Coherent THz Spin Dynamics in Antiferromagnets Beyond the Approximation of the N\'eel vector

Controlled generation of coherent spin waves with highest possible frequencies and the shortest possible wavelengths is a cornerstone of spintronics and magnonics. Here, using the Heisenberg antiferromagnet RbMF$_3$, we demonstrate that laser-induced THz spin dynamics corresponding to pairs of mutually coherent counter propagating spin waves with the wavevectors up to the edge of the Brillouin zone cannot be understood in terms of magnetization and antiferromagnetic (N\'eel) vectors, conventionally used to describe spin waves. Instead, we propose to model such spin dynamics using the spin correlation function. We derive a quantum-mechanical equation of motion for the latter and emphasize that, unlike the magnetization and antiferromagnetic vectors the spin correlations in antiferromagnets do not exhibit inertia.