Kugel-Khomskii materials

Abstract The Kugel-Khomskii super-exchange mechanism for orbital ordering is a pillar of orbital physics. Besides orbital phase transitions, it can give rise to a plethora of emergent phenomena, from exotic magnetic states, orbital-liquid phases, hidden order and much more. Yet, to identify real systems in which orbital-ordering arises purely from the Kugel-Khomskii mechanism has been a challenge. The first obstacle was that ions with orbital degrees of freedom are also of the Jahn-Teller kind. This poses a chicken-and-egg problem: electronic ordering can give rise to distortions and distortions can give rise to orbital ordering. This problem was eventually solved, showing that the two effects can be indeed disentangled. From this the next obstacle emerged: lattice distortions are very efficient in freezing orbital fluctuations, hampering the effects of orbital super-exchange. Thus, in most systems, orbital ordering occurs well above T KK , the critical temperature at which super-exchange can drive it. Representative Kugel-Khomskii systems were recently identified, however. The understanding gained provides guidelines for finding Kugel-Khomskii materials. It also indicates that experimental signatures of the Kugel-Khomskii mechanism should be mostly searched via the primary effect, electronic and magnetic properties, rather than the secondary effect, lattice distortions.