# Single-laser pulse toggle switching in CoHo and CoDy single-layer alloys: When domain wall motion matters

B Kunyangyuen, G Malinowski, D Lacour, J-X Lin, Y Le Guen, L D

Buda-Prejbeanu, S Mangin, J Gorchon, J Hohlfeld, Michel Hehn

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B Kunyangyuen, G Malinowski, D Lacour, J-X Lin, Y Le Guen, et al. Single-laser pulse toggle switching in CoHo and CoDy single-layer alloys: When domain wall motion matters. Physical Review B, 2025, 112, pp.094432. 10.1103/qntz-fw15. hal-05264216

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Single-laser pulse toggle switching in CoHo and CoDy single-layer alloys:
When domain wall motion matters

B. Kunyangyuen Ⓔ,¹ G. Malinowski Ⓔ,¹ D. Lacour,¹ J.-X. Lin Ⓔ,¹ Y. Le Guen Ⓔ,¹ L. D. Buda-Prejbeanu,²

S. Mangin,¹ J. Gorchon Ⓔ,¹ J. Hohlfeld Ⓔ,¹ and M. Hehn Ⓔ¹,*

¹Université de Lorraine, CNRS, IJL, F-54000 Nancy, France

²Université Grenoble Alpes, CEA, CNRS, Grenoble INP, SPINTEC, F-38000 Grenoble, France

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

(Received 6 May 2025; revised 21 July 2025; accepted 3 September 2025; published 16 September 2025)

We report single-pulse all-optical helicity-independent toggle switching in CoHo and CoDy alloy thin films, demonstrating a magnetization reversal mechanism distinct from previously observed ultrafast or precessional pathways. Unlike the subpicosecond switching in Gd-based ferrimagnets, we show that reversal occurs on a microsecond timescale via domain wall motion and coalescence processes. This dynamic is initiated by complete demagnetization of the Co sublattice following ultrafast laser excitation, with angular momentum transfer from the rare-earth element (Ho or Dy) leading to deterministic toggle behavior. Using both time-resolved magneto-optical Kerr effect measurements and Hall bar electrical detection, we establish that the reversal process is inherently slow and governed by domain dynamics. Complementary micromagnetic simulations support a model in which slight asymmetries induced by a spin current during the recovery from a demagnetized state guide the system toward a reversed saturated final magnetization. These results extend the class of materials that can exhibit deterministic magnetization reversal without magnetic fields or helicity, offering promising new routes for optically driven spintronic applications.

DOI: 10.1103/qntz-fw15

I. INTRODUCTION

All-optical helicity-independent switching (AO-HIS) en-
ables the reversal of magnetization in magnetic thin films
using a single femtosecond laser pulse, without the appli-
cation of an external magnetic field. This phenomenon has
attracted significant interest due to its potential for ultrafast,
energy-efficient magnetic recording technologies. The fastest
reported AO-HIS occurs on the subpicosecond timescale and
was first demonstrated in ferrimagnetic GdFeCo alloys [1–4].
In these systems, ultrafast laser-induced heating creates a far-
from-equilibrium state where antiferromagnetically coupled
rare-earth (RE) and transition-metal (TM) sublattices evolve
with different dynamics. The angular momentum transfer be-
tween these sublattices drives a transient ferromagneticlike
state, ultimately leading to magnetization reversal. Beyond
GdFeCo, AO-HIS has been reported in a range of ferrimag-
netic systems, including synthetic ferrimagnets [5], Gd/Co
multilayers [6], and Mn₂RuₓGa Heusler compounds [7].
However, attempts to extend AO-HIS to Co-RE alloys such as
CoTb and CoDy have been only partially successful. In these
systems, single-pulse switching is partial and limited to a few
initial laser shots [8]. This limitation is attributed to weaker
angular momentum transfer or the lack of favorable dynamical
asymmetries between RE and TM sublattices. Notably, adding
Gd to CoTb or CoDy alloys reintroduces AO-HIS, suggesting
that Gd’s particular dynamics play a decisive role [9]. While
Co/Ho multilayers have shown AO-HIS [10], the underlying

reversal mechanisms remain unclear and appear to be con-
siderably slower than in Gd-based systems. To date, there
has been no comprehensive study of AO-HIS in amorphous
CoHo or CoDy single-layer alloys, and the role of domain
wall dynamics and remagnetization pathways in such systems
remains poorly understood.

