# Micromagnetic Modeling of All Optical Switching of Ferromagnetic Thin Films: The Role of Inverse Faraday Effect and Magnetic Circular Dichroism

^{*}

## Abstract

**:**

## Featured Application

**Existing magnetic recording devices require the application of pulsed strong magnetic fields and/or electrical currents. The duration of these typical pulses needed to reverse the initial state at the nanoscale lies in the nanosecond regime, which imposes a limit for the maximum speed of writing operations. Manipulation of the magnetic state by ultrashort laser pulses is interesting for the future development of novel magnetic recording devices. Differently from conventional field or current pulses, the deterministically control of the magnetic state by means of ultrashort laser pulses with duration of a few femtoseconds will constitute a major step for next future of laser induced recording devices. The present manuscript provides novel and efficient numerical methods which allow us to explore the physics behind all-optical switching and domain wall motion observations in ferromagnetic systems with perpendicular anisotropy.**

## Abstract

## 1. Introduction

^{2}, solving the full micromagnetic problem is a complicated task. Moreover, the involved time scales in these processes also differ over a wide range, going from the femtosecond scale of the laser pulses, the picosecond scale of the temperature evolution, and nanosecond scale for the magnetization dynamics and temperature dissipation to the substrate. Additionally, the temperature even exceeds the Curie temperature (${T}_{C}$), and consequently, LLB equation must be numerically solved. This requires small time stepping, which makes the numerical problem even more time-consuming. To date, there has been no full micromagnetic simulator that takes into account all the physics involved in extended samples and consequently, a realistic description of available HD-AOS experiments is still missing. Therefore, it has not been possible to realistically elucidate the real role of the IFE and the MCD in helicity-dependent all-optical switching or domain wall motion processes, which is precisely the aim of the present work.

## 2. Micromagnetic Model

## 3. Results

#### 3.1. Helicity-Dependent All Optical Switching (HD-AOS)

#### 3.1.1. Helicity-Dependent All Optical Switching with Inverse Faraday Effect

#### 3.1.2. Helicity-Dependent All Optical Switching with Magnetic Circular Dichroism

#### 3.2. Helicity-Dependent Domain Wall Motion (HD-DWM)

#### 3.2.1. Helicity-Dependent Domain Wall Motion with Inverse Faraday Effect

#### 3.2.2. Helicity-Dependent Domain Wall Motion with Magnetic Circular Dichroism

## 4. Conclusions

## Supplementary Materials

**Video S1**: Comparison of temporal magnetization evolution of the HD-AOS for the IFE and the MCD scenarios under 25 laser pulses. Up and down initial states and right-handed and left-handed circular polarization are evaluated in both cases.

**Video S2**: Comparison of the HD-DWM for the IFE and the MCD scenarios. Right-handed and left-handed circular polarization, and two different locations of the laser spot (either at the left side or the right side of the down-up DW) are presented for both IFE and MCD simulations.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic of the Pt/Co thin film and the laser setup. (

**b**) Time dependence of electron (red line) and lattice (blue line) temperatures obtained from the 2TM model for two laser pulses. (

**c**) Detail of the temperature evolution during the time interval when the laser pulse is present, showing the differences between both electrons (red) and lattice (blue). The green line represents the normalized laser pulse power for comparison. (

**d**) Temporal evolution of the averaged out-of-plane component of the magnetization (${m}_{z}$) showing the ultrafast reduction due to the heating generated by the laser pulses.

**Figure 2.**Snapshots of the magnetization after different laser pulses for different combination of the initial state ($\overrightarrow{m}\uparrow ,\overrightarrow{m}\downarrow $) corresponding to (

**a,b**) and (

**c,d**) respectively and laser helicities (${\sigma}^{+},{\sigma}^{-}$ ) corresponding to (

**a–c**) and (

**b–d**) respectively under the influence of the IFE ($F=0.55\text{}\mathrm{J}/{\mathrm{m}}^{2}$, ${B}_{MO}^{0}=5\text{}\mathrm{T}$ ). Each pulse is applied every $\mathsf{\Delta}{t}_{L}=1\mathrm{ns}$. The last snapshot shows the final relaxed state after 25 laser pulses. A video of these HD-AOS is provided as Supplementary Material (video S1).

