Non-Abelian Berry transport, spin coherent states, and Majorana points

TL;DR

This paper explores the adiabatic evolution of spin states in molecular magnets using Majorana's parametrisation, revealing complex quantum dynamics and classical Hamiltonian descriptions, with applications to Mn4 molecular magnets.

Contribution

It introduces a novel analysis of spin state evolution via Majorana points, linking quantum and classical descriptions in molecular magnets.

Findings

Majorana points' motion can be described by a classical Hamiltonian.

The frequency of magnetization variation differs from the rotation frequency.

Application to Mn4 magnets demonstrates the theory's practical relevance.

Abstract

We consider the adiabatic evolution of Kramers degenerate pairs of spin states in a half-integer spin molecular magnet as the molecule is slowly rotated. To reveal the full details the of the quantum evolution, we use Majorana's parametrisation of a general state in the $2j+1$ dimensional Hilbert space in terms of $2j$ Majorana points. We show that the intricate motion of the Majorana points may be described by a classical hamiltonian which is of the same form, but of quite different origin, as that which appears in the spin-coherent-state path integral. As an illustration we consider molecular magnets of the $j=9/2$ Mn4 family and compute the frequency with which the magnetization varies. This frequency is generally different from the frequency of the rotation.