Macroscopic Quantum Dynamics of a Free Domain Wall in a Ferromagnet

TL;DR

This paper investigates the quantum behavior of a free domain wall in a ferromagnet using a discrete-time path integral approach, revealing conditions for wave-packet spreading and non-spreading phenomena due to spin non-linearity.

Contribution

It introduces a discrete-time spin-coherent-state path integral method to analyze domain wall quantum dynamics, highlighting the role of chirality and non-linear spin effects.

Findings

Chirality is approximately conjugate to the domain wall position.

Wave-packet spreading occurs under certain conditions.

Non-linear spin effects can prevent wave-packet spreading.

Abstract

We study macroscopic quantum dynamics of a free domain wall in a quasi-one-dimensional ferromagnet by use of the spin-coherent-state path integral in {\it discrete-time} formalism. Transition amplitudes between typical states are quantitatively discussed by use of {\it stationary-action approximation} with respect to collective degrees of freedom representing the center position and the chirality of the domain wall. It is shown that the chirality may be loosely said to be canonically conjugate to the center position; the latter moves with a speed depending on the former. It is clarified under what condition the center position can be regarded as an effective free-particle position, which exhibits the phenomenon of wave-packet spreading. We demonstrate, however, that in some case the non-linear character of the spin leads to such a dramatic phenomenon of a non-spreading wave packet as to completely invalidate the free-particle analogy. In the course of the discussion, we also point out various difficulties associated with the continuous-time formalism.