Spin Flips versus Spin Transport in Nonthermal Electrons Excited by Ultrashort Optical Pulses in Transition Metals

A joint theoretical and experimental investigation is performed to understand the underlying physics of laser-induced demagnetization in Ni and Co films with varying thicknesses excited by 10 fs optical pulses. Experimentally, the dynamics of spins is studied by determining the time-dependent amplitude of the Voigt vector, retrieved from a full set of magnetic and nonmagnetic quantities performed on both sides of films, with absolute time reference. Theoretically, ab initio calculations are performed using time-dependent density functional theory. Overall, we demonstrate that spin-orbit induced spin flips are the most significant contributors with superdiffusive spin transport, which assumes only that the transport of majority spins without spin flips induced by scattering does not apply in Ni. In Co it plays a significant role during the first $\sim 20\mathrm{fs}$ only. Our study highlights the material dependent nature of the demagnetization during the process of thermalization of nonequilibrium spins.

Figure 1

Ultrafast magnetization dynamics of a 10 nm Ni film excited with 10 fs pump pulses. The sample is probed on the front face. Short delay dynamics of (a) reflectivity $R_F$ (left axis) and transmission $T_F$ (right axis). (b) Real and imaginary parts of the diagonal dielectric tensor $\epsilon 1_{xxF}$ (left axis) and $\epsilon 2_{xxF}$ (right axis). (c) Dynamics of the amplitude $Q_F$ (right axis) and phase ${\phi }_F$ (left axis) of the complex Voigt “vector.” Panels (d)–(f) show the same quantities when the charges and the spins are relaxing to the lattice. The pump energy density is $5\times {10}^{-5}{\mathrm{J}\mathrm{cm}}^{-2}$.

Figure 2

Ultrafast magnetization dynamics of Ni and Co films excited with 10 fs pulses probed on their front ($F$) and back ($B$) faces. Nonthermal regime in (a) 10 nm Ni, (b) 40 nm Ni, (d) 10 nm Co, (e) 40 nm Co samples. Panels (c) and (f) are the differences between $B$ and $F$ faces for Ni and Co samples, respectively.

Figure 3

Layer averaged majority (left axis) and minority (right axis) as a function of time (in femtoseconds). The results for Ni are shown in the left panel and for Co in the right panel. As compared to the $t=0$ case there is a decrease in the majority and an increase in the minority spins.

Figure 4

Total (a),(c) and layer resolved (b),(d) normalized magnetic moment for Ni and Co films as a function of time (in femtoseconds). The layer resolved results are calculated in two ways: (1) by time propagating the full Hamiltonian in Eq. (1) of the Supplemental Material [31] (shown in black), and (2) by setting the last term to zero in Eq. (1) of the Supplemental Material [31] (shown in blue). The layer resolved data are for a representative layer (third layer) of a seven monolayer thick film. The vertical dotted lines in panels (b) and (d) show the time at which demagnetization due to spin diffusion starts to saturate.