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