  Rectification describes the generation of a quasistatic component from an
oscillating field, such as an electric polarization in optical rectification,
or a structural distortion in nonlinear phononic rectification. Here, we
present a third fundamental process for magnetization, in which spin precession
is rectified along the coordinates of a nonlinearly driven magnon mode in an
antiferromagnet. We demonstrate theoretically that a quasistatic magnetization
can be induced by transient spin canting in response to the coherent excitation
of a chiral phonon mode that produces an effective magnetic field for the
spins. This mechanism, which we call nonlinear magnonic rectification, is
generally applicable to magnetic systems that exhibit infrared-active chiral
phonon modes. Our results serve as an example of light-induced weak
ferromagnetism and open a promising avenue towards creating dynamical spin
configurations that are not accessible in equilibrium.
