Ferro-quadrupolar ordering in PrTi${}_2$Al${}_{20}$

Origin of the non-magnetic phase transition in PrTi${}_2$Al${}_{20}$, reported earlier in the macroscopic study, has been asserted microscopically using elastic and inelastic neutron scattering techniques. It has been shown spectroscopically that the crystalline-electric-field ground state is a non-magnetic ${\mathrm{\Gamma }}_3$ doublet, whereas the excited states are two triplets (${\mathrm{\Gamma }}_4$ and ${\mathrm{\Gamma }}_5$) and a singlet (${\mathrm{\Gamma }}_1$). The diffraction experiment under external magnetic field shows that the non-magnetic transition is indeed ferro-quadrupolar ordering, which takes place as a consequence of cooperative removal of the ground-state-doublet degeneracy. It is therefore concluded that PrTi${}_2$Al${}_{20}$ is another rare example of Pr compounds exhibiting non-magnetic quadrupolar order.