Abstract
The exchange stiffness coefficient, A_{ex}, represents the strength of direct exchange interactions among neighboring spins. A_{ex} is linked to most of the magnetic properties such as skyrmion formation, magnetic vortex, magnetic domain wall width, and exchange length. Hence, the quantification of A_{ex} is essential to understanding fundamental magnetic properties, but little is known for the dynamics of A_{ex} on a subpicosecond timescale. We report the ultrafast dynamcis of A_{ex} in an ordered magnetic state in Co/Pt ferromagnetic multilayer. Timeresolved magnetooptical Kerr effect and reflectivity measurements were analyzed for various pump fluences. We reveal that the significant dynamical reduction of A_{ex} is responsible for the dramatic increase of remagnetization time for high fluences. The analysis shows that A_{ex} dynamically varies, strongly affecting overall ultrafast demagnetization/remagnetization process. The investigation demonstrates the possibility of A_{ex} engineering in femtosecond timescale and thereby provides a way to design ultrafast spintronic devices.
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Introduction
The exchange interaction is a fundamental aspect of ferromagnetism^{1,2,3}; this interaction, underpinning the existence of ordered magnetic states, allows the alignment of neighboring spins in a system. The origin of the direct exchange interaction is ascribed to the overlapping of electron wave functions among neighboring atoms with no classical analogy, and its strength depends sensitively on the atomic and lattice structure^{4,5}, while there also exist other exchange mechanisms such as DzyaloshinskiiMoriya interaction^{6,7}, and superexchange interaction^{8}. The strength of the direct exchange interaction is represented by the exchangestiffness coefficient A_{ex}, which is a material parameter mostly depending on the atomic and lattice structure and detailed characteristics of which are determined by the electronic band structure^{9,10,11}. Fundamental mechanisms of novel spin phenomena, such as magnetic vortices^{12,13} and skyrmions^{14,15}, might be understood based on a quantitative analysis of A_{ex}. It has been known that A_{ex} is temperaturedependent^{16,17}. As the temperature increases, thermal agitation reduces the degree of the ordering of neighboring spins, effectively lowering the value of A_{ex}.
Although the temperaturedependence of A_{ex} is relatively well recognized in static cases^{17}, very little is known regarding how A_{ex} varies on an in the ultrafast timescale. In case of ultrafast photoinduced demagnetization, as the fluence F_{P} of a pump laser increases, the disorder in a spin system should increase so that the effective spin temperature should also increase. It is then expected that the remagnetization time of the system from an excited disordered state to a stable equilibrium state should increase as F_{P} increases. Recent reports of the dynamics of the exchange interaction on ultrafast timescale have shown that a fundamental exchange interaction varies on scales of several tens of femtoseconds in ferromagnetic NiFe alloy^{18} and antiferromagnetic KNiF_{3}^{19}. A possibility of ultrafast control of exchange interaction by using a femtosecond pump laser has been proposed theoretically^{20,21,22}. All of these results indicate that the exchange interaction or exchange splitting dramatically changes by a femtosecond pump laser. However, to our best knowledge, no systematic study has been conducted to quantify the dynamics of A_{ex} on ultrafast timescale.
Here, we report, the dynamics of A_{ex} on a femtosecond timescale in Co/Pt multilayers for a range of F_{P}, demonstrating that A_{ex} varies rapidly, affecting spin dynamics and its variation can be controlled by the pump fluence. While the electronspin interaction strength is kept constant all the time in the conventional threetemperature model (3TM) in the study of ultrafast magnetism, the dynamic change of A_{ex} is considered, adopting the generalized threetemperature model (G3TM) developed by A. Manchon et al^{23}.
