  In magneto-optics the spin angular momentum $S_z$ of a sample is indirectly
probed by the rotation angle and ellipticity, which are mainly determined by
the off-diagonal susceptibility $\chi^{(1)}_{xy}$. A direct and analytic
relation between $S_z$ and $\chi^{(1)}_{xy}$ is necessary and of paramount
importance to the success of magneto-optics, but is often difficult to acquire
since quantum mechanically the relation is hidden in the sum-over-states. Here
we propose a new and simple model to establish such a much needed relation. Our
model is based on the Hookean model, but includes spin-orbit coupling. Under cw
excitation, we show that $\chi^{(1)}_{xy}(\omega)$ is indeed directly
proportional to $S_z$ for a fixed photon frequency $\omega$. Such an elegant
relation is encouraging, and we wonder whether our model can describe spin
dynamics as well. By allowing the spin to change dynamically, to our surprise,
our model predicts that an ultrafast laser pulse can induce a spin precession;
with appropriate parameters, the laser can even reverse spin from one direction
to another. This works for both the circularly and linearly polarized light.
The spin reversal window is narrow. These unexpected results closely resemble
all-optical helicity-dependent magnetic switching found in much more
complicated ferrimagnetic rare earth compounds. Therefore, we believe that our
spin-orbit coupled model may find some important applications in spin switching
processes, a hot topic in femtomagnetism.
