Abstract
Understanding of ultrafast spin dynamics is crucial for future spintronic applications. In particular, the role of nonthermal electrons needs further investigation in order to gain a fundamental understanding of photoinduced demagnetization and remagnetization on a femtosecond time scale. We experimentally demonstrate that nonthermal electrons existing in the very early phase of the photoinduced demagnetization process play a key role in governing the overall ultrafast spin dynamics behavior. We simultaneously measured the timeresolved reflectivity (TRR) and the magnetooptical Kerr effect (TRMOKE) for a Co/Pt multilayer film. By using an extended threetemperature model (E3TM), the quantitative analysis, including nonthermal electron energy transfer into the subsystem (thermal electron, lattice, and spin), reveals that energy flow from nonthermal electrons plays a decisive role in determining the type I and II photoinduced spin dynamics behavior. Our finding proposes a new mechanism for understanding ultrafast remagnetization dynamics.
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Introduction
The photoinduced ultrafast demagnetization behavior of ferromagnetic systems by a femtosecond laser has attracted considerable attention due to possible applications for future ultrafast spin devices and magnetic information techniques^{1,2,3}. Photoinduced spin dynamics allows us to control magnetic moments on a femtosecond time scale simply by optical pulses^{4,5}, as well as by external field or spin current^{6,7}. Since the seminal work on a Ni single layer by Beaurepaire et al.^{8}, numerous studies have investigated the underlying mechanism of ultrafast photoinduced spin dynamics^{9,10,11,12,13}. It has been generally accepted that energy from photons is transferred first into the electron subsystem within a few tens of femtoseconds and hot electrons then transfer their energies into the spin and the lattice subsystems, leading to a final equilibrium state among electron, spin, and lattice subsystems^{8,9,10}.
Ultrafast spin dynamics triggered by the femtosecond laser is inevitably associated with hot electrons^{14,15,16}. The irradiation of samples with laser pulses induces a change of the electron distribution near the Fermi energy, and further excitation could result in the temporary existence of nonthermal electrons off the thermal FermiDirac distribution^{17,18,19,20,21}, as illustrated in Fig. 1. The initial excitation of nonthermal electrons implies that they will be critically involved with energy flow in a very early phase among electron, spin, and lattice subsystems^{22,23}. Although the ultrafast behavior of the nonthermal electrons in normal metals^{18,20,24} and gapped materials^{25,26} has been explored, little is known about the nonthermal electron behavior in ferromagnetic materials^{23,27,28}. Moreover, recent reports indicate that the hot electrons can not only contribute to demagnetization but also enhance magnetization on an ultrafast timescale^{29}, implying that the understanding and control of nonthermal electron dynamics could be crucial in future ultrafast spin applications.
Here, we have investigated the effect of nonthermal electrons in the early phase of the dynamics and demonstrated that (1) the thermalization of nonthermal electrons is slowed down as pump fluence increases and (2) the energy flow among electrons, spins, and lattices, including nonthermal electrons, naturally explains type I and II remagnetization dynamics. We systematically and simultaneously measured both the timeresolved reflectivity (TRR) and the timeresolved magnetooptical Kerr effect (TRMOKE) for Co/Pt multilayer films. Then the extended threetemperature model (E3TM) was used for analysis. The analysis clearly shows that the MOKE signal is rather insensitive to the thermalization of nonthermal electrons, which confirms the necessity of simultaneous measurement ofthe reflectivity.
Results
TRR and TRMOKE were measured for [Co (6.2 Å)/Pt (7.7 Å)]_{5} multilayer film for pump fluences F_{P}: 1.7 ≤ F_{P} ≤ 29.0 mJ cm^{−2}. An external magnetic field of 1.7 kOe was applied normal to the film surface. The coercivity and saturation field determined by static magnetic hysteresis were 0.94 and 1.58 kOe, respectively. The change of measured reflectivities (ΔR) was normalized by their peak values for a given laser fluence, as seen in Fig. 2. At lower fluences (Fig. 2(a)), the photoinduced ΔR depends on F_{P} such that the reflectivity rapidly decreases, reaching the minimum on a subps time scale, and then is recovered afterward. It is interesting to note that at higher fluences (Fig. 2(b)), ΔR does not exhibit the same simple behavior, as in the case of lower fluences. For example, in the case of F_{P} = 13.2 mJ cm^{−2}, the reflectivity reaches the maximum at t = ~300 fs, but decreases to the minimum at t = ~900 fs, and then relaxes on a longer timescale. The initial abrupt increase of ΔR could be a typical signature of the nonthermal electron excitation, as observed for other noble metals^{18,30}. Another possible origin for the nontrivial TRR trend is a strain effect triggered by laser pulse^{31,32}, whereas a timescale of the acoustic wave generated by the laser pulse is on a sub or few tens of picoseconds, which is much longer than the time window (2 ps) in the present study. In supplementary information Note S3, we have discussed coherent phonon oscillation, where the coherent phonon oscillation periods are about 5–10 ps. Therefore, we consider that the nontrivial TRR behavior is still due to the nonthermal electron excitation above the Fermi energy without being involved with any specific gap structure or strain effect.