Results
Fluence dependent remagnetization time
We performed timeresolved magnetooptical Kerr effect (TRMOKE) measurements for [Co (6.2 Å)/Pt (7.7 Å)]_{5} multilayer film, of which the magnetic properties such as perpendicular magnetic anisotropy and saturation magnetization are well known^{7,24,25,26,27}. A detailed experimental configuration was reported elsewhere^{28}. TRMOKE signals were measured for 1.7 ≤ F_{P} ≤ 28.5 mJ cm^{−2} for time delays of up to 30 ps. To exclude the dichroic bleaching effect, the experiments are carried out by pump beam at both 400 and 800 nm wavelength (λ_{pump}). TRMOKE vs. time at different fluences is plotted in Fig. 1a for the case of λ_{pump} = 800 nm, while no significant difference is observed in the overall trend for the case of λ_{pump} = 400 nm. The signals were normalized by their maximum changes to compare the dynamical behaviors in remagnetization for different conditions. An external magnetic field of 1.7 kOe was applied normally to the film surface. All the measured curves exhibit clearly the dynamics of photoinduced demagnetization and subsequent remagnetization. The maximal change of demagnetization is observed around t = 0.3 ps for all the fluence cases. In case of λ_{pump} = 800 nm, as F_{P} was increased from 1.7 to 28.5 mJ cm^{−2}, the remagnetization was slowed down for F_{P} > 9.9 mJ cm^{−2}. The remagnetization behavior at 1.7 ≤ F_{P} ≤ 16.5 mJ cm^{−2} wellfitted with a single exponential curve (Fig. 1a, dotted lines), yielding the characteristic time τ_{R} of remagnetization (open square in Fig. 1b). We note that τ_{R} increased drastically as F_{P} increased by only a factor of a few. Fitting with a single exponential curve was not valid for F_{P} > 16.5 mJ cm^{−2}. A similar trend is observed for the case of λ_{pump} = 400 nm, where τ_{R} is fitted with a single exponential curve as well.
G3TM analysis
For further understanding, we conducted G3TM analysis for the TRMOKE data^{23,28,29}. G3TM is composed of three coupled equations (see Supplementary Note 1 for more details):
where T_{e}, T_{l}, and T_{s} are the electron, lattice, and spin temperatures, respectively. C_{e}, C_{l,} and C_{s} are the specific heats of the electron, lattice, and spin, respectively. G_{el}, G_{es}, and G_{ls} are the electronlattice, electronspin, and latticespin interaction channels, respectively. P(t) is a laser source term with a Gaussian temporal profile. The term that contains K_{l} represents lattice thermal diffusion, which is modeled to be proportional to the third power of the temperature increase of lattice system^{30}. A typical relation between the magnetization and the spin temperature: ∝ (1 – (T_{s} / T_{C}))^{0.5}, where T_{C} is Curie temperature of 1131 K^{17}, to match the normalized TRMOKE signal (∆θ_{Kerr}/∆θ_{peak}).
In conventional 3TM, G_{el}, G_{es}, and G_{ls} have been set to be constant over time. However, in our study, for correct analysis, the electronspin interaction channel(G_{es}) was allowed to change over time. Adopting the G3TM, G_{es} can be written as
where a is a lattice constant, A_{ex0} an exchangestiffness coefficient at 0 K, V unit cell volume, T_{F} Fermi temperature, S = 3/2 spin quantum number, M magnetization and G_{2} a function based on the secondorder Debye function^{23} (Eq. (3)). T_{F} is Fermi temperature, chosen to be that of fcc Co (T_{F} = 16.87 Ry/k_{B})^{31}. D = S M[T_{s}] q_{m}^{2} a^{2}, where q_{m} is magnon wave number q_{m} = k_{F} = (6π^{2})^{1/3}a^{−1}, and k_{F} is Fermi wave number. Features of G_{e}[T_{e}, T_{s}] is described in detail in Supplementary Note 1. G_{es0} (Eq. (4)) is a temperatureindependent electronspin interaction channel. In static case, it is well known that A_{ex} \( \propto \) (J_{ex} a^{−1}) <S^{2} > , where J_{ex} is an exchange interaction constant, a is a lattice constant. The proportionality depends on material parameters such as a periodic lattice configuration. Since A_{ex} can be easily measured rather than J_{ex}, we focus on qauntifying A_{ex} on an ultrafast timescale. When the relation between A_{ex} and J_{ex} is extended, we have put A_{ex}(T) \( \propto \) A_{ex0} < M(T)^{2} > \( \propto \) (J_{ex} a^{−1}) <S(T)^{2} > , where the temperature T dependence is included in <M(T)^{2} > without affecting J_{ex}. For simplicity, we have used the approximation, J_{ex} ~ 2aA_{ex0}^{16}. In the G3TM, G_{el} is still assumed to be constant because the relaxation rate between the electron and the lattice is expected to be simply proportional to the temperature difference. G_{ls} was also set to be constant throughout the simulations.
