An electronic mechanism for electron pairing in antiferromagnetic bridged mixed-valence systems

Abstract

One- and two-dimensional bridged mixed-valence systems consisting of metal atoms M and polarizable ligands L are discussed. It is argued that when the valence state of the metal atom is changed, the energy gap and the effective resonance integral between M and L orbitals are also changed. The former is due to electron–electron repulsion and the latter to ligand polarization. A Hubbard model Hamiltonian with an occupation-dependent resonance integral is adopted to describe these systems. Approximate solutions are obtained by the Hartree–Fock method. One-dimensional chains and two-dimensional nets are studied, in which metal ions are joined together by bridging ligands. The fully oxidized system is taken to have one electron per metal orbital, with the ligand orbitals vacant. The electron spin vectors are aligned in an antiferromagnetic fashion. Upon the addition of extra electrons, low-lying vacancies can be formed under certain conditions, which can lead to interesting p-type conductive properties in one or two dimensions. In the one-dimensional system, the formation of such a low-lying vacancy requires that the regional orbitals which contain the added electron are delocalized over seven units or more. (If the bridging ligands are monatomic and the metal–ligand bond distance is about 2 Å, then the delocalization length is about 12 Å.) This phenomenon is unlikely to be realizable in one dimension for the present type of system since it only occurs in parts of parameter space with an unrealistically small value for the electron–electron repulsion U. However, in two dimensions, low-lying vacancies are sometimes predicted by the present model for reasonable values for U. Furthermore, the minimum delocalization radius required for the generation of low-lying vacancies is somewhat smaller in two dimensions than in one. The relative stability of one isolated versus two paired excess electrons is also explored, although some crude assumptions about the delocalization lengths of two vs one excess electrons had to be made. When a single excess electron is delocalized over three units or more, the total energy for two paired excess electrons may be lower than that for two isolated excess electrons. Possible superconductivity by such an electronic mechanism is discussed.