1-D Simulation of Ultrafast-Pulsed Laser into Nano-Sized Multilayered Structure (Ni81Fe19/Cu/YIG/GGG) for Memory Device Applications

Spintronic offers a solution by exploiting spin instead of electron charge since spin current propagation can occur in principle without dissipation. One of the applications involve within this project for storage media is heat-assisted magnetic recording (HAMR). The objective of this study is to simulate the behavior of thermal gradient to generate a pure spin current using an ultrafast femtosecond (fs) laser in a nano-sized multilayered structure of (Al2O3/Ni81Fe19 (Py)/Cu/Y3Fe5O12 (YIG)/Gd3Ga5O12 (GGG)) at room temperature. A ferromagnetic/spacer/magnetic insulator nano-sized multilayered is the proposed structure for this study. Electron spin, directed by the external applied magnetic field, is transferred via the spacer to the magnetic insulator, leading to the generation of a spin-wave within the last layer. The ultrafast laser generates a spark of spin diffusion to get spin current. The thermal behavior within the trilayer simulated using COMSOL Multiphysics (v 5.5) is presented and supported by the theoretical model. Simulation results showed the effect of thickness and time on the generated spin current. Moreover, the thickness of the permalloy layer plays an essential role in generating a high-temperature gradient within a magnetic insulator to generate a spin current.


Introduction
Pure spin currents that are unassociated to charge transport, can control a new generation of environmentally sustainable and energy-sensitive spintronic (electron spin in electronics) systems. The absorption by a ferromagnetic (FM) layer results angular momentum that occurs during spin currents. This can cause or adjusts the dynamics of magnetization by producing a torque of a spin-transfer [1][2][3]. Recently, considerable effort has been spent in obtaining spin current, whether by thermal gradients via Seebeck effects [4][5][6][7][8], or the spin current synthesized by the spin hall effect, in which spin-orbit interaction (SOI) is used [9][10][11][12]. Moreover, the ultrafast laser generates a spark of spin diffusion to obtain the spin current. This can be result from spin current using an ultrafast fs laser in a multilayer thin film. Frequently, Heat-Assisted Magnetic Recording (HAMR) is considered a technique that requires increasing memory capacities [13]. Bit-Patterned Media (BPM) [14], Shingled Magnetic Recording (SMR) [15] and Microwave-Assisted Magnetic Recording (MAMR) [16] are other recording techniques for improving the density of hard disk storage. The amount of data transferred between the head and the media is much higher in HAMR [17]. Therefore, the high temperature due to the laser within HAMR to transfer data remains a task that needs to be addressed [18].Chen et al.presented a study of the head-disk interface in hard disk drives, which comprises the surface of a disk and a slider surface moving at a different relative velocity [19]. Kiely et al. presented a study of the driving forces, mechanisms of the growth, and writestimulated head contamination growth rates. The combination between an evaporation and condensation model with shear forces proposes that the flow of the lubricant on the head might cause contamination [20]. Sakhalkar and Bogy presented the effect of head, media temperature, and the thickness of lubricant on the lubricant transfer process [21], claiming that initially largely thermally driven was due to the transfer mechanism. According to a previous study, Mohamad et al. succeeded in experimentally generating spin current by ultrafast laser in multilayer thin films, but they did not consider the effect of ferromagnetic layer thickness on the spin current generation, which can be explored in detail by studying the effect of the layer thickness [22]. In the present study, a thermal behavior, induced by ultrafast fs laser within the nano-sized trilayer Ni 81 Fe 19 (Py)/Cu/Y 3 Fe 5 O 12 (YIG) using COMSOL Multiphysics (v 5.5)was simulated, where a one-dimensional model was designed. The ferromagnetic over-layer is partially demagnetized by the fs laser pulse, resulting in a high thermal gradient within the trilayer structure sample. Electron spin is passed to the magnetic insulator through a spacer. Thereby, spin current, which plays an important role in spintronic devices and their applications, was obtained. The challenge is to simulate the ultrafast pulsed laser and study the temperature gradient within the sample as a function of time and sample thickness. Therefore, both ferromagnetic and magnetic insulator are important in this case. Ultra fast pulsed laser generates heat along all layers with different percentage due to the layer heat conductivity.

Theoretical Consideration
Within the time scale of the femtosecond, pulses of ultrafast laser energy can penetrat into the sample layers. The temperature increases rapidly within the sample, therefore it is easy to be explained by the one-dimensional heat diffusion equation [23]. Many important studies have focused on the heat diffusion equation within a metal [24] to describe the electron, lattice, and spin interaction [25]. The description of this interaction is written as [26]: Where z is a layer thickness, T is the temperature, t is time, and ℊ( , ) is the absorbed power density in the sample. Thermal diffusivity D could be represented by (D = k /ρ C p ),where k, ρ, C p are the thermal conductivity, the material density, and the heat capacity per unit mass, respectively. All these parametres are well known and were collected from different litretures. Spin current describes the flow of spin angular momentum within materials. The waveform shape of a spin current equals in energy term flipping the spin magnetization from up to down. This saves energy on the microscopic scale and leads to the spintronic devices. The structure of the spintronic device is vital; therefore, the suggested structure is considered to generate spin current within the nano-sized YIG layer. Using an ultrafast laser directed to the sample structure, the temperature gradient was solved. The sample structure considered is a trilayer of ferromagnetic/spacer/magnetic insulators. Inside the trilayer sample, the transient temperature distribution has cylindrical symmetry. Since the stack thickness is of a lower value than the diameter of the laser spot, lateral heat diffusion at the sample's surface can be overlooked. The absorbed power density (heat source) in the heat diffusion equation and the temperature in each layer in the stack were determined using the distribution of the electric field in the active layer(s). By considering multiple reflection and propagation, the model specified the transmission/reflection coefficients at the film interfaces [27]. Only the (lossy) permalloy and/or copper layers are thought to absorb light; the other layers in the stack have either comprehensive or negligible value of the extinction coefficients (imaginary part of the refractive index -). Consequently, only a two-layer absorption model as shown in Figure 1 was used here, with the outer layers considered to be semi-infinite in extent. The Poynting vector links a complex wave's time-averaged power per unit area (W/m 2 ) to electric and magnetic fields by the relation: ⟨ ⟩ * + (2) The normalized power density can be written as [28,29] : where ⟨ ⟩ is the time-averaged power density of the incident electric field, is the wave number at the laser wavelength ( ), n m and n i are the refractive indices of the transmitted and incident media, respectively, E is the transmitted electric field in layer m, and I is the incident electric field magnitude that takes the form for the first layer, where ( ), n 1 and n 2 being the refractive indices of the incident and transmitted media. For air/Al 2 O 3 interface, n 1 and n 2 represent the refractive index of air and Al 2 O 3 layer, respectively. Figure 1 presents the optical system that was used to simulate laser beam that has high penetration depth.