The G3TM is composed of several free parameters, so the fitting should be processed with care. First, timeresolved reflectivity R(t) data were utilized to estimate values for C_{e}, C_{l}, and G_{el}, considering only the electron and lattice, based on the 2temperature model^{32,33}. In the full analysis using the G3TM, the reflectivity and MOKE data were fitted. As a constraint in the analysis, the measured values for the degree of demagnetization (D_{demag}) were used (Fig. 2a, d). Hysteresis loop measurement is the best way to estimate the D_{demag}. The hysteresis loops were measured at t = −2 ps and 0.3 ps (the maximal demagnetization) using the same TRMOKE setup with probebeam modulation for all the F_{P} (Methods section). An example of measurements for F_{P} = 13.2 mJ cm^{−2} (Fig. 2a, inset) shows that a D_{demag} is 70%. The excellent match has been established in all the cases (See Supplementary Note 2, where the utilization of R(t) measurement and the D_{demag} for fitting is described).
The G3TM fitting determines temporal evolutions of spin, electron, and lattice temperature at wavelength of pump pulse λ_{pump} = 800 nm (Fig. 2b, c) and λ_{pump} = 400 nm (Fig. 2e, f). The cases for very high F_{P} corresponding to T_{s} being very close to Curie temperature (1131 K) are not considered, where the G3TM may not be valid. The fitted value of C_{e} was 1.8 ~ 2.1 × 10^{3} J (m^{3} K^{2})^{−1} and, C_{l} was 1.8 ~ 5.0 × 10^{6} J (m^{3} K)^{−1} ^{34,35}. (all the fitting parameters are summarized in Supplementary Note 2). C_{s} should depend on the spin temperature T_{s}. In the original Manchon’s paper^{23} which the G3TM on, C_{s} is determined from the numerical derivative of the spin energy. In fitting our data, we have found that the fitting becomes quite good if C_{s} is smaller than ~10^{4} J (m^{3}K)^{−1} in all cases. Thus, we used a small value of C_{s} = 100 J (m^{3}K)^{−1} for all cases. The upper limit of fitted C_{s} value (~10^{4} J (m^{3}K)^{−1}) in the present work seems to be a little bit smaller than the reported values determined from 3TM. For instance, in Ref. ^{35}, C_{s} of Ni and FeCuPt are 0.2 × 10^{6} J (m^{3} K)^{−1} and 0.17 × 10^{6} J (m^{3} K)^{−1}.
The maximum values of electron temperature T_{e}^{max} and spin temperature T_{s}^{max} at t = 0.3 ps increased as F_{P} increased; e.g., T_{s}^{max} at t = 0.3 ps changes from 564 to 1040 K as F_{P} increases from 1.7 to 9.9 mJ cm^{−2} (λ_{pump} = 800 nm). High F_{P} increases the amount of energy transferred to the subsystems, so the increase of T_{e}^{max} and T_{s}^{max} is expected. The equilibrium temperature at which T_{e} = T_{l} = T_{s} also increased consistently as F_{P} increased, but it is very interesting to note that the difference between T_{e}^{max} and T_{s}^{max} got larger substantially as F_{P} increased (Fig. 2b, c, Fig. 2e, f). In the context of the G3TM, this observation indicates that the interaction channel G_{es} between the electron and spin subsystem is reduced, resulting in the increase of the thermal separation of the spin system from the electron subsystem as well as thereby the increase of the time required to reach thermal equilibrium. This phenomenon may be a reason for the increase of τ_{R} as F_{P} increases as observed in Fig. 1b.
