and rarefactions.

Prediction of stationary solitons and oscillatory wavetrains under magnetic supersonic conditions.

Abstract

The unsteady, nonlinear magnetization dynamics induced by spin injection in an easy-plane ferromagnetic channel subject to an external magnetic field are studied analytically. Leveraging a dispersive hydrodynamic description, the Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for the magnetization's perpendicular component (spin density) and azimuthal phase gradient (fluid velocity). Spin injection acts as a moving piston that generates nonlinear, dynamical spin textures in the ferromagnetic channel with downstream quiescent spin density set by the external field. In contrast to the classical problem of a piston accelerating a compressible gas, here, variable spin injection and field lead to a rich variety of nonlinear wave phenomena from oscillatory spin shocks to solitons and rarefaction waves. A full classification of solutions is provided using nonlinear wave modulation theory by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the classical piston problem such as rarefaction (expansion) waves and shocks manifest in their spin-based counterparts as smooth and highly oscillatory transitions, respectively. The spin shock is an example of a dispersive shock wave, which arises in many physical systems. New features without a gas dynamics counterpart include composite wave complexes with "contact" spin shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced piston edge behaviors including a stationary soliton and an oscillatory wavetrain. These coherent wave structures have physical implications for the generation of high frequency spin waves from pulsed injection and persistent, stable stationary and/or propagating solitons in the presence of magnetic damping. The analytical results are favorably compared with numerical simulations.