Magnetic order and energetics of dipolar coupling in magnetic superconductors

Abstract

The exact (notjust nearest-neighbor) dipolar coupling energy densities for the observed structures ofthe rare earth Chevrel compounds are calculated by the method ofLuttinger and Tisza. The dipolar coupling energy density for the most probable spin configuration is comparable to the observed magnetic transition temperature, TM, but the most probable ground state is not found experimentally. The discrepancy between the observed magnetic ground state and that predicted from dipole coupling may arise from conduction electron effects or possibly from some strong crystal field effect and should be included in any electronic theory of the superconductive state below TM.The antiferromagnetic interaction energy of the rare earth Chevrel (1) compounds is calculated on the basis of simple dipolar coupling (2). The compounds are of special interest because they are also superconductors, and the connection between their superconductive and magnetic properties is the object of much current experimental (3-6) and theoretical (7-10) effort.If the antiferromagnetic transition temperature, TM, could be accounted for by dipole coupling ofthe rare earth moments, the connection between superconductive and antiferromagnetic ordering would be simplified. Essentially, different electrons would give rise to the two effects.In the rare earth Chevrels, the magnetic moments are very large and well-separated spatially, and there is a relatively low density of conduction electrons. Thus, it seemed possible that the molecular field model of the transition temperature due only to dipole coupling could make a significant contribution to the stability ofthe magnetic phases ofthe rare earth Chevrels.The Chevrel compounds are characterized by sulfur cubes filled in alternate layers by Mo6 octahedra or metal, M,, each M-or Mo6-filled cube being separated from the next by an empty sulfur cube; the sulfur cubes themselves form a bodycentered cubic lattice. This structure permits the inclusion of a great variety of M,. When M. is a superconductor (Sn, Pb), the Chevrel compound is found to be superconducting with a raised transition temperature. The superconducting transition temperature, T,, is increased more for those with lowest original transition temperature, T%. If M. is not superconducting (Ag, Cu), the Chevrel compound becomes superconducting. If M. is a rare earth having a large free-ion magnetic moment, the Chevrel compounds exhibit both magnetic and superconducting ordering. In particular, TbMo6S8, DyMo6S8, and HoMo6S8 are found to be superconducting and at lower temperatures to exhibit antiferromagnetic and ferromagnetic order. METHOD OF LUTTINGER AND TISZAThe rare earth atoms lie on a nearly cubic lattice (rhombohedral angle a 89.40). The exact mean-field dipole coupling interaction energy for an ordered array of moments can be calculated by the group theoretic method of Luttinger and Tisza (11). A simple cubic dipole array is denoted by placing a dipole of definite moment and direction at every lattice point. The lowest energy-o...