Interplay of Three Antiferromagnetic Modulations in the Nuclear Spin System of Copper.

摘要

Nuclear spins in copper have become a prototype system for testing theoretical models of magnetism against experiments. Copper nuclei are well localized, their spins are isolated from the electronic and lattice degrees of freedom at low temperatures, and the interactions between the nuclear spins can be calculated from first principles. The nuclear magneton is small, and the critical temperature for spontaneous magnetic ordering is in the nanokelvin range. Antiferromagnetic nuclear spin configurations of copper were investigated in the mean-field theory. All single-k(vector) and double-k(vector) structures with the k(vector) = (0,2/3,2/3) modulation were determined as a function of the external magnetic field. The theoretical selection rules for the 12 cubic-symmetry-related (0,2/3,2/3) ordering vectors are in perfect agreement with neutron-diffraction measurements. The authors also found structures in which the (0,2/3,2/3) and (1,0,0) spin modulations are superposed in a single magnetic domain. The calculated variations of the (0,2/3,2/3) and (1,0,0) modulations as functions of the magnetic field are in good agreement with experiments. The ordered spin structures were further studied by means of numerical mean-field simulations. Overall, the theoretical phase diagram is in good agreement with experiments.