Neutron Scattering Study on the Field-Induced $O_{xy}$-type Antiferroquadrupolar Ordering of Heavy-Fermion Superconductor $PrOs_4Sb_{12}$

Neutron scattering experiments have revealed a field-induced antiferroquadrupolar order parameter in the Pr-based heavy-fermion superconductor PrOs$_4$Sb$_{12}$. We observed the field-induced antiferromagnetic dipole moment with the propagation vector {\textit{\textbf{q}}} = (1 0 0) for the applied field direction both {\textit{\textbf{H}}}${\parallel}$[1 1 0] and [0 0 1]. For {\textit{\textbf{H}}}${\parallel}$[1 1 0] at 8 T, it should be noted that the induced antiferromagnetic moment of 0.16(10) ${\mu}_{\rm B}$/Pr orients parallel to the field within our experimental accuracy. This observation is strong evidence that the $O_{xy}$ electric quadrupole to be the primary order parameter for {\textit{\textbf{H}}}${\parallel}$[1 1 0]. A mean-field calculation, based on ${\Gamma}_1$ singlet and ${\Gamma}_4^{(2)}$ excited triplet with the $O_{xy}$ quadrupolar interaction, reproduces the induced moment direction and its field response. These facts indicate the predominance of $O_{xy}$-type antiferroquadrupolar interaction in PrOs$_4$Sb$_{12}$.