Figure 3a is the plot of G_{es} (Eq. (4)) as a function of T_{e} and T_{s}. As T_{s} increases, G_{es} increases then decreases for a given electron temperature. The values T_{e}, T_{s}, and G_{es} determined from fitting to our experimental data at λ_{pump} = 800 nm are shown in a gray curved line in Fig. 3a, and again in Fig. 3b for various F_{P}. The case of T_{s} = T_{e} is also presented as a dotted curve for guidance in Fig. 3b. The nonmonotonic nature of G_{es} with respect to T_{s} is a direct consequence of Eq. (3). G_{es} increased monotonically with an increase in T_{s} at low F_{P} = 1.7 and 3.3 mJ cm^{−2}, but the increasingthendecreasing behavior is observed at high F_{P} > 6.6 mJ cm^{−2}. We suspect that diverse experimental results of ultrafast demagnetization dynamics might be originated from this different trend of G_{es} at high F_{P}^{36,37,38}.
The dynamical variation of G_{es} on a femtosecond timescale is plotted for various F_{P} in Fig. 3c. At low F_{P}, the simple increaseanddecrease behavior of G_{es} is observed, with a maximum at t = 0.3 ps. The time of the maximum G_{es} coincides with the time at which the D_{demag} is the greatest. At high F_{P}, G_{es} quickly reaches the first peak right after the arrival of a pump pulse, decreased to a minimum at around the time of maximal D_{demag} (t = 0.3 ps), and then increased again. A comparison between the behaviors of G_{es}, G_{ls}, and G_{el} at t = 0.3 ps under various F_{P} (Fig. 3d) reveals that G_{el} is the strongest channel, G_{es} increased at low F_{P}, but decreases at high F_{P}; this trend may be the result from the feature of G_{es} (Fig. 3a, b). On the other hand, G_{ls} is the weakest channel (as often neglected) but becomes comparable to G_{es} as F_{P} increases. G_{ls} is involved with spinorbit coupling^{23}, which might get stronger as T_{e} or D_{demag} ^{39}.
The above discussion indicates that the dynamics of the photoinduced demagnetization and remagnetization in Co/Pt spin system is mostly governed by G_{es} and G_{ls}. Figure 3e shows a ratio of G_{es} to G_{ls} at t = 0.3 ps for various fluences. G_{es}/G_{ls} is larger than 10 for F_{P} < 6.6 mJ cm^{−2} for λ_{pump} = 800 and 400 nm. This imbalance implies that the spinelectron interaction is dominant in this F_{P} regime. For F_{P} ≥ 6.6 mJ cm^{−2}, G_{es}/G_{ls} approaches unity asymptotically, indicating that spinlattice interaction becomes increasingly important. The G3TM fitting yields the values for G_{es}. Equations (2) and (4) allow us to calculate A_{ex0}, temperatureindependent exchangestiffness coefficient. The estimated value of A_{ex0} turns out to be 10.01 pJ m^{−1} at all the F_{P}; this value agrees well with a reported value for a Co/Pt multilayer^{40,41}. Other analysis methods^{42,43} could also reproduce the slow rate of magnetization at high fluences. It should be commented that the G3TM based on the Hamiltonian for laserinduced demagnetization^{23} allows us to separately monitor timedependent G_{es} and G_{ls} as well as their ratio G_{es}/G_{ls}. In this work, we note that the ratio particularly seems to play an important role in determining the energyexcessive spin dynamics on a subps timescale.
