Cumulant expansion for ferrimagnetic spin (S_1, s_2) systems

TL;DR

This paper extends cumulant expansion techniques to large-spin ferrimagnetic systems, deriving effective classical Hamiltonians and analyzing thermodynamic properties for both isolated and interacting molecules at high temperatures.

Contribution

It introduces a generalized cumulant expansion method for large-spin ferrimagnetic systems and applies it to both noninteracting and interacting molecules, including effects of spin inhomogeneity.

Findings

Good agreement with exact results at high temperatures

Negligible correlation beyond nearest neighbors at moderate/high T

Single molecule results applicable to chains for T > JS_1s_2

Abstract

We have generalized the application of cumulant expansion to ferrimagnetic systems of large spins. We have derived the effective Hamiltonian in terms of classical variables for a quantum ferrimagnet of large spins. A noninteracting gas of ferrimagnetic molecules is studied systematically by cumulant expansion to second order of ($Js/T$) where $J$ is the exchange coupling in each molecule, $s$ is the smaller spin ($S_1, s_2$) and $T$ is temperature. We have observed fairly good results in the convergent regime of the expansion, i.e $T > Js$. We then extend our approach to a system of interacting ferrimagnetic molecules. For one dimensional nearest neighbor interaction we have observed that the correlation of more than two neighboring sites is negligible at moderate and high temperature behavior. Thus the results of a single molecule can be applied to the chain of interacting molecules for temperatures greater than classical energy scale, i.e $T>JS_1s_2$. Finally we will discuss the effect of spin inhomogeneity on the accuracy of this method.