# Magnetization manipulation using ultra-short light pulses

Y.Xu ¹,² and S. Mangin ³,⁴ *

1) MIIT Key Laboratory of Spintronics, School of Integrated Circuit Science and Engineering, Beihang University, Beijing 100191, China

2) Hefei Innovation Research Institute, Beihang University, Hefei 230013, China

3) Université de Lorraine, Institut Jean Lamour-UMR CNRS 7198, F-54000 Nancy, France

4) Cavendish Laboratory, Cambridge University, Cambridge CB3 0HE, United Kingdom

*Stephane.mangin@univ-lorraine.fr

## Abstract

In this review, we discuss the different results demonstrating deterministic magnetization switching using ultra-fast laser pulses, named all-optical switching (AOS). The response of these magnetic systems can be separated into two groups depending on whether the helicity of the incident light affects the switching behaviour. All optical helicity-independent switching (AO-HIS) occurs after a single laser pulse and is mostly observed in Gd based alloys and multilayers while all optical helicity-dependent switching (AO-HDS) occurs following multiple laser pulses and is observed in a diverse range of magnetic thin films. Our discussion focuses on the experimental and theoretical aspects of AO-HIS from Gd-based systems and other emerging materials. For AO-HDS, we highlight recent progress on the influence of domain size, state diagrams, mechanisms, and interlayer coupling. Finally, we discuss the potential application of all-optical switching in data-storage and logic devices, such as magnetic tunnel junctions, racetrack memories, and logic computation.

## 1. Introduction

Magnetic recording and memory utilizes magnetic moments to store binary information. The binary information is represented by bistable magnetic states, which are separated by an energy barrier due to magneto-crystalline anisotropy in the recording material. Therefore, the magnetization has to be switched deterministically to write binary information. In conventional magnetic recording and memory devices (Åkerman 2005; Fert 2008) such as magnetic hard disks, magnetic tapes and conventional magnetic random access memory, magnetization manipulation is performed using an external magnetic field.

However, this approach suffers from low switching speed and high energy consumption due to the difficulty in generating a strong magnetic field in devices. Therefore, in the last 20 years there has been great focus dedicated to the development and study of new ways of manipulating magnetization and magnetic structures(Dieny et al. 2020; Sander et al. 2017; Vedmedenko et al. 2020). Researcher has endeavored to use new external stimuli to overcome the energy barrier and manipulate the magnetic moments of the recording material. Current induced magnetization reversals were first proposed in 1996 together with the concept of spin transfer torque(Slonczewski 1996; Berger 1996; Ralph and Stiles 2008) which quickly gave rise to STT-MRAM(Brataas, Kent, and Ohno 2012; Kent and Worledge 2015). Spin orbit torque was then introduced(Miron et al. 2011; Manchon et al. 2015; Ning et al. 2022; Soumyanarayanan et al. 2016) following the studies on the interplay of charge
and spin transport (Žutić, Fabian, and Das Sarma 2004; Sinova et al. 2015). Later, it was found the interplay between heat current, charge current, and spin currents could be used to affect magnetization dynamics (Uchida et al. 2008; Bauer, Saitoh, and van Wees 2012; Matsukura, Tokura, and Ohno 2015). Other exploitable behaviors allow for magnetization to be manipulated via electric fields (Bauer, Emori, and Beach 2012; Shirahata et al. 2015) as well as strain (Eerenstein, Mathur, and Scott 2006; Okabayashi, Miura, and Taniyama 2019).

In this review, we focus on how the interaction between ultrafast light and magnetism opens a new way to achieve ultrafast and energy-efficient magnetic recording. As the shortest known stimulus, an ultrafast laser pulse has a high peak power on a short time scale. Unlike other thermodynamic approaches, the intensive ultrafast light breaks the thermal equilibrium and brings the system to a temperature close to the Curie temperature (Kimel and Li 2019; Kirilyuk, Kimel, and Rasing 2011; Kirilyuk, Kimel, and Rasing 2010; Kirilyuk, Kimel, and Rasing 2013). Because of the ultrafast energy transfer, the amplitude of magnetization changes and the switching is not limited to the slow switching trajectory in thermal equilibrium. The magnetic order is manipulated at the sub-picosecond timescale, comparable to the typical time for interactions between electrons and spins (Beaurepaire et al. 1996; Koopmans et al. 2010).

The interplay between femtosecond laser pulses and spin leads to at least two kinds of deterministic magnetization switching, i.e., multiple-pulses AO-HDS and single-pulse AO-HDS. In the case of AO-HDS, first discovered in GdFeCo, the magnetization direction is determined by the helicity of light. Later, AO-HDS is found to be a universal effect that appears in various kinds of perpendicularly magnetized materials, such as ferrimagnets, ferromagnets, multilayers, etc. However, in the case of AO-HIS, the magnetization direction is determined by the number of pulses. AO-HIS is only observed in the Gd-based systems and Mn₂RuₓGa alloys. While both effects stem from the interaction between laser pulses and spin, the mechanisms of the two effects are uncorrelated (Xu et al. 2019).

