Field Induced Phase Transition with Quadrupole Fluctuation in HoFe^sub 2^Al^sub 10^ with Orthorhombic Symmetry

To explore phase transitions in HoFe^sub 2^Al^sub 10^ with an orthorhombic structure, we performed ultrasonic measurements on transverse elastic moduli C^sub 55^ and C^sub 66^ under magnetic fields H. At zero magnetic field, C^sub 55^ and C^sub 66^ show an elastic softening down to 0.5 K without a clear anomaly, suggesting that no phase transition exists at zero magnetic field. However, in H along the a- and c-axes, the softening of C^sub 55^ under 0.6 (0.4) T stops at T^sub Q^ = 0.8 (0.75) K for H || a (c). Below T^sub Q^, C^sub 55^ shows an elastic hardening. With further increasing H, we observed a remarkable softening of C^sub 55^ toward T^sub Q^. C^sub 66^ also shows a kink anomaly at T^sub Q^ in H || a and c. From the results, we clarified the field induced phase transition for H || a and c in HoFe^sub 2^Al^sub 10^. The minimum point of C^sub 55^ at T^sub Q^ suggests that the field induced phase transition results from a quadrupolar ordering with the order parameter of quadrupole O^sub zx^ despite a singlet ground state under an orthorhombic crystal electric field in HoFe^sub 2^Al^sub 10^.