FRUSTRATION IN ISING-TYPE SPIN MODELS ON THE PYROCHLORE LATTICE

We compare the behaviour of ferromagnetic and antiferromagnetic Ising- type spin models on the cubic pyrochlore lattice. With simple 'up-down ' Ising spins, the antiferromagnet is highly frustrated and the ferrom agnet is not. However, such spin symmetry cannot be realized on the py rochlore lattice, since it requires a unique symmetry axis, which is i ncompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local (1 1 1) anisotropy axes, w hich direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We: show how the local 'in-out' magnetic a nisotropy reverses the roles of the ferro-and antiferromagnetic exchan ge couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in-out ferromagn et is a magnetic analogue of the ice model, which we have termed the ' spin ice model'. it is realized in the material Ho2Ti2O7. The up-down antiferromagnet is also an analogue of the ice model, albeit a less di rect one, as originally shown by Anderson. Combining these results sho ws that the up-down spin models map onto the in-out spin models with t he opposite sign of the exchange coupling. We present Mont : Carlo sim ulations of the susceptibility for each model, and discuss their relev ance to experimental systems.