Spin–orbital liquid state and liquid–gas metamagnetic transition on a pyrochlore lattice*

Crystal structures with degenerate electronic orbitals are generally unstable, as the system lowers the overall energy by lifting the degeneracy through Jahn-Teller (JT) distortions. Typically, in e.g. 3d transition metal compounds, energy scales of orbital-lattice couplings and exchange interactions are orders of magnitude different, which ensures that the JT distortions occur independently from magnetic orderings. Therefore, it is hard to suppress orbital order down to low temperatures, not to mention to obtain a “spin-orbital liquid” state. Nevertheless, rare earth systems provide a promising platform for realizing such novel states. In even number electron (non-Kramers) systems, e.g. Pr³⁺, an interlocking between the spin and the orbital moment is realized due to the strong spin-orbit coupling. Our focus is in the pyrochlore oxide Pr₂Zr₂O₇, a multipolar spin ice whose ground doublet comprises of longitudinal magnetic dipole and transverse electric quadrupole (orbital) moments. Such non-Kramers doublet is extremely sensitive to disorders/ distortions, setting a high bar for the sample quality.

Here, we prepared ultrapure single crystal Pr₂Zr₂O₇, in which a sharp metamagnetic anomaly is observed. The presence of such anomaly differentiates our samples from those of the literatures and enables us to investigate more intrinsic physics of Pr₂Zr₂O_7. We present the data from a broad range of thermodynamic measurements including lattice expansion, ultrasound, magnetization and dielectric constants. Interestingly, our observation of a highly anisotropic metamagnetic transition -characteristic to spin-ice- with strong lattice softening, suggests spin-orbital dynamics at low temperature and low fields.