Observation and formation mechanism of 360° domain wall rings in synthetic anti-ferromagnets with interlayer chiral interactions

The interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) is an interlayer-mediated antisymmetric exchange interaction observed in multilayer heterostructures, which promotes orthogonal coupling between spins in different magnetic layers.^1–4 This interaction contrasts with the well established intralayer DMI,^5,6 which chirally couples spins within the same magnetic layer. IL-DMI is a coupling mechanism that may find interesting applications in 3D nanomagnetism, as it provides the opportunity of inducing chiral magnetic states in a layer controlled by the magnetic state of another.

IL-DMI can be understood as an effective unidirectional magnetic field breaking the symmetry of the reversal process, leading to a chiral exchange bias.² This exchange bias field has been for instance utilized to achieve field free spin-orbit torque mediated deterministic switching of perpendicularly magnetized thin film systems,^7–11 as an alternative to exchange bias generated at ferromagnet/anti-ferromagnet interfaces. So far, samples with IL-DMI have been typically investigated with magnetometry and magnetotransport techniques, such as the magneto-optical Kerr effect (MOKE)¹ and anomalous Hall effect.^2,12,13

Here, the remanent magnetic domain configurations present in a synthetic anti-ferromagnet (SAF) with chiral exchange coupling due to IL-DMI are investigated using x-ray magnetic circular dichroism photo-emission electron microscopy (XMCD-PEEM). The states imaged are obtained after performing a demagnetizing^14,15 process with different external field offsets added to the cycling sequence. By combining multiple XMCD-PEEM projections measured at different azimuthal angles, the magnetization vector is reconstructed, evidencing the formation of 360° domain wall (DW) rings. The IL-DMI is found to be key for the stability of these structures, as rings are only observed when the exchange bias IL-DMI field is not fully compensated by the external field offset. Experiments are complemented with micromagnetic simulations, which highlight the importance of the relative orientation of external and demagnetizing dipolar magnetic fields with the in plane anisotropy axis of the sample for the formation of the 360° DW rings.

The SAF structure under investigation consists of Si/Ta (4 nm)/Pt (10 nm)/Co (1 nm)/Pt (0.5 nm)/Ru (1 nm)/Pt (0.5 nm)/CoFeB (2 nm)/Pt (2 nm)/Ta (4 nm), deposited by sputtering. The Co layer has dominating strong perpendicular magnetic anisotropy (PMA) provided by the Pt at the interfaces (surface anisotropy K_s = 1.2 mJm⁻²)¹ i.e., it is a hard out-of plane (OOP) layer. In contrast, the CoFeB (Co: 60%, Fe: 20%, B: 20%) has been tailored to exhibit moderately low in-plane (IP) anisotropy, achieved by tuning its thickness slightly above the spin reorientation transition which takes place at 1.55 nm. The transition thickness occurs when the surface anisotropy (K_s = 0.7 mJm⁻²)¹ balances the thin film shape anisotropy, i.e., $K eff = 2 K s / t − 0.5 μ 0 M s 2 = 0$⁠, with M_s being the saturation magnetization (⁠ $M s CoFeB = 1.2 × 10 6$ Am⁻¹, $M s Co = 1.4 × 10 6$ Am⁻¹). During deposition, a magnetic field of ∼100 mT was applied providing further IP anisotropy in the CoFeB layer along the field direction. This effect is negligible on the Co layer, due to dominating PMA. The Pt layers in between both ferromagnetic layers serve several purposes. They provide PMA to the ferromagnetic layers, high spin orbit coupling to enhance the DMI, and also damp the antiferromagnetic Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions due to the Ru spacer. Lastly, the Ta seed layer provides an appropriate basis for the growth of the remaining layers, whereas the top Ta protects the sample from oxidation.

In this type of SAFs, a chiral exchange bias due to IL-DMI has been previously observed under measurement of minor IP hysteresis loops on which solely the CoFeB layer reverses while the Co stays fixed in the OOP direction. Upon reversal of the orientation of the Co layer, the exchange bias changes sign. The unidirectional nature of the effect is manifested by the IP angular dependence of the bias,¹ which shows opposite sign for the two possible directions parallel to the IP anisotropy easy axis (EA), and zero for the directions orthogonal to it. In particular for the sample investigated here, the magnitude of the exchange bias field along the EA is 3.3 mT, compared with a coercivity of 4.0 mT, as evidenced by Figs. 2(c) and 2(d).