In this work, we demonstrate fully deterministic single-
pulse toggle switching in CoHo and CoDy alloy thin films
with perpendicular magnetic anisotropy, i.e., the ability of the
magnetization of those materials to be switched back and forth
using a single laser pulse without any other external stimulus.
We reveal that switching does not occur on the femtosecond
or picosecond scale, but rather in a range between a few hun-
dred nanoseconds and a few microseconds. This slow reversal
involves domain wall motion and domain coalescence after
complete ultrafast demagnetization of the Co sublattice. Using
the time-resolved magneto-optical Kerr effect (TR-MOKE),
Hall voltage measurements, and micromagnetic simulations,
we uncover a reversal mechanism initiated by angular mo-
mentum transfer from the RE sublattice to the TM lattice,
followed by a deterministic remagnetization process through
domain wall propagation and rearrangement. Our findings
establish a original type of AO-HIS process and extend the
class of materials and mechanisms relevant for magnetization
control using single laser pulses.

II. EXPERIMENTAL DETAILS

Despite the extensive investigations into the magnetic and
magneto-optical properties of Co-RE alloys from 1975 to
1990 for magneto-optical recording applications [11–13], the

<footnote>*Contact author: michel.hehn@univ-lorraine.fr</footnote>
magnetic behavior of ultrathin CoₓHo₁₋ₓ films (thickness ≤3 nm) remains largely unexplored. In Co-RE alloy thin films, particularly with heavy rare earths such as Gd, Tb, Dy, Ho, and Er, the Co and RE sublattices are antiferromagnetically exchange coupled. When these elements are codeposited at room temperature, the significant atomic size mismatch between Co and the RE leads to the formation of amorphous alloys. To investigate all-optical switching (AOS) in this class of materials, we prepared multilayers, namely, glass (substrate)/Ta(5)/Pt(5)/CoₓHo₁₋ₓ(3)/Ta(5)/Pt(1) (thicknesses in nanometers), deposited using DC magnetron sputtering in an AJA system. The base pressure before deposition was below 2×10⁻⁸ mbar, and the typical deposition rates of the materials were 0.5 Å/s. The film thickness was set to 3 nm to satisfy the domain size criterion required for the observation of AOS [14], ensuring that the lateral size of laser-switched magnetic domains remains bigger than the intrinsic domain size, thus allowing for domain stabilization. A range of Co atomic concentrations (x = 0.64–0.79) was selected to encompass the magnetic compensation point of the alloy, which, for 30 nm thick CoₓHo₁₋ₓ films, has been reported to occur near 74.5% Co at room temperature [15].

All samples were magnetically characterized using polar MOKE hysteresis measurements at room temperature. The films consistently displayed perpendicular magnetic anisotropy (PMA), square hysteresis loops, and full remanence (see Fig. S1 in the Supplemental Material [16]). All loops exhibited the same polarity across the tested composition range, indicating that the magnetization is dominated by a single sublattice. Based on the positive sign of the Kerr rotation at high positive fields, we attribute the dominant contribution to the TM, confirming that the Co sublattice governs the net magnetization across all tested compositions. This observation implies that no magnetic compensation point is reached within the probed range of ultrathin films, in contrast to the behavior of thicker (30 nm) CoₓHo₁₋ₓ layers, where compensation is observed near 74.5% Co [15]. As also reported for CoFeGd thin films [17], we attribute this shift in the compensation point for 3 nm thick films to interface effects, in particular the spin polarization induced in adjacent Pt layers by the Co sublattice.

### A. Optical switching of CoₓHo₁₋ₓ alloys

To investigate the possibility of all-optical switching in CoₓHo₁₋ₓ alloys, we performed static and time-resolved magneto-optical Kerr measurements on a series of thin films with varying Co concentration. Optical switching experiments and TR-MOKE dynamics were carried out using a Ti:sapphire femtosecond laser system with 800 nm pump and 400 nm probe pulses. For single-pulse measurements, the resulting domain structure was imaged several seconds after exposure. In the TR-MOKE experiments, a mechanical delay line up to 1.2 ns allowed time-resolved probing of the magnetization dynamics. The laser repetition rate was 5 kHz, and an out-of-plane magnetic field was applied to reset the magnetization. Reproducible toggle switching, i.e., reversal of magnetization after each laser pulse, was observed in films with Co concentrations between 74.8% and 79% (Fig. S2) [16], which coincides with and slightly exceeds the