The TRMOKE signal, also normalized by the maximum demagnetization signal, is plotted in Fig. 2(c) (F_{P} ≤ 9.9 mJ cm^{−2}) and 2(d) (F_{P} ≥ 13.2 mJ cm^{−2}). In the case of low F_{P} (Fig. 2(c)), demagnetization is followed by subsequent remagnetization, where the characteristic remagnetization time gets longer as F_{P} increases, which is conventionally categorized as type I remagnetization dynamics^{10,14}. For higher F_{P} (Fig. 2(d)), the characteristic remagnetization time becomes indefinitely long, indicating the transition to type II remagnetization dynamics. Once F_{P} becomes greater than a threshold value of F_{P} (13.2 mJ cm^{−2}), the normalized TRMOKE curves are found to fall into the universal one regardless of fluences.
Discussion
To better understand the dynamics and associated energy flows between electrons, spins, and lattices, we initially used the conventional 3temperature model (3TM), not considering nonthermal electrons. We failed to fit both TRR and TRMOKE experimental data (Supplementary information Note S1 for a more detailed discussion). We then adopted an extended 3TM (E3TM) that considers nonthermal electrons^{22,23}. Four coupled differential equations of E3TM are written as
N is the optically pumped, nonthermal electron energy density, and p[t] is a pump laser source with a Gaussian temporal profile. p_{e}[t], p_{l}[t], and p_{s}[t] represent the energy flows from nonthermal electrons to thermal electrons, lattices, and spin system, respectively, which are defined as in Eq. (2)^{18}. C_{e}, C_{l,} and C_{s} are the specific heats of the electron, lattice, and spin, respectively. T_{e}, T_{l}, and T_{s} are the electron, lattice, and spin temperatures, respectively. G_{el}, G_{es}, and G_{ls} are energy exchange coefficients representing the electronlattice, electronspin, and latticespin channel, respectively. G_{ee} is an energy exchange coefficient between nonthermal and thermal electrons. The K_{l} term describes the thermal diffusion of energy via the lattice, which is modeled to be proportional to the third power of the temperature increase of the lattice system^{12,33}.
It turns out that the reflectivity in the early phase depends sensitively on G_{ee}, as shown in Fig. 3. At both low and high fluences, TRMOKE fitting is not much affected by G_{ee} (Fig. 3(a,c)), while TRR fitting is quite sensitive to G_{ee} (Fig. 3(b,d)). This clearly reveals the critical role of nonthermal electrons and their interactions with thermal electrons and demonstrates that the simultaneous measurement of R and MOKE is crucial in the analysis of energy flow.
The examples of E3TM fitting are plotted in Fig. 4. In Fig. 4(a), wellfitted TRMOKE data are plotted for F_{P} = 1.7, 6.6, 13.2, and 23.1 mJ cm^{−2}. TRR data are also well fitted, as depicted in Fig. 4(b). The contribution to the reflectivity from nonthermal electrons, thermal electrons, and lattice is extracted (Supplementary information Note S1) and plotted in Fig. 4(b). The contribution from thermal electrons (green) exhibits a sharp decrease on a subps time scale, followed by a relatively slow recovery. The subsequent recovery dynamics of thermal electrons are sensitively dependent on F_{P} and the reflectivity dip is delayed, which is a direct consequence of heating, particularly in the case of higher F_{P}.
Very interestingly, there seems to be a nonnegligible contribution from nonthermal electrons (black) for all cases of F_{P}. Even for lower pump fluences such as F_{P} = 1.7 mJ cm^{−2}, the nonthermal electrons contribute, although weak. For higher fluence cases such as F_{P} = 13.2 mJ cm^{−2}, the contribution from nonthermal electrons becomes comparable to that from thermal electrons. The contribution from nonthermal electrons exists only in the early phase and rapidly vanishes within ~2 ps under higher fluences. The degree of the nonthermal electron contribution is high, and the decaying time is extended. With lower fluences, the overall reflectivity behavior is mostly determined by thermal electrons (green) and lattice (blue). Positive lattice contribution with much longer recovery time and negative thermal electron contribution with much shorter recovery time are summed, leading to a typical TRR behavior of rapid decrease, reaching a minimum, and then subsequent recovery.