To investigate the effect of IL-DMI on the domain states forming in these samples, magnetic microscopy measurements were taken at CIRCE¹⁶ beamline in ALBA Synchrotron, using XMCD-PEEM (see sketch in Fig. 1). In this setup, the azimuthal angle of the sample with respect to the x-rays can be modified in the full 360° angular range, while the incidence angle is fixed to 16° with respect to the surface plane, giving large sensitivity to IP components. Both circular polarization images are recorded and combined exploiting XMCD for magnetic contrast,^17–19 measured at both Fe and Co's L₃ absorption edges at each magnetic state. Prior to the experiments, 50 nm thick $Pt x C 1 − x$ squares and rectangles were deposited using focused electron beam induced deposition (FEBID) on top of the film, serving as non-magnetic references for equalizing both circular polarization images in order to properly compute the final XMCD image. The holder used for mounting the sample into the PEEM chamber has an embedded dipolar electromagnet,^16,20 giving the possibility of applying in-plane uniaxial magnetic fields (⁠ $B → ext$⁠). The nominal IP EA of the CoFeB (⁠ $x ̂$⁠), given by the rectangle alignment mark's long axis, is mounted parallel to the electromagnet's axis after previously saturating the Co layer in one of the OOP directions.

In order to obtain a magnetically non-trivial remanent state, a demagnetization protocol, which consists of consecutively decreasing IP sinusoidal $B → ext$ signals, is applied. $B → ext$⁠, thus, consists of an AC oscillating component (⁠ $B → ext A C$⁠), and a DC or external field offset component (⁠ $B → ext D C$⁠). The protocol is demonstrated in Fig. 2, where the magnetization is probed in a separate x-ray resonant magnetic scattering (XRMS) experiment, performed at SEXTANTS beamline in SOLEIL synchrotron. For this, XRMS hysteresis loops are taken where the specularly reflected signal is recorded, using field sequences where the IL-DMI exchange bias field (⁠ $B → I L − DMI$⁠) is either fully or partially compensated by $B → ext D C$⁠. The x-ray beam spot used is 300 μm in diameter,²¹ and the x-ray beam was set to 13° of incidence with respect to the sample plane, giving large sensitivity to the IP magnetization.²² 

Figures 2(c) and 2(d) show the XRMS hysteresis loops for the two demagnetizing sequences in Figs. 2(a) and 2(b). In the green (fully demagnetized case) shown in Fig. 2(c), $B → I L − DMI$'s $x ̂$ component is fully compensated by $B → ext$⁠, i.e., B_x = 0, with $B → = B → ext − B → I L − DMI$⁠, yielding final zero net magnetic signal. This state corresponds to the one observed via XMCD-PEEM in Fig. 2(e), where the area of black and white domains within the field of view (FOV) is indeed approximately equal. The situation is different for the red (partially demagnetized case) shown in Fig. 2(d), where $B → I L − DMI$'s $x ̂$ component is not fully compensated (⁠ $B x ≠ 0$⁠), reaching a final state with non-zero net magnetic signal. This agrees with the corresponding PEEM experiment shown in Fig. 2(f), where there is a clear dominating magnetic configuration aligned with $B → ext$⁠. In the partially demagnetized case, a number of ring-like magnetic textures (0.5–3.0 μm in diameter) are frequently observed by PEEM, for instance, the one marked by the white arrow in Fig. 2(f). The emergence of a large number of rings is found in partially demagnetized states as the one in Fig. 2(g), where an area with a larger field of view is shown. All the images shown here are taken at the Co L₃ edge and refer to states forming on the CoFeB layer, since the magnetic features are identical at both Fe and Co edges, with Co showing a significantly better signal-to-noise ratio due to the stoichiometry of the CoFeB layer (see the supplementary material).

In the experiments, other demagnetizing sequences with offset fields of different magnitude were performed. The maximum offset investigated was 0.8 mT larger than the one that perfectly compensates the exchange bias, i.e., B_x = 0.8 mT. We observe a decrease in the number of rings as the offset field increases, with a few of them still present at this maximum offset.

To understand better the magnetic configuration of these spin textures, vector imaging of one of the rings is performed by measuring several x-ray beam/sample projections. For this, the sample is rotated in the PEEM chamber with respect to the x-ray direction, as shown in Fig. 1. XMCD images are obtained for a total of eight azimuthal angles, see Fig. 3(a). The images have been previously rotated and aligned with respect to each other in order to have the same spatial orientation, following a similar procedure to the one described in.²³ Additionally, deformations in different projection images are corrected by an algorithm, which makes use of a combination of image registration techniques, using the $Pt x C 1 − x$ marker's geometrical shape as reference landmarks. These deformations arise from the fact that the used PEEM microscope does not inherently present circular symmetry. Some of the electron optical elements, in particular, the 120° beam splitter, typically introduce image distortions, which become relevant when overlaying images for different sample orientations.

