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 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 . 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 Monte Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.

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Neutron scattering and ac-susceptibility techniques have been performed on the spin ice material Ho 2 Ti 2 O 7 to study the spin relaxation processes in the 'hot' paramagnetic phase (T > 1 K). Neutron spin echo (NSE) proves that above T 15 K the spin dynamics are governed by a thermally activated single-ion process. At lower temperatures (T < 15 K) this cannot account for the spin dynamics found in ac-susceptibility measurements. It is inferred that a second, slower process, with a different thermal signature dominates. We suggest that this is a quantum-mechanical tunnelling process between different spin states separated by a large energy barrier.

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