Proposal for methods to measure the octupole susceptibility in certain cubic Pr compounds

Direct means of measuring the susceptibility toward an octupole order parameter are proposed via a sixth-rank tensor property. Equivalent derivatives more conventionally measured properties, including elastic stiffness, magnetic susceptibility, and elastoresistivity, written in full, as constrained by symmetry experimentally motivated ${O}_{h}$ point group. For simplicity, we consider specific case ${\text{Pr}}^{3+}$ ions cubic with ${\mathrm{\ensuremath{\Gamma}}}_{3}$ crystal-field ground state, but ideas somewhat general. The experimental feasibility these various quantities is discussed.