Tunable skyrmion–edge interaction in magnetic multilayers by interlayer exchange coupling

Magnetic skyrmions are topologically nontrivial spin textures that are stabilized because of the interplay of various magnetic interactions, e.g., antisymmetric Dzyaloshinskii–Moriya (DM) interaction, symmetric Heisenberg exchange interaction, perpendicular magnetic anisotropy (PMA), and magnetostatic interaction.^1,–4 Apart from their topological stability, magnetic skyrmions exhibit intriguing transport properties,^5,–8 for example, the current density required to drive skyrmion motion is orders of magnitude smaller than that for domain wall motion.⁹ Therefore, the skyrmions are recognized as promising candidates for information carriers in future data storage and processing devices.^10,–12 Under a current, the skyrmions with nonzero topological charges exhibit the skyrmion Hall effect (SkHE), which describes the phenomenon that the trajectory of a moving skyrmion deviates from the current direction.^13 –15 In nanowires, generally, the skyrmions move toward the edge due to the SkHE, which restricts the applications of skyrmions in devices.

To suppress the SkHE, several proposals have been addressed. For example, the antiferromagnetic skyrmions,^16,–18 skyrmion/antiskyrmion pairs,¹⁹ and hybrid skyrmions²⁰ avoid showing the SkHE. It is worth noting that, in a reconfigurable scheme, a stripe domain wall situated near the edge of a nanowire can offset the SkHE and promote the longitudinal motion of magnetic skyrmions.^21,–23 The potential well induced by the locally lowering PMA can also be used to guide the skyrmions to move along an artificially set pathway.²⁴ Conversely, the interaction between the skyrmion and film edge (skyrmion–edge interaction) also protects skyrmions from being annihilated. Recently, two groups have made advances in this regard. Iwasaki et al. proposed that, in the presence of the DM interaction, a potential barrier forms around the film edge that can repel the moving skyrmions and protect skyrmions driven by a small current density from being annihilated.¹⁴ Nevertheless, when the current density is excessively large, magnetic skyrmions can overcome this potential barrier; eventually, the repulsive potential becomes an attractive one, leading to skyrmion annihilation. Spethmann et al. experimentally demonstrated that an artificially introduced ferromagnetic rim²⁵ can prevent the occurrence of skyrmion annihilation at the film edge in the zero field.

In this paper, we investigate, experimentally, the skyrmion–edge interaction in magnetic multilayer samples with varying interlayer exchange coupling strength, by employing the magneto-optic Kerr effect (MOKE) microscope. Our samples have the nominal structure: Ta(3)/[Pt(0.5)/Co(0.5)]₃/Ru(1.6)/[Co(0.5)/Pt(0.5)]₃ (hereinafter referred to as “the S1 sample”), Ta(3)/[Pt(0.5)/Co(0.5)]₃/Ru(1.8)/[Co(0.5)/Pt(0.5)]₃ (hereinafter referred to as “the S2 sample”), and Ta(3)/[Pt(0.5)/Co(0.5)]₃/Ru(2.0)/[Co(0.5)/Pt(0.5)]₃ (hereinafter referred to as “the S3 sample”), which are prepared by magnetron sputtering. In the three samples, as expected, the film edge repels the skyrmion bubbles. However, the strength of the repulsive potential is tailored by the strength of the interlayer exchange coupling. Our study suggests that the feature of the skyrmion–edge interaction can be harnessed by tailoring the interlayer coupling strength, providing an impetus to the development of skyrmion-based devices.

Three multilayer stacks with PMA and ferromagnetic interlayer exchange coupling interaction are prepared by the AJA magnetron sputtering on the silicon wafers with 300 nm oxide. The thin films were deposited using DC magnetron sputtering at a base pressure of 4 × 10⁻⁵ Pa. The device (nanowire with 20 µm width and 110 µm length) is prepared by the lift-off process. The MOKE microscope with the perpendicular field is used to measure the hysteresis loops and observe the skyrmion bubbles directly. The MOKE microscope uses a 50× objective lens. The current pulses are applied by the Keithley 6221 current source. The 80 mA current corresponds to a current density of 2.9 × 10¹¹ A/m². By characterizing the shift of out-of-plane hysteresis loops under different DC currents and in-plane bias fields, the spin-orbit torque (SOT) efficiency can be obtained. The effective DMI field H_DMI is also estimated from the dependence of the SOT efficiency on the in-plane bias field.

