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All-optical switching of magnetic domains in Co/Gd heterostructures with Dzyaloshinskii-Moriya Interaction

Given the development of hybrid spintronic-photonic devices and chiral magnetic structures, a combined interest in all-optical switching (AOS) of magnetization and current-induced domain wall motion in synthetic ferrimagnetic structures with strong Dzyaloshinskii-Moriya Interaction (DMI) is emerging. In this study, we report a study on single-pulse all-optical toggle switching and asymmetric bubble expansion in specially engineered Co/Gd-based multilayer structures. In the absence of any external magnetic fields, we look into the AOS properties and the potential role of the DMI on the AOS process as well as the stability of optically written micro-magnetic domains. Particularly, interesting dynamics are observed in moon-shaped structures written by two successive laser pulses. The stability of domains resulting from an interplay of the dipolar interaction and domain-wall energy are compared to simple analytical models and micromagnetic simulations.

In this paper, we employed synthetic-ferrimagnetic Pt/Co/Gd stacks for AOS. The strong anti-ferromagnetic coupling at the Co/Gd interface [16] and the large contrast in demagnetization times between Co and Gd [17,18] ensure the opticalswitching of our samples, in a scenario that recently was explained in more detail [19,20]. To manipulate the strength of DMI through structural (a)symmetry, structures with a single ferrimagnetic interface (Co/Gd) and double ferrimagnetic interface (Co/Gd/Co) are proposed. We also prepared another group of samples with different capping materials to investigate the effect of the intermixing between the capping layer and the under-layers. Asymmetric domain wall motion is observed indicating the existence of DMI. After the comparison of AOS properties, we focus on the potential role of the DMI on the field-free AOS process and the stability of optically written magnetic domains. Two successive laser pulses were produced to write elongated moon-shaped magnetic domains in our synthetic-ferrimagnetic thin-films. A simple model including the competition between dipolar interaction and domain-wall energy is proposed, which describes the domain shrinkage at the sharp ends and expansion at their waist. Both the micromagnetic simulation and experimental observations exhibit obvious shrinkage and negligible expansion. Moreover, DMI is found to stabilize the AOS-written small-size domain stripes as expected.
To distinguish the strength of DMI through structural asymmetry, we grow samples (see Figure 1 (a)) with single and double Co layers by magnetron sputtering and marked them as S/Pt: Ta(4 nm)/Pt(4 nm)/Co(1 nm)/Gd(3 nm)/Pt(4 nm) and D/Pt: Ta(4 nm)/Pt(4 nm)/Co(1 nm)/Gd(3 nm)/Co(1 nm)/Pt(4 nm), where 'S' and 'D' refers to single and double. Since time-dependent intermixing (particularly at the Gd/Pt interface) over time scales of days to weeks were observed in a similar structure, we also prepared another pair of structures with different capping layers, S/Ta and D/Ta, as reference.
All of the structures are deposited on 2 types of substrates, Si:B and silicon with a 100-nm thermal silicon oxide layer (Si/SiO 2 ). The base pressure of our ultrahigh vacuum deposition system is around 2 × 10 -9 mbar. The (111) texture of the bottom Pt was ensured by a Ta seed layer [21], which promotes perpendicular magnetic anisotropy (PMA) induced by the lower Pt/Co interfaces. The PMA is confirmed by polar MOKE, as seen in Figure 1 (b).
The Curie temperature of bulk Co is 1403 K while the Curie temperature of bulk Gd (289K) lies below room temperature (298K). Considering that the Curie temperature for nanometer-thin films is even lower, the Gd layer will be paramagnetic at room temperature. However, due to the strong anti-ferromagnetic exchange interaction at the Co/Gd interface, a layer of roughly 1-2 atomic layers will be magnetized oppositely to Co at room temperature. This process is possibly enhanced by thermodynamically driven interdiffusion [22] between Co and Gd, which is expected to be of particular relevance for the top Gd/Co interface in the double-layer structures, leading to a composition at the interface close to a Gd 40 Co 60 alloy [23,24]. The compensation temperature ( . ) is defined as the temperature for which the total magnetic moment of the whole structure vanishes. As a rule of thumb, the higher . , the more Gd is inversely magnetized at the Co/Gd interface at room temperature.
