Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field

TL;DR

This paper investigates the thermodynamic properties of one- and two-dimensional Heisenberg ferromagnets with arbitrary spin in a magnetic field using Green-function theory and quantum Monte Carlo simulations, revealing detailed field and temperature dependencies.

Contribution

It combines second-order Green-function theory with quantum Monte Carlo simulations to analyze thermodynamics of ferromagnets with arbitrary spin, providing new insights into their magnetic behavior.

Findings

Good agreement between Green-function theory and Monte Carlo simulations.

Field dependence of susceptibility maximum fits power law at low fields and linear at high fields.

Identification of maxima in specific heat and correlation lengths depending on spin and dimensionality.

Abstract

The thermodynamic properties (magnetization, magnetic susceptibility, transverse and longitudinal correlation lengths, specific heat) of one- and two-dimensional ferromagnets with arbitrary spin S in a magnetic field are investigated by a second-order Green-function theory. In addition, quantum Monte Carlo simulations for S= 1/2 and S=1 are performed using the stochastic series expansion method. A good agreement between the results of both approaches is found. The field dependence of the position of the maximum in the temperature dependence of the susceptibility fits well to a power law at low fields and to a linear increase at high fields. The maximum height decreases according to a power law in the whole field region. The longitudinal correlation length may show an anomalous temperature dependence: a minimum followed by a maximum with increasing temperature. Considering the specific heat in one dimension and at low magnetic fields, two maxima in its temperature dependence for both the S= 1/2 and S = 1 ferromagnets are found. For S>1 only one maximum occurs, as in the two-dimensional ferromagnets. Relating the theory to experiments on the S= 1/2 quasi-one-dimensional copper salt TMCuC [(CH_3)_4NCuCl_3], a fit to the magnetization as a function of the magnetic field yields the value of the exchange energy which is used to make predictions for the occurrence of two maxima in the temperature dependence of the specific heat.