Spin-charge-orbital structures and frustration in multiferroic RFe2O4

We examine theoretically the spin, charge and orbital states in a frustrated system RFe2O4. We suggest that the orbital degree of freedom is active in an Fe2+ ion. To describe the spin, charge and orbital states, the effective Hamiltonian for the electronic state is derived. By utilizing the Monte Carlo simulation in a finite-size cluster, we investigate the charge, spin and orbital structures. It is shown that the obtained charge and spin states are consistent with experimental results in RFe2O4. The numerical simulation for the effective orbital model does not show the conventional orbital order. We discuss possible orbital states at low temperatures.