Why spin ice obeys the ice rules

Details Why spin ice obeys the ice rules Why spin ice obeys the ice rules

2005-02-04

arxiv.org/abs/cond-mat/0502137v2

Phys. Rev. Lett. 95, 217201 (2005)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.95.217201

The low temperature entropy of the the spin ice compounds, such as Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, is well described by the nearest-neighbor antiferromagnetic Ising model on the pyrochlore lattice, i.e.\ by the ``ice rules''. This is surprising since the dominant coupling between the spins is their long ranged dipole interaction. We show that this phenomenon can be understood rather elegantly: one can construct a model dipole interaction, by adding terms of shorter range, which yields {\it precisely} the same ground states, and hence T=0 entropy, as the nearest neighbor interaction. A treatment of the small difference between the model and true dipole interactions reproduces the numerical work by Gingras et al in detail. We are also led to a more general concept of projective equivalence between interactions.

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