Thermodynamics of layered Heisenberg magnets with arbitrary spin

TL;DR

This paper develops a Green-function theory for layered Heisenberg magnets with arbitrary spin, accurately predicting thermodynamic properties and comparing well with numerical and experimental data for quasi-2D and 3D systems.

Contribution

It introduces a spin-rotation-invariant Green-function approach applicable to arbitrary spin S, providing comprehensive thermodynamic predictions for layered Heisenberg magnets.

Findings

Good agreement with quantum Monte Carlo and series-expansion data.

T_N > T_C for quasi-2D S=1/2 magnets with small interlayer coupling.

Theoretical results match experimental data on specific heat and correlation lengths.

Abstract

We present a spin-rotation-invariant Green-function theory of long- and short-range order in the ferro- and antiferromagnetic Heisenberg model with arbitrary spin quantum number S on a stacked square lattice. The thermodynamic quantities (Curie temperature T_C, N\'eel temperature T_N, specific heat C_V, intralayer and interlayer correlation lengths) are calculated, where the effects of the interlayer coupling and the S dependence are explored. In addition, exact diagonalizations on finite two-dimensional (2D) lattices with S>=1 are performed, and a very good agreement between the results of both approaches is found. For the quasi-2D and isotropic 3D magnets, our theory agrees well with available quantum Monte Carlo and high-temperature series-expansion data. Comparing the quasi-2D S=1/2 magnets, we obtain the inequalities T_N>T_C and, for small enough interlayer couplings, T_N<T_C. The results for C_V and the intralayer correlation length are compared to experiments on the quasi-2D antiferromagnets Zn_2VO(PO_4)_2 with S=1/2 and La_2NiO_4 with S=1, respectively.