Strong ultrafast demagnetization due to the intraband transitions*

Laser-induced ultrafast demagnetization in ferromagnetic transition

metals has attracted extensive attentions over several decades, but

its underlying mechanism has been very puzzling.  Using experimental

laser parameters, none of the current theories is able to reproduce

the same amount of demagnetization.  This is true for both model

simulations and first-principled calculation, including the

time-dependent density functional theory and Liouville formalism.

This is partly because for a long time, since 1990s, there has been a

long misconception that in the crystal momentum space, the velocity

gauge automatically includes intraband transitions. In the meantime,

it has been claimed that the length gauge the dipole transition matrix

elements are are diagonal in the crystal momentum space and must

include an extra derivative term to include the intraband

transition. In fact, none of these two is correct.  In this talk, we

will show why they are incorrect and will propose a method to

incorporate intraband transitions within the velocity gauge through a

convective derivative in the crystal momentum space.  It turns out

that length gauge cannot be used to simulate laser-induced dynamics in

metals as it violates the Maxwell equation. 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. Our finding has a

far-reaching impact on understanding of ultrafast demagnetization, and

opens the door to all dynamical processes in superconductors and

topological insulators.