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Femtosecond (fs) coherent control of collective order parameters is importantfor non--equilibrium phase dynamics in correlated materials. Here we propose apossible scheme for fs control of a ferromagnetic order parameter based onnon--adiabatic optical manipulation of electron--hole ($e$--$h$)photoexcitations between spin--orbit--coupled bands that are exchange--split bymagnetic interaction with local spins. We photoexcite fs carrier spin--pulseswith controllable direction and time profile without usingcircularly--polarized light, via time--reversal symmetry--breaking bynon--perturbative interplay between spin--orbit and magnetic exchange couplingof coherent photocarriers. We manipulate photoexcited {\em fs spin--orbittorques} to control complex switching pathways of the magnetization betweenmultiple magnetic memory states. We calculate the photoinduced fs magneticanisotropy in the time domain by using density matrix equations of motionrather than the quasi--equilibrium free energy. By comparing to pump--probeexperiments, we identify a "sudden" magnetization canting induced by laserexcitation, which displays magnetic hysteresis absent in staticmagneto--optical measurements and agrees with switchings measured by Hallmagnetoresistivity. The fs magnetization canting switches direction withmagnetic state and laser frequency, which distinguishes it from nonlinearoptical and demagnetization longitudinal effects. By shaping two--colorlaser--pulse sequences analogous to multi--dimensional Nuclear MagneticResonance (NMR) spectroscopy, we show that sequences of clockwise orcounter--clockwise fs spin--orbit torques can enhance or suppress magneticringing and switching rotation at any desired time. We propose protocols thatcan provide controlled access to four magnetic states via consequative 90$^{o}$switchings.

Manipulating Femtosecond Spin--Orbit Torques with Laser Pulse Sequences to Control Magnetic Memory States and Ringing