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Abstract
With the feature of low-power and ultrashort time magnetization manipulation, all optical magnetic switching (AOMS) has been propelled to the forefront in investigations. To further speed up the magnetization reversal, in this paper, based on the combination of heating and Inverse Faraday Effect (IFE), an ultrashort square-wave laser (USWL) pulse is explored to excite the reversal of magnetization in a Co/Pt system, and all the parameters necessary for our simulation are well within the current theoretical estimates. Simulation results show that the switching time of magnetization is 3 times faster than the using of a traditional ultrashort Gaussian wave laser (UGWL) under the same laser fluence F = 4 mJ/cm2 and pulse duration t0 = 35 fs, and the threshold of AOMS for the ferromagnet is 0.67 mJ/cm2. We furthermore demonstrate that the heat accumulating effect of a laser-pulse is an important factor that influences the switching time, and a USWL has a larger effect of heat accumulating than a UGWL. At present, the debate on the origin of helicity dependent AOMS is still going on, and the model we propose provide a guideline for achieving helicity dependent AOMS more rapidly. We believe that the results could potentially be used to the field of storage technology especially for the using of AOMS.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrafast magnetization dynamics is drawing great interest since the observation of a ps-time scale demagnetization dynamics in Ni films after a fs-time scale pulsed-laser excitation [1]. All optical magnetic switching (AOMS), which has the feature of low-power and an ultrashort time magnetization manipulation, has been propelled to the forefront in investigations in ultrafast magnetization dynamics [2–4]. This novel phenomenon was first observed in a perpendicularly magnetized ferrimagnetic GdFeCo alloy [5], and later a wider range of materials were discovered [6,7]. One of the most promising applications of AOMS is the manipulation and storage of magnetic information, by using laser pulses to switch the magnetization rapidly without any external magnetic field [8]. Recently, by fine tuning of the excitation parameters, G. kichin et al reduced the number of pulses required to obtain all optical helicity-dependent switching (AO-HDS) from hundred pulses to 10 pulses in a Co/Pt system [9]. By optimizing the excitation parameters of the laser, compositions of the Co/Pt system, and the thickness of the capping, one single AO-HDS is possible in the future [10]. To further speed up magnetization reversal by manipulating ultrashort optical pulses, triggering magnetization switching on shorter time scales is a promising strategy [11]. However, conventional ultrashort Gaussian wave lasers (UGWLs), as the only one candidate, were applied to excite AOMS in the past two decades [12,13]. To switch the magnetization more rapidly, in this paper, an ultrashort square-wave laser (USWL) is first employed to excite AOMS in a Co/Pt system. Comparing with a traditional UGWL, where each pulse has a Gaussian temporal profile, the pulse generated by a USWL has a flattop [14], and the switch time of magnetization is 3 times faster, which is more suitable for the application of magnetic data storage.
USWLs, which can be used for potential applications including laser micromachining, optical sensing, and optical square-wave clocks, have recommend themselves to be a topic of great interest in optics [15], and many new technologies have been proposed to generate USWL pulses, e.g. passively mode-locked fiber lasers [16], and femtosecond pulse shaping method [17,18]. With these technologies proliferating, manipulating the reversal of magnetization of ferromagnets by using of a USWL is possible. Previous studies have confirmed that two main mechanisms, which are inverse Faraday effect (IFE) and thermal effect, are responsible for AOMS [19]. And several theories have successfully uncovered the underlying mechanism of AOMS, e.g. momentum resolved Boltzmann scattering [20], atomistic Landau-Lifshitz Gilbert (LLG) [21], and Landau-Lifshitz-Bloch (LLB) [22]. The theory of IFE is still not quite mature, and it is generally applied for transparent media where optical losses a small. Recently, IFE is applied to explain switching in metallic systems as well. In 2016 a quite simple model, which is termed as microscopic three-temperature model (M3TM), is successfully accounted for the helicity dependent AOMS of a Co/Pt system [19]. In this model, free electrons, phonons accord to the Einstein or Debye model, and spin excitation is represented by a mean-field Weiss model. In this paper, M3TM is re-employed to describe the helicity dependent AOMS exciting by a USWL in a Co/Pt system, and the IFE, which is induced by the helicity of the USWL, acts as one of the driving mechanisms. In spite of more than twenty years of development, the origin of AOMS is still debated [13,19,23–26]. In this paper we unveil a path for the reversal of the magnetization more rapidly by using a USWL.
