Orbital-selective singlet dimer formation and suppression of double exchange in 4d and 5d systems

One of the main mechanisms of ferromagnetic ordering in conducting materials is the double exchange (DE). It is usually supposed in DE model that the Hund’s coupling $J_H$ is much larger than electron hopping $t$; in this case one stabilizes the state with maximum spin per pair of ions, which finally leads to ferromagnetism in bulk systems. We show that in the dimerized $4d/5d$ transition metal oxides for which $J_H$ is reduced and $t$ is in contrast enhanced, another situation is possible, when formation of the spin-singlets on delocalized orbitals is more favorable. This leads to suppression of the DE and to a strong decrease of the total spin. The model calculations using the dynamical mean-field theory show that this effect survives even in the extended systems, not only for dimers. Such a situation is realized, e.g., in Y$_5$Mo$_2$O$_{12}$, CrO$_2$ under pressure and in many other $4d/5d$ based materials. Another mechanism, which may suppress DE and which is also typical for $4d/5d$ compounds is the spin-orbit coupling (SOC). We show on the example of Ba$_5$AlIr$_2$O$_{11}$, that in this system it is the combination of molecular-orbital formation and SOC that strongly decreases magnetic moment on Ir.