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

We present a theoretical framework of resonant x-ray scattering (RXS) to study orbital order-disorder phase transition in manganites. The scattering cross section (SCS) of RXS is given by the correlation function of the pseudospin operator for the orbital degree of freedom in Mn ions. The order parameter, critical fluctuation, and their critical exponents in the phase transition are studied like those of spin and charge done in neutron and x-ray scatterings, respectively. The temperature, momentum, and polarization dependences of the SCS are calculated independently of detailed scattering processes. The theory may also be applied to RXS in other compounds with an orbital degree of freedom.