Angular momentum redistribution in laser-induced demagnetization

The ultimate fate of the spin moment in ultrafast demagnetization is to appear as a gain in momentum of the lattice. However, the route by which it occurs remains to be conclusively demonstrated. Employing state-of-the-art time-dependent density functional theory we show that spin-orbit coupling at femtosecond timescales drives a transfer of spin angular momentum into orbital angular momentum, which via the Coulomb term transfers from this orbital angular momentum instantaneously to the lattice. The rate of change of angular and spin momenta have, respectively, predominantly extrinsic (the pulse duration) and intrinsic (spin-orbit coupling) timescales. This facilitates the design of pulses to clearly disentangle the physics of angular momentum redistribution. While experiments predominantly use bulk elemental Ni, we propose Co in thin film geometry with an experimentally realizable time resolution for ultrashort pulses will allow clear observation of the ultrafast transfer of momentum via orbital degrees of freedom to the lattice.

Figure 1

Spin dynamics of $L_z$ and $S_z$ for a laser pulse of full width at half maximum (FWHM) 25 fs, central frequency 1.55 eV, and incident fluence 3.55 mJ/${\mathrm{cm}}^2$. The normalized orbital angular momentum, $L_z\left(t\right)/L_z\left(0\right)-1$, and spin angular moment, $S_z\left(t\right)/S_z\left(0\right)-1$, are shown for (a) Ni and (b) Co. The negative of the excited charge and the $A$ field of the pump pulse are also shown.

Figure 2

Dynamics of spin and angular momenta for an ultrashort pulse of full width at half maximum 5 fs. The normalized orbital angular momentum, $L_z\left(t\right)/L_z\left(0\right)-1$, and spin angular moment, $S_z\left(t\right)/S_z\left(0\right)-1$, are shown for (a) Ni and (b) Co. The $A$ field of the pump pulse and negative of the excited charge are also presented. The pump pulse has an incident fluence of 5 mJ/${\mathrm{cm}}^2$ and central frequency 1.55 eV. Note that in contrast to the longer pulse of FWHM 25 fs shown in Fig. 1, a significant change in $L_z$ and $S_z$ can be seen postpulse during which no change in the amount of excited charge is seen. This results from the continuous loss of $S_z$ into the lattice via the orbital angular angular momentum $L_z$ of the electron system.

Figure 3

Dependence of the dynamics of $L_z$ and $S_z$ angular momenta on the spin-orbit coupling (SOC) constant. Shown are the (a) the change in spin angular moment, $S_z\left(t\right)-S_z(t=0)$, and (b) the change in orbital angular momentum, $L_z\left(t\right)-L_z(t=0)$, for Co, with the $A$ field of the pump pulse also presented. Increasing the SOC results both in an increased loss of $L_z$ during the pulse, but also a subsequently larger increase after the pulse as the enhanced SOC drives increased $S_z$ transfer into $L_z$.