Resonant Soft Energy X-Ray Diffraction of Charge, Spin and Orbital Ordering

Abstract

Soft X-ray resonant diffraction is a new technique pioneered by our group. Huge resonant enhancements of charge and magnetic scattering can be obtained at the L-edges of 3d transition metal oxides. We review the technique of soft X-ray diffraction as well as giving recent examples of charge, spin and orbital ordering from bulk single crystals. We have studied the low temperature phase of La$_{0.5}$Sr$_{1.5}$MnO$_4$. Previous claims of orbital ordering in such materials have relied on observations at the K edge. These claims have attracted a barrage of controversy from theoretical studies. Instead we have employed resonant soft X-ray scattering at the manganese $L_{III}$ and $L_{II}$ edges which provides a direct measurement of the orbital ordering. Energy scans at constant wavevector have been compared to theoretical predictions and show that at all temperatures there are two separate contributions to the observed scattering, direct Goodenough orbital ordering and strong cooperative Jahn-Teller distortions of the Mn$^{3+}$ ions.