<figure><img src="image_3.png" /><figcaption>FIG. 1. Magneto-optical Kerr microscopy images obtained on a glass/Ta(5)/Pt(5)/(Co₇₅.₇Ho₂₄.₃)(3)/Ta(5)/Pt(1) thin film. (a) Single-pulse experiments showing the domain pattern after four successive pulses, with fluence increasing from left to right. (b) Single-pulse toggle switching at a constant fluence of 10 mJ/cm² and pulse duration of 50 fs, with domain configurations shown after 1, 2, 11 111, 11 112, 21 111, 21 112, 31 111, and 31 112 pulses. Each pulse induces deterministic magnetization reversal.</figcaption></figure>

magnetic compensation point for thick films (~74.5% Co [15]). For the composition Co₇₅.₇Ho₂₄.₃, a single laser pulse of 10 mJ/cm² fluence and 50 fs duration produced deterministic toggle switching over more than 30 000 pulses (Fig. 1). This represents a demonstration of full helicity-independent toggle reversal in amorphous CoHo alloy thin films. The switching behavior observed here significantly extends previous work in Co/Ho multilayers [10] and is particularly noteworthy given that Ho, with stronger spin-orbit coupling and larger magnetic moment than Tb or Dy, was not previously thought to support robust single-pulse switching since only a partial single-pulse all-optical switching was observed in the case of Dy and Tb [8].

To characterize the laser parameters governing switching, we constructed a state diagram of fluence versus pulse duration [Fig. 2(a)]. The critical fluence for toggle switching *F*<sub>SW</sub> increases with pulse duration, while the threshold for the emergence of multidomain states *F*<sub>MD</sub> remains nearly constant. This diagram is similar to the one for FeCoGd alloys [18]. At moderate fluences (typically, 10.5 mJ/cm²), circular reversed domains are obtained for pulse durations up to ~1 ps. Beyond this limit, domains become distorted and dendritic, and the toggle efficiency decreases significantly [Figs. 2(c) and S3 [16]]. At higher fluences (typically, 12.5 mJ/cm²), a multidomain state forms at the beam center, while toggle switching persists in the peripheral region due to the Gaussian laser beam profile. These observations point to a delicate balance between full demagnetization and thermal stability of domains. Time-resolved MOKE measurements [Fig. 2(b)] reveal an ultrafast demagnetization of the Co sublattice on a subpicosecond timescale, followed by a recovery whose rate depends on the applied field. At 50 fs pulse duration, the fluence for which toggle switching occurs (~6 mJ/cm²) corresponds to a full demagnetized state in the TRMOKE experiment. Furthermore, no magnetization precession or in-plane reorientation is detected, indicating that the PMA is preserved throughout. However, no clear signature of magnetization reversal is seen within the 1.2 ns temporal window.
<figure><img src="image_4.png" /><figcaption>FIG. 2. Measurements performed on a glass/Ta(5)/Pt(5)/(Co<sub>75.7</sub>Ho<sub>24.3</sub>)(3)/Ta(5)/Pt(1) thin film. (a) State diagram of laser pulse duration versus fluence. The black curve marks the critical fluence $F_{\text{SW}}$ required to induce magnetization switching. The red curve indicates the threshold fluence $F_{\text{MD}}$ beyond which a multidomain state forms. (b) Time-resolved magnetization dynamics measured by the TR-MOKE under an out-of-plane applied field of 9.5 mT and for a 50 fs pulse duration. (c) Evolution of the magnetic domain configuration for fluences of 10.5 mJ/cm² (blue arrow) and 12.5 mJ/cm². For 12.5 mJ/cm², dotted white lines are added in the first two domains images to delimit regions of toggle switching and multidomain at the center of the laser beam.</figcaption></figure>

This suggests that the actual toggle switching occurs on longer timescales. From these measurements, two important conclusions emerge: (1) Toggle switching requires complete ultrafast demagnetization of the Co sublattice, and (2) the remagnetization proceeds through slow micromagnetic dynamics, consistent with a micron timescale reversal mechanism, as explored further in subsequent sections.

