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

TL;DR

This paper investigates how orthorhombic crystalline field splitting influences the orbital and magnetic orders in KCuF₃, revealing stabilization mechanisms and anisotropic magnetic interactions through a cluster self-consistent field approach.

Contribution

It demonstrates the crucial role of crystalline field splitting in stabilizing orbital and magnetic structures in KCuF₃, using a novel cluster self-consistent field method.

Findings

Orbital ordering stabilized by crystalline field splitting with specific orbital proportions.

Significant reduction of Cu magnetic moment to 0.49μ_B.

Highly anisotropic magnetic coupling with J_c/J_ab ≈ 26.

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.