Discovery of magnon self-interaction in a strongly driven antiferromagnet

Nonlinear dynamics govern a wide array of natural phenomena and are essential for understanding nonequilibrium behaviors in condensed matter systems. In magnetically ordered materials, magnons - the quanta of spin waves - exhibit intrinsic nonlinearities that are of great interest in fundamental research and practical applications. Despite progress in the nonlinear control of magnon modes in antiferromagnetic materials, the transition from perturbative to non-perturbative regimes of magnon coherences has remained elusive. Here, we explore the nonlinear dynamics of a magnon mode in an antiferromagnet using two-dimensional terahertz spectroscopy with waveguide-enhanced terahertz fields. By driving the magnon mode far from equilibrium, we demonstrate the emergence of high-order magnon coherences and delineate a distinct transition into non-perturbative magnon nonlinearities. This behavior originates from the intrinsic anharmonicity of the magnetic potential and marks a regime dominated by magnon self-interactions at large spin deflection angles. These findings provide fundamental mechanistic insights that might be exploited for ultrafast switching and other advanced magnonic applications.