Magnetization reversal more rapidly by using an ultrashort square-wave laser pulse

With the feature of low-power magnetization manipulation at an ultrashort time scale, all optical switching (AOS) has been propelled to the forefront in investigations. To further speed up the magnetization reversal by manipulating ultrashort optical pulses, in this paper, one single square-wave laser pulse (SWLP) vie the combination of heating and Inverse Faraday Effect (IFE) is explored to excite the reversal of magnetization in a Co/Pt system. Simulation results show that the switching time of magnetization is 3 times faster than the using of a traditional Gaussian wave laser pulse (GWLP) under the same laser energy and pulse duration, and the threshold of AOS for the ferromagnet is 0.67 mJ/cm2. We furthermore demonstrate that the"heat accumulating effect"of laser-pulse is an important factor that influences the switching time, and a SWLP has a larger effect of heat accumulating than a GWLP.

can be controlled by the linear polarizer (LP) and the quarter wave plate (QWP) easily, and "Left" or "right" circular polarization of the pulse can be switched by rotating the QWP by ±45° with respect to the plane of LP. In the sketch, the SWLP is introduced to heat up the electron system of the sample, and then a rapid increase of the electron temperature (Te) and phonon temperature (Tp). After a few picoseconds, the heat will dissipate from the electron system into the substrate. The thermodynamic process of electron and lattice can be gotten from the following two differential equations: [11] ( ) ( where Ce and Cp are the electron and phonon heat capacities, respectively, gep is the electron-lattice coupling constant, κ is the heat diffusion constant, Tamb is the ambient temperature, and P(r, t), which is determined by the square-wave laser pulse and the amount of laser energy absorbed by the sample, is the heat source, and P(r, t) has a Gaussian space profile, [11] which coincides with the profile of the laser pulse. In Eq. 1.1 and Eq. 1.2, Ce can be assumed to have a linear approximation of Ce = γTe, where γ is a materials-dependent parameter, and Cp is independent of the lattice temperature. In this manuscript, the temporal profile of the SWLP is investigated only, and the Gaussian distribution in space can be ignored when we consider one fixed point of the ferromagnet only. Then, the heat source P(r, t) in Eq. 1.1 can be rewritten as P(t).
As shown in Fig. 1 (b), the fluence of SWLP has a square-wave time-profile, and the heat source can be described as PSWLP(t)=I0·F·rect(t), where I0 is assumed to be the amount of laser energy absorbed by the sample [19,20] , F is the total fluence of the square-wave pulse, and rect(t) is a square wave. The temporal profile of rect(t) has the following form: where t0 is the pulse duration and t1 is the center of the pulse duration.
Based on the M3TM, the magnetization dynamics of the spin can be completely specified as follow: [15] ( where M is the magnetization normalized to the saturation value, Heff is the effective magnetic field induced by IFE, and Tc is the Curie temperature. R is the demagnetization rate and asf the spin-flip probability, kB the Boltzmann constant, TD the Debye temperature, and Ds the atomic magnetic moment divided by Bohr magneton μB. To the best of our knowledge, in experiment, the effective magnetic field induced by IFE is still very difficult to characterize, and the theory accounted for IFE is under development as well. [21][22][23] Therefore, the strength and the duration of the Heff are estimated basing on existing theories, and given by where σ is the polarization of the SWLP and is equal to ±1 and 0 for a right-hand or left-hand circularly polarized and linearly polarized light pulse, respectively, β is the magneto-optical susceptibility, c is the speed of light, k is the unit vector along the wave vector of the SWLP, and f(t) is the temporal profile of induced Heff. Similar to Ref. [22], the lifetime of Heff lasts somewhat longer than the laser pulse, and the temporal profile of f(t) can be introduced as where tdecay is defined as the decay time of IFE. As for conventional GWLP, where each pulse has a Gaussian temporal profile, tdecay is in the range of 20 < tdecay < 3000 fs, [22] and in our simulation, we select tdecay = 200 fs. this can be gotten easily by an external magnetic field. Figure 2 (a) shows the magnetization dynamics of the same one sample after excitation by three different polarized SWLPs with equal fluence and pulse width. In Fig. 2 (a), we can find the magnetization reversal appears directly when a right-hand circularly polarized SWLP induced on the sample. While the case of σ = 0 or σ = -1, no magnetization reversal is observed, and only a rapid demagnetization and slower re-magnetization process exist. This because that the right-hand circularly polarized SWLP will introduce a positive effective magnetic field induced by IFE, which is opposite to the original direction of magnetization. While for the case σ = -1 will produce a negative field, which is agreement with the original direction of magnetization, and for the case σ = 0, none magnetic field is introduced. As a result, no reversal can be observed, and only a demagnetization and slower re-magnetization process occur due to the thermal effect. Since the laser energy is a crucial parameter in determining whether the reversal of magnetization will proceed, the dynamics of the magnetization under different laser fluences and the same pulse duration are surveyed. As shown in Fig.   2 (b), when the laser fluence F < 0.67 mJ/cm 2 , no switching is performed, and only a demagnetization and slower re-magnetization process exist. However, with the increase of laser energy, AOS is observed.
