# Role of domain nucleation and domain wall motion in all-optical helicity-dependent switching

Tian Xun Huang, Wei Zhang, Michel Hehn, Grégory Malinowski, Stéphane

Mangin, Julius Hohlfeld

► To cite this version:

Tian Xun Huang, Wei Zhang, Michel Hehn, Grégory Malinowski, Stéphane Mangin, et al., Role of domain nucleation and domain wall motion in all-optical helicity-dependent switching. Physical Review B, 2025, 111 (14), pp.144408. 10.1103/PhysRevB.111.144408. hal-05156763

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# Role of domain nucleation and domain wall motion in all-optical helicity-dependent switching

Tian Xun Huang,¹ Wei Zhang,¹,² Michel Hehn,¹ Grégory Malinowski,¹ Stéphane Mangin,¹,*, and Julius Hohlfeld¹

¹Université de Lorraine, CNRS, Institut Jean Lamour, F-54000 Nancy, France

²National Key Laboratory of Spintronics, Hangzhou International Innovation Institute, Beihang University, Hangzhou, China

<figure><img src="image_2.png" /></figure>

(Received 19 November 2024; revised 14 February 2025; accepted 17 March 2025; published 8 April 2025)

Since the discovery of femtosecond laser pulse induced magnetization switching, all-optical helicity- dependent switching (AO-HDS) has emerged as a powerful technique in the manipulation of magnetization across various magnetic materials, notably without any applied magnetic field. Nevertheless, the underlying mechanisms of AO-HDS remain a subject of intensive debate. Here, we investigate the AO-HDS phenomenon through a complementary approach, employing anomalous Hall effect and microscope optical Kerr effect analyses on a 10 × 10 µm² square Co/Pt multilayer with strong perpendicular magnetic anisotropy. Our focus is on the dynamics of magnetization switching induced by multiple picosecond circularly polarized laser pulses. We meticulously record the evolution of the anomalous Hall voltage as a function of time, revealing distinct “jump” and “relaxation” phases in the Hall signal. These phases are intricately linked to the processes of magnetic domain nucleation and domain wall propagation. Furthermore, we consider the influence of helicity-independent laser heating, domain pressure, and temperature gradients to understand the domain dynamics during the magnetization switching process. This comprehensive analysis not only sheds light on the role of micromagnetic evolution but also constitutes a pivotal step toward unraveling the complex mechanics of AO-HDS.

DOI: 10.1103/PhysRevB.111.144408

## I. INTRODUCTION

The increasing demand for information and communication technology (ICT), driven by advancements such as 5G and 6G communication, the Internet of things (IoT), artificial intelligence (AI), and autonomous vehicles, is leading to an exponential growth in data production and a concerning rise in energy consumption [1]. Emerging technologies, including spintronics, are being explored to provide sustainable, fast, and energy-efficient solutions [2]. In this context, light—recognized as the fastest external stimulus—offers a promising avenue for rapid and energy-efficient magnetization manipulation, crucial for magnetic data storage, memory, and logic. A pioneering study by Stanciu *et al.* demonstrated the feasibility of reversing magnetization in ferrimagnetic rare earth–transition metal (RE-TM) GdFeCo using ultrashort laser pulses without an applied magnetic field [3]. Subsequent research has identified three primary methods of optical magnetization switching: all-optical helicity-independent switching (AO-HIS) [4]; all-optical helicity-dependent switching (AO-HDS) [5–12]; and, more recently, all-optical precessional switching (AO-PS) [13].

While AO-HIS is mainly limited to Gd-based ferrimagnetic alloys and multilayers, with the exception of Mn₂RuₓGa [14], AO-HDS is a more general phenomenon demonstrated in a wide variety of magnetic materials, including pure ferromagnetic films such as [Pt/Co] and [Ni/Co] multilayers, as well as FePt granular media [7]. These materials are commonly used in spintronic devices. In contrast to AO-HIS,

which leads to toggle switching of the magnetization after each single laser pulse, AO-HDS requires multiple pulses to reverse the magnetization but allows one to deterministically control the final state of the magnetization by the helicity of circularly polarized light. AO-HDS was first demonstrated by sweeping a laser beam with a certain pulse repetition rate (typically a few kilohertz) across the surface [3], and later by keeping the laser static with regard to the sample [5]. Experimental investigations have studied the effects of laser pulse parameters—such as pulse duration, beam size, fluence, and the number of pulses—on AO-HDS in ferromagnetic Co/Pt multilayers. Their results were summarized in so-called state diagrams that, by mapping the final magnetic state as a function of laser fluence and pulse duration, highlight the conditions necessary to observe AO-HDS [12].

However, no consensus has been reached regarding the driving force of AO-HDS, the necessity of multiple pulses, and the micromagnetic mechanisms leading to full switching. With respect to the underlying driving force, two primary theories have been proposed. One theory involves magnetic circular dichroism (MCD), which accounts for helicity-dependent magnetization switching by considering the difference in light absorption between left- and right-circular polarization. In this scenario, it is understood that for a given light helicity, the probability of switching from up to down or down to up differs because the temperatures reached for up and down domains are different [11,15]. The other theory suggests helicity-dependent creation of magnetization via the inverse Faraday effect (IFE) as a potential driving force for AO-HDS. According to this theory, it is an associated effective magnetic IFE field that causes an imbalance between probabilities for switching from up to down and

<footnote>*Contact author: stephane.mangin@univ-lorraine.fr</footnote>
down to up. It is worth noting that several other mechanisms for the impact of light helicity on magnetization have been proposed [3,16–21].

