Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 30-38. © 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 30 PACS: 71.70.Gm, 75.30.Et, 71.38.-k. Polaron effects in exchange clusters (V 2+ − F - −V 2+ in KMgF 3 ) N.I. Kashirina V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 45, prospect Nauky, 03028 Kyiv, Ukraine, E-mail: kashirin@class.semicond.kiev.ua 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 KMgF 3 . 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 + 2 Cu ions in O 2H CuCl K 2 4 2 ⋅ 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 1 1 0 Σ ) 1 ( − − − ≈ x e I I I , where Σ I is the complete exchange interaction in a system including the phonon contribution (the second term) , T k x 0 / δ = with the parameters Κ 29 . 0 0 ≅ I , Κ 22 . 0 1 ≅ I , Κ 192 ≅ δ . The parameter δ corresponds to the splitting of a doubly degenerated lowest term of the copper ion in the crystalline field. Keywords: an orbital-lattice interaction, exchange-coupled pairs, indirect spin-spin interactions. Manuscript received 30.05.05; accepted for publication 25.10.05. 1. Introduction The account of permutation symmetry effects in wavefunction for many-electron system is a basis of the microscopic theory of magnetism. For a long time in the theory of exchange interactions (EI), the influence of a phonon system on the size of an exchange splitting (as well as the influence of elementary excitations of another nature on EI) was not taken into account. Aggregate colour centers (an exchange-coupled pairs of F-centers or F 2 -centers) in alkali-halide crystals were intensively studied in the Kiev school in the 50s of the last century by M.F. Deigen [1]. The historical analysis of the first works devoted to the theory of the aggregate colour centers and bipolarons (BPs) [1-3] shows that the nonrelativistic magnetic exchange takes place in addition to the electron-phonon interaction (EFI) taken into account in functionals of the ground state. The stability of two-center BPs is provided by the exchange contribution caused by electron-phonon interaction to the energy of a two-electron system (in this system, the Coulomb exchange is ferromagnetic). For the first time, the phonon contribution to the energy of the simplest aggregate centers such as F 2 - centers and BPs was investigated in the framework of continuum approximation [1-4]. This direction of the aggregate center theory is currently developed, too [5-8]. The availbility of the coupled two-electron states such as F 2 -centers and two-center BPs was possible to be explained only due to the account of permutation symmetry in these electron systems. The functional of the ground state in these systems, besides terms, concerning the kinetic energy and Coulomb energy, contained the contributions caused by interaction of electrons with the field of optical E opt and acoustical E ac waves. These additional terms depend on a distance R between centers of the polarizing well for two polarons and between vacancies for two F-centers. In spite of the