Symmetry Classes of Spin and Orbital Ordered States in a t_<2g> Hubbard Model on a Two-Dimensional Square Lattice(Condensed Matter Physics)

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To study quasi two-dimensional ruthenate compounds, we consider a t_<2g> Hubbard model on a two-dimensional square lattice. To find more systematically possible spin and orbital ordered ground states in this system, we used a group theoretical bifurcation theory of the Hartree-Fock (HF) equation and obtained 30 types of orbital ordered states and 41 types of spin and orbital ordered states that bifurcate from the normal state through one-step transition in cases of commensurate ordering vectors Q_0=(0,0), Q_1=(π,π), Q_2=(π,0), and Q_3=(0,π). Furthermore, we obtained five types of magnetic states bifurcating through two-step transitions from the normal state. To grasp the phase diagram of the ruthenate compounds, we calculated HF energies of all the above states (76 states in total) for some parameter sets. We determined the most stable state on some lattice points in the space (δ,U) spanned by onsite Coulomb interaction U and the splitting of crystal fields δ=∈_<yz>-∈_<xy> between {d_<yz>, d_<zx>} and d_<xy> levels. It is shown that the value of δ has a large effect on the type of ground state. Then we found that three types of broken symmetry states in addition to the conventional antiferromagnetic state can be the ground state. It is shown that for small U and J, many states with various broken symmetries have nearly degenerate HF energies.
理論物理学刊行会の論文
2009-02-25