Until now, the micromagnetic evolution of magnetization reversal in thin films, typically understood in terms of domain nucleation and domain growth mediated by domain wall motions, has not been thoroughly studied in the context of all-optical switching. The primary reason for this omission is that time-resolved studies of optically induced magnetization dynamics are typically conducted using optical pump-probe techniques, where it is nearly impossible to study dynamics at times longer than a few nanoseconds.

Our experimental study aims to elucidate the underlying mechanisms and pathways of helicity-dependent magnetization switching in ferromagnetic materials by example of a Co/Pt multilayer. To this end, we combine time-resolved measurements of the anomalous Hall effect (AHE) with quasistatic magneto-optical Kerr effect (MOKE) microscopy to monitor the evolution of AO-HDS within a $10 \times 10 \mu m^2$ square Co/Pt multilayer with perpendicular magnetic anisotropy located in the middle of a Hall cross. While the quasistatic MOKE images reveal the spatial magnetization configuration after a single laser pulse with micrometer lateral resolution, the complementary time-resolved measurements of Hall resistance monitor the dynamics of the net magnetization with microsecond time resolution. Our approach enables us to separate the contributions of magnetic domain nucleation and of domain wall propagation to the magnetization reversal, and therefore to study the response of both mechanisms to variations of the pump pulse helicity, fluence, and duration individually. Our measurements indicate that temperature differences and temperature gradients induced by MCD play a crucial role in the micromagnetic evolution of the net magnetization. In particular, they show that MCD related effects are the driving force for AO-HDS during its approach of reversed saturation.

## II. METHODS

### A. Details of magnetic device and experimental setup

The sample is a multilayered stack of Ta (3 nm)/Pt (3 nm)/Co (0.6 nm)/Pt (3 nm), grown on a glass substrate by dc sputtering at room temperature. Through standard lithography and etching processes, the sample was structured so that a $10 \times 10 \mu m$ square of the top Co (0.6 nm)/Pt (3 nm) layers remained on top of a Ta (3 nm)/Pt (3 nm) Hall cross. The magnetic element exhibits strong perpendicular magnetic anisotropy (PMA), and the measured hysteresis loop with an applied field perpendicular to the film shows a square loop with a coercivity of $H_c = 11$ mT as shown in Fig. S1 in the Supplemental Material [22].

The geometry of the sample as well as the configurations used for magneto-optical Kerr imaging and electric transport measurements are illustrated in Fig. 1. Laser fluence dependent optical excitation was performed using ultrashort laser pulses from a commercial Coherent Elite system with an adjustable pulse duration ranging from 300 fs to 3 ps with a wavelength of 800 nm. The full width at half maximum (FWHM) of the laser beam is approximately 70 µm, which

<figure><img src="image_3.png" /><figcaption>FIG. 1. Schematic representation of the experimental setup combining Hall resistance measurements and MOKE microscopy for the study of all-optical helicity-dependent switching.</figcaption></figure>

is significantly larger than the $10 \times 10 \mu m^2$ Co/Pt square, ensuring uniform excitation across the magnetic element. Laser fluence dependent optical excitation was performed using ultrashort laser pulses with durations ranging from 300 fs to 3 ps and a wavelength of 800 nm.

Note that fluence represents the total energy delivered per unit area by a laser pulse. Therefore, at a fixed fluence, increasing the pulse duration does not change the total energy deposited on the sample but does lower the peak intensity. In contrast, if both the fluence and pulse duration are increased by a factor of 2, the total energy absorbed will increase by a factor of 2 as well.

Single-pulse and multiple-pulse measurements were conducted at a 5 kHz repetition rate, delivering one pulse every 200 µs. Hall resistance was measured by applying a 0.5 mA dc current and recording the anomalous Hall voltage, as illustrated in Fig. 1. The low current and the symmetric stack design enable us to rule out any current-induced magnetization manipulation and minimize heating effects. Fast electrical measurements allowed us to record Hall resistance every 0.05 µs. By using a transparent glass substrate, we were able to image the magnetic domain configurations through the substrate using magneto-optical Kerr effect (MOKE) microscopy with a resolution of around 1 µm.

Note that multiple Hall crosses were studied due to damage induced by high laser fluence and occasional mishandling. While all samples originated from the same nominal Co/Pt multilayer stack, measurements were conducted over a period of 1 year, with laser exposures occurring on different days. As a result, while the switching dynamics is fully reproducible, precise fluence values may vary slightly from one figure to another. However, for a given figure, all data were obtained on the same exact Hall cross and on the same measurement day, ensuring internal consistency.

## III. RESULTS

To identify the optimal pulse fluence and duration for our investigations, we first used MOKE microscopy on a nominally identical, but unstructured film to obtain the AO-HDS state diagrams shown in Fig. 2. During these measurements,
<figure><img src="image_4.png" /></figure>

FIG. 2. All-optical switching state diagram obtained on a Co/Pt full film: Magnetization state as a function of the laser fluence (F) and pulse duration (PD), obtained with a left circularly polarized laser beam in both static and sweeping laser configurations, starting from a saturated Ta (3 nm)/Pt (3 nm)/Co (0.6 nm)/Pt (3 nm) sample. For a given pulse duration, the black and red solid squares indicate the critical fluence for switching magnetization (Fc) and for creating multidomain formation (Fm) when the laser is static. In the case of the laser sweeping the surface with a 5 kHz pulse repetition rate at a sweeping rate of approximately 20 µm/s, Fc and Fm are indicated by blue and pink hollow triangles, respectively.

