Antiferro-quadrupolar ordering and multipole interactions in PrPb₃

Antiferro-quadrupolar (AFQ) ordering in the cubic Γ₃ ground state system PrPb₃ has been studied by means of magnetization and specific heat measurements under magnetic fields H. Field variation of the AFQ transition temperature T_Q (0.4 K at H = 0) has been determined for the three crystallographic directions 〈100〉. 〈110〉 and 〈111〉. The obtained T_Q(H) is strongly anisotropic, with T^〈100〉_Q (H) the largest (∼0.7 K at 6 T). The AFQ phase diagram and the magnetization behavior observed for H ∥ 〈100〉 are well explained by a model that incorporates both antiferromagnetic and antiferroquadrupolar interactions. The interactions between field-induced staggered magnetic moments stabilize the AFQ order. This simple model, however, seriously fails to explain the observed anisotropy: T^〈100〉_Q (H) > T^〈110〉_Q (H) > T^〈111〉_Q (H). Reconsidering the field-induced multipole moments in the AFQ phase, we propose that inclusion of a weak ferro-octupolar interaction between Γ₅ type octupole moments is important in reproducing the anisotropic phase diagram of PrPb₃.