  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.
