Effects of anharmonic lattice distortion on orbital and magnetic orderings in KCuF3

Lattice, magnetic and orbital structures in KCuF₃ areself-consistently determined by our cluster self-consistent fieldapproach based on a spin-orbital-lattice Hamiltonian. Two stablestructures are obtained and found to be degenerate, which confirmsthe presence of the coexistent phases observed experimentally. Weclearly show that due to the inherent frustration, the ground stateof the system only with the superexchange interaction is degenerate;while the Jahn--Teller distortion, especially the anharmonic effect,stabilizes the orbital ordered phase at about 23% in thex²--y² orbit and at 77% in the 3z²--r² orbit.Meanwhile the magnetic moment of Cu is considerably reduced to0.56μ_B, and magnetic coupling strengths are highlyanisotropic, J_z/J_xy approx 18. These results are ingood agreement with the experiments, implying that the anharmonicJahn--Teller effect plays an essential role in stabilising theorbital ordered ground state of KCuF₃.