  Demagnetization in ferromagnetic transition metals driven by a femtosecond
laser pulse is a fundamental problem in solid state physics, and its
understanding is essential to the development of spintronics devices. Ab initio
calculation of time-dependent magnetic moment in the velocity gauge so far has
not been successful in reproducing the large amount of demagnetization observed
in experiments. In this work, we propose a method to incorporate intraband
transitions within the velocity gauge through a convective derivative in the
crystal momentum space. Our results for transition-element bulk crystals (bcc
Fe, hcp Co and fcc Ni) based on the time-dependent quantum Liouville equation
show a dramatic enhancement in the amount of demagnetization after the
inclusion of an intraband term, in agreement with experiments. We also find
that the effect of intraband transitions to each ferromagnetic material is
distinctly different because of their band structure and spin property
differences. Our finding has a far-reaching impact on understanding of
ultrafast demagnetization.
