Molecular magnetic X-ray scattering with ultrashort X-ray free-electron lasers: from spin-orbit dynamics to Berry phase detection.

The emergence of X-ray free-electron lasers (XFELs) with attosecond capabilities has opened unprecedented opportunities for probing ultrafast spin dynamics in molecules. Magnetic X-ray scattering (MXS), while well-established in condensed matter physics, remains nascent for isolated molecules. Here we review the theoretical framework and computational methodology for molecular MXS on femtosecond and attosecond timescales. Using circular dichroism to separate spin-dependent contributions from dominant charge scattering, MXS enables direct probing of spin-dependent dynamics during ultrafast processes. We demonstrate these capabilities through three paradigmatic examples: femtosecond spin-orbit beating in NO molecules, sub-femtosecond singlet-triplet oscillations in core-excited TiCl4, and Berry phase detection during CH2OH photodissociation. We connect this molecular framework to established condensed-matter magnetic X-ray techniques and compare with the recent proposal of time-resolved XMCD for molecular photodynamics. Together, these theoretical and computational developments position molecular MXS as a powerful tool for understanding spin-resolved electron dynamics inaccessible by other ultrafast techniques.