the laser pulse repetition rate was 5 kHz, and the sample was either kept stationary or moved in a raster scan mode with a linear velocity of approximately 20 µm/s relative to the fixed laser beam. In both cases, AO-HDS switching is clearly

observed for pulse durations longer than 600 fs and the fluence window for switching becomes wider as the pulse duration increases, as previously observed [12]. However, the critical fluence thresholds for controlled switching and for the appearance of randomly oriented domains are both smaller when the beam is stationary than when it is moving. While the increase in the switching threshold can be attributed to reduced heat accumulation resulting from the beam's motion [23], the much more significant rise in the multidomain threshold is likely due to the moving beam dragging the inner domain wall(s) of a ring-shaped reversed domain, effectively erasing the random domain pattern within its interior. Thus, random domain patterns become only visible at very high fluences where the width of the ring-shaped reversed domain becomes so narrow that the reversed domain becomes unstable [24]. The state diagram for the stationary beam taught us that longer pulses lead to larger fluence windows for controlled AO-HDS but require larger minimum fluences to switch the magnetization than shorter pulses. As a compromise between our desire to maximize both the size of the fluence window and the energy efficiency of AO-HDS, we chose to use 2 ps pulses for all subsequent studies presented below.

Figures 3(a) and 3(b) show typical results for full AO-HDS induced by a static laser beam illuminating the center of a 10 × 10 µm² Co/Pt square as measured by MOKE imaging and Hall measurements, respectively. As shown in Fig. 3(a), starting from a saturated state with the magnetization pointing up, $M^↑$, we observe full magnetization switching toward $M^↓$, measured by MOKE, using 1000 consecutive circularly polarized laser pulses with helicity $\sigma^-$, a repetition rate of 5 kHz, and a laser fluence $F = 2.1$ mJ/cm$^2$. Figure 3(a) also shows that the switching can be reversed by changing the light helicity to $\sigma^+$. This process is clearly deterministic and reversible.

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FIG. 3. AO-HDS using 2 ps circularly polarized laser pulses on a 10 × 10 µm² Co/Pt square: (a) MOKE images obtained at different stages of the experiment: (1) after saturation in the $M^+$ state using a positive perpendicular magnetic field $H^+$; (2) after 1000 consecutive laser pulses ($\sigma^-$, 5 kHz repetition rate, 2.1 mJ/cm²) under no applied field; (3) after 1000 consecutive laser pulses ($\sigma^+$, 5 kHz, 2.1 mJ/cm²) under no applied field; (4) reproducing step (2). The contrast in these images is obtained by background subtraction in the $M^+$ configuration, which explains why the dot appears only when it switches to the $M^-$ state. (b) Hall resistance measurements as a function of time, starting from the negative saturated state $M^-$, followed by the application of $H^+$ and then $H^-$ to resaturate the sample. Subsequently, 1000 $\sigma^-$ laser pulses, 1000 $\sigma^+$ pulses, and finally another 1000 $\sigma^-$ pulses are applied. The laser fluence is 2.1 mJ/cm². (c) Magnetic configuration after 12 consecutive $\sigma^-$ pulses. The delay between pulses is approximately 10 s to allow imaging, leading to a slightly higher effective fluence (2.5 mJ/cm²) compared to the 5 kHz repetition rate case.
<figure><img src="image_6.png" /><figcaption>FIG. 4. Normalized Hall resistance ($R^H/R_S^H$) as a function of the number of laser pulses starting from a sample saturated in the negative perpendicular direction ($M^-$ with $R^H/R_S^H = -1$). One thousand laser pulses linearly polarized (L) and circularly polarized right and left ($\sigma^-$ and $\sigma^+$) are shone on the Hall cross with a 5 kHz repetition for a fluence (a) $F = 2.1 \text{ mJ/cm}^2$, (b) $F = 2.3 \text{ mJ/cm}^2$, (c) $F = 2.4 \text{ mJ/cm}^2$, and (d) $F = 2.6 \text{ mJ/cm}^2$.</figcaption></figure>

Figure 3(b) compares Hall resistances measured when the magnetic element is saturated by an external field to those measured after AO-HDS. First, the $10 \times 10 \text{ µm}^2$ Co/Pt square was saturated using an applied magnetic field $H^+$ (respectively, $H^-$) to saturate the magnetization in the $M^+$ (respectively, $M^-$) direction, and the corresponding saturated Hall resistance value was recorded. Under the same conditions as used for the Kerr images presented in Fig. 3(a), starting from $M^+$ (respectively, $M^-$), 1000 $\sigma^-$ (respectively, $\sigma^+$) pulses were applied and a full magnetization reversal could be deduced from the Hall resistance levels.

As displayed in Fig. 3(c), we found that only 12 pulses of 2 ps duration with a fluence of $2.5 \text{ mJ/cm}^2$ are sufficient to achieve full switching in our Co/Pt device. In this case, the time interval between each pulse is approximately 10 s to allow enough time to record the MOKE images. From these images, both domain nucleation and domain growth can be clearly observed. Note that the 10 s delay between two pulses likely plays an important role, as domain wall motion can be observed by eye long after the laser pulse. Moreover, these experiments are not reproducible. If we repeat the same procedure, the initial reversals do not appear at the same positions, and the number of pulses needed to achieve full saturation can vary significantly. This point will be addressed in more detail in Fig. 5 and its description, where we discuss the stochastic nature of domain nucleation and domain wall motion, which leads to variations in the switching dynamics between repeated measurements.

