Ultrafast giant magnetic cooling effect in ferromagnetic Co/Pt multilayers

The magnetic cooling effect originates from a large change in entropy by the forced magnetization alignment, which has long been considered to be utilized as an alternative environment-friendly cooling technology compared to conventional refrigeration. However, an ultimate timescale of the magnetic cooling effect has never been studied yet. Here, we report that a giant magnetic cooling (up to 200 K) phenomenon exists in the Co/Pt nano-multilayers on a femtosecond timescale during the photoinduced demagnetization and remagnetization, where the disordered spins are more rapidly aligned, and thus magnetically cooled, by the external magnetic field via the lattice-spin interaction in the multilayer system. These findings were obtained by the extensive analysis of time-resolved magneto-optical responses with systematic variation of laser fluence as well as external field strength and direction. Ultrafast giant magnetic cooling observed in the present study can enable a new avenue to the realization of ultrafast magnetic devices.


Supplementary Note 2. Comparison of static and TR-MOKE hysteresis loops
We compared two loops measured by TR-MOKE with a pump-beam modulation at t = 700 ps (red open circle) and static MOKE (black open square) measurement without pump-beam, as shown in Supplementary Figure 2. The static MOKE hysteresis loops were found to be the same as the loop measured by VSM, where the loop shape variation with respect to n was also as expected from previous reports [1][2][3][4][5] . Interestingly, for n = 5, the TR-and static MOKE loops were different, which is a typical aspect of the "irreversible" process observed frequently in the stroboscopic pump-probe experiment 6,7 .
The irreversible trend appears to be weakened as n increases. In the case of n = 15, the two loops are similar, but a detectable difference in the coercive field exists between the static MOKE and stroboscopic TR-MOKE loops.    First, the two temperature model (2TM) was applied to fit the TR-MOKE signals at H = 0 with a conventional assumption that a spin temperature promptly follows an electron temperature [8][9][10][11][12] . The 2TM equation is then simplified as where the thermal diffusion term is neglected. For convenience, the following Supplementary Equation 2 was used to account for a real MOKE signal that was modulated by the pump beam to give a zero background signal before time zero.
where A is an arbitrary amplitude parameter. Numerical analysis was performed to check the effects of the parameters, C e0 , G el and C l . In the simulation, P(t) was set to be a Gaussian function with a fluence In previously reported low-temperature experiments, C s was reported to be less than 10 4 J m -3 k -1 13, 14 .
The overall fitting in this study is not affected by a selection of the C s value if C s < 10 4 J m -3 K -1 .
Therefore, a C s value of 100 J m -3 K -1 was chosen in all the fits. In addition, the C s values for several materials were quite low, as in the case of the fitting 13,15 . Similarly, C e was also set to be constant, irrespective of n because there is no reason for the effective electron number density around the Fermi energy to change substantially with n. Therefore, as in previous studies 11,16,17 , C e was just assumed to be linearly proportional to T e for all samples. On the other hand, the fitting suggests that C l increases with n. This is understandable because the Co/Pt multilayer is considered to be a repeated superlattice structure 18 , possibly generating a coherent phonon in an initial phase after laser pulse illumination. The increased C l should lower the equilibrium temperature of spin, electron and lattice, considering that C s is negligibly small and C e does not depend on n.
The validity of the 3TM fitting was also checked by systematic variations of the field strength. The best 3TM fitting results of the TR-MOKE signals under a range of magnetic fields for n = 5, 10 and 15 were plotted together with the experimental data in Supplementary Figure 9, where excellent agreement between the experimental data and 3TM fittings were found in all cases of n and H.
The 3TM was also applied to analyze the TR-MOKE signal with variation of fluences as in Supplementary Figure 10, where the external field was applied normal to the films. As seen in the figure, 3TM is found to still fit the data well, where same values for heat capacities of spin, electron, and lattice are used with only freeing G el , G es , and G ls parameters. The fitting results are listed in Table 1.  The magnetic anisotropy was determined via analysis of the easy-and hard-axis hysteresis curves measured by vibrating sample magnetometer 19 . The results are shown in Supplementary Figure 12, where the effective anisotropy (K eff ) and anisotropy field (H k ) for n = 5, 10, and 15 samples are plotted.
Both K eff and H k decrease from 6.3 × 10 6 to 2.3 × 10 6 erg cm -3 and 12.6 to 6.6 kOe, respectively, with respect to n. H k of all the samples are greater than 5 kOe, stronger compared to the external field strength (1.70 kOe). Thus, the external field applied along the film-normal direction could affect the sample responses more directly.