Competition between exchange and anisotropy in a pyrochlore ferromagnet

¹ University College London, Department of Chemistry 20 Gordon Street, London WC1H0AJ, UK
² Laboratoire de Physique, Ecole Normale Supérieure 46 Allée d'Italie, F-69634 Lyon cedex 07, France
³ ISIS Facility, Rutherford Appleton Laboratory Chilton, Didcot, Oxon OX11 0QX, UK

Received: 9 March 2001
Accepted: 19 October 2001

Abstract

The Ising-like spin ice model, with a macroscopically degenerate ground state, has been shown to be approximated by several real materials. Here we investigate a model related to spin ice, in which the Ising spins are replaced by classical Heisenberg spins. These populate a cubic pyrochlore lattice and are coupled to nearest neighbours by a ferromagnetic exchange term J and to the local axes by a single-ion anisotropy term D. The near-neighbour spin ice model corresponds to the case . For finite D/J we find that the macroscopic degeneracy of spin ice is broken and the ground state is magnetically ordered into a four-sublattice structure. The transition to this state is first order for D/J > 5 and second order for D/J < 5 with the two regions separated by a tricritical point. We investigate the magnetic phase diagram with an applied field along [001] and show that it can be considered analogous to that of a ferroelectric.