Orbital ordering in transition-metal spinels

Transition-metal spinels ( general formula AB(2)X(4)) have been, for many years, the subject of intense experimental and theoretical activity. Structurally, the most interesting feature of these systems is the fact that the B cation occupies the nodes of a pyrochlore lattice, which is known to be geometrically frustrated. Therefore, one can explore how the natural tendency of the transition metals to order in the charge, magnetic and orbital sectors is affected by geometrical frustration. Recently, orbital ordering has become a topical subject in a variety of both non-frustrated systems, such as manganites and other perovskites, and in the spinels. In this paper, I review the recent experimental activity on the subject of orbital ordering in transition-metal spinels and relate this to models of orbital ordering that are being developed by theoreticians.