# Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet

## TL;DR

This study investigates the thermodynamic properties of the pyrochlore-lattice quantum Heisenberg antiferromagnet using RGM and HTE methods, revealing no magnetic long-range order and aligning well with experimental data for specific compounds.

## Contribution

It provides a comprehensive analysis of thermodynamic quantities and excitation spectra for the pyrochlore Heisenberg antiferromagnet, including quantum effects and comparison with experiments.

## Key findings

- No magnetic long-range order detected for any spin value.
- Dynamical structure factor matches experimental observations for NaCaNi2F7.
- High-temperature series indicate weak order by disorder effects.

## Abstract

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as various thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=1/2$ and $S=1$. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound NaCaNi$_2$F$_7$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 \ldots 8~meV for NaCaNi$_2$F$_7$. We analyze the static structure factor ${S}_{\bf q}$ to find regions of maximal ${S}_{\bf q}$. The high-temperature series of the ${S}_{\bf q}$ provide a fingerprint of weak {\it order by disorder} selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $\pi$.