In this review, we discuss AO-HIS and AO-HDS separately. For each effect, we discuss various aspects of the ultrafast manipulation of magnetic order, including material properties, mechanisms and modeling, laser parameters, and exchange-coupled systems. We also discuss recent progress on skyrmions generated using ultrafast laser pulses.

## 2. AO-HIS

In 2012, Oster et al. reported a toggle-type switching without an external magnetic field, which is referred to as AO-HIS (Ostler et al. 2012). The magnetization of GdFeCo switches back and forth when the film is exposed to a sequence of laser pulses. The visualization of AO-HIS was first achieved by Oster et al. using a magneto-optic Kerr microscope (Figure 2-1). For AO-HIS, the final state depends on the number of pulses. AO-HIS is driven by ultrafast heating, consistent with the helicity-independent property.
<figure><img src="image_1.png" /></figure>

Figure 2-1. The magneto-optical images of a Gd24Fe66.5Co9.5 continuous film were obtained after the action of a sequence of N 100 fs laser pulses. (a) and (b) Initial homogeneously magnetized state of the film with magnetizations 'up' and 'down' as represented by the circled dot and cross, respectively. The light (dark) grey region represents magnetization pointing down (up). (c) and (d) The film after an excitation with N (N = 1, 2...5) pulses with a fluence of 2.30 mJ cm⁻². Each laser pulse excites the same circular region of the film and reverses the magnetization within it. The scale bar on the right corresponds to 20µm. From (Ostler et al. 2012).

The ultrafast temporal (sub-ps) behavior of AO-HIS received much attention in the past decade. Stanciu et al. first identified that the magnetization of a GdFeCo layer switches within 0.7 ps using the pump-probe technique (Stanciu, Tsukamoto, et al. 2007). Radu et al. performed an element-specific study on ultrafast dynamics of Gd and Fe sublattices using X-ray magnetic circular dichroism (Radu et al. 2011). They found that the two sublattices demagnetize on different timescales despite the exchange coupling between them. The demagnetization of Fe takes 300 fs, while that of Gd is much slower at 1.5 ps (Radu et al. 2011). The difference in the timescale of demagnetization results in a transient ferromagnetic-like state which is vital for triggering AO-HIS, especially when the pulse duration is very short (sub-100 fs).

The magnetization dynamics in the picosecond timescale were visualized by a time-resolved imaging technique. In 2014, Hashimoto et al. developed a time-resolved single-shot pump-probe microscopy with a micrometer space resolution and a sub-picosecond time resolution (Hashimoto et al. 2014). They managed to record the domain images at different time delays during the reversal process. Recently, Wang et al. explored the frequency limit via the dual-shot pump-probe technique (Wang et al. 2021). They showed that a reliable rewriting of GdFeCo by the second shot requires separating the shots by at least 300 ps, defining the upper-limit of repetition rate for AO-HIS to ≈3GHz.

The single pulse switching of Mn2RuxGa (MRG) films (Banerjee et al. 2020) at room temperature is another milestone for AO-HIS as it was the first observation of the phenomena outside a Gd-based alloy or multilayer. In MRG, the Mn atoms occupy two inequivalent sublattices with antiferromagnetic coupling, leading to a compensation temperature $T_{comp}$ (Banerjee et al. 2020). Time-resolved study shows that MRG switches in 2 ps or less with the two Mn-sublattices having different demagnetization rates, as shown by Bonfiglio et al. The temperature of the two spin subsystems in MRG follows a similar relaxation path already at ~2 ps (Bonfiglio et al. 2019). The faster demagnetization rate leads to deterministic all-optical switching of MRG with switching times of ~ 1 ps. The observation of single-pulse switching in Gd-free MRG compensated ferrimagnets challenged the understanding of AO-HIS.

Unlike the AO-HIS in metal systems described above, Stupakiewicz et al. observed a distinct single-pulse switching in the dielectric YIG:Co (Stupakiewicz et al. 2017). Depending on the polarization, the linearly polarized femtosecond laser pulse deterministically sets the magnetization. Szerenos et al. studied the magnetization dynamics using the double-pulse excitation approach. Write-rewrite cycles can be
achieved for a temporal separation greater than 60ps, setting a maximum repetition
frequency of 20GHz(Szerenos et al. 2019). Single pulse switching has also been
observed in Tb/Co multilayers(Avilés-Félix et al. 2020) but the state diagram and the
dynamic also is completely different from AO-HIS in metal systems. The following
discussion is limited to AO-HIS in ferrimagnetic metals.

