Figure 2: Dynamics of spin and orbital momenta for Co and Gd in Co_0,8Gd_0.2.

(a) Time-resolved XMCD at the Co L₃ (filled red circles), Co L₂ (empty red circles), Gd M₅ (filled black circles) and Gd M₄ edges (empty black circles) measured on a 15-nm Co_0,8Gd_0.2 alloy film. The XMCD values at negative time delays match the XMCD magnitude recorded at the Co L₃, Co L₂, Gd M₅ and Gd M₄ edges during quantitative static XMCD measurements²⁷. The pump fluence used during our experiment was adjusted to 8 mJ cm⁻². (b) Ultrafast dynamics of the spin and orbital momenta −S^Co(t) (black circles) and −L^Co(t) (red circles) for Co as extracted by applying the sum rules. The values of L^Co(t) and S^Co(t) at negative delays are normalized to the static values L^Co and S^Co at thermodynamic equilibrium²⁷. The continuous lines are the simulations of S^Co(t) (black line) and L^Co(t) (blue line; see Methods) with characteristic thermalization times of τ^Co_therm=200±20 fs for both momenta. The ratio L^Co(t)/S^Co(t) (green circle) obtained as a function of the delay time shows that the orbital momentum reduces more than the spin momentum during the ultrafast demagnetization. (c) Ultrafast dynamics of the spin and orbital momenta S^Gd(t) (black circles) and L^Gd(t) (red circles) for Gd. The values at negative delays are normalized to the static values of L^Gd and S^Gd provided by the static XMCD measurements²⁷. A constant value of L^Gd(t)=0 is evidenced during the ultrafast demagnetization process. The continuous line is a simulation of S^Gd(t) (black line) with a characteristic thermalization time of τ^Gd_therm=480±40 fs. The simulations of Lⁱ(t) and Sⁱ(t) (where i stands for Co, Gd or Tb) have been obtained using a nonlinear least square fitting procedure. The extracted error bar on τⁱ_therm is the s.d., which is given as an output parameter of the fitting procedure. The error bars obtained for Lⁱ(t) and Sⁱ(t) as shown in b and c are given by the s.d. of the experimental data with respect to the fitting functions (see Methods).