The multiorbital Hubbard model in the strong-coupling limit is analyzed for the effectively antiferromagnetic Hund's coupling relevant to fulleride superconductors with three orbitals per molecule. The localized spin-orbital model describes the thermodynamics of the half-filled (three electron) state with total spin 1/2, composed of a singlon and a doublon placed on two of the three orbitals. The model is solved using the mean-field approximation, and magnetic and electric ordered states are clarified through the temperature dependences of the order parameters. Combining the model with the band structure from ab initio calculation, we also semiquantitatively analyze the realistic model and the corresponding physical quantities. In the A15-structure fulleride model, there is an antiferromagnetic ordered state, and subsequently the two-orbital ordered state appears at lower temperatures. It is argued that the origin of these orbital orders is related to the $T_h$ point-group symmetry. As for the fcc fulleride model, a time-reversal-broken orbital ordered state is identified. Whereas the spin degeneracy remains in our treatment for a geometrically frustrated lattice, it is expected to be lifted by some magnetic ordering or quantum fluctuations, but not by the spin-orbital coupling, which is effectively zero for fullerides in the strong-coupling regime.

中文翻译：

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富勒烯的自旋轨道模型

强耦合极限下的多轨道哈伯德模型分析了与每个分子具有三个轨道的富勒德超导体相关的有效反铁磁 Hund 耦合。局部自旋轨道模型描述了总自旋为 1/2 的半填充（三个电子）态的热力学，由放置在三个轨道中的两个轨道上的单粒子和双粒子组成。该模型使用平均场近似求解，磁和电有序状态通过有序参数的温度依赖性得到澄清。将模型与从头算起的能带结构相结合计算，我们还对现实模型和相应的物理量进行了半定量分析。在 A15 结构的富勒德模型中，存在反铁磁有序态，随后在较低温度下出现双轨道有序态。有人认为，这些轨道顺序的起源与${吨}_H$点群对称。对于 fcc fulleride 模型，确定了时间反转破坏的轨道有序状态。尽管自旋简并在我们对几何受挫晶格的处理中仍然存在，但预计它会被一些磁序或量子涨落解除，但不会被自旋轨道耦合解除，在强耦合状态下，自旋轨道耦合实际上为零。