For fluences above 6.2 mJ/cm², a fully demagnetized state is reached and then recovers slowly over time. These measurements reveal a clear correlation: When the fluence is sufficient to induce complete demagnetization of the Co sublattice, magnetization reversal is achieved. Conversely, if full demagnetization is not reached, no reversal occurs. At higher fluences, however, a multidomain state becomes stabilized. At this stage, our time-resolved optical setup does not allow for direct observation of the long-lived demagnetized state beyond 1.2 ns, making it impossible to resolve the magnetic configuration (e.g., domain size or the detailed reversal pathway) during this delayed evolution. Thus, an estimate of the reversal timescale is required. To overcome this temporal limitation and gain deeper insight into the magnetization dynamics beyond 1 ns, we fabricated Hall cross structures from the same thin films and performed long-timescale electrical measurements. Special attention was paid to minimizing thermal effects during the lithography and etching steps to preserve the magnetic properties of the alloy. The fabrication process began with spin coating S1803 photoresist onto the sample, followed by a soft bake at 100°C for 1 min. The

first lithography step defined the Hall cross geometry, which was then etched using RF Ar ion milling. A second lithography step was used to define contact electrodes, followed by thermal evaporation of Ti (10 nm) and Au (100 nm). As shown in Fig. 3(a), clear magnetization reversal is observed on a timescale of approximately 1 µs, with a relaxation tail extending up to ~300 µs. A second laser pulse reverses the magnetization back to its initial state with a similar timescale. Pulses 3 and 4 confirm the reproducibility of this toggle behavior. Kerr microscopy images taken after the switching events [Fig. 3(b)] confirm that the final state corresponds to a full magnetic reversal. The slow timescale of this process strongly suggests that it is governed by domain wall dynamics. A similar interpretation was proposed in the case of Co/Pt with close dynamical timescales [19]. In that case, the reversal was attributed to thermally assisted nucleation and domain wall propagation, constrained by the static magnetization surrounding the laser-irradiated region.

Beyond magnetic fields, magnetic domains and domain walls can be deterministically manipulated using various external stimuli, including electric fields [20], lattice strain [21], electric currents [22,23], and thermal gradients [23,24]—the latter often generated by localized femtosecond laser pulses [25,26]. To determine which mechanism governs the switching observed in our system, we performed the experiment presented in Fig. 4. Starting from a uniformly magnetized state ($M^+$, shown in red in Fig. 4), a single laser pulse induces the formation of a reversed domain ($M^-$), visible as a
<figure><img src="image_5.png" /><figcaption>FIG. 3. Experiments performed on a Si/SiO(500)/Ta(5)/Pt(5)/(Co<sub>76.5</sub>Ho<sub>23.5</sub>)(3)/Ta(5)/Pt(1) thin film. (a) Normalized Hall voltage as a function of time after laser pulses 1, 2, 3, and 4. Inset: zoom on the first microsecond of the response. Pulse parameters are fluence = 5 mJ/cm² and pulse duration = 50 fs. (b) Kerr microscopy image acquired after the laser pulses. The initial magnetic state was $M^-$ and corresponds to the blue contrast. Toggle switching results in the appearance of the red $M^+$ contrast. The fluence required for switching is slightly lower than in Fig. 2 due to the use of a Si/SiO substrate instead of glass.</figcaption></figure>

blue region. The laser beam is then repositioned so that its center overlaps the previously written domain (the center of the laser is located at the black cross in Fig. 4), and a second pulse is applied. This results in a clear toggle: The previously reversed (blue) area switches back to $M^+$ (red), while parts of the surrounding $M^+$ background flip to $M^-$. A third pulse at the same position restores the magnetic configuration to that after the first pulse. This sequence clearly demonstrates

deterministic toggle behavior and excludes stray-field-driven or thermally induced gradient mechanisms as the dominant reversal pathway. Instead, the results point to a highly local and intrinsic process—likely triggered by spin or angular momentum transfer during the ultrafast demagnetized state.