**2.1 Material properties**

For AO-HIS, most research advances are reported in GdFeCo alloy. GdFeCo is
an amorphous rare-earth transition-metal ferrimagnet that shows a strong magneto-
optic response. GdFeCo received intensive attention in the 1980s due to its
technological importance as a magneto-optical media. The magnetic moments of the
Gd sublattice and FeCo sublattice are antiferromagnetically coupled. The alloy is
labeled Gd-rich (resp FeCo-rich) if the net magnetization is aligned with the Gd (resp
FeCo) magnetic sublattice. For a given alloy composition, GdFeCo has a
magnetization compensation temperature (T<sub>M</sub>) and an angular momentum
compensation temperature (T<sub>A</sub>, slightly higher than T<sub>M</sub>).

The stoichiometry ratio of GdFeCo is critical for magnetic properties, such as
saturation magnetization, anisotropy, T<sub>M</sub>, T<sub>A</sub>, et al (etc is more commonly used here).
Thus, the effect of the stoichiometry ratio on AO-HIS received much attention. AO-
HIS is observed in a large range of compositions(Xu et al. 2017). As the percentage of
the Gd in GdFeCo increases, the maximum pulse duration capable of enabling AO-
HIS increases (Davies et al. 2020). For a given thickness, the threshold switching
fluence F<sub>switch</sub> is minimized with the Gd composition close to the magnetization
compensation point of ~25%. Recently, Wei et al. examined the interplay between the
stoichiometry ratio, pulse duration, and laser fluence(Wei et al. 2021). Zhang et al.
showed that CoTb alloy with just 1.5 % of Gd is enough to induce single pulse
switching(Zhang et al. 2022).

To explore the potential of AO-HIS for high-density data storage, researchers
studied the size effect and fabricated micro- and nano-sized structures. In a typical
AO-HIS experiment, the femtosecond laser is focused to a dimension of several tens
of micrometers, which is much larger than the bit size in magnetic storage media.
Savoini et al. demonstrated that the energy requirements decreased for micropatterned
samples due to enhanced light absorption for micrometer-sized structures(Savoini et
al. 2012). Le Guyader studied via time-resolved photo-emission electron microscopy
that nanoscale magnetic switching can be pushed to the sub-100 ps regime(Le
Guyader et al. 2015). Those studies establish that AO-HIS is valid for fabricated
micro- and nano-sized GdFeCo structures.

**2.2 Mechanisms and modeling**

As AO-HIS is driven by heat, the temperature evolutions of electrons and
phonons play an important role and are calculated conveniently using the two-
temperature model. The electronic thermal bath is coupled to that of the phonons, and
the phonon thermal bath is coupled to an external bath at room temperature. When a
laser pulse radiates on the metallic system, the electrons absorb the photon energy,
and the electronic temperature increases rapidly. The coupling between electrons and
phonons enables the energy transfer between electrons and phonons, allowing the
electronic temperature to decrease on the picosecond timescale. The coupling between
phonons and the environment brings the system back to room temperature on the
nanosecond timescale. In addition, the ultrafast energy transfer is usually
accompanied by the ultrafast transfer of angular momentum(Bergeard et al. 2016; Malinowski et al. 2008; Eschenlohr et al. 2013).

Mentink et al. (Mentink et al. 2012)considered the longitudinal spin dynamics and proposed equations of motion for two nonequivalent collinear sublattices:

$$ \dot{S}_1 = \lambda_e(H_1 - H_2) + \lambda_1 H_1 \dot{S}_2 = -\lambda_e(H_1 - H_2) + \lambda_2 H_2 $$

where $\lambda_1$ and $\lambda_2$ are of relativistic origin and describe the transfer of angular momentum between the sublattice (1 or 2) and the environment. $\lambda_e$ is of exchange origin and stems from spin-spin interactions, allowing for the transfer of angular momentum between the sublattices. Depending on the electronic temperature, the spin dynamics are classified into three regimes: the temperature-dominated regime (< 1 ps), where relativistic relaxation yields distinct dynamics for sublattices with different magnetic moments; the exchange-dominated regime (ps timescale); the critical regime, where both relaxation parameters are important. This theoretical framework is used for explaining the spin dynamics methods for both GdFeCo(Davies et al. 2020) and MRG alloys(Jakobs and Atxitia 2022).

The magnetization dynamics of AO-HIS are well reproduced with the atomistic spin model(Ostler et al. 2012; Radu et al. 2011). In this model, the spin dynamics of this problem are computed using the Landau-LifshitzGilbert (LLG) equation with Langevin dynamics, which is a stochastic differential equation with multiplicative noise

$$ \frac{dS_i}{dt} = -\frac{\gamma_i}{(1 + \lambda_i^2)\mu_i} S_i \times [H_i + \lambda_i S_i \times H_i] $$

where $\lambda_i$ is the microscopic thermal bath coupling constant, $\gamma_i$ is the gyromagnetic ratio, $\mu_i$ is the atomic moment, and $H_i = -\frac{\partial E_i}{\partial S_i} + \zeta_i$, $\zeta_i$ is the thermal fluctuation field. The atomistic simulation successfully reproduced the ultrafast magnetization dynamics for a wide range of pulse durations and alloy compositions(Jakobs et al. 2021).

