Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields

TL;DR

This paper investigates the potential for lattice distortions in high magnetic fields to lower energy in 2D and 3D pyrochlore antiferromagnets, revealing a spin-Peierls instability through analytical and numerical methods.

Contribution

It provides the first rigorous analytical demonstration of spin-Peierls instability in pyrochlore lattices under high magnetic fields, supported by numerical data.

Findings

Existence of spin-Peierls instability in pyrochlore lattices

Analytical proof using localized magnons

Numerical evidence from exact diagonalization

Abstract

We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to N=64 sites. We discuss a scenario of the field-tuned changes in the ground-state properties of the frustrated spin lattices due to the coupling between spin and lattice degrees of freedom.