On the other hand, with higher fluences, the contribution from nonthermal electrons (black) becomes nonnegligible, particularly in the early phase (t < 1 ps), leading to a complex TRR behavior as observed in Fig. 2(b). Additional contribution from the nonthermal electrons in the early phase fits the observed nontrivial TRR behavior very well, as demonstrated in Fig. 4(b).
In Fig. 4(c), the temperatures, T_{s} (red), T_{e} (green), and T_{l} (blue), together with nonthermal electron energy density N (black), are plotted for various F_{P}. For low F_{P} (1.7 mJ cm^{−2}), T_{s} and T_{e} exhibit a typical behavior during photoinduced demagnetization^{8,9,10}, where T_{s} and T_{e} are almost identical to each other; hence, a simplified 2temperature model could be valid. However, as F_{P} increases, the nonthermal electrons influence the temperatures of the other subsystems. In the case of F_{P} = 6.6 mJ cm^{−2}, T_{e} is only slightly higher than T_{s}, whereas for F_{P} = 13.2 mJ cm^{−2}, T_{e} and T_{s} differ substantially, with T_{s} arising slightly faster than T_{e}, although the maximum temperature of T_{e} is still higher than that of T_{s}. The quicker increase of T_{s} in the early phase is directly linked to the role of nonthermal electrons since nonthermal electrons take the photon energy first and then redistribute the energy to thermal electrons, spin, and lattice subsystems, as in Eq. (1). Therefore, the observed behavior of T_{e} and T_{s} implies that G_{ee} significantly changes under high fluences. In the case of F_{P} = 23.1 mJ cm^{−2}, the temperature discrepancy between T_{e} and T_{s} becomes even bigger due to the more considerable influence of the nonthermal electrons. Within 1 ps, nonthermal electrons absorb most of the photon energy and distribute it into spin, thermal electrons, and lattice. It should be noted that T_{s} increases faster than T_{e}, implying further modification of the energy exchange coefficients. At higher fluences (13.2 and 23.1 mJ cm^{−2}), T_{s} rapidly approaches T_{C} (1131 K) and exhibits a very slow decrease afterward, where the rapid increase of T_{s} is dominated by the transferred energy from the nonthermal electrons. The maximum T_{s} is less than T_{C} in all the cases, and hence, the application of E3TM remains valid. As seen in Fig. 4(a), at the fluence of 23.1 mJ cm^{−2}, the TRMOKE experiment data indicate the maximum demagnetization of 76%, which reveals the continued presence of significant magnetic ordering even at this high fluence, which seems to be consistent with the consideration that the nonthermal electrons take more energy as F_{P} increases so that the spin system does not become fully demagnetized. While T_{s} approaches T_{C}, thermal electrons and lattice still receive energy from nonthermal electrons and the excessive energy in thermal electrons and lattice continues to interact with the spin subsystem, which could effectively lead to the slow recovery of the spin system.
These fitting results reveal how the energy exchange coefficients between subsystems change. Figure 5(a) shows the change of G_{ee}, G_{el,} and G_{es} with respect to the fluences. G_{es} in all the cases is in the order of about 10^{16} W (m^{3}K)^{−1}, substantially less than G_{el}, which is in the order of 10^{18} W (m^{3}K)^{−1} for all fluences; on the other hand, G_{ee} exhibits the significant variation. For F_{P} = 1.7 mJ cm^{−2}, G_{ee} ~ 2 × 10^{20} W (m^{3}K)^{−1}, which is the largest among all the energy exchange coefficients. G_{ee} remains dominant in low F_{P} cases (F_{P} < 9.9 mJ cm^{−2}). The larger G_{ee} should lead to the faster relaxation of energy from nonthermal electrons to thermal ones. However, at lower fluences, the nonthermal electron density is substantially low, as seen in Fig. 4(c); hence, the contribution of nonthermal electrons is negligible. G_{ee} significantly decreases as F_{P} increases and becomes comparable to G_{el} for F_{P} = 13.2 and 16.5 mJ cm^{−2}, and even smaller than G_{el} for F_{P} = 23.1 and 29.0 mJ cm^{−2}. Along with the reduction of G_{ee}, the effective nonthermal electron density dramatically increases, as shown in Fig. 4(c); hence, the nonthermal electrons play a significant role in the overall spin dynamics. It should be mentioned that the total effective energy exchange coefficients get smaller under higher fluences, leading to a longer remagnetization time, as observed in the experiment.