## 2.3 Laser parameters

The influence of laser pulse duration on AO-HIS is one of the most intriguing questions in this field. It was believed that the pulse duration should be shorter than the electron-lattice interaction time $\tau_{e-l}$ (~ 2 ps for GdFeCo) to trigger AO-HIS. If the pulse duration is shorter than $\tau_{e-l}$, the electron temperature increases more rapidly than the lattice temperature because the lattice temperature increases in a timescale governed by $\tau_{e-l}$. The temperature difference between electrons and lattices generates a strong nonequilibrium state, such as the transient ferromagnetic-like state. However, Gorchon et al. observed AO-HIS in GdFeCo even with laser pulse durations up to 15 ps(Gorchon et al. 2016), which is much longer than $\tau_{e-l}$. Over such a long duration, the pump pulse cannot induce dramatic overheating of the free electrons. Therefore, claiming that a nonequilibrium state is a prerequisite for AO-HIS is controversial.

For a given pulse duration, there exists a fluence window for AO-HIS. The fluence window corresponds to the range between the threshold switching fluence $F_{switch}$, and the fluence above which multiple random domains are created, Fmulti. Wei et al. found that the fluence window decreases with increasing pulse duration(Wei et al. 2021), forming a triangle-shaped switching region (Figure 2-3). The maximum pulse duration of AO-HIS corresponds to the pulse duration at which
the switching window closes. The study of Wei et al. established that the maximum pulse duration greatly exceeds $\tau_{e-l} \sim 2$ ps.

<figure><img src="image_2.png" /><figcaption>Figure 2-2 AO-HIS state diagram: switching fluence $F_{switch}$ (open black square and full blue square) and multidomain fluence $F_{multi}$ (full red dot) as a function of the pulse duration for a single linearly polarized laser pulse. From(Wei et al. 2021)</figcaption></figure>

To explain AO-HIS induced by slow heating (several ps), Davies et al. proposed a distinct path for magnetization reversal based on two assumptions: (i) there is more angular momentum in rare-earth sublattice than in transition metal sublattice, and (ii) the total angular momentum of the two sublattices is conserved(Davies et al. 2020). The ferromagnetic-like state occurs when laser pulses fully demagnetize the transition metal sublattices. The transition-metal sublattice receives angular momentum from the rare-earth sublattice until the latter's magnetization crosses zero (Figure 2-2). Experiments on the interplay of pulse duration and Gd-concentration(Davies et al. 2020; Wei et al. 2021) support the mechanism proposed by Davies et al. Using atomistic spin dynamics simulations, Jakobs et al. suggested that large $\alpha Fe/\alpha Gd$ is helpful for AO-HIS under slow heating(Jakobs et al. 2021).
<figure><img src="image_3.png" /></figure>

Figure 2-3 Conceptual phase map showing the different pathways for thermally induced relaxation and recovery of the angular momentum S of the ferrimagnet $A_{100-x}B_x$. The thick green dots indicate positions of equilibrium, and by varying x, these states are translated across the map. Excitation of the ferrimagnet by thermal pulses of varying duration $τ$ lead to different trajectories. Shown in the inset is the adiabatic thermal dependence of the angular momentum. From (Davies et al. 2020).

The lateral dimension of the laser beam defines the domain size of AO-HIS. Due to the limitation of diffraction criteria, AO-HIS is limited to a lateral size of about 200 nm, which is a major obstacle to high-density magnetic storage. Using the dual-shot method, Wang et al. demonstrated that the lateral switching size can be pushed into the sub-diffraction range (Wang et al. 2021). Ignatyeva et al. increased the storage density by a factor of 2 using layer-resolved all-optical switching in GdFeCo/Si3N4 (80 nm)/GdFeCo (Ignatyeva et al. 2019). The layer selectivity is achieved through the excitation of surface plasmon polariton using s- or p-polarized laser pulses.

Besides the direct excitation by laser pulses, the indirect excitation by hot electrons has also been used to induce AO-HIS. For example, in GdFeCo/Au (>50 nm) bilayers, when laser pulses were pumped from the Au layer side, the majority of energy was absorbed by the Au electrons (Wilson et al.). The electronic heat currents pulses are sufficient to trigger AO-HIS for GdFeCo (Gorchon et al. 2016; R. B. Wilson et al. 2017; Richard B. Wilson et al. 2017). Later, Xu et al. studied the ultrafast magnetization dynamics in GdFeCo-based structures to compare the effect of femtosecond laser and hot-electron pulses. They found that a single femtosecond hot-electron pulse causes deterministic magnetization reversal in either Gd-rich or FeCo-rich alloys in a similar way to a femtosecond laser pulse (Bergeard et al. 2016; Xu et al. 2017). Those studies established that heat is the driving force for AO-HIS.

