Paper detail

Mn L$_{2,3}$ edge resonant x-ray scattering in manganites: Influence of the magnetic state

We present an analysis of the dependence of the resonant orbital order and magnetic scattering spectra on the spin configuration. We consider an arbitrary spin direction with respect to the local crystal field axis, thus lowering significantly the local symmetry. To evaluate the atomic scattering in this case, we generalized the Hannon-Trammel formula and implemented it inside the framework of atomic multiplet calculations in a crystal field. For an illustration, we calculate the magnetic and orbital scattering in the CE phase of \lsmo in the cases when the spins are aligned with the crystal lattice vector ${\vec a}$ (or equivalently ${\vec b}$) and when they are rotated in the $ab$-plane by 45$^{\circ}$ with respect to this axis. Magnetic spectra differ for the two cases. For the orbital scattering, we show that for the former configuration there is a non negligible $σ\to σ'$ ($π\to π'$) scattering component, which vanishes in the 45$^\circ$ case, while the $σ\to π'$ ($π\to σ'$) components are similar in the two cases. From the consideration of two 90$^\circ$ spin canted structures, we conclude there is a significant dependence of the orbital scattering spectra on the spin arrangement. Recent experiments detected a sudden decrease of the orbital scattering intensity upon increasing the temperature above the N\' eel temperature in \lsmo. We discuss this behavior considering the effect of different types of misorientations of the spins on the orbital scattering spectrum.