Momentum-dependent light scattering in a 2D Heisenberg antiferromagnet

Motivated by the achievements of the $X$-ray scattering technique, we analyzed the profile of the light scattering intensity $R(q, \omega)$ at a finite $q$ in a 2D Heisenberg antiferromagnet. Previous Raman scattering studies at $q=0$ identified the two-magnon peak in $B_{1g}$ scattering geometry. We found that the $B_{1g}$ peak disperses downwards at a finite $q$, and its intensity increases, reaching its maximum at $q= q_0 = (0, \pi)$ and symmetry related points. In addition, the intensity in the $A_{1g}$ geometry becomes non-zero at a finite $q$, and also displays a two-magnon peak which gains strength and disperses to larger frequencies with increasing $q$, and reaches its highest intensity at $q_0$. We found that the profile of $R(q_0, \omega)$ is equivalent in $A_{1g}$ and $B_{1g}$ geometries.