In Fig. 5(b), the nonthermal electron energy density (N) for various fluences is plotted with respect to time. It is clearly observed that the N becomes more abundant with higher fluences and the overall shape is elongated with time at higher fluences. In the inset figure at F_{P} = 1.7 mJ cm^{−2}, N sharply increases initially and then decreases in the very early phase. The decreasing part of N is fitted by an exponential decay (gray dotted line) to determine the characteristic decay time τ_{N}, which is then plotted with respect to F_{P} in Fig. 5(c); τ_{N} and F_{P} exhibit a clear proportionality. The increase of τ_{N} for higher fluences is consistent with the observed decrease of G_{ee} in Fig. 5(a). The inverse of τ_{N} (τ_{N}^{−1}) is also plotted in Fig. 5(a), and shows the same fluencedependent trend as observed for G_{ee}. This confirms that τ_{N} is effectively inversely proportional to G_{ee}^{18}. τ_{N} can be written as \({ < \tau }_{{\rm{N}}} > =\frac{1}{\langle {{\rm{\nu }}}^{{ee}}\rangle }=\frac{\int \Delta {\rm{f}}({\rm{E}}){{\rm{\tau }}}_{{\rm{ee}}}({\rm{E}}){\rm{dE}}}{\int \Delta {\rm{f}}({\rm{E}}){\rm{dE}}}\) averaged over the distribution function. ∆f(E) is a deviation from Fermi distribution, representing the excitation of electrons and \(\langle {{\rm{\nu }}}^{{ee}}\rangle \) the electronelectron collision rate. ∆f(E) has been typically modeled to be uniform around the Fermi energy^{18,34}. However, recently, a nonuniform excited distribution ∆f(E) has been reported for Au slabs^{35} and Au nanoparticles^{34}, where more excitation near the Fermi energy is implied. The relatively slower timescale of excited electrons near the Fermi energy might lead to a slower timescale of \({ < \tau }_{N} > \). Moreover, based on Fermi liquid theory, the electronelectron collision rate follows as^{36,37} \(\langle {{\rm{\nu }}}^{{\rm{ee}}}({\rm{T}},{\rm{\omega }})\rangle ={{{\rm{\nu }}}^{{\rm{ee}}}}_{0}({\rm{T}},{\rm{\omega }})\left[1+{\left(\frac{{\rm{\hslash }}{\rm{\omega }}}{2{\rm{\pi }}{\rm{kT}}}\right)}^{2}\right]\), where \({{{\rm{\nu }}}^{{\rm{ee}}}}_{0}({\rm{T}},{\rm{\omega }})\) is the corresponding classical collision frequency proportional to T^{2}. In the cases where the 2^{nd} term can be neglected, \(\langle {{\rm{\nu }}}^{{ee}}\rangle \) is proportional to T ^{2}. In our case, the pump photon energy of 1.5 eV is significantly larger than kT so that \({\left(\frac{{\rm{\hslash }}{\rm{\omega }}}{2{\rm{\pi }}{\rm{kT}}}\right)}^{2}\) ≫ 1 and \(\langle {{\rm{\nu }}}^{{ee}}\rangle \) is more or less constant implying that the thermalization of nonthermal electron decay time might take longer. Very recently, B. K. Nayak et al. has reported the experimental observation of a slower thermalization with increasing pump fluence^{38}, similar to our observation. On the other hand, in plasma physics, where hot electrons move freely, the electronelectron collision has been well known to behave as T^{−3/2}, which has been called as Spitzer resistivity^{39}. The hot electrons in the conduction band of metal have a similarity to those in hightemperature plasma in a sense that they are free to move around but yet are different in a sense that the density is much higher and so electronelectron correlation effect might be larger. Hence, the hot electrons in the conduction band of metal may show the same trend as in hightemperature plasma but with different scaling, as shown in Ref. ^{38}.
