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 ferromagnet is not. However, such spin symmetry cannot be realized on the pyrochlore lattice, since it requires a unique symmetry axis, which is incompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local (1 1 1) anisotropy axes, which direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We: show how the local 'in-out' magnetic anisotropy reverses the roles of the ferro-and antiferromagnetic exchange couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in-out ferromagnet 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 direct one, as originally shown by Anderson. Combining these results shows that the up-down spin models map onto the in-out spin models with the opposite sign of the exchange coupling. We present Mont : Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.