Figure 1-
The transmission/reflection model within the multilayer concept. I, R and T are the incidents, reflected, and transmitted field amplitudes respectively, while S is the amplitude of the field reflected from the next interface, d is the layer thickness [27].

Experimental Consideration
The model is described in theoretical consideration and was achieved using simulation software COMSOL Multiphysics version 5.5. A one-dimensional model was build using a time-based study in heat transfer in solids (ht) interface as shown in Figure 2. The model was based on the measurement of a multilayer thin metallic film (Al 2 O 3 /Cu/Ni 81 Fe 19 /YIG/GGG) heated by an ultrafast laser, as shown in Figure 3. The sample was not damaged by the laser pulses due to its properties. The theoretical concepts considered the 3D tempreture model which determine the lattice, electron, and spin relationship. The data of materials parameters was taken from previous works [30][31][32][33][34][35]. A summary of these parameters with descriptions and corresponding references are presented in Table 1. The geometry of the sample was made as shown in Figure 4. The laser pulse plays an essential role in this work, as it represents the source of heat falling on the sample, which has a Gaussian shape and spot diameter of 120 µm. The FWHM laser pulse width (t) is assumed to be 74 fs, while the laser repetition rate (f) is 100 kHz. Therefore, the peak power (P) in mW takes the following form [36]: Thermal-Boundary Resistance (TBR) interface conditions were used in the numerical simulations in COMSOL software to account for the imperfect interaction between the various layers in the stack of multi-nano-size composite layer. The TBR values related to the interfaces between each layer in the structure are not well understood and are dependent on the structure of the interface formation [37]. An assumed value of 1/R th was (2×10 8 W/m 2 /K) for the Al 2 O 3 /Ni 81 Fe 19 and Cu /YIG interfaces [38,39], whereas the values of (1×10 9 and 2.04×10 8 W/m 2 /K) were gathered for Ni 81 Fe 19 /Cu and YIG/GGG [39], respectively. Figure 2 shows the front layout of the Comsol software with the designed code for the presented sample. Figure 3 (a) presents the studied sample in 3D design with the input laser beam. Figure 3 (b) shows the sketch of the spin current (J) and the concept of the spin transfer [22]. While, Figure 4 shows the final 1D designed code and the line on the top of the figure was drawn to clarify the sample structure only.

Results and Discussion
Simulation results describe the effect of time and thickness in generating spin current induced by optical pumping within a trilayer (Py/Cu/YIG). The temperature profile within the sample at different time delays is shown in Figure 5 with the inclusion of TBR. The time dependence of the change in temperature at designated depths in the sample is revealed in Figure 6 with the inclusion of TBR. The temperature gradient at different positions within the YIG layer is plotted in Figure 7. Change in temperature as a function of the depth of Py within the YIG sample at time 0.05 ns is shown in Figure 8. Thermal modeling in Figure 5 illustrates the relationship between temperature variation with depth that occurs in the trilayer sample as a result of excitation by fs laser pulse at selected time intervals. A significant rise in the temperature of the permalloy layer was observed, also an increase in the energy absorption in the copper film was noted , which leads to a thermal gradient inside the sample (YIG) at a time of 1 and 0.05 ns, indicating the generation of spin current.   The temperature gradient is shown in Figure 7, which is highly influenced by the sample's position z relative to the surface. The presence of a large thermal gradient at the Cu/YIG interface highlights the importance of using TBR in the calculations. The temperature change in the YIG layer at different permalloy layer thicknesses is shown in Figure 8. The change in the thickness of the Py leads to an increase in the temperature difference in the YIG layer. This can save energy and use small power with the applied laser. The maximum temperature was observed at 8 nm thickness and 0.05 ns time.

Conclusion
The HAMR is considered a challenging task to explore due to the microscopic details that need to be addressed. This study presented a simulation of spin current in a one-dimensional model. The spin current was generated by the temperature gradient within the magnetic insulator (YIG). The obtained simulation results described the effect of thickness and time on the generation of spin current induced by optical pumping within a trilayer (Py/Cu/YIG). The Cu/YIG interface was noticed to be very important in the spin current generation, indicating the importance of including TBR values in calculations. Furthermore, it was shown that the thickness of the permalloy layer is essential in generating a high-temperature gradient within the magnetic insulator in order to generate spin current. This leads to reducing the laser power used to generate the temperature gradient within the sample and so energy is saved.