Correlated Quantum Tunnelling of Monopoles in Spin Ice*

The spin ice materials Ho₂Ti₂O₇ and Dy₂Ti₂O₇ are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour – both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution – is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single ion subject to the crystal, exchange and dipolar fields from neighbouring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates which depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr₂Sn₂O₇ and Pr₂Zr₂O₇, we find an even more pronounced separation of time scales signalling the likelihood of coherent many-body dynamics
that is likely to have signatures in the behaviour of these systems.