In Fig. 4 we show the evolution of the Hall resistance as a function of time for a $10 \text{ µm}^2$ wide Ta (3nm)/Pt (3nm)/Co (0.6nm)/Pt (3nm) Hall device under the action of 1000

consecutive 2 ps pulses with a 5 kHz repetition rate, different laser polarizations [circularly polarized left ($\sigma^+$) and right ($\sigma^-$) and linearly polarized (L)] and four different laser fluences. The measured Hall resistance is normalized such that +1 corresponds to the upward saturated magnetization state ($M^+$), -1 corresponds to downward saturated $M^-$, and 0 represents a balanced multidomain state whose average perpendicular magnetization is zero. In Fig. 4, the initial magnetization state $M^-$ is obtained by applying a large negative field, and the four different fluences $F = 2.1 \text{ mJ/cm}^2$; $F = 2.3 \text{ mJ/cm}^2$; $F = 2.4 \text{ mJ/cm}^2$, and $F = 2.6 \text{ mJ/cm}^2$ are chosen such that they lead to distinct characteristic behaviors. Note that once again, these experiments are not reproducible; the same procedure will not lead to the same results, highlighting the stochastic nature of the AO-HDS effect as highlighted in Fig. 5.

For a fluence lower than a threshold value (here $2 \text{ mJ/cm}^2$), the laser has no effect on the magnetization switching whatever the laser polarity (not shown). For $F = 2.1 \text{ mJ/cm}^2$, representative for fluences just above the switching threshold, the magnetization is reversed by $\sigma^+$ circularly polarized laser pulses whereas linearly and right circularly polarized ($\sigma^-$) laser pulse have almost no impact on the magnetization. This behavior is shown in Fig. 4(a), where the normalized Hall signal represents the normalized magnetization. For a slightly larger fluence, $F = 2.3 \text{ mJ/cm}^2$ in Fig. 4(b), the magnetization reversal induced by $\sigma^+$ circularly polarized laser pulses requires far fewer pulses [100 instead of the 800 needed for $F = 2.1 \text{ mJ/cm}^2$ in Fig. 4(a)] but still reaches saturation. However, unlike the results in Fig. 4(a), linearly (L) polarized laser pulses significantly affect the magnetization and lead to
<figure><img src="image_7.png" /><figcaption>FIG. 5. Normalized Hall resistance ($R^H/R_S^H$) measured on a Hall cross with a $10 \times 10 \ \mu\text{m}^2$ Co/Pt square initially saturated in the negative direction ($M$ − with $R^H/R_S^H = -1$) as a function of time while a 5 kHz repetition laser with a $\sigma^+$ helicity shines on the Co/Pt Square for 400 ms. (a) For a fluence $F = 2.06 \ \text{mJ/cm}^2$ the same measurement is repeated five times and the average is presented. (b) Average over ten measurements for various laser fluences ranging from 1.89 to 2.6 mJ/cm$^2$.</figcaption></figure>

full demagnetization. When the laser fluence is further slightly increased, to $F = 2.4 \ \text{mJ/cm}^2$ in Fig. 4(c), linear polarization continues to lead to a zero magnetization multidomain state, but the magnetic states obtained using circularly polarized light of both helicities are now far from saturation. Nevertheless, the final values of magnetization obtained for $\sigma^+$ and $\sigma^-$ light are still clearly distinct and of opposite sign. Figure 4(d) shows that for an even larger fluence of $F = 2.6 \ \text{mJ/cm}^2$, thermal multidomain states are induced almost independently of the laser pulse polarization. Those measurements show that picosecond laser pulses induce both helicity-dependent and helicity-independent effects, which are competing. Below a lower threshold ($\sim 2.3 \ \text{mJ/cm}^2$ in our case), the final state is dominated by the helicity, whereas for fluences above an upper threshold ($\sim 2.6 \ \text{mJ/cm}^2$ in our case) the helicity-independent effects are dominant and a multidomain state with zero net magnetization is generated. For fluences between these thresholds, a gradual transition from helicity-dependent to helicity-independent behavior occurs. This result is consistent with the simulation from [15].

In Fig. 5(a), we present the temporal evolution of the normalized Hall resistance ($R^H/R_S^H$) measured over several repeated 400 ms exposures to $\sigma^+$ polarized laser pulses (2 ps, $2.06 \ \text{mJ/cm}^2$, 5 kHz repetition rate). Before each measurement, the sample was initialized in the $M - (R^H/R_S^H = -1)$ saturation state. These data confirm that AO-HDS is inherently nondeterministic: while the final magnetic state is governed by the laser polarization and fluence, the intermediate magnetization dynamics vary from one attempt to another. Note that the primary difference between the $R$ vs time curves is the waiting time before a significant change in resistance is observed. It appears that full reversal only occurs once substantial domain nucleation has taken place, after which the switching dynamics proceeds in a similar manner. This behavior arises from the highly stochastic nature of laser-induced domain nucleation. Recognizing this, we opted to further investigate the fluence dependence of AO-HDS by averaging ten repeated measurements per fluence value, as shown in Fig. 5(b). While we agree that simple averaging may obscure certain details of the stochastic process, the averaged

curves still provide meaningful insight into the overall trends, reinforcing the conclusions drawn from Fig. 4. Specifically, they reveal that larger fluences lead to a faster magnetization response, and when exceeding a certain threshold, a loss of saturation. In addition, they show that the critical switching threshold is not sharply defined. Starting from a low fluence of $1.9 \ \text{mJ/cm}^2$, we find incomplete reversal that only approaches saturation when increasing the fluence to $2.06 \ \text{mJ/cm}^2$.

These findings emphasize the necessity of fluence optimization for achieving reliable AO-HDS with the fewest possible laser pulses. They also highlight the importance of considering switching probabilities in future AO-HDS phase diagrams, rather than treating switching as a strictly deterministic process.

