  Understanding spin-lattice interactions in antiferromagnets is one of the
most fundamental issues at the core of the recently emerging and booming fields
of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear
spin-lattice coupling was discovered in an antiferromagnet which opened the
possibility to control the nonlinear coupling strength and thus showing a novel
pathway to coherently control magnon-phonon dynamics. Here, utilizing intense
narrow band terahertz (THz) pulses and tunable magnetic fields up to 7 T, we
experimentally realize the conditions of the Fermi magnon-phonon resonance in
antiferromagnetic $CoF_{2}$. These conditions imply that both the spin and the
lattice anharmonicities harvest energy transfer between the subsystems, if the
magnon eigenfrequency $f_{m}$ is twice lower than the frequency of the phonon
$2f_{m}=f_{ph}$. Performing THz pump-infrared probe spectroscopy in conjunction
with simulations, we explore the coupled magnon-phonon dynamics in the vicinity
of the Fermi-resonance and reveal the corresponding fingerprints of an
impulsive THz-induced response. This study focuses on the role of nonlinearity
in spin-lattice interactions, providing insights into the control of coherent
magnon-phonon energy exchange.
