Effect of Jahn-Teller distortion on the exchange interactions in KCuF3. Two model studies

In an analysis of the influence of the Jahn-Teller (JT) distortion in KCuF₃ on the exchange-coupling constants (ecc) along (J_S ≈ -190K), and perpendicular to (J_AS ≈ 0) the c-axis, two models are considered. First, a three-center, four-electron model is adopted with d(e_g)- and p_σ-orbitals at the cations and anion, respectively. Experimental values of ionization potentials and electron affinities are employed. The model accounts for the JT-distortion by using the induced admixtures of the e_g-orbitals on the copper cations. The computations involve CI. Secondly, taking s-orbitals at all centers, we perform three-center, four-electron model calculations supplemented with two-anion non-additive exchange contributions obtained from four-center, six-electron model calculations. The latter contributions, strongly geometry dependent, account for the effect of JT-distortion on the ecc's. First-order exchange-perturbation theory is used. In the applications to KCuF₃ we adopt in the two models the same orbital parameterization, based on atomic properties, with which the ecc's in the regular perovskites KMF₃ : M = Mn, Co and Ni, are reproduced. The resulting values for J_S and J_AS agree with experiment. The vanishing value of J_AS is structural in the first (pd-) model and accidental in the second (s-) model. This discrepancy is discussed.