Figure 1(a) shows the schematic cross-sectional view of the multilayers. By employing the lift-off process, each multilayer is patterned into a nanowire (20 µm width and 110 µm length) with two rectangular electrodes. Figure 1(b) illustrates the top view of the device. The magnetic properties of the multilayers are measured by using the MOKE microscope. As shown in Fig. 1(c), the hysteresis loop of the S1 sample is square with a coercive field of 11 mT. Remarkably, for the S1 and S2 samples, the loops are identical, indicating that they have almost a constant PMA field. In ultrathin films lacking inversion symmetry, the DM interaction is expected to occur at the interfaces.^26,27 We estimate the DM interaction strength in terms of the shift of the out-of-plane hysteresis loops under different DC currents and in-plane bias fields;²⁸ the results are shown in Fig. 1(d). It is seen that, for a sample with the nominal structure of Ta(3)/[Pt(0.5)/Co(0.5)]₃/Ru(1.6), the effective DM field is ∼10 mT, which is one order of magnitude smaller than the reported values.^29,–31 However, as shown in Ref. 32, the micrometer-sized skyrmion bubble with an integer topological charge can be stabilized in the presence of a weak DM interaction with the strength ∼0.1 mJ/m². Because of the low signal-noise ratio of the electron microscopy images due to the thickness of the Co layer, J_ex is hard to be measured accurately by the transmission electron microscopy³³ or the scanning electron microscope with the polarization analysis³⁴ method. However, in our previous study, tuning of J_ex in the antiferromagnetic exchange-coupling area for similar multilayers has been realized by varying the thickness of the Ru layer.³⁵ Therefore, the dependence of J_ex in the ferromagnetic exchange-coupling area for the multilayers in this work is also expected, leading to a weaker J_ex value in the S1 and S3 samples and a stronger one in the S2 sample.

The influence of the Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction strength on skyrmion bubble dynamics is studied. Figure 2 displays the trajectories of skyrmion bubbles in the three samples. In the S1 sample, the skyrmion bubbles are created by a 78 mA sine-wave current pulse with a duration of 27 µs without applying field. Then, a train of repeating square-wave current pulses with a duration of 10 µs and an amplitude of 82 mA is applied to the sample. It is seen that, soon after the action of the first several pulses, some of the skyrmion bubbles are annihilated. However, a skyrmion bubble survives and moves against the charge current pointing −x. As expected, the skyrmion bubble moves toward the edge of the device, indicative of the skyrmion Hall effect. As shown in Fig. 2(a), the skyrmion trajectory is straight but spans a ∼10° angle with respective to the edge. When the skyrmion bubble reaches the edge, the amplitudes of the external magnetic field and the current pulses are increased to 4 mT and 86 mA, respectively, to adjust the shape and size of the skyrmion bubble. During the entire process, the skyrmion bubble remains circular while its diameter is around 1 µm. Before reaching the edge, the skyrmion trajectory in the S2 and S3 samples is analogous to that in the S1 sample, as shown in Figs. 2(b) and 2(c).

Once approaching the edge, the skyrmion bubbles in the three samples behave in distinct manners. In the S1 and S3 samples with the weaker J_ex, the moving skyrmion bubble cannot overcome the repulsive potential from the film edge; as a result, the skyrmion bubble cannot touch the edge, and instead, the skyrmion bubble proceeds along the edge. Before the final annihilation, the skyrmion bubble moves at least 10 µm. During the moving process, the repulsive potential from the film edge cancels out the Magnus force, and the moving skyrmion bubble avoids showing the SkHE, namely, the transverse skyrmion motion pointing +y is halted. However, in the S2 sample with the stronger J_ex, the skyrmion bubble overcomes the repulsive potential from the film edge. Then, the skyrmion bubble rapidly expands and converts to a stripe domain around the film edge, as illustrated in Fig. 2(b). It is worth knowing that, in the three samples, the driven current pulses have a constant current density (∼2.9 × 10¹¹ A/m²). Therefore, the distinct dynamic behaviors of skyrmion bubbles in the three samples may indicate the tailored strength of the repulsive potential from the film edge.

Several possible mechanisms might lie underneath different behaviors of the skyrmion bubbles in the three distinct samples. Among them, the interaction between the magnetization at the sample edge (boundary magnetization) and that at the periphery of the skyrmion bubbles should contribute considerably. As a widely accepted fact, the boundary magnetization develops an in-plane component due to the DM interaction.^27,36 The boundary magnetization can form a repulsive potential barrier, which can repel the skyrmions at the film edge. Meanwhile, two types of skyrmion dynamics have been predicted.¹⁴ If the driven current density is small, the moving skyrmion cannot overcome the potential barrier and bounces back; nevertheless, when the driven current density is excessively large, the skyrmion can overcome this potential barrier, which leads to skyrmion annihilation. Recently, the skyrmion–edge interaction induced by boundary modification is also observed in the Pd/Fe/Ir system with the Co/Fe-decorated edge.¹⁷ At the Pd/Fe island rim, the skyrmion is protected by the edge against annihilation. This mechanism plays a decisive role in the situation that the DM interaction predominates in the total free energy and defines the chirality of the domain walls.

