Jahn-Teller effect and electron correlation in manganites

Jahn-Teller (JT) effect in manganites is studied theoretically both in the absence and presence of the Coulomb interaction. The focus is on the role of orbital degeneracy, i.e., multiband effect, in the electron-phonon (el-ph) interaction. The kinetic energy gain K, which is directly related to the spin-wave stiffness, is calculated to compare with the experiments. Without the Coulomb interaction, the perturbative analysis gives the reduction ΔK of K due to the JT coupling as ΔK(0.7--1.9)(Ω/t₀)(g²/MΩ²) with the prefactor determined mostly by the density of states at the Fermi energy $[g:$ electron-phonon (el-ph) coupling constant, M: mass of the oxygen atom; Ω: frequency of the phonon; t₀: transfer integral]. Although there occur many second-order perturbative processes, ΔK roughly scales with the density of states at the Fermi energy. The magnitude of ΔK is at most 3% of K and is negligible in this case. In the limit of strong electron correlation, on the other hand, the magnitude of the orbital polarization saturates and the relevant degrees of freedom are its direction. An effective action is derived, and it is found that the JT interaction is enhanced compared with the noninteracting case, and ΔK is given by the lattice relaxation energy EL for the localized electrons, although the electrons remains itinerant with the bandwidth of the order of t₀, which is larger than EL. Therefore there should be an appreciable reduction of the spin stiffness due to JT coupling in manganites.