## 2.4 Exchange-coupled systems

For Gd-based systems, AO-HIS exists not only in ferrimagnetic alloys GdFeCo but also in Gd-based ferrimagnetic multilayers. Gorchon et al. explored the single pulse switching of Co/Pt via the direct exchange coupling between Co/Pt and GdFeCo (Gorchon et al. 2017). Lalieu et al. achieved single-pulse all-optical switching in Pt/Co/Gd stacks using linearly polarized laser pulses (Lalieu et al. 2017). However, the
intermixing at the Co/Gd interface, which results in a thin layer similar to GdCo alloy, is critical for AO-HIS(Beens et al. 2019). The roles of the Dzyaloshinskii-Moriya Interaction(Cao et al. 2020) and magnetic field(Peeters, van Ballegooie, and Koopmans 2022) are investigated for AO-HIS of Co/Gd-based multilayer structures. Li et al. observed that the switching threshold fluence decreased by 80% for the Co/Gd/Pt stack sandwiched by two dielectric SiO2 layers(Li et al. 2021) (Figure 2-4). AO-HIS of ferromagnetic Co is enabled by using the exchanged-coupling with Gd or GdFeCo layers. It is thus inferred that AO-HIS of other thin magnetic layers could be enabled similarly.

<figure><img src="image_4.png" /><figcaption>Figure 2-4 The switched domain size as a function of pulse energy for various samples with different ICP-CVD SiO2 layer thicknesses, which is marked as a number (unit nm) next to each corresponding curve. All curves are for samples without top-dielectric, except for the blue data set, which is for Co/Gd with both a 100 nm thermal SiO2(t-SiO2) underlayer and a 100 nm ICV-CVD SiO2(c-SiO2) top layer. The threshold fluence for each curve obtained by the method proposed by Lalieu(Lalieu et al. 2017) is displayed in the inset. From(Li et al. 2021)</figcaption></figure>

AO-HIS has been further extended to exchange-bias systems. Guo et al. succeeded in manipulating the exchange bias with a single femtosecond laser pulse in AFM/CoGd bilayers (unpublished). Recently single pulse AO-HIS and demagnetization in GdFeCo layer have shown to generate enough spin current to induce a single pulse switching of a ferromagnetic layer in a spin-valve structure such as GdFeCo/Cu/[Co/Pt] or GdFeCo/Cu/[Co/Ni] (Iihama et al. 2018; Igarashi et al. 2020; Remy et al. 2020; Iihama et al. 2021) which could open the field of ultra-fast spintronics.

## 3. AO-HDS

All-optical helicity-dependent switching (AO-HDS) was first demonstrated by Stanciu *et al.* in GdFeCo. Circularly polarized (left-circularly polarized $\sigma^-$ or right-circularly $\sigma^+$) polarized fs laser pulses deterministically switch the magnetization of perpendicularly magnetized $Gd_{22}Fe_{74.6}Co_{3.4}$ thin films(Stanciu, Hansteen, et al. 2007). Unlike AO-HIS, which appears only for a limited number of materials, AO-HDS is observed for a broader range of materials, such as Co/Pt and Co/Ni, CoTb, CoDy,
FePt granular films, etc(Mangin et al. 2014; Lambert et al. 2014). The rich material choices pave the way for the application of AO-HDS.

## 3.1 Material properties

AO-HDS in perpendicular ferromagnetic multilayers depends strongly on the total thickness of the layers. In 2014, Lambert et al. investigated a variety of ferromagnetic multilayers with perpendicular magnetic anisotropy(Lambert et al. 2014). For [Co(0.4 nm)/Pt(0.7 nm)]<sub>N</sub> multilayers, the influence of total thickness was studied by changing the repetition number N (Figure 3-1). Multidomain states were observed from samples with N=8 or 5, regardless of the laser helicity. Deterministic AO-HDS was obtained from the sample with N=3. AO-HDS tends to appear in thin perpendicular magnetic layers.

<figure><img src="image_5.png" /><figcaption>Figure 3-1 (a-c) Kerr images of [Co(0.4 nm)/Pt(0.7 nm)]<sub>N</sub> multilayer samples, where (a) N=8, (b) N=5, (c-d) N=3. For (a-c), left-circularly (σ-) or right-circularly (σ+) polarized laser beams are swept over a region of the sample, while for (d), the laser beam was fixed at individual spots over a region of the sample with different laser powers. From (Lambert et al. 2014).</figcaption></figure>