**Figure 3.**(

**a**) Phase diagram of final states as a function of the fluence ($F$) and the maximum amplitude of the magneto-optical field (${B}_{MO}^{0})$ starting from a uniform up magnetization ($\overrightarrow{m}\uparrow $ ). The results were obtained by applying a train of laser pulses with left-handed helicity (${\sigma}^{-}$ ). Snapshots (

**b**–

**e**) represent typical final possible states. The black squares correspond to no-inversion combinations (

**b**). The red dots correspond to cases where the local magnetization under the laser beam reverses its initial state (

**c**). The green triangles correspond to a multi-domain final state (

**d**), and the blue stars depict combinations of where the central area below the laser beam becomes demagnetized with an inverted ring around a multi-domain pattern (

**e**).

**Figure 4.**(

**a**) Inverted area (${S}_{inv}$) normalized to the area of the laser spot (${S}_{Laser}=\pi {r}_{0}^{2}$ with ${r}_{0}={d}_{0}/2$ being the FWHM laser radius) as a function of the number of pulses for several of the separation time between consecutive pulses ($\mathsf{\Delta}{t}_{L}$ ). (

**b**) Normalized inverted area (${S}_{inv}/{S}_{Laser}$ ) as a function of separation time ($\mathsf{\Delta}{t}_{L}$ ) between consecutive laser pulses. (

**c**) Normalized inverted area (${S}_{inv}/{S}_{Laser}$ ) as a function of the normalized delay time between the magneto-optical field and the laser duration (${\tau}_{d}/{\tau}_{L}$ ) for two different values of ${B}_{MO}^{0}$. (

**d**) Normalized inverted area (${S}_{inv}/{S}_{Laser}$ ) as a function of the ${B}_{MO}^{0}$ when the magneto-optical field and the laser duration are the same (${\tau}_{d}=0$ ).

**Figure 5.**Magnetization snapshots after several pulses under the influence of the MCD. Results are shown for right-handed (${\sigma}^{+}$) (

**a**) and (

**c**) and left-handed (${\sigma}^{-}$ ) (

**b**) and (

**d**) circular polarization of the laser beam, and initial magnetic states pointing up ($\overrightarrow{m}\uparrow $ ) (

**a**) and (

**b**) or down ($\overrightarrow{m}\downarrow $ ) (

**c**) and (

**d**). The fluence and the MCD absorption rate are $F=\text{}0.5\text{}\mathrm{J}/{\mathrm{m}}^{2}$ and MCD = 10% respectively. A video of these HD-AOS is provided as Supplementary Material (video S1).

**Figure 6.**(

**a**) Phase diagram showing the final states as a function of the fluence and MCD absorption rate starting from a uniform up magnetization ($\overrightarrow{m}$↑) and applying a train of 25 laser pulses with left-handed helicity (${\sigma}^{-}$ ). (

**b**–

**e**) are representative snapshots of the four possible final states.

**Figure 7.**Initial and final snapshots of a down-up DW after 100 laser pulses of 200 ps of duration. The magneto-optical effective field due to the IFE has maximum amplitude of ${B}_{MO,MAX}=10\text{}\mathrm{T}$, and its direction, either up or down, is given by the circular polarization (${\sigma}^{-}$ and ${\sigma}^{+}$ for top and central graphs). The fluence is $F=0.3\text{}\mathrm{J}/{\mathrm{m}}^{2}$. The results for linear polarization (${B}_{MO,MAX}=0$ ) are shown in bottom graphs. The red dotted circles indicate the location of the laser beam. The in-plane size is $1.5\text{}\mathsf{\mu}\mathrm{m}\times 1.5\text{}\mathsf{\mu}\mathrm{m}$, and the center of laser was displaced 192 nm to the left (