In the next section we are investigating the time evolution of the magnetization after each individual laser pulse throughout the switching. Figure 6(a) shows the evolution of the Hall resistance as a function of time starting from the saturated down-state $M^\downarrow$ for the three laser light polarizations $\sigma^+$, $\sigma^-$, and linear, and a laser pulse repetition rate of 5 kHz. The laser pulses excite the sample every 200 ms and values of the resulting transient Hall resistance are recorded in 50 ns intervals. Figures 6(b) and 6(c) present the time evolution of the Hall signal within the first 2 ms and between 2 and 4 ms after the excitation by $\sigma^+$ polarized pulses, respectively. Starting from the low Hall resistance state represented by the −1 level in Fig. 6(b), the first laser pulse leads to pronounced positive jumps of the Hall signal that are followed by slower negative relaxation toward the initial state until the next pulse is sent. The $\sim 2 \ \mu\text{s}$ rise time of the jumps reflects the limited response time of our electronics. When $R^H$ exceeds a certain positive value $R_{\text{SW,crit}}^H$, the jumps become negative and the relaxation positive as most notably in Fig. 6(c).

Along the line of these observations, we will divide the magnetization reversal process into two stages: The initial stage I where the normalized net magnetization $M_{\text{net}}$ switches from a saturated state to a partially reversed state with magnetization $M_{\text{SW,crit}}$, and the subsequent stage II where $M_{\text{net}}$, starting from $M_{\text{SW,crit}}$ approaches reversed saturation. During stage I [see Fig. 6(b)], after each pulse, the fast jump is
<figure><img src="image_8.png" /><figcaption>FIG. 6. Normalized Hall resistance ($R^H/R_S^H$) measured on a Hall cross with a $10 \times 10$ µm$^2$ Co/Pt square initially saturated in the negative direction ($M$- with $R^H/R_S^H = -1$) as a function of time while a laser pulse train is shone with a 5 kHz repetition rate and a 2.3 mJ/cm$^2$ fluence. (a) For the three helicity linearly polarized (L) and circularly polarized right and left ($\sigma$- and $\sigma^+$) recorded during the first 4 ms. (b) Close-up of the first part of the magnetization reversal (from 0 to 2 ms); a positive jump and a slow negative relaxation are observed after each laser pulse. (c) Close-up of the second part of the magnetization reversal (from 2 to 4 ms); a negative jump and a positive relaxation are observed after each laser pulse.</figcaption></figure>

positive and brings $M_{net}$ toward the reversed state, whereas the slow relaxation brings $M_{net}$ back toward the initial state. Since the jump amplitude is larger than the relaxation, after several pulses, the system reaches the partially reversed state $M_{SW,crit}$. In stage II [see Fig. 6(c)] the situation is inverted: jumps tend to bring the system back toward $M_{SW,crit}$ whereas the relaxation pushes the system toward reversed saturation. Moreover, the amplitude of the relaxations is larger than the one of the jumps so that the system ends in the reversed state.

Since each pulse generates a jump followed by a relaxation, we could extract the values of the jumps, $\Delta M_{jump}$, and relaxations, $\Delta M_{relaxation}$, for different net magnetizations, laser fluences, and helicities. In order to account for the stochasticity of the reversal, we repeated the switching measurements ten times at various fluences, with a repetition rate of 5 kHz and a maximum pulse number of 2000. The corresponding values of $\Delta M_{jump}$, $\Delta M_{relaxation}$ and their sum ($\Delta M_{jump} + \Delta M_{relaxation}$) are shown in Fig. 7 as a function of the initial net magnetization for a fluence of 2.57 mJ/cm$^2$. The smaller symbols present the individual values for each laser pulse in every experiment while the larger full dots represent their average. All results are normalized.

The large scatter of the individual data results from the above-mentioned stochasticity of the involved processes. Nevertheless, the averages clearly show that $\Delta M_{jump}(M_{net})$ is positive and $\Delta M_{relaxation}(M_{net})$ is negative as long as $M_{net} \le M_{SW,crit}$, and that both change sign for larger values of $M_{net}$. Moreover, the sum ($\Delta M_{jump} + \Delta M_{relaxation}$), indicated by the large black dots in Fig. 7, is always positive independent of the net magnetization which assures deterministic switching.

Figures 8(a) and 8(b) present $\Delta M_{jump}(M_{net})$ and $\Delta M_{relaxation}(M_{net})$ for various fluences, respectively. They show that the laser fluence has only a marginal impact on the shape of the measured curves (the variations of $\Delta M_{jump}$ and $\Delta M_{relaxation}$ with $M_{net}$) but affects their magnitude. Most strikingly, we find that the value of the slightly reversed magnetization $M_{SW,crit}$, where $\Delta M_{jump}$ changes sign, is fluence

independent. In contrast, the value of $M_{net}$ where $\Delta M_{relaxation}$ changes sign seems to move from 0 to slightly negative values with increasing fluence. Moreover, the laser fluence seems to have a larger impact on $\Delta M_{relaxation}$ during the approach to reversed saturation (stage II, $M_{net} > M_{SW,crit}$) than during the initial stage of the reversal (stage I, $M_{net} < M_{SW,crit}$).

