Invariant Form of Multipolar Interactions and Relation between Antiferro-Quadrupolar Order and Field-Induced Magnetic Moments

Abstract

The invariant interaction form between multipoles, including the octupoles, is studied for three types of cubic lattices: s.c., b.c.c. and f.c.c. The coupling terms can be arranged in a form similar to the hopping matrices between LCAO's. By using it, order parameters in the magnetic field are classified into groups in which they couple with each other, and the symmetry of the antiferro-quadrupolar (AFQ) moment is analyzed through induced antiferromagnetic moments (AFM). In this way the table for s.c. by Shiina et al. [J. Phys. Soc. Jpn. 66 (1997) 1741] is generalized for general wave vectors of the three lattice types. Recent experimental results of TmTe having the f.c.c. structure are analyzed from this viewpoint. The nature of the ferromagnetic moment below the AFM transition in the AFQ phase is also discussed. Finally brief comments are given also on field-induced moments in PrFe 4 P 12 and NpO 2 .