Theory of orbital ordering, fluctuation, and resonant x-ray scattering in manganites

We present a theoretical framework of resonant x-ray scattering (RXS) to st udy orbital order-disorder phase transition in manganites. The scattering c ross section (SCS) of RXS is given by the correlation function of the pseud ospin operator for the orbital degree of freedom in Mn ions. The order para meter, critical fluctuation, and their critical exponents in the phase tran sition are studied like those of spin and charge done in neutron and x-ray scatterings, respectively. The temperature, momentum, and polarization depe ndences of the SCS are calculated independently of detailed scattering proc esses. The theory may also be applied to RXS in other compounds with an orb ital degree of freedom.