  The recent accessibility of high quality, charge neutral monolayer transition
metal dichalcogenides with narrow exciton linewidths at the homogeneous limit
provides an ideal platform to study excitonic many-body interactions. In
particular, the possibility to manipulate coherent exciton-exciton
interactions, which govern the ultrafast nonlinear optical response, by
applying an external magnetic field has not been considered so far. We address
this discrepancy by presenting a nonlinear microscopic theory in the coherent
limit for optical excitations in the presence of out-of-plane, in-plane, and
tilted magnetic fields. Specifically, we explore the magnetic-field-induced
exciton and biexciton fine structure and calculate their oscillator strengths
based on a Heisenberg equations of motion formalism. Our microscopic
evaluations of pump-probe spectra allow to interpret and predict coherent
signatures in future wave-mixing experiments.
