Charge ordering as alternative to Jahn-Teller distortion

It was pointed out in the seminal paper of Jahn and Teller that a partially occupied degenerate molecular level, often a doubly degenerate $E_{g}$ level in a cubic ligand field, is unstable against a distortion that splits the level and lowers the total energy of the occupied states. Since then, this effect has been commonly found in solids where it takes a form of a \textit{cooperative} Jahn-Teller (JT) effect (orbital ordering), when the crystal lattice distorts coherently so as to lift orbital degeneracy at each site or, in band language, to split an entire band ($e.g.$, $e_{g}$) and thus open a gap at the Fermi level. Upon the gradual delocalization of degenerate electrons, the JT distortion and corresponding orbital ordering becomes less and less favorable, but, as we show, below a crossover region exists with the possibility of lifting degeneracy not by an \textit{orbital ordering}, but by a \textit {charge ordering} (CO): an electron can be transferred from one ion to another, so that, say, the doubly degenerate $e_{g}$ level on one site will be fully occupied, and on the other site empty. In this paper we demonstrate, experimentally and by first principles calculations, that just such a ``JTCO'' effect actually occurs in the rare earth nickelates such as YNiO$_{3}$ and LuNiO$_{3}$. Apparently this novel phenomenon can also take place in other similar systems.