High field properties of geometrically frustrated magnets

TL;DR

This paper reviews the phase transitions and thermodynamic properties of geometrically frustrated quantum antiferromagnets, highlighting exact solutions and mappings that reveal critical behavior and large magnetocaloric effects near saturation fields.

Contribution

It introduces a detailed theoretical framework mapping frustrated magnets to classical models, enabling precise predictions of their critical phenomena and thermodynamic responses.

Findings

Exact critical behavior at magnon crystal transition

Universal entropy value at saturation field

Large magnetocaloric effect due to finite entropy

Abstract

Above the saturation field, geometrically frustrated quantum antiferromagnets have dispersionless low-energy branches of excitations corresponding to localized spin-flip modes. Transition into a partially magnetized state occurs via condensation of an infinite number of degrees of freedom. The ground state below the phase transition is a magnon crystal, which breaks only translational symmetry and preserves spin-rotations about the field direction. We give a detailed review of recent works on physics of such phase transitions and present further theoretical developments. Specifically, the low-energy degrees of freedom of a spin-1/2 kagom\'e antiferromagnet are mapped to a hard hexagon gas on a triangular lattice. Such a mapping allows to obtain a quantitative description of the magnetothermodynamics of a quantum kagom\'e antiferromagnet from the exact solution for a hard hexagon gas. In particular, we find the exact critical behavior at the transition into a magnon crystal state, the universal value of the entropy at the saturation field, and the position of peaks in temperature- and field-dependence of the specific heat. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain. The finite macroscopic entropies of geometrically frustrated magnets at the saturation field lead to a large magnetocaloric effect.