We measured the magnetic moment of our samples using the vibrating sample magnetometer (VSM) mode of a superconducting quantum interference device (VSM-SQUID) to evaluate the magnetic moment of our stacks as a function of temperature, and, more specifically, comp. , from which we can extract the amount of magnetized Gd at the syntheticferrimagnetic Co/Gd interfaces [13]. For each sample, we applied + 6 T external field to saturate the film at the start, then turn off the field, and measure the perpendicular component of the magnetic moment at different temperatures. The magnetic moments per unit surface area versus temperature are shown in Figure 1 (c). While the temperature decreases, the magnetization of the Gd layer increases, and below comp. , the Gd, instead of the Co layer, starts to dominate the total moment. Upon further decrease of the temperature, the total magnetic moment will rapidly increase (in the direction of the Gd moment), whereby the (in-plane) shape anisotropy will overcome the (perpendicular) interfacial anisotropy, and starts to be dominant. As a result, the easy axis will rotate from out of plane to in-plane, as seen in the measurements by a sharp collapse of the magnetic moment for lower temperature (indicated by pointers in Figure 1 (c)). More details about measuring comp. with a bias field and the corresponding temperature-dependent magnetic moments are given in Supporting Information part I.
For a proper interpretation, it is of relevance to note that for structures with two Co layers and a double Co/Gd interface, one would ideally expect both a doubling of the Co moment, as well as the Gd moment. Thus, based on the assumption that the top (Gd/Co) and bottom (Co/Gd) interface are their exact mirror image, one would expect that the comp. of double Co/Gd interface structures will be comparable with comp. of the single (Co/Gd) interface group. However, as seen in that compared with the case when Co is deposited on Gd, less rapid intermixing is observed when Gd is deposited on Co [22]. The same trend is observed for the samples capped with Pt, albeit they display a higher comp. compared to their Ta counterparts, and the difference between S and D structure is larger. For structures with a single Co layer, the sample capped with Pt (S/Pt) exhibits less intermixed Gd compared with S/Ta, which might be caused by the intermixing between Gd and the Pt capping layer. Furthermore, note that we did not observe comp. below room-temperature for D/Pt in Figure   1 (c). However, the inverse Kerr signal, shown in Figure 1 (b), indicates an inverse total moment of the whole structure which means the Gd moment is larger than the Co moment in D/Pt. Therefore, we deduce that D/Pt has a comp. above room-temperature indeed. We quantified the strength of DMI in our samples employing a magneto-optical Kerr microscope to observe asymmetric DW movement in the creep regime with an in-plane field x and a perpendicular field z . The dependence of DW velocities on the in-plane field is found to display a minimum occurring at a non-zero value of x , which we use as an indication of the strength of DMI and mark it as DMI [25]. A typical result of asymmetrical DW motion in the presence of an in-plane field x is shown in Figure 2 (a). The applied 0 z is around tens of milli-tesla, and the in-plane field 0 x is in the range of ± 350 mT. Due to strong pinning and comp. being close to room-temperature, we failed to observe DW motion in sample D/Pt. The other three samples displayed a very pronounced asymmetry in the DW velocity which indicates a sizable DMI. We employed a procedure using an empirical function (see Supporting Information part II) by which we obtained the values of the effective DMI field , as shown in Figure 2 (b) -(d). In a ferromagnetic system, the DMI energy can be extracted by | | = 0 S | DMI |√ / eff [26], where S is the saturation magnetization, the exchange stiffness and the eff effective anisotropy. As we mentioned above, in a Co/Gd system, there is a very thin layer of Gd antiferromagnetically coupled with Co at the Co/Gd interface. It has been reported that the thickness of the antiferromagnetic Gd layer is about 0.5 nm. Although extracting a quantitative value of the DMI parameter is far from trivial for this system, we performed a simplified analysis to derive a rough estimate. By assuming the thickness of We stress that our estimate of | | is just a rough estimate for several reasons, including but not limited to the uncertainty of and . Hereon, we leave the exact value of | | in our Co/Gd system as an open question for further research. We carried out all-optical switching experiments on these synthetic-ferrimagnetic multilayers. All samples were firstly saturated with an external field and then excited by single laser pulses without applying a magnetic field. Each structure was exposed to linearly polarized laser pulses with 700 nm central wavelength, ~100 fs duration, and a pulse energy up to 1 μJ, focused on typically a spot size of ~50 μm diameter. The all-optically written domains were imaged after mounting the samples in a Kerr microscope. In this section, we will discuss experiments aimed at exploring the AOS efficiency of the various samples. In the following sections will report on experimental investigations aimed at understanding the stability of small, optically written micro-magnetic domains, after first having provided some physical insight by introducing some simple models.
