$\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce$_2$Zr$_2$O$_7$

The Ce$^{3+}$ pseudospin-1/2 degrees of freedom in Ce$_2$Zr$_2$O$_7$ possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. Here we report new muon spin relaxation and rotation ($\mu$SR) measurements on single crystal samples of Ce$_2$Zr$_2$O$_7$ in zero magnetic field and in magnetic fields directed along the $[1,\bar{1},0]$ and $[1,1,1]$ crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field $\mu$SR measurements on a powder sample of Ce$_2$Zr$_2$O$_7$, and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for Ce$_2$Zr$_2$O$_7$ in zero-field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation, and correspondingly, the high stoichiometry of our single crystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in Ce$_2$Zr$_2$O$_7$ remain dynamic at $T = 0.1$ $\mathrm{K}$. For both $[1,\bar{1},0]$ and $[1,1,1]$ magnetic fields, our $\mu$SR Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbour exchange parameters of Ce$_2$Zr$_2$O$_7$.