In Fig. 5(d) to 5(f), the energy flow of p_{e}[t], p_{l}[t], p_{s}[t], and the laser energy profile p[t] are plotted. With the increase of F_{P}, p_{e}[t] and p_{l}[t] become smaller and broader compared to p[t]. The inset shows that with the increase of F_{P}, p_{s}[t] increases, gets sharper, and develops a tail unlike p_{e}[t] and p_{l}[t]. The peak position of p_{s}[t] is around t ~300 fs, which coincides with the temporal moment of the maximal demagnetization time regardless of the fluences in the TRMOKE data (Fig. 2(c,d)). Further details of p_{s}[t] are described in Supplementary information Note S2^{40}. An interesting development of the tail in p_{s}[t], lasting up to 2 ps in the case of high fluences, originates from the broadening nonthermal electron energy density N since p_{s}[t] is proportional to the product of N and G_{es}, as shown in Fig. S3 of Supplementary information Note S2.
Such an analysis of energy flow reveals, the energetics of type I and II remagnetization dynamics in detail. In Fig. 6, the energy terms of the spin subsystem in the 4^{th} equation of Eq. (1) are plotted for the early phase of ultrafast photoinduced demagnetization in Fig. 6. As discussed in Fig. 2, the type I (Fig. 2(a)) and type II (Fig. 2(b)) remagnetization dynamics are categorized based on the TRMOKE behavior. In the case of the low fluence (1.7 mJ cm^{−2}), \({C}_{s}\frac{d{T}_{s}}{{dt}}\) (net energy of the spin subsystem) shows a sharp increase boosted by p_{s}[t] (the energy flow from nonthermal electrons), and \(\sum _{i=e,l}{G}_{is}({T}_{s}{T}_{i})\) (the sum of interaction energy flows involved with other subsystems). However, later, \({C}_{s}\frac{d{T}_{s}}{{dt}}\) becomes negative, due to the change of the sign of \(\sum _{i=e,l}{G}_{is}({T}_{s}{T}_{i})\), letting the net energy flow out of the spin subsystem. The resulting rapid cooling of the spin by the net flow out of the spin system corresponds to the observed rapid recovery of the TRMOKE signal, resulting in the type I behavior. A similar trend occurs at F_{P} = 6.6 mJ cm^{−2}. The negative \(\sum _{i=e,l}{G}_{is}({T}_{s}{T}_{i})\) contribution implies that the energy flows from the spin subsystem to other subsystems after all. The same behavior is observed for the case of F_{P} = 6.6 mJ cm^{−2}. As seen in the T_{s} profile in Fig. 4(c), the spin subsystem is excited fast in the early phase due to its much lower heat capacity than that of the thermal electrons and lattice, so that the net energy can flow into other subsystems (the negative value of \(\sum _{i=e,l}{G}_{is}({T}_{s}{T}_{i})\), as seen in Fig. 6(a)). The fact that \({C}_{s}\frac{d{T}_{s}}{{dt}}\) becomes negative indicates the fast recovery of the spin subsystem (type I remagnetization dynamics).
On the other hand, at higher fluences of 13.1 and 23.1 mJ cm^{−2} (Fig. 6(b)), \(\sum _{i=e,l}{G}_{is}({T}_{s}{T}_{i})\) contribution remains negative; however, p_{s}[t] is strong and has a positive tail, which can cancel out so that \({C}_{s}\frac{d{T}_{s}}{{dt}}\) remains nearly zero through the later stage of the ultrafast remagnetization process, leading to the slow remagnetization behavior (type II remagnetization dynamics). These results demonstrate that nonthermal electrons play a significant role in determining the overall ultrafast spin dynamics, particularly in determining the type of remagnetization dynamics (type I or II). With respect to the cause of different remagnetization dynamics, although a few mechanisms involved with ElliotYafet scattering^{10,41,42,43} and spin current^{6,7,11,44} have been discussed. Very recently, a quantitative study and comparison between fluencedependent experiments and a model that includes nonequilibrium effects microscopically has been reported^{45}. This investigation revealed that the nonthermal electron contribution could be another critical mechanism in understanding ultrafast photoinduced spin dynamics.
Lastly, a strain wave effect is considered in a more systematic way. Although the timescale of the acoustic phonon oscillation is found to be about 5 –10 ps, as described in the Results and Supplementary Information (S3), there might still be a possibility to have a strain wave with modifying the observed TRReflectivity and TRMOKE signal. If any, strain waves will be launched from the surface, respectively from the interface to the substrate with the maximum strength of the strain when the acoustic waves meet in the middle. We have carried out a more careful analysis to exclude the transient strain by carrying out thicknessdependent experiments. We have varied repeat number n of [Co/Pt]_{n} multilayer (n = 5, 7, and 9) so that the total thickness is varied from 8.5 to 15.3 nm. Timeresolved nonthermal electron density (N) at various fluences is plotted for 3 thickness cases. In Fig. 7(a), at the fluence of 3.5 mJ cm^{−2}, N increases as the total thickness increases, since more photon energy is absorbed for thicker samples. The same is observed at the fluence of 13.7 mJ cm^{−2} as in Fig. 7(b). For the thickest sample (n = 9), increases with respect to the fluence, similar to the case of n = 5, as in Fig. 7(c). It should be noted that the timescale of τ_{N} remains almost the same regardless of the total film thickness at each fluence (Fig. 7(d)), indicating that the strain wave effect can be neglected in our analysis.