It is now well established that ultrafast demagnetization of a ferro- or ferrimagnetic layer can generate spin currents on subpicosecond timescales or lead to angular momentum transfer between sublattices in ferrimagnets [2,3]. It is also known that TMs and RE elements exhibit markedly different demagnetization dynamics. Using element-specific time-resolved x-ray magnetic circular dichroism, previous studies showed that Co demagnetizes on a timescale of ~200 fs [27,28], whereas RE elements respond more slowly: ~480 fs for Gd [27,28], 280–500 fs for Tb [27,28], and 610–980 fs for Dy [29,30]. To the best of our knowledge, no experimental data are currently available for Ho. We thus hypothesize that Ho demagnetizes more slowly than Co, with a characteristic timescale similar to that of Dy. Based on this assumption, we model the transfer of angular momentum from Ho to Co as a spin-transfer torque–like pulse of 1 ps duration (its typical demagnetization time), applied to a fully demagnetized state. This is consistent with the experimental prerequisite for switching established in Fig. 2. After the pulse, the micromagnetic system is allowed to evolve freely, without additional assumptions such as time-dependent anisotropy, saturation magnetization variation, and thermal effects. Micromagnetic simulations were carried out using mumax3 [31]. The simulated volume was discretized using a cell size of 3×3×9 nm³ and a grid size of 2000×2000×1. Periodic boundary conditions (PBCs) were applied in the x and y directions [PBC = (10, 10, 0)] to emulate an infinite thin film. The magnetic parameters were set to $M_{sat} = 400$ kA/m, $A_{ex} = 15 \times 10^{-12}$ J/m, and $K_{u1} = 1 \times 10^6$ J/m³ corresponding to strong perpendicular magnetic anisotropy. The damping parameter $\alpha$ was varied in the simulations, and the temperature was fixed at $T = 0$ K unless otherwise specified. The initial magnetization

<figure><img src="image_6.png" /><figcaption>FIG. 4. Sequential single-pulse laser switching experiment on a glass/Ta(5)/Pt(5)/(Co<sub>75.7</sub>Ho<sub>24.3</sub>)(3)/Ta(5)/Pt(1) thin film (fluence = 9 mJ/cm², pulse duration = 50 fs). Starting from a uniformly magnetized state ($M^+$, red contrast), the first pulse creates a reversed domain ($M^-$, blue contrast). The laser beam is then repositioned (black cross) so that the second pulse overlaps both the reversed and nonreversed regions. This induces a toggle: the previously switched (blue) domain returns to red ($M^+$), while a new reversed region forms in the previously unexposed background. A third pulse restores the configuration observed after the first pulse. This deterministic behavior confirms that the reversal mechanism is local and not driven by long-range stray fields or laser-induced thermal gradients.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 5. Micromagnetic simulation of reversal dynamics. (a) Out-of-plane normalized magnetization as a function of time for different micromagnetic parameters. Black (red) curves correspond to negative (positive) spin polarization. Dashed lines indicate $\alpha = 0.1$, solid lines show $\alpha = 0.01$, and dotted lines show $\alpha = 0.001$. Red circles correspond to positive spin polarization, negative current, and $\alpha = 0.01$; red disks correspond to positive spin polarization, positive current, $\alpha = 0.01$, and $T = 300$ K. (b) Domain configuration calculated for seed 24563. (c) Time evolution of the bubble configuration derived from (b), showing the number of red (black circles) and blue (green circles) bubbles as a function of time.</figcaption></figure>

configuration was randomized using the RandomMagSeed() function.

The spin-transfer torque (STT) was applied assuming a fixed, fictitious bottom electrode with the spin polarization vector *p* aligned along the *z* axis. This STT simulates the generated spin currents on subpicosecond timescales or angular momentum transfer from the RE subnetwork towards the Co subnetwork. The current density *J* was also applied along *z*, with a magnitude of $2.0 \times 10^{11}$ A/m$^2$. The polarization was set to 1, with both positive and negative polarities explored. The nonadiabaticity parameter $\epsilon'$ was set to zero, and the spin torque asymmetry parameter $\lambda$ was fixed at 1. While future simulations incorporating time-dependent temperature profiles near the Curie temperature would better capture thermal fluctuations and cooling dynamics, our present zero-temperature simulations already reveal key trends. As shown in Fig. 5, a small initial asymmetry induced by STT during the 1 ps current pulse can evolve into a deterministic saturated state. In the simulated domain images, red (blue) regions

correspond to normalized out-of-plane magnetization $m_z = +1$ ($-1$).