Discussion
The previous studies^{17,44,45,46} in static cases have shown that the temperature dependence of A_{ex} is expressed as power of M with a scaling exponent ranging from 1.79 to 1.82 in case of Co. We set the exponent to be 1.8 and write the temporal variance of A_{ex} as
Based on Eq. (5), timedependent A_{ex} is plotted in Fig. 4. The increase in F_{P} results in the reduction of A_{ex}, as generally expected in static cases. However, the recovery of reduced A_{ex} depends sensitively on F_{P}. A_{ex} decreases asymptotically as F_{P} increases, and saturates at F_{P} ≈ 9.9 mJ cm^{−2} (λ_{pump} = 800 nm) or 12.1 mJ cm^{−2} (λ_{pump} = 400 nm) without further decrease with respect to the fluence higher than this value, which is expected from the saturated behavior of the D_{demag} at high F_{P}. At F_{P} > 9.9 mJ cm^{−2}, A_{ex} was ~1 pJ m^{−1}. The maximal decrease of A_{ex} occurred at t = 0.3 ps when the maximum D_{demag} occurs in the TRMOKE measurement. TRMOKE data (Fig. 1a) show a similar trend to the trend in A_{ex} (Fig. 4). The magnetization M and A_{ex} recovered quickly at low F_{P} whereas the recovery becomes significantly slow for high F_{P}.
It should be noted that Eq. (5) is valid for the steadystate case and we use the very rough assumption that considering that even in the outofequilibrium case, there could be a rough relation between A_{ex} and temperaturedependent M^{9}. Indeed, although we use 3TM^{23,28,29}, 3 temperatures are not fundamentally well defined in the outofequilibrium state and only phenomenologically defined once 3TM is used. On the other hand, we consider that the M[T] might not be totally different compared to the steadystate case, since the estimated spin temperature is still below T_{C}. The pump pulse excites the electrons around the Fermi energy so that the excited electrons occupy the allowed energy levels above the Fermi energy, while remaining electrons still follow the FermiDirac distribution. Moreover, the thermal equilibrium among 3 temperatures is achieved around ~10 ps and thus, the M[T] will be soon replaced back to the equilibrium case after this timescale. Therefore, we think that there might be a deviation of M[T] from the steadystate case, but the M[T] can be roughly approximated based on the Eq. (5). We have varied the exponent value from 1.6 to 2.0 in our analysis, where no significant difference in the analysis result is observed.
Possible mechanisms of A_{ex} reduction might be involved with Stoner exchange splitting reduction^{9}, where it has been reported that dynamic exchange splitting is determined by timedependent magnetization M(t). On the other hand, magnon generation should be also an important factor^{47}, where it has been reported that the magnon contribution to demagnetization is dominant only on a very short (700 fs) timescale. Thus, in our case, we consider that the magnon contribution could exist on a subps timescale, while the Stoner exchange splitting reduction is lasting longer up to few tens of ps since there is still a substantial amount of demagnetized M(t) in the present work. It should be also noted that G3TM, which our whole analysis is based on, includes the magnon generation by hot electron as a key mechanism in the model. In G3TM, electronspin interaction Hamiltonian intrinsically deals with the effect of magnon generation, which might be reflected in the A_{ex} dynamics, particularly on the subps timescale. The effective Stoner exchange splitting reduction is understood based on the reduced M(t) over the whole process of demagnetization and remagnetization. It should be mentioned that our film is prepared on a Si substrate with no doping, which can be approximated to be an insulator so that the spin diffusion effect could be negligible in the process of demagnetization.