<figure><img src="image_9.png" /><figcaption>FIG. 7. The magnitude of jumps $\Delta M_{jump}$ and relaxations $\Delta M_{relaxation}$ as a function of normalized net magnetization, which is measured on a Hall cross with a $10 \times 10$ µm$^2$; Co/Pt square. The laser fluence we used is $F = 2.57$ mJ/cm$^2$ and 2000 pulses were applied. The small scatters are the results of numerous tests and the large solid dots (red and blue) are the average of these measurements which are $\Delta M_{jump}$ and $\Delta M_{relaxation}$. The black dots are the sum of averaged jumps and relaxations ($\Delta M_{jump} + \Delta M_{relaxation}$); the shadow area indicates that the total contribution of jumps and relaxations accomplishes the switching.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>FIG. 8. (a) The evolution of $\Delta M_{jump}$ as a function of the net magnetization for various laser fluences with 1000 pulses, which is measured on a Hall cross with a $10 \times 10 \mu m^2$ Co/Pt square by applying 1000 pulses. (b) Evolution of the relaxations $\Delta M_{relaxation}$ with the net magnetization for various laser fluences.</figcaption></figure>

## IV. DISCUSSION

We can start by highlighting that our work shows that the magnetization dynamics induced by single ultrashort laser pulses during AO-HDS proceeds on at least two distinct timescales as evidenced from the fast jumps and slow relaxations in the time-resolved Hall signals. The latter relaxation dynamics proceeds on a microsecond to millisecond timescale which is not accessible in ultrafast optical pump-probe experiments and has thus not been studied so far.

Second, our observation that fast jumps start to work against the magnetization reversal as soon as the magnitude of the reversed magnetization exceeds $M_{SW,crit}$ demonstrates that the inverse Faraday effect might only play an important role in the initial partial magnetization reversal, but does not contribute to the subsequent approach of the fully reversed state. The latter approach is solely driven by $\Delta M_{relaxation}$ at times when the inverse Faraday effect has long vanished.

The main assumptions underlying our discussion of the origins of the observed jumps and relaxations are (i) that the observed jumps are the sole result of fast domain nucleation driven by highly elevated electron temperatures and/or the inverse Faraday effect during and shortly after the optical excitation, and (ii) that the subsequent relaxation results from domain wall tension and temperature gradient driven domain wall motion only.

### A. Jumps of the Hall signal: Domain nucleation

The overall evolution of the jump, $\Delta M_{jump}$, as a function of the net magnetization, $\Delta M_{net}$, indicates that the laser tends to nucleate domains with random orientations. Specifically, when the magnetization is negative, it is more

likely to nucleate a positive domain, and vice versa. In a purely stochastic process, we would expect $\Delta M_{jump} = 0$ at $\Delta M_{net} = 0$. However, a closer inspection of Figs. 7 and 8(a) reveals that $\Delta M_{jump}$ is not entirely antisymmetric around $\Delta M_{net} = 0$. Instead, $\Delta M_{jump}$ exhibits larger positive values than negative values and crosses zero at a finite positive value of $\Delta M_{net} \sim 20\%$. These findings demonstrate the presence of a helicity-dependent effect during the jumps. In particular, $\sigma$+polarization favors the nucleation of domains with positive magnetization. This helicity-dependent effect appears to be enhanced by increasing laser fluence.

All these observations can qualitatively be explained when assuming that the nucleation of opposite domains follows an Arrhenius law with a polarization-dependent activation energy (due to the inverse Faraday effect) and/or temperature (due to magnetic circular dichroism). Thus, our data prove the presence of helicity-dependent nucleation rates but do not allow us to distinguish whether the helicity dependence originates from MCD, IFE, or both.

### B. Relaxation of the Hall signal

After each jump a slow relaxation of the Hall resistance takes place during the 200 µs before the following laser pulse. Since the Hall resistance does not depend much on temperature as shown in Fig. S2 [22], its temporal evolution mainly monitors changes in the net magnetization given by the difference of the total areas of up and down domains. Thus, we must consider the following laser-induced forces acting on domain walls, which may alter the relative areas of up and down domains: (i) a surface tension-induced pressure that increases with domain wall curvature and tends to eliminate small domains [25], and (ii) temperature gradient-driven forces arising from the Seebeck effect [26] and/or a corresponding gradient in domain wall energy [27,28]. For our quasihomogeneous excitation of the sample, sizable temperature gradients can only result from different heating rates of oppositely oriented domains caused by magnetocircular dichroism. Thus the temperature gradient induced forces (ii) are helicity dependent.

As shown in Figs. 7 and 8(b), the relaxation always goes toward the closest saturated state for laser fluences close to the switching threshold. This can be explained by the helicity-independent force (i). Domains with a magnetization opposite to the net magnetization are on average smaller than those aligned with it. This leads to a net magnetostatic pressure on the domain walls which tends to further shrink their size. Consequently, the resulting $\Delta M_{relaxation}$ will bring the magnetization toward the closest saturated state and vanish for $M_{net} = 0$. The large scatter of the data shown in Fig. 8(b) hinders the clear identification of polarization-dependent contributions to $\Delta M_{relaxation}$ at higher laser fluences that might originate from the helicity-dependent forces (ii). Nevertheless, the fact that all traces analyzed to obtain the data shown in Fig. 7 led to a fully reversed state demonstrates the crucial role of $\Delta M_{relaxation}$ for AO-HDS. Without $\Delta M_{relaxation}$ the magnetization reversal would have stopped at $M_{net} \sim 20\%$, where $\Delta M_{jump}$ changes sign. Note that the average total magnetization changes per laser pulse, represented by the sum $\Delta M_{jump} + \Delta M_{relaxation}$ in Fig. 7, stays opposite to the initial magnetization for any value of $M_{net}$ while its magnitude varies
as expected from the helicity controlled S-shaped reversal represented by the yellow curve in Fig. 5(b).

