Exploring Dimensional Crossover in Heisenberg Magnets using RIXS Spectroscopy

Resonant Inelastic X-ray scattering (RIXS) is a novel experimental technique to characterize the properties of magnetic materials. The goal of this research is to theoretically investigate the effect of spatial anisotropy and next-nearest neighbor interaction on the multiple peak location of the bimagnon RIXS spectrum. Utilizing a Green function approach within the Bethe-Salpeter scheme we wrote a python code to simulate the indirect RIXS spectrum. Using a spin wave theory magnetization phase diagram and the associated spatial anisotropy parameter (zeta) and next nearest neighbor interaction parameter (eta) we notice that the RIXS spectrum can develop multiple peaks. By fitting the location of the peaks we observe that a pattern emerges in how these peaks are affected by interaction. In the vast majority of the parameter space the peak of a fixed zeta with increasing eta combination shifts downward in frequency with each consecutive increase in eta. However, there are a couple of parameters where an upshift was observed. Based on our fits of the peak location we conclude that the pattern follows either a linear or non-linear dependence on eta for a fixed zeta. We also draw connections to the peak movement and dimensional crossover in quantum Heisenberg magnets.