The above analysis reveals that the significant increase of the remagnetization time (τ_{R}) (Fig. 1b) for high fluence is directly related to the reduction of A_{ex}. In order to confirm how much A_{ex} or demagnetization state affects the remagnetization process, we have carried out another series of independent micromagnetic simulations. The micromagnetic simulation was performed using the ObjectOriented Micromagnetic Framework^{48} based on the LandauLifshitzGilbert (LLG) equation:
where the gyromagnetic ratio γ = 2.210 × 10^{5} m (A s)^{−1} and H_{eff} is the effective magnetic field. Since the micromagnetic simulation does not consider the temperature variation, it is not suitable to dynamics study but still provides valuable information about the material properties for remagnetization at a fixed temperature. We set the initial degree of magnetization according to the measurement and simulated how the remagnetization proceeds for different magnetic parameters such as A_{ex} and magnetic anisotropy. In the simulations, an external magnetic field of 1.7 kOe was applied with an angle of 0° to the surface normal of the film as in the experiments. The saturation magnetization M_{s} of the film was set as 10^{3} kA m^{−1}. Magnetic anisotropy constant K was set as 6 × 10^{5} J m^{−3}. Gilbert damping constant α was set as 0.05. The cell size was 0.5 × 0.5 × 0.5 nm^{3} and the sample size was 50 × 50 × 7.5 nm^{3}. The initial demagnetization state is set by the experimentallymeasured D_{demag} for various F_{P} (Fig. 1b is replotted with respect to D_{demag} corresponding to various F_{P} (black open squares) as shown in Fig. 5a). As the D_{demag} increases, τ_{R} increases, drastically at larger D_{demag} than 60 %. To determine parameters that are most responsible for the abrupt increase of τ_{R} with the increase of F_{P} (or high D_{demag}), we performed micromagnetic simulations for A_{ex} = 1, 8, and 15 pJ m^{−1}. In each simulation, A_{ex} was fixed throughout the simulation. Simulations with A_{ex} = 8 (Fig. 5a, green triangle) and 15 pJ m^{−1} (Fig. 5a, red circle) agree well with experiments at low F_{P} (or low D_{demag}). The literature value^{40,41} of A_{ex} of Co/Pt multilayer for a static case is ~ 10 pJ m^{−1}, which is consistent with the range of our simulation parameter. In the simulation with A_{ex} = 1 pJ m^{−1}, τ_{R} was substantially higher than the experimental observations (low D_{demag}).
Magnetic anisotropy is another important parameter that might affect τ_{R}. The magnetic anisotropy is determined mostly by the crystal structure, sample shape, and multilayer interfaces. This anisotropy produces a perpendicular magnetic anisotropy in the Co/Pt multilayer used in the present study. The micromagnetic simulation of τ_{R} for various magnetic anisotropy constants K for various D_{demag} from 47 to 80 % showed no significant change of τ_{R} at 0.01 ≤ K ≤ 1.2 MJ m^{−3} (Fig. 5b). The measured value of K for the Co/Pt multilayer in the present study is K = 0.6 MJ m^{−3}, which is within our simulation range. Thus, we infer that the variation in K is not responsible for the increase of τ_{R}. This independence is expected because the variation of K will mostly affect the total effective field without directly modifying spinspin or spinelectron interactions.
We also systematically changed A_{ex} in micromagnetic simulations with the D_{demag} being fixed at 80% (Fig. 5c). As A_{ex} was varied from 4.0 to 0.1 pJ m^{−1}, τ_{R} increased from 10.8 to 30.1 ps. In particular, at A_{ex} < 1 pJ m^{−1}, τ_{R} increases rapidly in a similar manner to the experimental observation (near high F_{P} in Fig. 1b, or near high D_{demag} in Fig. 5a). The increase in F_{P} can be expected to reduce A_{ex} significantly, resulting in a large increase of τ_{R}. The decrease in A_{ex} is generally expected to cause the increase in τ_{R}, because the reduced spinspin interaction weakens the ordering among neighboring spins. This micromagnetic simulation also confirms the analysis by G3TM.
