Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

TL;DR

This paper uses quantum Monte Carlo methods to accurately analyze low temperature magnetization and excitation spectra of antiferromagnetic Heisenberg spin rings, providing improved energy eigenvalues and insights relevant for experimental magnetic molecules.

Contribution

It introduces a numerically exact quantum Monte Carlo approach to determine energy levels of Heisenberg spin rings, surpassing previous approximations and revealing scaling relations for different spins and sizes.

Findings

More accurate energy eigenvalues than rotational band approximation.

Energy gap approaches zero as 1/N^a with specific exponents.

New estimate of exchange constant for Fe12 magnetic molecule.

Abstract

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s <= 5/2, data are presented for all even N <= 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.