2. Model for AOMS
Figure 1(a) shows the sketch of the AOMS setup with a USWL. The polarization of generated USWL pulse 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, a USWL 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, and the thermodynamic process of electron and lattice can be gotten from the following two differential equations [13]:
Fig. 1. (a) Sketch of the AOMS setup with a USWL. Laser, femtosecond square-wave laser; LP, linear polarizer; QWP, quarter wave plate; L, lens; WLS, white light source; M, mirror; A, analyzer, C: CCD camera, BS: beam splitter. (b) The temporal profile of a USWL pulse centered t = t1, and the pulse duration is t0.
As shown in Fig. 1(b), the fluence of the USWL pulse has a square-wave time-profile, and the heat source can be described as PUSWL(t) = I0·F·rect(t), where I0 is assumed to be the amount of laser energy absorbed by the sample [27,28], F is the total fluence of the USWL, and rect(t) is a square wave. In Fig. 1(b), the temporal profile of rect(t) has the following form:
Based on the M3TM, the magnetization dynamics of the spin can be completely specified as follows [19]:
3. Results and analysis
Employing the model as introduced in the foregoing, the dynamics response of magnetization of the same one sample after excitation by the USWL with three different polarization is surveyed, and the parameters used for the simulations, which are based on those for Co/Pt found by Kuiper et al [11], are listed in Table 1. During the simulations, the initial magnetization M = -1, and this can be gotten easily by an external magnetic field. In Fig. 2(a), we can find that the magnetization reversal appears directly when a right-hand circularly polarized USWL pulse (σ = 1) induced on the sample. However, in 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 phenomenon is introduced by the IFE, where a right-hand circularly polarized USWL pulse will introduce a positive effective magnetic field pulse, and its direction is opposite to the initial direction of the magnetization. However, in the case of σ = -1, a negative field pulse is produced, and its direction is agreement with the initial direction of the magnetization. In the case of 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. The insets of Fig. 2(a) show the final magnetization state after a USWL pulse with different polarization, which are obtained by the M3TM simulations [19], and the white and black corresponding to opposite magnetizations. This pattern is caused by the Gaussian spatial profile of the laser spot. In the center of the laser spot, the sample is heated to such a degree that a multi-domain state is formed, and AOMS is observed in a small outer circle region only [25].
Fig. 2. (a) The magnetization dynamics after excitation by a USWL pulse with polarization of right-hand circularly polarized (σ = 1), linearly polarized (σ = 0), and left-hand circularly polarized (σ = -1), respectively, and the insets show the schematic diagram of the final magnetization state, obtained by the M3TM simulations. The laser fluence and pulse width of these three pulses are 4 mJ/cm2 and 35 fs, respectively. (b) The magnetization dynamics after excitation by a right-hand circularly polarized laser with different laser fluences, and the laser fluences are 0.4 mJ/cm2, 0.67 mJ/cm2, 1 mJ/cm2, 5 mJ/cm2, 7 mJ/cm2, and 9 mJ/cm2, respectively. Note: the 6 laser pulses have the same pulse width, and t0 = 35 fs.
Table 1. Parameters used in the modeling
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 same pulse duration are surveyed. As shown in Fig. 2(b), when the laser fluence F < 0.67 mJ/cm2, no switching is performed, and only a demagnetization and slower re-magnetization process exist. However, with the increase of laser energy, AOMS is observed. And further increasing the laser energy, thermal demagnetization appears 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 AOMS for the ferromagnet is about 0.67 mJ/cm2.