In our samples, nevertheless, the Ru layer is almost irrelevant in inducing the DM interaction; accordingly, the DM interaction strength can hardly be engineered by varying its thickness. Therefore, the distinct skyrmion dynamics in the three distinct samples cannot be attributed to the tailored DM interaction strength. Conversely, our work determines that the strength of the repulsive potential can be tailored by the interlayer exchange interaction strength in the multilayers. With constant current density, in the S1 and S3 samples with weaker J_ex, the skyrmion bubble cannot overcome the potential and the transverse skyrmion motion is halted; in the S2 sample with stronger J_ex, a moving skyrmion bubble overcomes the repulsive potential and is annihilated at the film edge. The interlayer exchange interaction strength is a key factor in determining the strength of the repulsive potential, which determines the dynamics of the skyrmion bubbles close to the edge.

We also study the shape and size of the skyrmion bubbles that are controlled by the out-of-plane field. As shown in Fig. 3, initially, the skyrmion bubbles are created without applying magnetic field; after nucleation, each set of skyrmion bubbles is subject to a different constant field [see Figs. 3(b), 3(d), and 3(f)]. The behavior of the skyrmion bubbles in the 0 mT field resembles that depicted in Fig. 2, except that the skyrmion bubbles tend to expand in the 0 mT field. However, under a +2 mT field, most skyrmion bubbles are annihilated in situ since the field along +z destabilizes the skyrmion bubbles; for a −2 mT magnetic field, most skyrmion bubbles are elongated horizontally.

The effect of the external field can be understood as follows: Generally, the shape and size of the isolated skyrmion sensitively depend on the external field.^37,–39 Meanwhile, the charge current pointing −x induces an accompanying Oersted field. Following the Biot–Savart law, the Oersted field is computed; the results are shown in Fig. 4. In the interior of the nanowire, the Oersted field is small; at the edges, this field increases remarkably and reaches ±3 mT.⁴⁰ When nucleated in the interior, the skyrmion bubble experiences a small field and remains circular. The skyrmion Hall effect leads to a transverse skyrmion motion along +y; hence, the skyrmion bubble experiences a negative field and expands at the upper half of the nanowire [see Fig. 3(b)]. When a +2 mT external field is applied, the spatial distribution of the net field (vector sum of the Oersted field induced by the current pulse and the external field generated by the electromagnet) will differ. As the skyrmion bubble moves across the upper half of the nanowire, it experiences a positive field and tends to be annihilated [see Fig. 3(d)]. On the contrary, if we apply a −2 mT external field, the skyrmion bubble experiences a larger negative field and tends to expand [see Fig. 3(f)]. Recent experiments on [CoB/Ir/Pt]₅ have also shown that the Oersted field gradient can slightly decrease the skyrmion diameter as the skyrmions traverse the nanowire.⁴⁰ If an additional external field gradient can offset the Oersted field gradient induced by the current pulses, the skyrmion bubbles will experience a zero net field when moving across the nanowire. Alternatively, for an isolated skyrmion, a temporally varying external field with an opposite spatial profile can also offset the Oersted field gradient. Following this, in our sample, the external field is increased from 0 to 3 mT as the skyrmion bubble moves across the upper half of the nanowire. Consequently, the skyrmion bubbles in the three samples remain circular while their diameter is around 1 µm, as shown in Fig. 2.

In conclusion, we experimentally demonstrate the tunable skyrmion–edge interaction by interlayer exchange coupling using the MOKE microscope. At the film edge, the skyrmion bubbles behave in distinct manners due to various interlayer exchange interaction strengths. We argue that the interaction between the boundary magnetization and magnetization at the periphery of the skyrmion bubble is responsible for different behaviors. In general, the boundary magnetization can form a repulsive potential barrier, which repels the moving skyrmions at the film edge. Our work demonstrates that the strength of the potential barrier is tunable by the interlayer exchange interaction, and the shape and size of the skyrmion bubbles are controllable by the external field.

This work was supported by Guangdong Basic and Applied Basic Research Foundation (2021B1515120047), Shenzhen Fundamental Research Fund (Grant No. JCYJ20210324120213037), the Shenzhen Peacock Group Plan (Grant No. KQTD20180413181702403), the Guangdong Special Support Project (Grant No. 2019BT02X030), the Pearl River Recruitment Program of Talents (Grant No. 2017GC010293), and the National Natural Science Foundation of China (Grant Nos. 11974298 and 61961136006). Y.L.Z. acknowledges support from the National Natural Science Foundation of China (Grant No. 12004319).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.