Theory of orbital ordering due to exchange interactions

稀土离子的开放壳层中有4f电子。由于4f电子的局域性，它们对晶格的凝聚贡献很小，因此晶格与4f电子的相互作用很弱。如果基态f多重态中存在轨道简并，则稀土化合物中的轨道有序很可能是由交换作用引起的，而不是由晶格与4f电子相互作用引起的，即Jahn-Teller效应。本项目的目的是在交换相互作用引起的轨道反铁磁性或交换作用引起的反铁-四极有序的框架内解释在CeB_6中观察到的反常磁性。在两个亚晶格模型中发展了平均场近似理论，通过假设较小的唯象各向异性能量，自洽地确定了30个序参数。计算结果证实了作者在…零阶近似下得到的结果更多的离子，这与实验一致：i)在中温区的相，被称为相II，被指定为轨道反铁磁态。最低温度相被指定为自旋反铁磁性和轨道反铁磁性共存。Ii)在没有磁场的情况下，第二相中不存在反铁磁矩，而在有磁场的情况下，出现反铁磁矩。3)弹性常数的各向异性与观测值一致。IV)在相II中，铁磁矩近似出现在自旋1/2的布里渊函数中，但饱和磁矩大于观测到的磁矩或零阶近似值。这一矛盾可以用近藤效应和交换作用之间的竞争来解释。竞争还可以解释CeNi1-x&Gt；Ptx的饱和磁矩与铂含量x的函数关系。竞争理论被进一步发展并应用于最近发现的铜氧化物的高温超导电性。较少

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