  Irradiating ${\rm Cu}_2{\rm Mo}({\rm CN})_8\cdot 8{\rm H}_2{\rm O}$ with blue
light induces a global magnetization, whereas succeeding irradiations with red
or longer-wavelength light demagnetize this material. We solve the
time-dependent Schr\"odinger equation for an extended Hubbard model to
reproduce the photoreversible magnetism. Monitoring the photoinduced
optical-conductivity and angle-resolved-photoemission spectra, we reveal that
the magnetic round trip by way of ferromagnetism is far from a return in terms
of electronics. While visible-light-induced magnetization has never been
observed in the tungsten analog ${\rm Cu}_2{\rm W}({\rm CN})_8\cdot 5{\rm
H}_2{\rm O}$, infrared-light irradiation may magnetize this material as well.
