Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$

TL;DR

This study investigates the thermodynamic behavior of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice using RGM and HTE methods, revealing how lattice geometry and spin quantum number influence magnetic properties.

Contribution

It provides a comprehensive analysis of thermodynamic quantities for the pyrochlore ferromagnet across different spins, highlighting geometric effects on magnetic ordering.

Findings

Pyrochlore lattice shows suppressed magnetic order compared to simple cubic.

Spin quantum number $S$ significantly affects temperature-dependent properties.

Geometric frustration impacts excitation spectra and thermodynamics.

Abstract

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number $S$ on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number $z=6$. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.