Polaron effects in exchange clusters (V²⁺ - F⁻ - V²⁺ in KMgF₃)

Abstract

We have calculated the phonon contribution to the energy of a superexchange. It is shown that the phonon contribution to the exchange interaction is comparable on the order of magnitude with the Coulomb superexchange. The numerical calculations are performed for a molecular cluster consisting of an exchange-coupled pair V ²⁺−F–−V ²⁺ and 10 nearest ions F- in KMgF₃. The distinctions of a temperature dependence of the exchange interaction caused by phonons are discussed. In systems with the close located electronic levels, the account of interaction with a phonon field reduces in occurrence of resonant terms in the exchange interaction of paramagnetic ions. The similar terms result in occurrence of the exponential temperature dependence in an exchange interaction. As an example, the exchange pair of Cu²⁺ ions in K₂CuCl₄ ⋅ 2H₂O ⋅ has been considered. The experimentally observed anomalously strong temperature dependence of the exchange interaction of copper ions in this system can be described by the contribution of the resonant terms caused by a phonon contribution to the exchange interaction. The total exchange can be described by the dependence IΣ = I₀ - I₁(ex -1)⁻¹ where IΣ is the complete exchange interaction in a system including the phonon contribution (the second term) x = δ/k₀T with the parameters I₀ ≅ 0.29 Κ , I₁ ≅ 0.22 Κ , δ ≅ 192 Κ. The parameter δ corresponds to the splitting of a doubly degenerated lowest term of the copper ion in the crystalline field.