  High intensity THz lasers allow for the coherent excitation of individual
phonon modes. The ultrafast control of emergent magnetism by means of phonons
opens up new tuning mechanisms for functional materials. While theoretically
predicted phonon magnetic moments are tiny, recent experiments hint towards a
significant magnetization in various materials. To explain these phenomena, we
derive a coupling mechanism between the phonon angular momentum and the
electron spin. This coupling introduces the transient level-splitting of
spin-up and spin-down channels and a resulting magnetization. We estimate this
magnetization on the example of the lowest infrared active mode in the
perovskite KTaO$_3$. Our results show an electronic magnetic moment of $\approx
10^{-1}$ $\mu_B$ per unit cell, depending on the doping level and electron
temperature.
