Mean-Field Theory of Antiferromagnetic Spin Hamiltonian with Four Spin Interactions for bcc Lattice

Abstract

An antiferromagnetic spin Hamiltonian with four spin interactions for bcc lattice is investigated on the assumption of four sublattices within the mean-field approximation. Phase diagrams are calculated in the parameter space for zero field. They possess a weak ferromagnetic phase. The effects of the magnetic field on the model are discussed in detail. The susceptibility of the antiferromagnetic phase becomes dependent on temperature in contrast to the usual cases. There is the case where the susceptibility of the SCAF ⊥ phase in the magnetic field on the spin plane can become much larger than the perpendicular susceptibility of this phase. On the basis of these results we examine to what extent this model can be compatible with the recent experimental results obtained in solid ³He. The magnitudes of exchange integrals are determined so as to fit to low-temperature behavior as well as high-temperature behavior of solid ³He. For these parameter values, it is shown that the paramagnetic phase undergoes a second-kind transition into the AF phase. In this phase the susceptibility increases more rapidly with lowering temperature than the extrapolation of the high-temperature Curie-Weiss law, and it shows a sudden drop to a nearly constant value from a peak value at T_c1, where this phase makes a first-kind transition to the SCAF // phase contrary to the case of Hetherington and Willard. This behavior is qualitatively similar to that of the solid ³He.