**a**) or to the right (

**b**) of the DW.

**Figure 8.**Initial and final snapshots of the magnetization of a sample with down and up domains separated by a domain wall. The final magnetic state is obtained after 100 laser pulses of ${\tau}_{L}=200\mathrm{ps}$. A MCD absorption rate of 10% is considered for both circular polarizations (top (${\sigma}^{-}$ ) and bottom (${\sigma}^{+}$ ) graphs). The case of linear polarization (MCD = 0) is depicted in bottom graphs. Red dotted circles indicate the location of the laser beam. The in-plane sample size is $1.5\text{}\mathsf{\mu}\mathrm{m}\times 1.5\text{}\mathsf{\mu}\mathrm{m}$ and the center of laser spot is displaced $192\text{}\mathrm{nm}$ to the left (

**a**) or to the right (

**b**) of the DW.

${\mathit{M}}_{\mathit{S}}\left(\frac{\mathbf{k}\mathbf{A}}{\mathbf{m}}\right)$ | ${\mathit{k}}_{\mathit{u}}\left(\frac{\mathbf{M}\mathbf{J}}{{\mathbf{m}}^{3}}\right)$ | ${\mathit{A}}_{\mathit{e}\mathit{x}}\left(\frac{\mathbf{p}\mathbf{J}}{\mathbf{m}}\right)\text{}$ | $\mathit{D}\left(\frac{\mathit{m}\mathit{J}}{{\mathbf{m}}^{3}}\right)$ | ${\mathit{K}}_{\mathit{e}}\left(\frac{\mathbf{W}}{\mathbf{m}\xb7\mathbf{K}}\right)$ | ${\mathit{\gamma}}_{\mathit{e}}\left(\frac{\mathbf{J}}{{\mathbf{m}}^{3}{\mathbf{K}}^{2}}\right)$ | ${\mathit{C}}_{\mathit{L}}\left(\frac{\mathbf{M}\mathbf{J}}{{\mathbf{m}}^{3}\mathbf{K}}\right)$ | ${\mathit{g}}_{\mathit{e}\mathit{l}}\left(\frac{\mathbf{W}}{{\mathbf{m}}^{3}\mathbf{K}}\right)$ | ${\mathit{T}}_{\mathit{C}}\left(\mathbf{K}\right)$ | ${\mathit{\tau}}_{\mathit{s}\mathit{u}\mathit{b}\mathit{s}}\left(\mathbf{n}\mathbf{s}\right)$ |
---|---|---|---|---|---|---|---|---|---|

1.1 | 1.25 | 15 | 2.25 | 91 | 930 | 3.7 | $6\times {10}^{17}$ | 550 | 0.9 |

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**MDPI and ACS Style**

Raposo, V.; Guedas, R.; García-Sánchez, F.; Hernández, M.A.; Zazo, M.; Martínez, E.
Micromagnetic Modeling of All Optical Switching of Ferromagnetic Thin Films: The Role of Inverse Faraday Effect and Magnetic Circular Dichroism. *Appl. Sci.* **2020**, *10*, 1307.
https://doi.org/10.3390/app10041307

**AMA Style**

Raposo V, Guedas R, García-Sánchez F, Hernández MA, Zazo M, Martínez E.
Micromagnetic Modeling of All Optical Switching of Ferromagnetic Thin Films: The Role of Inverse Faraday Effect and Magnetic Circular Dichroism. *Applied Sciences*. 2020; 10(4):1307.
https://doi.org/10.3390/app10041307

**Chicago/Turabian Style**

Raposo, Victor, Rodrigo Guedas, Felipe García-Sánchez, M. Auxiliadora Hernández, Marcelino Zazo, and Eduardo Martínez.
2020. "Micromagnetic Modeling of All Optical Switching of Ferromagnetic Thin Films: The Role of Inverse Faraday Effect and Magnetic Circular Dichroism" *Applied Sciences* 10, no. 4: 1307.
https://doi.org/10.3390/app10041307