As outlined above, we start by exploring the AOS efficiency. A threshold fluence 0 is defined as the threshold pulse energy 0 divided by the laser spot area 0 (defined at 1/e intensity). Considering the thermal switching mechanism, demagnetization of the magnetic layer is a precondition for magnetization switching. We varied the pulse energy by a neutral density filter wheel and wrote circular domains by single laser pulses, shown in Figure 3 (a). It can be seen that above the threshold energy 0 , the domain area exhibits a positive correlation with pulse energy. The areas of domains written on the four samples are plotted in Figure 3 (b) as a function of pulse energy. Supposing the energy of the laser pulse shows a Gaussian spatial profile, in the case of an elliptical laser spot, the relation between the domain area and the pulse energy has been derived to be [28] where is the length of the short axis for the elliptical Gaussian spot and the ratio between the long and short axis. and were determined from the Kerr images, after which 0 and 0 can be fitted using Equation (1). The fitted 0 of the four structures grown on Si/SiO 2 are smaller than 0 for structures with Si:B substrate, due to more efficient optical absorption.
More details are discussed in Supporting Information part III. To understand the stability of small domains after AOS, we will distinguish two types of domains, as can be simply produced by one or two laser pulses. (i) Circular bubbles are written by AOS and using a single pulse, such as shown in Figure 3 (a). Note that these domains are expected to form skyrmionic bubbles, i.e., Né el-type domain walls with net chirality at zero fields when the DMI is strong enough. (ii) Moon shape patterns are produced by two successive, slightly displaced laser pulses, which converge to extremely thin, curved stripes if the displacement of the laser pulses is much smaller than the diameter of the laser spot, see Figure 4 (a). The latter one (type (ii)) will be discussed in the following part.
We propose that the small domains display shape changes due to the laser's heating effect or the following creep processes.
To describe the creep-like deformation of the narrow-stripe-domain, we successively address two parts: the sharp tip and the middle region.
For an ideal writing process, governed by an entirely local switching event with a well-defined threshold fluence, two moon-shaped domains are formed, touching in two singularities at opposite sides of the laser spot, where two domain walls cross. Such a structure is intrinsically unstable, as we verified by micro-magnetic simulations below. At a time-scale of nanoseconds, the two touching domains will detach as illustrated in Figure 4 (a), ending up in two tapered domains with rounded ends. To further reduce their micromagnetic energy, these tapered ends will shrink like Figure 4 (b) illustrates.
This shortening process is dominated by the reduction of domain wall energy to lower the total energy, where the domain wall energy density is defined as σ = 4 √ − (per unit area) [29,30]. In this way, not only and eff but also the strength of DMI is related to the instability (shrinkage) of the domain at its tip end; the larger the DMI energy the larger its stability, so the slower the shrinkage.
