Orbital physics in transition metal compounds: new trends

The present review discusses different effects related to orbital degrees of freedom. Leaving aside such aspects as the superexchange mechanism of cooperative Jahn-Teller distortions and various properties of 'Kugel-Khomskii'-like models, we mostly concentrate on other phenomena, which are the focus of modern condensed matter physics. After a general introduction, we start with a discussion of the concept of effective reduction of dimensionality due to orbital degrees of freedom and consider such phenomena as the orbitally driven Peierls effect and the formation of small clusters of ions in the vicinity of the Mott transition, which behave like 'molecules' embedded in a solid. The second large part is devoted to orbital-selective effects, such as the orbital-selective Mott transition and the suppression of magnetism due to the fact that the electrons on some orbitals start to form singlet molecular orbitals. At the end, the rapidly growing field of so-called 'spin-orbit-dominated' transition metal compounds is briefly reviewed, including such topics as the interplay between the spin orbit coupling and the Jahn-Teller effect, the formation of the spin orbit-driven Mott and Peierls states, the role of orbital degrees of freedom in generating the Kitaev exchange coupling, and the singlet (excitonic) magnetism in 4d and 5d transition metal compounds.