| Various exotic phenomena in correlated electron systems are studied from the view point of the internal degrees of freedom of electron, i.e. charge, spin nd orbital degrees of freedom in strong Coulomb interaction. Recently, dilution effects on the orbital ordered state are examined experimentally in KCuF3 which is a prototypical material showing the long range orbital order. It is revealed that, by replacing Cu ion by Zn which does not have the orbital degree of freedom, a reduction of the orbital ordering temperature (Too) is more remarkable than that in diluted magnets, and Too disappears at a certain Zn concentration which is lower than the percolation threshold. We investigate theoretically dilution effects in orbital systems.
(1) The classical eg orbital model is analyzed by the Monte-Carlo (MC) simulation and the cluster expansion method. We show Too decreases more rapidly by increasing dilution in comparison with the diluted magnets, and reproduce the experimental results in KCu1-xZnxF3.
(2) We analyze the two dimensional version of the quantum eg orbital model, termed the orbital compass model by quantum Monte-Carlo simulation. It is known that at low temperatures, this model shows the orbital alignment along one direction in the two dimensional lattice, i.e. the directional order. We show that the directional ordering temperature decreases by dilution more rapidly than the diluted Ising model, but more slowly than the classical compass model. This result implies that the quantum effects stabilize the directional order.
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