A first series of micromagnetic simulations was performed using mumax3 [31], starting from a random magnetization state initialized with a cell size of 3 nm. The corresponding results are shown in Fig. 5(a). Regardless of the damping value used, the system systematically evolves toward a uniformly magnetized final state whose orientation is dictated by the sign of the spin polarization of the injected current. By inverting the current direction, the magnetization reverses accordingly [see red circles in Fig. 5(a)], confirming the deterministic nature of the toggle mechanism. Including thermal fluctuations at 300 K does not alter this behavior (red disks), indicating the robustness of the process. The characteristic reversal time extracted from the simulations is consistent with the experimentally observed timescale. To test the sensitivity of this mechanism to initial conditions, we repeated the simulations with different seeds for the random demagnetized state. For realistic damping values in the range 0.01 to 0.1—consistent
with expectations for CoHo [32]—the early dynamics (first 20 ns) remain unchanged regardless of the seed used (Fig. S4). However, the long-time calculations can be affected by periodic conditions when the sizes of the domains formed become comparable to the replicated 6 µm elementary cell. Indeed, it is clearly seen that depending on the seed used, an artificial periodic configuration stabilizes without saturation. We also investigated the influence of the spin torque pulse duration on the final state. For a fixed seed and $\alpha = 0.1$, we observe that pulse durations shorter than 0.4 ps lead to stochastic outcomes (Fig. S5) [16], suggesting that the spin-transfer torque or angular momentum injection must persist long enough to break the symmetry and steer the system toward a deterministic state. For further analysis, we focus on one representative seed over a 30 ns timescale, for which all tested seeds yield qualitatively similar evolution. During the reversal, small magnetic bubbles form—red domains within a blue background or vice versa, as shown in Fig. 5(b). The domain evolution is tracked in Fig. 5(c) by counting the number of red and blue bubbles as a function of time. It can clearly be seen that with a positive (negative) spin polarized current, an excess of red (blue) bubbles forms. Those bubbles, because of their small size, are unstable and will disappear over time. As a result, with a positive (negative) spin polarized current, the size of the blue (red) domains will increase at the expense of the red (blue) domains, leading to a full blue (red) saturated state. The reversal process relies solely on the priority disappearance of the smallest domains for a gain in demagnetizing field energy. The reversal mechanism is thus governed by a subtle initial imbalance, amplified by domain wall motion and demagnetizing field minimization. To confirm that this process is not an artifact of the periodic boundary conditions, we ran additional simulations without PBCs. The early-stage domain evolution is unchanged (Fig. S7) [16], validating the intrinsic nature of the observed mechanism.

Experimentally, we find that CoₓHo₁₋ₓ films near or slightly above the magnetic compensation point exhibit robust single-pulse toggle switching, sustained over more than 30 000 cycles for a 3 nm thick film. Full demagnetization of the Co sublattice is required, and any in-plane magnetization component must be minimized to allow the out-of-plane domain dynamics to proceed.

## B. Optical switching of CoₓDy₁₋ₓ alloys

Building on the insights gained from the CoHo system, we prepared glass/Ta(5)/Pt(5)/CoₓDy₁₋ₓ(3)/Ta(5)/Pt(1) multilayers (thicknesses in nanometers) to investigate all-optical switching in CoDy alloys. Previous studies placed the magnetic compensation composition for CoDy near room temperature between 75% and 78% Co [14,30,33]. Accordingly, we selected Co concentrations ranging from 80.4% to 83.3%, slightly above the expected compensation point. As with the CoHo samples, the films were deposited by DC magnetron sputtering using an AJA system under a base pressure below $2 \times 10^{-8}$ mbar. Their magnetic properties were then systematically characterized. All samples exhibit robust PMA, as confirmed in Fig. S8, and deterministic all-optical switching was observed across the entire composition range. Among the compositions, the one with 81% Co yielded the

most well-defined reversed domains [Fig. 6(a)]. For this optimized concentration, we performed a detailed analysis of the switching behavior, as summarized in Fig. 6. The resulting fluence vs pulse duration phase diagram [Fig. 6(b)] and the magnetization dynamics [Fig. 6(c)] closely mirror those obtained for the Co₇₅.₇Ho₂₄.₃ alloy. Notably, as in the CoHo case, no magnetization reversal is detectable within the 1 ns time window of our time-resolved MOKE setup, and no evidence of in-plane reorientation was observed. These findings confirm that the switching occurs on longer timescales and proceeds through domain wall motion, consistent with the microsecond-scale dynamics previously discussed. This constitutes a demonstration of complete, deterministic single-pulse toggle switching in amorphous CoDy alloy thin films, significantly expanding the class of RE-TM systems known to exhibit AO-HIS. Our results contrast with prior observations in CoDy alloys [8], where only partial or transient switching was reported, and underline the importance of composition, film thickness, and measurement timescale in accessing this novel switching regime.