The influence of layer thickness on AO-HDS was further explained using domain size. In 2016, El Hadri *et al.* investigated the role of domain size on AO-HDS(M. S. El Hadri et al. 2016; Mohammed Salah El Hadri et al. 2016) in ferromagnetic multilayers, e.g., [Co/Ni]. After reducing the number of repetitions *N*, the total magnetic layer thickness was reduced, and AO-HDS was observed (Figure 3-2). The thickness *t* is related to the stable magnetic domain size *D* with the following equation:

$$D = t \exp \left[ \frac{\pi D_0}{2t} + \ln \ln \pi - 1 + \mu \left( \frac{1}{2} - \ln \ln 2 \right) \right]$$
where $D_0=\sigma/E_d$ is the dipolar length, $\mu=1+E_d/K_u$ is the magnetic susceptibility. $E_d=2\pi M_S^2$ is the demagnetizing energy per unit volume, and $\sigma=4(A_{ex}K_u)^{1/2}$ is the domain wall energy per unit surface. If the domain size $D$ at room temperature is larger than the laser spot size, helicity-dependent all-optical switching could be achieved.

<figure><img src="image_6.png" /><figcaption>Figure 3-2 Kerr images of [Co(0.2 nm)/Pt(0.6 nm)]<sub>N</sub> multilayer samples with N from 2 to 6, where left-circularly (σ-) or right-circularly (σ+) polarized laser beam are swept over a region of the sample. From (Mohammed Salah El Hadri et al. 2016).</figcaption></figure>

## 3.2 Mechanisms and modeling

The physical origin of AO-HDS is still under debate. Two mechanisms from circularly-polarized light have been proposed to explain the AO-HDS, either the inverse Faraday effect (IFE) or the magnetic circular dichroism (MCD). The IFE, due to circularly-polarized light, would lead to either an effective field or an induced magnetization, whose direction would be opposite for left-circularly (σ-) or right-circularly (σ+) polarized light. The MCD model is based on the fact that left-circularly (σ-) or right-circularly (σ+) polarized laser is absorbed differently for one orientation of the magnetization direction.

The magnetic field induced by IFE, or equivalently the optomagnetic polarization, has been proposed as a main possible driver for the ultrafast magnetization response, including spin oscillations(Kimel et al. 2005; Choi, Schleife, and Cahill 2017) and AO-HDS. The right- and left-handed circularly polarized light induce magnetizations of opposite signs in the normal direction with respect to the film plane. The light-induced polarization in ferromagnetic metals has been calculated theoretically(Battiato 2014; Berritta 2016).

The IFE has been introduced in several theoretical models to interpret the action of circularly polarized laser pulses(John et al. 2017; Nieves and Chubykalo-Fesenko 2016; Cornelissen, Córdoba, and Koopmans 2016). In 2016, Cornelissen et al. developed a microscopic model for all-optical switching in ferromagnets based on the
magnetic three-temperature model (M3TM). The model describes the interactions between electrons, phonons, and spin(Cornelissen, Córdoba, and Koopmans 2016; Xiaoqiang Zhang et al. 2020). Figure 3-3 shows the simulation results of the magnetic dynamics with the fs laser excitation in Co/Pt multilayers. While linear polarized laser pulses induce only a magnetization quenching followed by a relaxation of magnetization, σ+ or σ- give a magnetization reversal to the up or down states. They also showed that a minimal IFE lifetime of 0.1 ps with an IFE field strength between 10 T and 24 T could achieve the all-optical switching.

<figure><img src="image_7.png" /><figcaption>Figure 3-3 The variation of magnetization in regard to the time after the excitation of laser pulses with σ-, σ+, and L. From(Cornelissen, Córdoba, and Koopmans 2016).</figcaption></figure>

However, it was argued that AO-HDS could be purely heat-driven (MCD)(Ellis, Fullerton, and Chantrell 2016; Gorchon, Yang, and Bokor 2016; Quessab et al. 2019). For a given circularly polarized laser pulses (σ+ or σ−), the absorption and thus the electron temperature depend on the magnetization direction (up or down) due to MCD. In 2016, Gorchon *et al.* developed a model for multi-shot helicity-dependent all-optical switching in ferromagnetic materials based on a purely heat-driven mechanism(Gorchon, Yang, and Bokor 2016). The laser pulse heats the magnetic sample close to the Curie temperature $T_C$ and lowers the energy barrier that separates the bistable magnetic states. Considering the MCD, the switching probabilities in regions with different magnetization directions are different. Given sufficient heating from the light pulses, split unevenly between the two spin populations by a strong MCD effect, stochastic switching occurs more favourably in the hotter regions than the colder(Fig. 3-4). With accumulated laser pulses, deterministic magnetization reversal could be achieved.
<figure><img src="image_8.png" /></figure>

Figure 3-4 The AOS model supposes an (a) Nx by Ny grid of cells, which present (b) temperature-dependent magnetic anisotropy energy barriers $E_{ab}$, resulting in (c) two stable possible states a (up) and b (down). As a (d) circularly polarized laser pulse arrives onto the grid, (e) cells in a and b states will absorb different amounts of energy due to MCD inducing a temperature distribution in the grid of hot and cold cells. This will lead to (f) different energy landscapes for the hot and cold cells, resulting mostly in stochastic switching of the hotter cells. From(Gorchon, Yang, and Bokor 2016).

