Theory of orbital ordering due to exchange interactions

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Rare earth ions have 4f electrons in their open shells. Since they contribute little to the condensation of lattices because of the localized nature of 4f electrons, the interaction between lattices and 4f electrons is weak. If there exists orbital degeneracy in the ground f multiplet, therefore orbital ordering due to exchange interactions is highly possible in rare earth compounds instead of that due to the interaction between lattices and 4f electrons, that is, the Jahn-Teller effect. The purpose of this project is to explain an anomalous magnetism observed in CeB_6 in the framework of orbital antiferromagnetism due to exchange interactions or antiferro-quadrupole ordering due to exchange interactions. A theory in the mean field approximation was developed in the two sub-lattice model; thirty order parameter were determined selfconsistently by assuming small phenomenological anisotropic energy. Calculated results confirmed the results obtained by the author in the zero-th approximat … More ion, which agree with the experiments: i)The phase in the intermediate temperature region, which is called phase II, is assigned as an orbital-antiferromagnetic state. The lowest temperature phase is assigned as the coexistence of spin antiferromagnetism and orbital antiferromagnetism. ii)No antiferromagnetic moments exist in phase II in the absence of magnetic fields, while antiferromagnetic moments appear in the presence of fields. iii)Anisotropy of elastic constants agree with observed ones. iv)Ferromagnetic moments appear approximately in the Brillouin function of spin 1/2 in phase II. However saturated moments are larger than observed ones or the values in the zero-th approximation. This contradiction can be explained by the competition between the Kondo effect and exchange interactions. The competition can also explain saturated magnetic moments in CeNi_<1-x>Pt_x as a function of Pt content x.The theory of the competition was further developed and applied to high-T_c superconductivity in Cu oxides recently discovered. Less