Field-induced switching of ferro-quadrupole order parameter in PrTi₂Al₂₀

We report magnetic-field-induced first-order phase transitions in the ferro-quadrupole (FQ) ordered state of PrTi₂Al₂₀, in which non-Kramers Pr³⁺ ions with two 4f electrons have a non-magnetic Γ₃ doublet ground state in the cubic T_d crystalline electric field. For magnetic fields along [111], ²⁷Al-NMR and magnetization experiments reveal Q_z ∝ 3z² − r² type FQ order below 2K independent of field strength. Magnetic fields along [001] or [110], however, induce discontinuous switching of order parameters within the two dimensional space spanned by Q_z and Q_x ∝ x² − y² at small field values less than a few tesla. A symmetry-based theoretical analysis shows that the transitions can be caused by competition between the magnetic Zeeman interaction and anisotropy in the quadrupole–quadrupole interactions, if the latter dominates over the former in low fields and vice versa in high fields. Furthermore, striking violation of proportionality between NMR Knight shift and magnetic susceptibility is observed in the symmetry-broken FQ phases, indicating significant influence of FQ order on the hybridization between conduction and f electrons, which in turn mediates the Ruderman–Kittel–Kasuya–Yosida (RKKY) type quadrupole interaction causing the FQ order. This feedback effect may be a specific feature of quadrupole orders not commonly observed in magnetic phase transitions and play a key role for inducing the discontinuous transitions.