Collinear and non collinear magnetic structures in anisotropic crystals with non primitive Bravais lattice: cubic case

The classical anisotropic exchange Hamiltonian is used for the analysis of the low-temperature magnetic structures of polyatomic crystals. The magnetic order is described by the wave-vector k of the Brillouin zone associated with the Bravais lattice in direct space. For cubic crystals it is shown that anisotropic terms of tetragonal symmetry in the exchange may determine the direction of the spins with respect to k and to the crystal axes. It follows that the experimental observation of longitudinal or transverse polarisation indicates that the spin-spin interaction is not of Heisenberg type. It is also shown that anisotropy is the basic mechanism for the formation of multiaxial non-helicoloidal spin configurations. The author has found two kinds of such spin arrangements, depending on the symmetry of k and on the configuration of the unit cell. Calculations of the exchange energy in the approximation of the next-nearest-neighbor interaction for crystals of cubic symmetry Oh with four atoms per unit cell are presented. A detailed discussion of multiaxial configurations of the triangular and multiple-k-type is given. Their occurrence in MnPt3 and in uranium monopnictides is accounted for in the framework of the present model