To further understand the switching mechanism behind AO-HDS, the light-driven domain nucleation and domain wall propagation should be taken into account. Quessab et al. demonstrate multiple-pulses helicity-dependent laser-induced domain wall motion (Quessab et al. 2018; Quessab et al. 2019) in all-optical switchable Co/Pt multilayers (Figure 3-5). The MCD-driven switching seems to have two steps. First, domains are nucleated by thermal demagnetization. Then, due to the temperature gradient across DWs arising from the MCD, the domain will shrink or expand depending on the magnetization direction and the light helicity.
<figure><img src="image_9.png" /><figcaption>Fig 3-5 Magneto-optical images of domain wall motion in [Co(6 Å)/Pt(7 Å)]<sub>x1</sub> induced by 40 fs- laser pulses with left- (s<sup>-</sup>) [right- (s<sup>+</sup>)] circular polarization with an energy per pulse of 12.5 mJ.cm<sup>-2</sup>. The white star indicates the center of the beam spot, and N the number of laser pulses. The laser beam spot is centered on the wall. The dashed line shows the initial position of the domain wall prior to laser exposure. From (Quessab et al. 2018).</figcaption></figure>

3.3 Laser parameters

In 2019 Kichin et al. (Kichin et al. 2019) studied the influence of laser pulse
parameters such as pulse duration, beam size, fluency, and the number of pulses in
order to better understand AO-HDS reversal in Ferromagnetic Co/Pt multilayers.
From this study, they could build a state diagram as a function of pulse duration and
laser fluence, which highlights the conditions for which AO-HDS is possible (Figure
3-3). Three different areas can be defined: For low fluences and long pulses, the laser
has no effect on the magnetic configuration. In the case of large fluences and short
pulse durations, a multidomain state is observed. In between the two areas, for a
certain range of pulse duration and laser fluence, full AO- HDS corresponding to the
reversal of a single magnetic domain is obtained. This state diagram reveals that for
all pulse durations, a threshold fluence is required for AO-HDS to be observed.
<figure><img src="image_10.png" /><figcaption>Fig 3-6. Magnetization state diagram as a function of the laser fluence, *F*, and the pulse duration, PD, for a circularly polarized static beam of different diameters (84 µm for triangles, 104 µm for squares, and 168 µm for dots) illuminating a Co/Pt. For a given fluence, the maximum (minimum) pulse duration for which we have AO HDS is plotted as filled (open) symbols. The inset shows a magnification of the diagram for the short pulse durations. From (Kichin et al. 2019).</figcaption></figure>

## 3.4 Exchange-coupled systems

AO-HDS is also demonstrated in synthetic ferrimagnets and exchange bias structures. Liao et al. studied helicity-dependent switching of synthetic ferrimagnetic heterostructures made from two antiferromagnetically exchange-coupled Co/Pt and CoFeB/Pt/CoFeB (Liao et al. 2019). The results on synthetic ferrimagnetic heterostructures show that the switching is controlled by both the light helicity and the relative Curie temperature of each ferromagnetic layer. Vallobra et al. (Vallobra et al. 2017) demonstrated the manipulation of exchange bias without any applied field using femtosecond laser pulses. For the IrMn/[Co/Pt] exchange biased multilayer, the roles of the circularly-polarized laser are two-fold: the laser pulse sets the magnetization direction of the [Co/Pt] and brings the temperature above the blocking temperature. Then the exchange bias is modified during the cooling process. Both studies highlight the importance of ordering temperature for individual layers.

## 3.5 Skyrmions

Even though the final state of multiple-pulse AO-HDS is deterministic, the domain formation after a single femtosecond layer is stochastic. Therefore, a femtosecond laser pulse is promising for generating magnetic structures such as skyrmions. Several studies demonstrated the creation of skyrmions by a femtosecond laser pulse. Finazzi et al. first demonstrated the creation of skyrmion bubbles in ferrimagnetic TbFeCo thin films(Finazzi et al. 2013) by applying infrared femtosecond laser pulses. Je et al. nucleated skyrmion bubble lattices in ferromagnetic CoFeB/Pt(Je et al. 2018) in ultrathin Ta(30 Å)/Fe72Co8B20 (wedge, 7.5–10.3Å)/TaOx(12 Å, naturally oxidized) trilayer films with ultrafast (35 fs) laser pulses. The interfacial DMI due to the asymmetric interfaces in these films gives rise
to Néel skyrmions. Bubbles with opposite magnetizations were created with opposite initial states (see Figure 4 a, b)

