Tunneling of a large spin via hyperfine interactions

TL;DR

This paper investigates quantum tunneling of a large spin interacting with many nuclear spins via hyperfine interactions, analyzing tunneling splittings, coherence, and relaxation behavior at different temperatures, with implications for Mn-12 acetate.

Contribution

It provides a perturbative analysis of tunneling splittings and resonance conditions for a large spin coupled to nuclear spins, highlighting temperature-dependent coherence and relaxation phenomena.

Findings

Quantum coherence persists at low temperatures (T << ASI).

At higher temperatures (T >= ASI), coherence is lost, leading to stretched relaxation dynamics.

The results are relevant for understanding spin dynamics in Mn-12 acetate.

Abstract

We consider a large spin \bf S in the magnetic field parallel to the uniaxial crystal field, interacting with N >> 1 nuclear spins \bf I_i via Hamiltonian \cal H = -DS_z^2 - H_zS_z+ A{\bf S}\cdot \sum_{i=1}^N {\bf I}_i with A << D, at temperature T. Tunneling splittings and the selection rules for the resonant values of H_z are obtained perturbatively. The quantum coherence exists at T << ASI while at T >= ASI the coherence is destroyed and the relaxation of \bf S is described by a stretched dependence which can be close to log t under certain conditions. Relevance to Mn-12 acetate is discussed.