The Quantum Noise of Ferromagnetic $\pi$-Bloch Domain Walls

TL;DR

This paper investigates the quantum noise and reversal probability of ferromagnetic $$-Bloch domain walls in nanowires at finite temperatures, using nonperturbative methods and entanglement entropy analysis.

Contribution

It introduces a nonperturbative approach based on Langer's Theory and importance sampling to quantify reversal probabilities and entanglement entropy in ferromagnetic nanowires.

Findings

Closed-form saddlepoint expression for free energy obtained.

Quantified geometric and non-geometric entanglement entropy contributions.

Analyzed Euclidean-time dependence of domain wall width and angular momentum transfer.

Abstract

We quantify the probability per unit Euclidean-time of reversing the magnetization of a $\pi$-Bloch vector, which describes the Ferromagnetic Domain Walls of a Ferromagnetic Nanowire at finite-temperatures, by evaluating the saddlepoint solution of the grand canonical partition function for the Ferromagnetic Nanowire consisting of $N$ such soliton and anti-soliton states. Our approach, based on Langer's Theory, treats the double Sine-Gordon model that defines the $\pi$-Bloch vectors via a procedure of nonperturbative renormalization, and uses importance sampling methods to minimise the free energy of the system, and identify the saddlepoint solution corresponding to the reversal probability. We identify that whilst the general solution for the free energy minima cannot be expressed in closed form, we can obtain a closed expression for the saddlepoint by maximizing the entanglement entropy of the system. We use this approach to quantify the geometric and non-geometric contributions to the entanglement entropy of the Ferromagnetic Nanowire, defined between entangled Ferromagnetic Domain Walls, and evaluate the Euclidean-time dependence of the domain wall width and angular momentum transfer at the domain walls, which has been recently proposed as a mechanism for Quantum Memory Storage.