  Nonlinear interactions of spin-waves and their quanta, magnons, have emerged
as prominent candidates for interference-based technology, ranging from quantum
transduction to antiferromagnetic spintronics. Yet magnon multiplication in the
terahertz (THz) spectral region represents a major challenge. Intense, resonant
magnetic fields from THz pulse-pairs with controllable phases and amplitudes
enable high order THz magnon multiplication, distinct from non-resonant
nonlinearities such as the high harmonic generation by below-band gap electric
fields. Here, we demonstrate exceptionally high-order THz nonlinear magnonics.
It manifests as 7$^\text{th}$-order spin-wave-mixing and 6$^\text{th}$ harmonic
magnon generation in an antiferromagnetic orthoferrite. We use THz
multi-dimensional coherent spectroscopy to achieve high-sensitivity detection
of nonlinear magnon interactions up to six-magnon quanta in strongly-driven
many-magnon correlated states. The high-order magnon multiplication, supported
by classical and quantum spin simulations, elucidates the significance of
four-fold magnetic anisotropy and Dzyaloshinskii-Moriya symmetry breaking.
Moreover, our results shed light on the potential quantum fluctuation
properties inherent in nonlinear magnons.
