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Recently there have been a number of experiments on Ce$_2$Zr$_2$O$_7$ andCe$_2$Sn$_2$O$_7$, suggesting that these materials host a three-dimensionalquantum spin liquid with emergent photons and fractionalized spinonexcitations. However, the interpretation of the data to determine the precisenature of the quantum spin liquids is still under debate. The Kramers doubletin Ce$^{3+}$ local moment offers unusual pseudo-spin degrees of freedom as the$x$ and $z$ components transform as a dipole and $y$ component as an octupole.This leads to a variety of possible quantum spin liquid (or quantum spin ice)phases on the pyrochlore lattice of Ce$^{3+}$ moments. In this work, wetheoretically propose that magnetostriction would be able to distinguish thedipolar (D-QSI) and octupolar (O-QSI) quantum spin ice, where the dipolar oroctupolar components possess the respective spin ice correlations. We show thatthe magnetostriction in various configurations can be used as a selection ruleto differentiate not only D-QSI and O-QSI, but also a number of competingbroken symmetry states.

Distinguishing dipolar and octupolar quantum spin ices using contrasting magnetostriction signatures