To make an order of magnitude estimate of the effective field governing the shrinkage process, we approximate the tip end by a sharp triangle with a semi-circular cap, where θ is the opening angle, is the diameter, and is the ferromagnetic layer thickness (see Figure 4 (b)). In the limit of → 0, this structure can be considered as a stripe with . Note that upon contraction, and assuming a small but finite value of θ, the value of will increase, leading to a gradually slowing down of the shrinkage process.
However, this contraction will not continue indefinitely. When the width of the stripe grows larger, dipolar energies, which strive to increase the stripe width, will increase. In order to obtain a simple estimate, we approximate the domain by a semi-infinite stripe with a straight cap. To avoid divergencies in the integral for dipolar energies, the domain wall width ∆ should be assumed to be finite. According to the Biot-Savart's Law and the difference of energy, we derived an approximate equation for the effective field associated with the dipolar interaction: eff di = 0 S ln [ where ∆ is the width of DW (see Supporting Information part IV). To be noticed, eff di has the opposite sign as eff DW . As a consequence, the total effective field of the shortening process can be expressed as Note that, as a consequence, eff sh will fade-out slowly with increasing .
Finally, we note that near the center of the moon-shaped domain, it can be modelled as a stripe of width with infinite length, corresponding to assuming → 0. In this limit, the broadening of the stripe at its center does not cost any domain wall energy, but dipolar interaction would result in a lower total energy with an increasing . As a consequence, in this limit, there will always be a tendency to broaden. In practice, this process stops because the effective field becomes too small to lead to measurable creep, or the domain transforms into a shape with a less pronounced aspect ratio, in which the net driving force to reduce the DW energy may result in a net shrinkage everywhere, ultimately leading to a collapse of the complete domain. Seen in Figure 4 (c), an expansion process driven by dipole interaction will be observed in the middle of the narrow domain. Regarding the infinite length of the stripe domain (compared with its width), we can obtain the effective field eff ex = 2 0 S .
Thus, it is found that the larger the domain width , the smaller the driving field associated with the expansion. With a specific and experimental S , eff ex of each structure can be quantitively obtained. For our structures, with a width of at least 1 micro-meter, and using typical parameters, this leads to effective fields of 0.4 mT or smaller. In order to make an estimate of the relevance of such an effective field for our samples, we measured the domain wall velocity as a function of perpendicular field (at zero in-plane field). We fitted the results for each sample using the relation between the creep velocity and the driving field ln( )~( 0 z ) − 1 4 , and extrapolated the trends according to these fits (more details can be found in Supporting Information part V). Thus, our estimate of eff ex extrapolates to a maximum velocity less than 1 μm in several days for all samples, which means that in our case the expansion process is expected to be negligible. We note that this weak tendency of widening a domain at its center is related to the small magnetization of our films, as a consequence of the compensating Co and Gd moments, leading to small dipolar effects. Besides, there isn't any clear expansion process during the short-term time scale for all of the step sizes in our simulation.
Finally, we note the asymmetry in shrinkage at the top and bottom end of the domain, particularly for the smallest step size ( Figure 5 (a)). This artefact is due to a combination of our finite mesh size and the point like anomaly in the initial state with crossing domain walls, but resolving it goes beyond the scope of this paper.  Figure 5. This demonstrates that an initial shortening process happened in the time interval between creating the domains and measuring the Kerr images. We also notice that the thinner domains (corresponding to largest and smallest ) produced with small step size suffer from stronger quenching processes, while more stable domains are produced with larger step sizes. We decreased the step sizes until the domains are unstable even at a time scale of minutes. For the S/Pt, D/Pt, S/Ta, and D/Ta structures, this led to a minimum step size of (roughly) 2 μm, 1 μm, 2 μm, and 5 μm respectively. According to Equation (2), the effective driving field of the shortening process eff sh has a contribution that is proportional to the DW energy, which is negatively correlated to the DMI energy .
