Reply to “Comment on ‘Ultrafast Demagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronic and Magnetic Contributions’ ”

In the following, we show that the conclusions of our article titled “Ultrafast Demagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronic and Magnetic Contributions” are correct. The Comment of Vodungbo et al. argues that a unique determination of the refractive index variation over time is not possible using the data set presented in our paper. Furthermore, it was suggested that the lack of uniqueness allows for the possibility of a very specific time-dependent trajectory of the refractive index in the complex plane that could give rise to a large nonmagnetic modulation of the measured asymmetry, in spite of a negligible change in the $s$-polarized reflectivity. In this Reply, we conclusively show that any nonmagnetic contribution to the measured asymmetry is indeed negligible ($<2\%$), below the noise level of the magnetic-asymmetry measurements. First, we use a few additional measurements to unambiguously rule out the presence of any nonmagnetic contributions to the signal. Second, we show that the scenario proposed by Vodungbo et al. would require both exotic time and energy dependences of the refractive index near the $M$ edge that are extremely unlikely (virtually impossible) in real materials. Thus, the conclusions of our original article are preserved.

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Figure 1

(a) Isoreflectivity contours of the complex refractive index for $R^S(\delta ,\beta )=R^S{}_0$ at two angles of incidence of 41° and 45°, for comparison with Fig. 1(a) in the Comment by Vodungbo et al. (b) Calculated asymmetry parameter for 41° and 45°, subject to the same isoreflectivity constraint, in the semi-infinite limit. (c) Same as (b), but calculated with a conventional, self-consistent multilayer-reflectivity model, for both a thick (1000 nm) and thin film (10 nm) of Ni on 3-nm Ta. Movement of $n$ away from point $O$, if restricted to the contours in (a), results in very different asymmetries for different angles of incidence. Experimentally, however, we do not observe any such dependence of the measured transient asymmetry on the incident angle (see Fig. 2).

Figure 2

(a) Demagnetization dynamics measured at a 41° angle of incidence for three different pump fluences. (b) Maximum demagnetization as a function of pump fluence. The red points are the original data from Ref. 2 measured at 45°, while the blue open circles are the new data measured at 41°. The deviation of the new data from the dashed red line, obtained from the original data via linear regression, is used to determine potential artifacts due to a pathological refractive index, which are found to be less than $2\%$.