Carriers binding to excitons: Crystal-field excitations in doped Mott-Hubbard insulators

We address the role played by orbital degeneracy in doped Mott-Hubbard insulators. We observe that in all but the simplest systems the carriers bind to d-d excitons because of Hund’s-rule interactions. These three-particle bound states have distinct spectroscopic signatures and at least in one case these seem already confirmed experimentally. If the crystal-field gaps become of the order of the kinetic energy of the carriers, doping might tend to stabilize phases characterized by a finite occupation of d-d excitons in the ground state. If the total spin of both the carrier state and the spin background are at maximum, the relevant excitons do not involve a change in spin. As a consequence, the orbital channel can be in the first instance considered independently from the spin channel and we find an exciton-carrier coupling that in essence interpolates between the carrier-spin-wave couplings of the t-J model and the conventional couplings to optical phonons. We work out in detail a case involving high-spin holes in a cupratelike system and we show that the exciton-carrier coupling tends to stabilize an orthorhombic type of orbital order. On the other hand, if either the carriers or the background are in a low-spin state, the relevant excitons also change total spin locally and more-exotic order parameters are possible. We analyze in detail the case of a nickelate close to the high-spin–low-spin transition where we show that doping will tend to stabilize an ordering related to superpositions of low-spin and high-spin states, characterized by an overall spin-rotational invariance. We argue that such a state might be realized in n-type ${\mathrm{La}}_2$ ${\mathrm{NiO}}_4$.