Spontaneous and impulsive stimulated Raman scattering from two-magnon modes in a cubic antiferromagnet

Exchange interactions govern the ordering between microscopic spins and the highest-frequency spin excitations - magnons at the edge of the Brillouin zone. As well known from spontaneous Raman scattering (RS) experiments in antiferromagnets, such magnons couple to light in the form of two-magnon modes - pairs of magnon with opposite wavevectors. Experimental works on two-magnon modes driven by exchange perturbation in impulsive stimulated Raman scattering (ISRS) experiment posed a question about consistency between spin dynamics measured in the ISRS and RS experiments. Here, based on an extended spin correlation pseudovector formalism, we derive the analytical expression for observables in both types of experiments to determine a possibly fundamental differences between the detected two-magnon spectra. We find that in both cases the magnons from the edge of the Brillouin zone give the largest contribution to the measured spectra. However, there is the difference in the spectra which stems from the fact that RS probes population of a continuum of incoherent modes, while in the case of impulsively driven modes, they are coherent and their phase and amplitudes are detected. We show that for the continuum of modes, the sensitivity to the phase results in a relative shift of the main peaks in the two spectra, and the spectrum of the ISRS is significantly broadened and extends to the range above the maximum two-magnon mode frequency. Formally, this is manifested in the fact, that the RS is described by an imaginary part of the Green function only, while the ISRS is described by the absolute value and hence additionally carries information about the real part of the Green function. We further derive two-magnon Raman tensor dispersion and the weighting factors, which define the features of the coupling to light of the modes from the different domains in the Brillouin zone.