V. CONCLUSION

Based on spatially resolved MOKE microscopy and time-
resolved Hall resistance measurements we have shown that
all-optical helicity-dependent switching of homogeneously
excited 10 × 10 µm² Co/Pt bilayers is a highly stochastic pro-
cess in both time and space. Our time-resolved Hall resistance
measurements revealed that the magnetization dynamics, in-
duced by each single laser pulse during multipulse AO-HDS,
proceeds via fast jumps (just after the laser pulse) that are
followed by much slower relaxation on the microsecond to
millisecond timescale. We have shown that the fast jumps are
the driving force for AO-HDS during the transition from the
initial state to a partially reversed state but that the slow relax-
ation is responsible for the subsequent transition to the fully
saturated reversed state. Since the inverse Faraday effect is
only present during the time of the jumps, it might contribute
to the initial partial magnetization reversal but is definitely
not the driving force for fully saturated multipulse AO-HDS
in homogeneously illuminated Co/Pt films. By attributing the
measured jumps to fast domain nucleation and the slow relax-
ation to changes of the domain pattern driven by domain wall
tension (pressure) and temperature gradient (MCD) induced
domain wall motion, we can explain key features of our data.
However, we are not able to explain the detailed response of
jumps and relaxations to variations of net magnetization and
laser fluence. We hope that our work will inspire additional
experimental and theoretical studies that will further enhance
our understanding of AO-HDS.

The sample is illuminated by 2 ps laser pulses, whose helic-
ity is controlled using a half-wave plate (HW), a quarter-wave
plate (QW), and a polarizer (P). The laser pulses are focused

onto a Hall cross, where the magnetic Co (0.6 nm)/Pt (3 nm)
layer is confined to the central 10 × 10 µm² region. The laser
spot size, approximately 70 µm in diameter, is significantly
larger than the Hall cross, ensuring uniform laser intensity
over the sample.

Hall resistance is measured by recording the applied cur-
rent (A) and the corresponding voltage (V). The magnetic
configuration of the Co/Pt square is visualized using a MOKE
microscope, which consists of an objective lens (OL), a beam
splitter (BS), a white LED (LED) for illumination, a polarizer
(P) and analyzer (A) for contrast, and a charge-coupled device
camera (CCD) for image capture.

ACKNOWLEDGMENTS

This work is supported by Project No. ANR-20-CE09-
0013S UFO and Project No. ANR-23-CE30-0047 SLAM; the
Institute Carnot ICEEL; the Région Grand Est; the Metropole
Grand Nancy for the project “OPTIMAG” and FASTNESS;
and the interdisciplinary project LUE “MAT-PULSE,” which
is part of the French PIA project “Lorraine Université
d’Excellence,” Ref. No. ANR-15-IDEX-04-LUE. This pa-
per is based upon work from COST Action No. CA23136
CHIROMAG, supported by COST (European Cooperation in
Science and Technology). This work was supported by the
ANR through the following France 2030 government grants:
PEPR Electronique- EMCOM (Grant No. ANR-22-PEEL-
0009), PEPR SPIN-CHIREX (Grant No. ANR-22-EXSP
0002), and PEPR SPIN – SPINMAT (Grant No. ANR-22-
EXSP-0007). W.Z. gratefully acknowledges the ZheJiang
Natural Science Foundation (Grant No. LZ25A040007),
Beijing Natural Science Foundation (Grant No. 1252026),
National Natural Science Foundation of China (Grant No.
12104030), and the China Scholarship Council. All funding
was shared equally among all authors.

[1] B. Dieny, I. L. Prejbeanu, K. Garello, P. Gambardella, P. Freitas, R. Lehndorff, W. Raberg, U. Ebels, S. O. Demokritov, J. Akerman *et al.*, Opportunities and challenges for spintronics in the microelectronics industry, Nat. Electron. **3**, 446 (2020).

[2] D. Sander, S. O. Valenzuela, D. Makarov, C. H. Marrows, E. E. Fullerton, P. Fischer, J. McCord, P. Vavassori, S. Mangin, P. Pirro *et al.*, The 2017 magnetism roadmap, J. Phys. Appl. Phys. **50**, 363001 (2017).

[3] C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and Th. Rasing, All-optical magnetic recording with circularly polarized light, Phys. Rev. Lett. **99**, 047601 (2007).

[4] I. Radu, K. Vahaplar, C. Stamm, T. Kachel, N. Pontius, H. A. Dürr, T. A. Ostler, J. Barker, R. F. L. Evans, R. W. Chantrell et al., Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins, Nature (London) **472**, 205 (2011).

[5] M. S. El Hadri, P. Pirro, C.-H. Lambert, S. Petit-Watelot, Y. Quessab, M. Hehn, F. Montaigne, G. Malinowski, and S. Mangin, Two types of all-optical magnetization switching

mechanisms using femtosecond laser pulses, Phys. Rev. B **94**,
064412 (2016).

[6] S. Mangin, M. Gottwald, C.-H. Lambert, D. Steil, V. Uhlíř, L. Pang, M. Hehn, S. Alebrand, M. Cinchetti, G. Malinowski et al., Engineered materials for all-optical helicity-dependent magnetic switching, Nat. Mater. **13**, 286 (2014).

[7] C.-H. Lambert, S. Mangin, B. S. D. Ch. S. Varaprasad, Y. K. Takahashi, M. Hehn, M. Cinchetti, G. Malinowski, K. Hono, Y. Fainman, M. Aeschlimann et al., All-optical control of ferromagnetic thin films and nanostructures, Science **345**, 1337 (2014).

