Resonant inelastic x-ray scattering study of vector chiral ordered kagome antiferromagnet

We study the resonant inelastic x-ray scattering (RIXS) features of vector chiral ordered kagome antiferromagnets. Utilizing a group theoretical formalism that respects lattice site symmetry, we calculated the $L$ -edge magnon contribution for the vesignieite compound BaCu${}_3$V${}_2$O${}_8$(OH)${}_2$. We show that polarization dependence of the $L$ -edge RIXS spectrum can be used to track magnon branches. We predict a non-zero $L$ -edge signal in the non-cross $\pi -\pi$ polarization channel. At the $K$ -edge, we derived the two-site effective RIXS and Raman scattering operator for two-magnon excitation in vesignieite using the Shastry-Shraiman formalism. Our derivation considers spin-orbit coupling effects in virtual hopping processes. We find vector chiral correlation (four-spin) contribution that is proportional to the RIXS spectrum. Our scattering operator formalism can be applied to a host of non-collinear non-coplanar magnetic materials at both the $L$ and $K$ -edge. We demonstrate that vector chiral correlations can be accessed by RIXS experiments.