Orbital-dependent singlet dimers and orbital-selective Peierls transitions in transition-metal compounds

We show that in transition-metal compounds containing structural metal dimers there may exist in the presence of different orbitals a special state with partial formation of singlets by electrons on one orbital, while others are effectively decoupled and may give, e. g., long-range magnetic order or stay paramagnetic. A similar situation can be realized in dimers spontaneously formed at structural phase transitions, which can be called the orbital-selective Peierls transition. This can occur in the case of strongly nonuniform hopping integrals for different orbitals and small intra-atomic Hund's rule coupling J(H). Yet another consequence of this picture is that for an odd number of electrons per dimer there exists competition between the double-exchange mechanism of ferromagnetism and the formation of a singlet dimer by the electron on one orbital, with the remaining electrons giving a net spin of a dimer. The first case is realized for strong Hund's rule coupling, typical for 3d compounds, whereas the second is more plausible for 4d-5d compounds. We discuss some implications of these phenomena, and consider examples of real systems, in which the orbital-selective phase seems to be realized.