Spin order on pyrochlore lattices studied by the Self-Consistent Cluster Approach

TL;DR

This study investigates magnetic ordering in quantum Heisenberg spins on pyrochlore lattices using the Cluster Variation Approximation, revealing no long-range order for antiferromagnetic exchange and complex phase behavior for ferromagnetic exchange.

Contribution

It applies the Cluster Variation Approximation to pyrochlore lattices, providing new insights into spin order, phase diagrams, and re-entrant phenomena in quantum spin systems.

Findings

No long-range spin order at finite temperature for antiferromagnetic exchange.

Finite order temperature for ferromagnetic exchange with s > 1/2.

Re-entrant behavior and magnetic field-induced transitions observed.

Abstract

In this paper we present a study of magnetic order of quantum Heisenberg spins on pyrochlore type lattices: a lattice of corner sharing tetrahedra. We use the Cluster Variation Approximation with the tetrahedron as basic cluster. We find that in case of anti-ferromagnetic nearest--neighbour exchange there is no long--range spin order at any finite temperature for any spin s. For ferromagnetic exchange and s=1/2 the spin system remains in a non-magnetic phase for all temperatures, while for s > 1/2 there is a finite order temperature. We derive the ground state phase diagram as a function of exchange anisotropy and tetragonal anisotropy and find regions of re--entrant behaviour. Magnetic fields can induce one or more magnetic transitions. Schottky--like anomalies appear in the specific heat, with on top signs of re--entrant behaviour. The limits of this Cluster Variation Approximations are discussed.