Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet

– 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 〈1, 1, 1〉 axes by a single-ion anisotropy term D. The near neighbour spin ice model corresponds to the case D/J → ∞. 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 secondorder for D/J < 5 with the two regions separated by a tricritical point. We investigate the magnetic phase diagram with an applied field along [1, 0, 0] and show that it can be considered analogous to that of a ferroelectric. Background. – Geometrical frustration represents a recipe by which condensed matter can be disordered even in the absence of substitutional disorder [1]. The canonical example is the proton disorder in ice, which was famously shown by Pauling to be the origin of the experimentally observed ground state entropy [2, 3]. Anderson later illustrated a direct mapping of Pauling’s model onto the Ising antiferromagnet on the pyrochlore lattice [4]. However, Anderson’s antiferromagnet does not appear to occur in nature and the mapping was for many years something of an academic curiosity, albeit one that inspired interest in frustrated magnetism [5–7]. Recently, however, this has changed with the presentation of an alternative mapping named “spin ice”, motivated by experiments on the cubic pyrochlore Ho2Ti2O7 [8]. This material is closely approximated by a pyrochlore ferromagnet with 〈1, 1, 1〉 Ising-like spins, which maps onto the ice model [8] and hence onto Anderson’s antiferromagnet [9, 10]. The behaviour of Ho2Ti2O7 [8] and the related compound Dy2Ti2O7 [13, 14] is described to