And further increasing the laser energy, thermal demagnetization appeared as the magnetization is heated up to a high temperature, where the ferromagnet cannot cool down, and the resulting value of M will be 0. In Fig. 2(b), we can get the threshold of AOS for the ferromagnet is about 0.67 mJ/cm 2 . Comparing with the traditional GWLP, we also confirm the superiority of using a SWLP to excite the reversal of magnetization. As far as we know, a GWLP has the temporal profile of where F, t0, and t2 are the total fluence, FWHM and the center of the pulse duration, respectively. [19] We also define another two parameters Feff (t) = P(t)/I0 and Δτ to study the evolution of laser pulse energy and magnetization reversal. As shown in Fig. 3, Δτ is the time from the center of the SWLP or GWLP to reach the maximum demagnetization of the ferromagnet. Figure 3 shows the magnetization dynamics after excitation by three right-hand circularly polarized laser pulses with the same laser energy W = 4×10 8 J·s/m 2 , where Fig. 3 (a) and Fig. 3 (b), the laser pulses are square waves, and the pulses width are 35 fs and 35 =62.04 fs fs   , respectively. Feff is a const, and they are 2 2 40 / =70.9 / J m J m   and 40 J/m 2 , respectively. Fig. 3 (c) shows the magnetization dynamics after excitation by a right-hand circularly polarized GWLP, and the pulse width and the peak value of Feff are 35 fs and 40 J/m 2 , respectively. In Fig. 3 (a), (b) and (c), Δτ is equal to 3.03×10 -14 s, 5.05×10 -14 s and 9.09×10 -14 s, respectively. Compare with Fig 3 (a) and Fig. 3 (c), we can see that a SWLP is more suitable for the exciting of AOS, and the switching time of AOS is three times faster than the using of a GWLP under the same laser energy and pulse duration. In Fig. 3 (a) and Fig. 3 (b), we can also find that with the increase of the pulse duration, the magnetization dynamics will slow down. We also explore the mechanism that why the reversal of AOS speed up, if a SWLP is selected as the heat source. Figure 4 (a) shows the temporal profile of a SWLP and a GWLP, where they have the same pulse width and laser energy, and we can see the rising or falling edge of the SWLP is sharp, and we believe that the accumulate of energy is rapider than the GWLP, which have a gently rising and falling. Figure 4 (b) confirms our assumption. In Fig. 4 (b), the laser energy of the first three laser pulses, which are a SWLP, a SWLP, and a GWLP, is 4×10 8 J·s/m 2 , and their pulse width are 35 fs, 62.04 fs and 35 fs, respectively. The last pulse is a SWLP with laser energy of 1×10 8 J·s/m 2 , which is corresponding to F = 10 J/m 2 , and the pulse is 35 fs. As shown in Fig. 4 (b), the rate of increase of laser energy, which is corresponding to the slope of W(t), is different, and under the same laser fluence, a SWLP has a larger slope than a GWLP. We can also find that, a SWLP with a shorter pulse-width will have a larger "heat accumulating effect" due to the larger peak value. From the analysis in the foregoing, we can confirm that "heat accumulating effect" play an important role during AOS.
In conclusion, we survey the AOS in a ferromagnet of Co/Pt system by a SWLP vie the combination of heating and IFE. Simulation result shows that the switching time of magnetization is 3 times faster than the using of a traditional GWLP under the same laser energy and pulse duration, and to further speed up the magnetization reversal, using a SWLP can be an effective candidate. We also predict that AOS for the ferromagnet in our model is possible with laser energy larger than 0.67 mJ/cm 2 . At last, we furthermore demonstrate that the "heat accumulating effect" of a laser-pulse is an important factor, which influences the AOS, and a SWLP has a larger effect of heat accumulating than a GWLP.