Theory of spin wave excitation in manganites

The role of the orbital degrees of freedom is studied theoretically for the spin dynamics of $R_{1-x}A_x$MnO$_3$. Based on the meanfield solution, an RPA calculation has been done and it is found that the $d_{x^2-y^2}$-type orbital is essential for the double-exchange (DE) interactions, i.e., the DE is basically two-dimensional interaction. Based on this results compared with experiments, we propose that the orbital wavefunction is $d_{x^2-y^2}$-type locally even in the metallic ferromagnetic state, which fluctuate quantum mechanically. Well agreement of the estimation with experiments suggest that the Jahn-Teller phonon has less importance on the spin dynamics.