The phase diagram of the final magnetization after excitation by the USWL with different laser fluences and pulse widths is shown in Fig. 3, and the polarization of the USWL is right-hand circularly polarized. In Fig. 3, the initial value of magnetization M = -1, and the laser fluence and pulse width are swept from 0.1 mJ/cm2 to 8 mJ/cm2, and from 5 fs to 120 fs, respectively. As shown in Fig. 3, for lower laser fluence and pulse width, no AOMS is observed. With the increase of laser fluence and pulse width, switching of magnetization becomes possible. However, if the fluence and pulse width continue to increase, thermal demagnetization will appear. In Fig. 3, the white star represents the threshold of AOMS when the pulse width of the USWL is 35fs, and the threshold is about 0.67 mJ/cm2. With the increase of pulse width, the threshold of AOMS is increasing, and the switching of magnetization is the most efficient when the laser fluence is about 1 mJ/cm2 and the pulse duration is about 10 fs. However, when the pulse width is larger than 100 fs, multidomain pattern is observed even though the laser fluence is lower. This is due to the fact that longer pulse can also induce a higher degree of demagnetization [30].
Fig. 3. Phase diagram of the final magnetization after excitation by a USWL with different laser fluence and pulse width. The polarization of the USWL is right-hand circularly polarized. The white star represents the threshold of AOMS when the pulse width of the USWL is 35fs.
Comparing with the traditional UGWL, we also confirm the superiority of using a USWL to excite the reversal of magnetization. As far as we know, a UGWL pulse has the temporal profile of ${P_{GWLP}}(t )= {I_0} \cdot F \cdot exp({ - {{[{{{({t - {t_2}} )} \mathord{\left/ {\vphantom {{({t - {t_2}} )} {{t_0}}}} \right.} {{t_0}}}} ]}^2}} )$, where F, t0, and t2 are the total fluence, FWHM and the center of the pulse duration, respectively [20]. 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. 4, Δτ is the time from the center of the USWL or UGWL to reach the maximum demagnetization of the ferromagnet. Figure 4 shows the magnetization dynamics after excitation by three right-hand circularly polarized laser pulses with the same laser energy W = 4×108 J·s/m2, where $W(t )= \int_0^t {P(t )dt}$. In Fig. 4(a) and Fig. 4(b), the laser pulses are square waves with pulse width 35 fs and $\sqrt \pi \times 35fs\textrm{ = 62}\textrm{.04 }fs$, respectively. Feff is a const, and they are $\sqrt \pi \times 40\textrm{ }J/{m^2}\textrm{ = }70.9\textrm{ }J/{m^2}$ and 40 J/m2, respectively. Figure 4(c) shows the magnetization dynamics after excitation by a right-hand circularly polarized UGWL, and the pulse width and the peak value of Feff are 35 fs and 40 J/m2, respectively. In Fig. 4(a)–4(c), Δτ is equal to 3.03×10−14 s, 5.05×10−14 s and 9.09×10−14 s, respectively. Comparing Fig. 4(a) with Fig. 4(c), we can see that a USWL is more suitable for the exciting of AOMS, and the switching time of AOMS is 3 times faster than the using of a UGWL under the same laser energy and pulse duration. In Fig. 4(a) and Fig. 4(b), we can also find that with the increase of the pulse duration, the magnetization dynamics will slow down. In Fig. 4, due to the thermal demagnetization, some fraction of the ferromagnet cannot cool down, and the final state of the ferromagnet is about 0.4. It is about t = 0.6ps that the ferromagnet relaxation to the final state when a USWL is used (Fig. 4(a)). However, it is about t = 1ps when a UGWL is applied (Fig. 4(c)). Therefore, we can say that a USWL also leads to a faster relaxation to the final state compared to a UGWL.
Fig. 4. The magnetization dynamics after excitation by three different laser pulses with right-hand circularly polarized. (a) A USWL pulse with a pulse width of t0 = 35 fs, and the maximum value of Feff is about 70 J/m2; (b) A USWL pulse with a pulse width of t0 = 62.04 fs, and the maximum value of Feff is 40 J/m2; (c) A UGWL pulse with a pulse width of t0 = 35 fs, and the maximum value of Feff is 40 J/m2.
