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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 singlon and doublon placed on the two of 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 semi-quantitavely 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, the time-reversal broken orbital ordered state is identified. Whereas the spin degeneracy remains in our treatment for the 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.

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The ground states and finite-temperature properties of mixed diamond chains with spins 1 and 1/2 are investigated in the limit of strong easy-axis anisotropy on the spin-1 sites. Magnetization curves, entropy, specific heat and magnetic susceptibility are exactly calculated using the method ofČanovà et al. [J. Phys.: Condens. Matter 18 4967 (2006)].We consider the mixed diamond chains with singlesite anisotropy D and magnetic field H described by the following Hamiltonian:where S l is a spin-1 operator, and τ (α) l (α = 1, 2) are spin-1/2 operators in the lth unit cell. The total number of unit cells is denoted by L. The ground state and finite temperature properties of this model have been investigated by one of the authors and coworkers. 1, 2) Defining the composite spin operators T l ≡ τ (1) l +τ(2) l , it is evident that ∀l [T 2 l , H] = 0. Thus, we have L conserved quantities T 2 l (≡ T l (T l + 1); T l = 0 or 1). The total Hilbert space of the Hamiltonian (1) consists of separate subspaces, each of which is specified by a definite set of {T l }.A spin pair with T l = 0 is a singlet dimer that cuts off the correlation between S l and S l+1 . The segment including n successive T l 's with T l = 1 and n + 1 S l 's coupled with them is called a cluster-n. A cluster-n is equivalent to a spin-1 antiferromagnetic Heisenberg chain of length 2n + 1 with alternating single-site anisotropy. A dimer-cluster-n (DCn) phase consists of an alternating array of cluster-n's and dimers.Since all eigenstates are constructed as direct products of the eigenstates of cluster-n's and dimers, the full thermodynamics of diamond chains can be formally formulated. However, the calculations of thermodynamic quantities include the contribution from cluster-n's of arbitrary size. This is intractable in practice. In the region where the ground state is a DCn phase with finite n, the contributions from large cluster-n's are small. Hence, the *

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