Magnetization dynamics of two interacting spins in an external magnetic field

TL;DR

This paper provides an exact analytical solution for the magnetization relaxation dynamics of two exchange-coupled spins in a strong magnetic field, covering all damping and barrier height regimes.

Contribution

It introduces a novel exact solution method for the two-spin relaxation problem using stochastic differential equations and matrix continued fractions.

Findings

Exact relaxation time calculated for all damping and barrier parameters.

Comparison with Langer's theory confirms asymptotic behavior in high barrier, high damping limits.

Complete characterization of two-spin magnetization dynamics in external magnetic fields.

Abstract

The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization, i.e., the Langevin equation of the process, over its realizations so reducing the problem to a system of linear differential-recurrence relations for the statistical moments (averaged spherical harmonics). The system is solved in the frequency domain by matrix continued fractions yielding the complete solution of the two-spin problem in external fields for all values of the damping and barrier height parameters. The magnetization relaxation time extracted from the exact solution is compared with the inverse relaxation rate from Langer's theory of the decay of metastable states, which yields in the high barrier and intermediate-to-high damping limits the asymptotic behaviour of the greatest relaxation time.