<figure><img src="image_11.png" /><figcaption>Figure 3-7 (a) Nucleated bubbles from a saturated state (+z) by a 35 fs single laser pulse with a laser fluence of 1.84 mJ/cm2 and linear polarization. (b) Bubble creation from an oppositely saturated state (−z) with linearly polarized light. From (Je et al. 2018).</figcaption></figure>

The timescales of the generation of skyrmions are further analyzed in recent studies. Berruto et al. used pump-probe Lorentz transmission electron microscopy and studied real-time and space-dependent nonequilibrium magnetization dynamics at the µs timescale (Berruto et al. 2018). Büttner et al. reported the skyrmion nucleation at hundreds of picosecond timescale induced by a laser pulse in CoFeB/Pt and Co/Pt (Büttner et al. 2021). However, the detailed domain structure of the intermediate magnetic state is not clear and needs to be explored in future studies.

# 4. Conclusion & Perspectives

Optically tunable magnetic tunnel junctions (MTJ) might pave the way toward a new category of integrated spintronic-photonic memory devices. Perpendicular magnetic tunnel junctions have become the building blocks of magnetic random-access memory, a promising candidate for next-generation nonvolatile memory architectures. Chen et al. used ferrimagnetic GdFeCo as the free layer and fabricated the optically switchable MTJ with a tunneling magnetoresistance ratio of 0.6%(Chen et al. 2017). Recently, Wang et al. demonstrated optically switchable MTJ with a relatively high tunnel magnetoresistance of 34.7%(Wang, Cheng, et al. 2022; Wang, Cai, et al. 2022). Attempts to combine single pulse switching of a ferromagnetic layer in a spin valve structure with the use of MTJ has been made by engineering VO2 based heterostructures (Fan et al. 2022:2). Overall, the ultrafast nature of AO-HIS is expected to significantly reduce the time for all-optical “writing” in MTJ base devices.

Researchers explored the possibility of combining AOS with racetrack memory, which is considered a future memory device. Co/Gd has a high domain wall velocity due to the compensation of the angular momentum. Lalieu et al. managed to nucleate a domain wall on Pt/Co/Gd synthetic-ferrimagnetic racetracks using AO-HIS and move the domain wall using electric current (Lalieu, Lavrijsen, and Koopmans 2019). Zhang et al. studied helicity-dependent domain wall motion by combining synchronized femtosecond laser pulses and electric current pulses (Zhang, Xu, Zhao, Zhu, Yang, et al. 2019; Zhang, Xu, Zhao, Zhu, Lin, et al. 2019). The electric current pulses apply spin-transfer torque or spin-orbit torque, depending on the multilayer stack. They proposed an optoelectronic logic-in-memory device based on the joint
effect combining spin-transfer torque/spin-orbit torque and helicity-dependent laser
pulses. Logic gates of AND, OR, NAND, and NOR are experimentally realized and
verified in their follow-up study(Boyu Zhang et al. 2020). Chakravarty et al.
demonstrated the possibility of using Co/Pt films as artificial synapses by
manipulating their magnetization state using circularly polarized ultrashort optical
pulses(Chakravarty et al. 2019).

Although much effort has been made, to develop and engineer new material
compatible with AOS many challenges will have to be faced before AOS can be
implemented in real devices. For example, all images shown in this paper are obtained
with a 50 to 100 micrometer laser beam. Solution such as plasmonic devices will have
to be used to go beyond the optical diffraction limit. Note that such solution has
already been implemented for Heat Assisted magneto Recording technology by
designing plasmonic antenna to focus optical energy at the nanometer scale(Zhou et al.
2014).

Nevertheless since magnetisation manipulation via ultra-fast laser is the fastest
known way to control magnetization and since its energy efficiency has been
demonstrated(Li et al. 2021), we believe that AOS has a strong potential for future
application. Moreover the combination of AOS with spintronic devices will enable a
new class of low-power spintronic-photonic devices beyond conventional approaches
for magnetic data storage, memories and logic.

Acknowledgment

This article is based upon work from COST Action CA17123 MAGNETOFON,
supported by COST (European Cooperation in Science and Technology). Y.X.
acknowledge the National Natural Science Foundation of China (Grants No.
11904016), and Beihang Hefei Innovation Research Institute Project (Grants No.
BHKX-19-01 and No. BHKX-19-02). This work was supported by the French PIA
project "Lorraine Université d'Excellence" reference ANR-15-IDEX-04-LUE, the
ANR UFO ANR-20-CE09-0013 and the ANR projects ANR-20-CE24-0003 SPOTZ,
by the European Union's Horizon 2020 research and innovation program COMRAD
under the Marie Skłodowska-Curie grant agreement No 861300 and the Institut
Carnot ICEEL, This work is part of the project PLUS supported by the "FEDER-FSE
Lorraine et Massif Vosges 2014-2020", a European Union Program and the Region
Grand est. The authors would like to thank Xinrui Zhai, for proofreading and fruitful
discussions.

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