## III. CONCLUSIONS

In this study, we demonstrated deterministic, single-pulse all-optical helicity-independent switching in amorphous CoDy and CoHo alloy thin films. This discovery expands the family of materials exhibiting AO-HIS and introduces a distinct class of magnetization reversal mechanism. Unlike the ultrafast switching observed in (FeCo)ₓGd₁₋ₓ alloys, which occurs on an ~1 ps timescale via angular momentum transfer between sublattices [2,3], or the precessional reversal occurring in ~100 ps as reported in [34–36], the mechanism revealed here unfolds over microsecond timescales. It is driven by domain wall motion and domain coalescence following full ultrafast demagnetization of the Co sublattice.

This slow, yet deterministic, process suggests a general framework: Any symmetry-breaking excitation introduced shortly after a laser-induced demagnetized state can steer the system toward a stable reversed configuration, even in the absence of light helicity or external fields. Our results offer a compelling explanation for previously puzzling experimental observations, such as the single-pulse switching reported by Zhang *et al.* [9] and Petty Gweha Nyoma *et al.* [37], where the role of interfacial Gd doping or RE substitution was unclear due to a lack of temporal resolution or study. Based on our findings, these cases likely involve similar slow reversal pathways, with angular momentum transfer taking place just after the pulse through sublattice demagnetization. Moreover, our results resonate with dual-pulse experiments such as that in [38], where delayed asymmetry during remagnetization triggered deterministic switching. Altogether, this points to a broader class of AO-HIS phenomena where the timing and nature of asymmetry—whether intrinsic or induced—govern the remagnetization/reversal trajectory. We anticipate that many additional material systems and engineered heterostructures could exhibit this reversal type, especially those combining ultrafast demagnetization with tunable postpulse asymmetries. These insights open promising avenues for designing optically controlled spintronic devices operating on new timescales and principles.
<figure><img src="image_8.png" /><figcaption>FIG. 6. All-optical switching in Co<sub>81</sub>Dy<sub>19</sub> thin films. (a) Kerr microscopy image illustrating the domain configuration after single-pulse excitation, confirming toggle behavior. These results mirror those obtained for Co<sub>75.7</sub>Ho<sub>24.3</sub> and demonstrate full deterministic AO-HIS in CoDy alloys. (b) Time-resolved magnetization dynamics measured by TR-MOKE under a 9.5 mT out-of-plane magnetic field and 50 fs pulse duration. No reversal is observed within the 1.2 ns time window. (c) Fluence versus pulse duration state diagram for a glass/Ta(5)/Pt(5)/Co<sub>81</sub>Dy<sub>19</sub>(3)/Ta(5)/Pt(1) multilayer, showing the critical fluence for toggle switching (black curve) and the threshold for multidomain formation (red curve).</figcaption></figure>

ACKNOWLEDGMENTS

This work is supported by the ANR through the
France 2030 government grants EMCOM (Grant No. ANR-
22-PEEL-0009), PEPR SPIN-TOAST (Grant No. ANR-
22-EXSP 0003), PEPR SPIN-SPINTHEORY (Grant No.
ANR-22-EXSP 0009), and PEPR SPIN-SPINMAT (Grant
No. ANR-22-EXSP-0007) and by the Grant No. ANR-
17-CE24-0007 UFO project, Grant No. ANR-23-CE30-
0047 SLAM project, and the interdisciplinary project LUE
“MAT-PULSE,” part of the French PIA project “Lorraine
Université d’Excellence” (Reference No. ANR-15-IDEX-04-

LUE). This work is part of OPTIMAG supported by ICEEL-
Carnot and Metropole du Grand Nancy. High-performance
computing resources were partially provided by the EXPLOR
center hosted by the University of Lorraine (Project No.
2020M4XXX1952).

DATA AVAILABILITY

The data that support the findings of this article are not
publicly available. The data are available from the authors
upon reasonable request.

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