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

Lattice, magnetic and orbital structures in KCuF₃ are self-consistently determined by our cluster self-consistent field approach based on a spin-orbital-lattice Hamiltonian. Two stable structures are obtained and found to be degenerate, which confirms the presence of the coexistent phases observed experimentally. We clearly show that due to the inherent frustration, the ground state of 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 the x²--y² orbit and at 77% in the 3z²--r² orbit. Meanwhile the magnetic moment of Cu is considerably reduced to 0.56μ_B, and magnetic coupling strengths are highly anisotropic, J_z/J_xy \approx 18. These results are in good agreement with the experiments, implying that the anharmonic Jahn--Teller effect plays an essential role in stabilising the orbital ordered ground state of KCuF₃.