Conclusion
In summary, we have systematically investigated the role of nonthermal electrons in ultrafast photoinduced demagnetization/remagnetization dynamics for a Co/Pt multilayer films and demonstrated that nonthermal electrons play a crucial role in understanding type I and II remagnetization dynamics. Using E3TM, which also considers the contribution from nonthermal electrons in addition to thermal electrons spin and lattice, the excellent fittings to the experimental TRMOKE and TRR data reveal the full details of energy transfers involved among subsystems. In competition with other energy exchange channels, the energy exchange channel of nonthermal electrons, which have been so far neglected, play a crucial role, particularly in the case of high pump fluences. Our findings support a new possible mechanism for explaining the ultrafast spin dynamics behavior.
Method
Timeresolved MOKE/reflectivity measurement
TRMOKE and reflectivity measurements with a pumpprobe stroboscope were performed on a Co/Pt multilayer. The pump pulses were generated by a Ti: sapphire multipass amplifier operating at a repetition rate of 3 kHz with a center wavelength of 780 nm and a pulse duration of 25 fs. The probe pulses with the same wavelength were generated by a beam splitter. Another beam splitter was placed in the probe beam path, before it was reflected from the sample, to obtain the reference beam and probe pulses for TRR measurements. Our experimental setup is a polar TRMOKE setup. The pump beam was focused on the sample along the normal direction (zaxis). The angle between the pump and probe beam was set to 35°. The sample plane is xyplane, the optical plane is zxplane, and the magnetization direction is along the zaxis. The incident pump fluence (F_{P}) was varied from 1.7 to 28.5 mJ cm^{−2} at a fixed probe fluence of 0.3 mJ cm^{−2}. A mechanical delay line was implemented in the pumpbeam line. A Wollaston polarizer was positioned in front of the two photodiodes to split out the s and ppolarization components. The resulting measurement generates a difference between the s and ppolarization components of the probe pulses, as modified by the TRMOKE at the reflection off a film surface. For the TRMOKE measurements, the pump beam was modulated using a mechanical chopper at 500 Hz. An external magnetic field of 1.7 kOe normal to the sample was applied throughout the measurements to keep the initial sample condition saturated before the subsequent pump pulse.
Samples
[Co(6.2 Å)/Pt(7.7 Å)]_{5} multilayer films were deposited by dc magnetron sputtering on Si substrates, then capped by a 22Å Pt layer to prevent surface oxidation. The structure of the Co/Pt multilayer films with welldefined interfaces was confirmed by a low angle Xray diffraction and extended Xray absorption fine structure analysis. The films exhibited perpendicular magnetic anisotropy (K = 0.63 MJ m^{−3}), and saturation magnetization (M_{s} = 1.04 × 10^{3} kA m^{−1}), which were measured by the ElectroMagnetic Property Measurement System developed in the Korea Basic Science Institute and were confirmed to be similar to literature values^{46,47,48}.
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Acknowledgements
This research has been supported in part by the Max Planck POSTECH/KOREA Research Initiative Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT[Grant No 2016K1A4A4A01922028]. The Basic Science Research Program supported this research through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [Grant No. 2017R1A6A3A04011173]. This study was supported by the Korea Research Foundation (NRF) grant No. 2018R1A2B3009569 and a KBSI Grant D39614.
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J.H.S., A.A.S., J.I.K., H.G.P., S.H.L., S.Y.P., and Y.S.C. collected data and performed all the analyses; K.M.L., H.J.K., J.R.J., and J.I.H. fabricated the samples; D.E.K. and D.H.K. were involved in study design. All authors discussed the results and commented on the manuscript.
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Shim, JH., Syed, A.A., Kim, JI. et al. Role of nonthermal electrons in ultrafast spin dynamics of ferromagnetic multilayer. Sci Rep 10, 6355 (2020). https://doi.org/10.1038/s41598020634523
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DOI: https://doi.org/10.1038/s41598020634523
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