Orthorhombic crystalline field splitting on orbital and magnetic orders in KCuF${}_3$

Abstract

Magnetic and orbital structures in KCuF${}_3$ are revisited by the cluster self-consistent field approach developed recently. We clearly showed that due to the inherent frustration, the ground state of the system with the superexchange and Jahn-Teller phonon-mediated orbital couplings is highly degenerate without broken symmetry; the orthorhombic crystalline field splitting arising from static Jahn-Teller distortion stabilizes the orbital ordering, about 42% in the $x^2-y^2$ orbit and 58% in the $3z^2-r^2$ orbit in sublattices. The magnetic moment of Cu is considerably reduced to 0.49${\mu }_B$, and the magnetic coupling strengths are highly anisotropic, J${}_c$/J${}_{ab}$ $\approx$ 26. These results are in agreement with the experiments, implying that as an orbital selector, the crystalline field plays an essential role in stabilizing the ground state of KCuF${}_3$. The 1s-3d resonant X-ray scattering amplitudes in KCuF${}_3$ with the {\it type-a} and {\it type-d} structures are also presented.

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