[8] J. Gorchon, Y. Yang, and J. Bokor, Model for multishot all-thermal all-optical switching in ferromagnets, Phys. Rev. B **94**, 020409(R) (2016).

[9] R. Medapalli, D. Afanasiev, D. K. Kim, Y. Quessab, S. Manna, S. A. Montoya, A. Kirilyuk, Th. Rasing, A. V. Kimel, and E. E. Fullerton, Multiscale dynamics of helicity-dependent all-optical magnetization reversal in ferromagnetic Co/Pt multilayers, Phys. Rev. B **96**, 224421 (2017).

[10] Y. Quessab, R. Medapalli, M. S. El Hadri, M. Hehn, G. Malinowski, E. E. Fullerton, and S. Mangin, Helicity-dependent
all-optical domain wall motion in ferromagnetic thin films, *Phys. Rev. B* **97**, 054419 (2018).

[11] Y. Quessab, M. Deb, J. Gorchon, M. Hehn, G. Malinowski, and S. Mangin, Resolving the role of magnetic circular dichroism in multishot helicity-dependent all-optical switching, *Phys. Rev. B* **100**, 024425 (2019).

[12] G. Kichin, M. Hehn, J. Gorchon, G. Malinowski, J. Hohlfeld, and S. Mangin, From multiple- to single-pulse all-optical helicity-dependent switching in ferromagnetic Co/Pt multilayers, *Phys. Rev. Appl.* **12**, 024019 (2019).

[13] Y. Peng, D. Salomoni, G. Malinowski, W. Zhang, J. Hohlfeld, L. D. Buda-Prejbeanu, J. Gorchon, M. Vergès, J. X. Lin, D. Lacour et al., In-plane reorientation induced single laser pulse magnetization reversal, *Nat. Commun.* **14**, 5000 (2023).

[14] C. Banerjee, N. Teichert, K. E. Siewierska, Z. Gercsi, G. Y. P. Atcheson, P. Stamenov, K. Rode, J. M. D. Coey, and J. Besbas, Single pulse all-optical toggle switching of magnetization without gadolinium in the ferrimagnet Mn₂RuₓGa, *Nat. Commun.* **11**, 4444 (2020).

[15] Y. Xiao, H. Wang, Y. Zou, Z. Zeng, L. Huang, K. Wang, and C. Xie, Magnetization switching of L₁₀-FePt nanoparticles by combination effect from multishot circularly polarized laser pulses, *IEEE Trans. Magn.* **54**, 1 (2018).

[16] P. Scheid, G. Malinowski, S. Mangin, and S. Lebègue, *Ab initio* theory of magnetization induced by light absorption in ferromagnets, *Phys. Rev. B* **100**, 214402 (2019).

[17] P. Scheid, S. Mangin, and S. Lebègue, Light-absorbed orbital angular momentum in the linear response regime arXiv:2311.14774.

[18] B. Assouline and A. Capua, Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation, *Phys. Rev. Res.* **6**, 013012 (2024).

[19] K. T. Yamada, A. V. Kimel, K. H. Prabhakara, S. Ruta, T. Li, F. Ando, S. Semin, T. Ono, A. Kirilyuk, and T. Rasing, Efficient all-optical helicity dependent switching of spins in a Pt/Co/Pt film by a dual-pulse excitation, *Front. Nanotechnol.* **4**, 765848 (2022).

[20] K. T. Yamada, C. S. Davies, F. Ando, T. Li, T. Ono, T. Rasing, A. V. Kimel, and A. Kirilyuk, Magnetization reversal of a ferromagnetic Pt/Co/Pt film by helicity dependent absorption of visible to near-infrared laser pulses, *Phys. Rev. B* **111**, L020406 (2025).

[21] P. Scheid, S. Sharma, G. Malinowski, S. Mangin, and S. Lebègue, *Ab initio* study of helicity-dependent light-induced demagnetization: From the optical regime to the extreme ultraviolet regime, *Nano Lett.* **21**, 1943 (2021).

[22] See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.111.144408 for the square loop with a coercivity of $H_c = 11$ mT of the sample in Fig. S1; the loop of Hall resistance and field under 300 and 350 K in Fig. S2(a); and Hall resistance decreases of 0.66% from 300 to 350 K, which is relatively much smaller than the magnitude of the relaxations in Fig. S2(b).

[23] U. Parlak, R. Adam, D. E. Bürgler, S. Gang, and C. M. Schneider, Optically induced magnetization reversal in [Co/Pt] N multilayers: Role of domain wall dynamics, *Phys. Rev. B* **98**, 214443 (2018).

[24] A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto, A. Itoh, and Th. Rasing, Role of magnetic circular dichroism in all-optical magnetic recording, *Phys. Rev. Lett.* **108**, 127205 (2012).

[25] X. Zhang, N. Vernier, W. Zhao, H. Yu, L. Vila, Y. Zhang, and D. Ravelosona, Direct observation of domain-wall surface tension by deflating or inflating a magnetic bubble, *Phys. Rev. Appl.* **9**, 024032 (2018).

[26] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, *Nature (London)* **455**, 778 (2008).

[27] J. Torrejon, G. Malinowski, M. Pelloux, R. Weil, A. Thiaville, J. Curiale, D. Lacour, F. Montaigne, and M. Hehn, Unidirectional thermal effects in current-induced domain wall motion, *Phys. Rev. Lett.* **109**, 106601 (2012).

[28] X. S. Wang and X. R. Wang, Thermodynamic theory for thermal-gradient-driven domain-wall motion, *Phys. Rev. B* **90**, 014414 (2014).