We have carried out a simulation with the variation of damping parameter (α), as seen in Fig. 5d. A_{ex} is set to be 11 pJ m^{−1}, anisotropy constant K is 0.6 MJ m^{−3}, and D_{demag} is set to be 80%. τ_{R} is found to be insensitive if α is larger than 0.005, as seen in the figure. For α smaller than 0.005, τ_{R} drastically increases due to the significant contribution of precessional oscillation. α of Co/Pt multilayer is reported in the range of 0.02–0.1^{49,50}, which is much larger than 0.005.
In summary, we have investigated the dynamical variation of A_{ex} on an ultrafast timescale, by TRMOKE and reflectivity measurements in a Co/Pt multilayer for various F_{P}. Our phenomenological analysis suggests that the ultrafast remagnetization mechanisms may be governed by the dynamically changing A_{ex}, which is also closely related to G_{es}, and G_{ls} also becomes nonnegligible in case of high F_{P}. Our comprehensive micromagnetic simulations implies that significantly reduced A_{ex} is responsible for the large remagnetization time. These results demonstrate the possibility of engineering magnetic properties on an ultrafast timescale by modifying G_{es}, G_{ls}, and G_{el}.
Methods
MOKE measurement
TRMOKE measurements with a pumpprobe stroboscope were performed on a Co/Pt multilayer. We used the femtosecond laser pulses generated by a Ti:sapphire multipass amplifier operating at a repetition rate of 3 kHz with a center wavelength of 800 nm and a pulse duration of 25 fs. We employed two pump wavelengths of 800 nm and 400 nm obtained from BBO (BaB_{2}O_{4}) crystal. As probe pulses, one wavelength of 800 nm was used. F_{P} was varied from 1.7 to 28.5 mJ cm^{−2} and probe fluence was 0.3 mJ cm^{−2}. For TRMOKE measurements, the pump beam was modulated using a mechanical chopper at 500 Hz. An external magnetic field of 1.7 kOe was applied throughout the measurements, with an angle of 0° to the surface normal of the film to keep the initial sample condition saturated before a subsequent pump pulse.
To estimate the D_{demag}, we conducted a series of hysteresis measurements at times of t = −2 ps and 0.3 ps under the same TRMOKE setup with only probebeam modulation at 500 Hz, while sweeping a magnetic field from −1.7 kOe to 1.7 kOe. The hysteresis measurement at t = −2 ps gives the magnetization of an intact sample.
Sample
[Co(6.2 Å)/Pt(7.7 Å)]_{5} multilayer films were deposited on Si substrates by dc magnetron sputtering, then capped by a 22Å Pt layer to prevent the oxidation of the surface. The structure of the Co/Pt multilayers with welldefined interfaces was confirmed by a low angle Xray diffraction and extended Xray absorption fine structure analysis. The film had a perpendicular magnetic anisotropy (K = 0.63 MJ m^{−3}) and saturation magnetization (M_{s} = 1.04 × 10^{3} kA m^{−1}), which are similar to literature values^{24,25,26,27}.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Code availability
The source codes used for G3TM fitting/micromagnetic simulation are available from the corresponding author upon reasonable request.
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Acknowledgements
This research has been supported in part by Max Planck POSTECH/KOREA Research Initiative Program [Grant No 2016K1A4A4A01922028] through the National Research Foundation of Korea (NRF) funded by Ministry of Science, ICT & Future Planning, partly by Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (P0008763, The Competency Development Program for Industry Specialist), partly by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education [Grant No 2017R1A6A3A04011173 and 2017R1A6A3A11032995] and partly by Korea Research Foundation (NRF) grant No. 2018R1A2B3009569 and a KBSI Grant D39614.
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J.H.S., A.A.S, Y.S., J.W.K., H.G.P. and S.H.L. collected data and performed all the analyses; K.M.L. and J.R.J. 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., Shin, Y. et al. Ultrafast dynamics of exchange stiffness in Co/Pt multilayer. Commun Phys 3, 74 (2020). https://doi.org/10.1038/s420050200346y
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DOI: https://doi.org/10.1038/s420050200346y
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