Antiferroquadrupolar correlations in the quantum spin ice candidatePr2Zr2O7

We present an experimental study of the quantum spin ice candidate pyrochlore compound ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ by means of magnetization measurements, specific heat, and neutron scattering up to 12 T and down to 60 mK. When the field is applied along the $[111]$ and $[1\overline{1}0]$ directions, $\mathbf{k}=0$ field-induced structures settle in. We find that the ordered moment rises slowly, even at very low temperature, in agreement with macroscopic magnetization. Interestingly, for $H\ensuremath{\parallel}[1\overline{1}0]$, the ordered moment appears on the so-called $\ensuremath{\alpha}$ chains only. The spin excitation spectrum is essentially inelastic and consists in a broad flat mode centered at about 0.4 meV with a magnetic structure factor which resembles the spin ice pattern. For $H\ensuremath{\parallel}[1\overline{1}0]$ (at least up to 2.5 T), we find that a well-defined mode forms from this broad response, whose energy increases with $H$, in the same way as the temperature of the specific-heat anomaly. We finally discuss these results in the light of mean field calculations and propose an interpretation where quadrupolar interactions play a major role, overcoming the magnetic exchange. In this picture, the spin ice pattern appears shifted up to finite energy because of those interactions. We then propose a range of acceptable parameters for ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ that allow to reproduce several experimental features observed under field. With these parameters, the actual ground state of this material would be an antiferroquadrupolar liquid with spin-ice-like excitations.