Non-collinear magnetism due to orbital degeneracy and multipolar interactions

The origin of non-collinear magnetism under quadrupolar ordering is investigated with CeB6 taken as a target system. The mode-mixing effect among 15 multipoles is analyzed based on the Ginzburg-Landau free energy. Then the lower magnetic transition temperature and the order parameters are derived within the mean-field approximation. In the presence of pseudo-dipole-type interactions for the next-nearest neighbors, the observed pattern of non-collinear ordering is indeed stabilized for certain set of interaction parameters. The stability of the phase III in the magnetic field is also explained, which points to the importance of the next-nearest-neighbor octupole-octupole interaction. Concerning the phase IV in CexLa1-xBe with x similar to 0.75, a possibility of pure octupole ordering is discussed based on slight modifications of the strength of interactions.