Triple-$q$ quadrupole-octupole order scenario for PrV$_2$Al$_{20}$

Abstract

We propose novel triple-q multipole orders in quadrupolar Kondo system PrV2Al20. Anisotropies of quadrupole moments stabilize a triple-q order, which further leads to the second transition to a coexisting phase with triple-q octupole moments. The mechanism for realizing these triple-q states is unique to time-reversal even multipolar systems. There, the cubic invariant of quadrupole moments with triple-q components in its free energy plays an important role. We analyze a multipolar exchange model by mean-field approximation and discuss the temperature and magnetic-field phase diagrams. Many of the microscopic results such as finite ferro octupole moments in the coexisting phase and the field-induced phases are qualitatively consistent with the experiments in PrV2Al20.