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The pyrochlore spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are well described byclassical Ising models down to very low temperatures. Given the empiricalsuccess of this description, the question of the importance of quantum effectsin these materials has been mostly ignored. We show that the common wisdom thatthe strictly Ising moments of Dy3+ and Ho3+ imply strictly Ising interactionsis too naive; a more complex argument is needed to explain the close agreementbetween theory and experiment. From a microscopic picture of the interactionsin rare-earth oxides, we show that the high-rank multipolar interactions neededto induce quantum effects are generated only very weakly by super-exchange.Using this framework, we formulate an estimate of the scale of quantum effectsin Ho2Ti2O7 and Dy2Ti2O7, finding it to be well below experimentally relevanttemperatures. We discuss the implications of these results for realizingquantum spin ice in other materials.

How quantum are classical spin ices?