We also explore the mechanism that why the reversal of AOMS is speeded up, when a USWL is selected as the heat source. Figure 5(a) shows the temporal profiles of two USWLs with pulse duration t0 = 35fs and t0 = 62.04fs, a UGWL with pulse duration t0 = 35fs, and a USWLs with pulse duration t0 = 35fs, respectively. In Fig. 5(a), the first three pulses have the same laser energies with fluence 40 J/m2. The fluence of the last USWL is 10 J/m2. The temporal energies of these four pulses are normalized to the maximum value of the USWL with pulse duration t0 = 35fs, fluence F = 40 J/m2, and the center of these four pulses are all set at 150 ps. We can see that the edge roll-off of a USWL pulse is much steeper comparing with the case of using a UGWL, and we believe that a USWL has a larger heat accumulating effect than a traditional UGWL. Figure 5(b) confirms our assumption. In Fig. 5(b), the laser energy W of the first three laser pulses, which are a USWL pulse, a USWL pulse, and a UGWL pulse, is equal, and it is 4×108 J·s/m2, and their pulse widths are 35 fs, 62.04 fs and 35 fs, respectively. The last pulse, in Fig. 5(b), is a USWL pulse with laser energy of 1×108 J·s/m2, which is corresponding to F = 10 J/m2, and the pulse width is 35 fs. As shown in Fig. 5(b), the rate of heating effect of the laser pulse, which is corresponding to the slope of W(t), is different, and under the same laser fluence, a USWL pulse has a larger slope than a UGWL pulse. Therefore, a USWL pulse is a more effective way of heating the electron bath compared to a UGWL. In Fig. 5(b), it is easy to see that the slope is relative to the laser fluence as well. We can also find that, a USWL pulse 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 and the laser fluence play an important role during AOMS.
Fig. 5. (a) Temporal profiles of 4 different laser pulses. The first three laser pulses, which are two USWL pulses, and a UGWL pulse, have the same laser fluence F = 40 J/m2, and their pulse widths are 35 fs, 62.04 fs and 35 fs, respectively. The last pulse is a USWL pulse, and the laser fluence is 10 J/m2 with pulse width 35 fs. The center of these four pulses are all set at 150 ps. Their temporal energies are normalized to the maximum value of the USWL pulse with pulse duration t0 = 35fs, fluence F = 40 J/m2. (b) Evolution of laser energy W(t) of the 4 different laser pulses. The carmine dashed line shows the center of these four pulses.
4. Conclusion
In conclusion, based on the combination of heating and IFE, we survey the helicity dependent AOMS in a ferromagnet of Co/Pt system by using a USWL pulse, and all the parameters necessary for our simulation are well within the current theoretical estimates. Simulation result shows that the switching time of magnetization is 3 times faster than the using of a traditional UGWL under the same laser energy and pulse duration, and to further speed up the magnetization reversal, using a USWL can be an effective method. We also predict that AOMS for the ferromagnet in our model is possible with laser energy larger than 0.67 mJ/cm2 when the pulse width is 35fs. In addition, we further demonstrate that the heat accumulating effect of a laser-pulse is an important factor, which influences the speed of AOMS, and a USWL has a larger effect of heat accumulating than a UGWL. At last but not least, we would like to underline that the question whether the magnetization switching in a Co/Pt system could be controlled by a single shot helicity dependent laser pulse on an ultrafast time scale is still open. In many senses, the model of single shot helicity dependent all optical switching in a Co/Pt system we propose is oversimplified, and many effects are either unknown or not taken into account properly, such as the magnitudes of the effective magnetic field induced by IFE, which is estimated carefully basing on existing theories. Notably, the model we put forward provides a path for speeding up the magnetization reversal in ferromagnetic systems like Co/Pt indeed, and in the future, the model should be clarified by more experiments.
Funding
China Postdoctoral Science Foundation (2019M650437); Beihang Hefei Innovation Research Institute Project (BHKX-19-01, BHKX-19-02); Natural Science Foundation of China (51602013).
Disclosures
The authors declare no conflicts of interest.
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