Comparing the domain images at 2 μm step size in Figure 6 (c) and (d), the sample with larger structural asymmetry (S/Ta) still shows some small domains, whereas all domains were completely quenched for the D/Ta sample. This behavior hints at a larger stability for domains in S/Ta structures, which is consistent with Equation (2). Since D/Pt exhibit comp. higher than room temperature, other complicated mechanisms might be involved in the domain's stability, we refrain from a discussion of the group capped by Pt (S/Pt and D/Pt) here. To describe the shape-change of domains more quantitatively and with specific emphasis on domain dynamics at a longer time scale, we analyzed the variance of the waist width and the opening angle, corresponding to the expansion and shrinkage respectively. The definitions of the width and the opening angle ( l and r ) are given in Figure 7 (a). In passing we note that the observed difference between l and r can be explained by an asymmetry of the laser spot. For that reason, we averaged l (left domain) and r (right domain) of each domain pair with the same step size. Furthermore, we averaged width of domains within ± 5˚ range around the x-axis. The averaged λ, as well as the averaged width, as a function of time (after AOS) for each structure are shown in Figure 7 (b) -(d).
We first focus on a possible widening effect. The dashed black lines in the top panels of Figure 7 (b) -(d) represent the averaged width of the ideal shape (without expansion), which is determined by the corresponding step sizes. Taking the error bars into account, the measured (averaged) width does not significantly deviate from the ideal values, i.e., there is not any observable expansion process in both the short-term and the long-term time scales after AOS.
Next, we address the shortening process, by inspecting the lower panels of Figure 7   Extrapolating the measured field-induced DW velocities using the creep law, we also estimated the experimental driving field 0 ex sh . The error bar of the experimental data comes from the standard error of the fitted . Next, we address how we derived the 'theoretical' values. The driving field for shortening can be obtained from Equation (2). eff sh can be calculated by adopting a value of exchange stiffness = 16 pJ/m from the literature [27], using the saturation magnetization and effective anisotropy eff from our experimental data (VSM data, assuming = 1. appreciably larger than ex sh and 0 ex sh , they can be attributed to several reasons. Firstly, as described by our physical model on the shrinkage, under the limitation of → 0, the length change of the semicircular cap ∆ (from to ′ shown in Figure 4 (b)) can be neglected. In the case of a specific , the contribution of ∆ would result in a smaller 2(4√ eff − ) s (positive term of Equation (2)) and a smaller eff sh . Secondly, with a specific , the dipole interaction would be larger, thus result in a larger 0 S ln [ ( −∆) 2 ∆ 2 ] (negative term of Equation (2)) and also a smaller eff sh . Thirdly, the estimations of the DMI energy and the ferromagnetic layer thickness are quite rough. Finally, taking the light blue areas (confidence interval) in Figure 7 (e) and (f), as well as the error bars into account, we conclude that our model is in reasonable qualitative agreement with the experiments.
In conclusion, we carried out a series of experiments on Pt/Co/Gd multilayers with single and double Co/Gd interfaces, which in the ideal case should correspond to asymmetric and symmetric structures, respectively. Firstly, the compensation temperature was measured to confirm the synthetic-ferrimagnetic behavior of these stacks. Then the DMI strength was estimated by measuring asymmetric field-induced DW motion in the presence of an in-plane field. Next, we proposed a physical model for two types of shape-change in narrow domain stripes, i.e., a shortening and a widening process.
Micromagnetic simulations and experimental observation on the optically written domains were also performed, which qualitatively and quantitively confirmed the shrinkage process and excluded the expansion process of domains. Through the comparison between the theoretical and experimental results on the shrinkage of domains, we demonstrated the applicability of our model, which describes the role of DMI on the shortening process of optically switched domains. More specifically, we conclude that DMI as inherently built into the Pt/Co/Gd stacks, is helpful for stabilizing AOS-written small-size domain stripes. We also notice that it is not trivial to scale down to sub-micron dimensions as would be required for large data densities, which can be another significant follow-up research to do.