Theory of antiferro-quadrupolar ordering in TmTe

Abstract

A theory of the antiferro-quadrupolar (AFQ) ordering in TmTe is presented on the basis of a classical description of multipoles. The phase diagram of the AFQ state and its relation to the type of crystal field and the form of multipolar interactions are studied in detail. It is shown that the Γ3-AFQ order parameter in a crystal field with the (001)-easy-axis type is uniquely consistent with the magnetic-field anisotropy observed in TmTe. A correlation is present between the spontaneous and field-induced antiferromagnetic orders through the magnetic interaction in the AFQ state; it leads to a natural interpretation of the phase diagram of TmTe. A large contribution from octupoles on the AFQ transition temperature is predicted in the high-field region due to the cooperative relation of octupoles and the magnetic field.