The spatially resolved normalized magnetization vector (⁠ $m →$⁠) is then reconstructed,^23–29 by performing a pixel-by-pixel least squares fitting of the XMCD profile (given by $k → · m →$⁠, with $k →$ being the incident x-ray wave-vector) as a function of the azimuthal rotation angle. The resulting vector directions of $m →$ are shown in the central image of Fig. 3(a). The line profiles in Fig. 3(b) evidence the presence of 360° DWs separating the outer and inner domains, whose orientation is the same, and the direction of $m →$ within them is the result of the EA and $B →$ directions. In the reconstruction, great precision is achieved in the determination of the IP components due to the grazing incidence of the x-rays, which on the other hand reduces the sensitivity to OOP components. Furthermore, the magnetic signal decreases in areas where the magnetization changes over small spatial lengthscales in comparison with the microscope's resolution, giving a larger uncertainty in the domain walls' OOP components.

360° DW rings have been previously observed in individual ferromagnetic Permalloy thin film layers,³⁰ in multilayered heterostructures,^31–33 in exchanged biased films,^15,34,35 and in magnetic tunnel junctions.³⁶ The role of Bloch lines,³¹ DW splitting,³² and dispersion in anisotropy¹⁵ have been proposed as mechanisms for explaining their formation.

In order to determine the dependence between the stability of 360° DW rings and the IL-DMI effective field, focus is first set on their topology and magnetic charge distribution. For this, the simplified sketch of the vector reconstructed configuration shown in Fig. 4(a) is used, assuming a fully IP texture. The figure shows an elongated, 360° DW ring with the EA along $x →$⁠. A 1D 360° DW is a topologically non-trivial structure, having been sometimes denominated 1D skyrmions in the literature.³⁷ However, when these DW form a ring structure as the one shown here, the net winding number computed along a line profile diametrically crossing the whole ring is zero due to the opposite chirality of the two encountered 360° DW. Therefore, a 360° DW ring as a whole is topologically trivial, which means that it can be continuously deformed into a single domain state.

Additionally, the elongation observed for the ring textures along the EA is expected based on magnetostatics arguments, i.e., Néel walls prefer to align parallel to the EA rather than perpendicular³⁸ to it. Furthermore, the magnetic charge distribution along the ring structure is anisotropic, as evidenced by the “+” and “−” in the figure. For both (top and bottom) walls parallel to the EA, the two 180° DW forming the 360° DW repel each other, which in combination with the ferromagnetic exchange promote the growth of the annular domain (cyan). In the absence of a net magnetic field, this magnetic texture would expand and relax into broader domains separated by consecutive 180° DW.³⁹ This contrasts with the (left and right) DW orthogonal to the anisotropy axis, where the demagnetizing field arising from the charge distribution now makes the two consecutive 180° DW attract each other, opposing the expansion of the annular domain promoted by ferromagnetic exchange. The competition of these interactions dictates the stability of the vertical 360° DW component at zero field.³⁹ Thus, for the overall 360° DW ring texture to remain stable, a net non-zero $B →$ field along the easy axis is required to compress from both inner and outer parts, preventing it from relaxing and expanding into broader domains, i.e., two consecutive domains separated by 180° DWs. Additionally, this field prevents the unwinding of the inner domain due to it being topologically trivial. This agrees well with previous observations of 360° DW rings in systems with exchange bias,^15,34,35 since the field sequences used there do not add field offsets, resulting in net non-zero fields at remanence.

Finally, we focus on investigating the mechanism behind the nucleation of the rings using micromagnetic simulations. For this, solely a single IP thin film is modeled representing the CoFeB layer of the SAF, whose simulation parameters are summarized in Table I. As in experiments, $B → I L − DMI$ is parallel to the EA (horizontal $x →$ direction), and it is modeled through the effective field $B →$⁠. In these simulations, we do not include additional effects related to the interaction between Co and CoFeB layers. In particular, the magnetostatic interaction in between the two layers is not considered. In the following, our simulations show a clear mechanism for the formation of the rings despite this approximation.

In order to model the formation process via micromagnetic simulations, the first step consists of obtaining a magnetic configuration formed by multiple domains, resembling an intermediate state during the demagnetizing protocol. For this, the simulation starts from a fully saturated $+ m x$ configuration. Then, a $B →$ field of increasing magnitude is applied along $− x ̂$ with a small $− y ̂$ component (5° with respect to $+ x ̂$⁠), which represents a misalignment between $B → ext$ and the EA. A circular defect of 0.8 μm radius and with 20% anisotropy value of the layer is included to trigger the nucleation of domains (cyan). Once $B →$ reaches the switching field magnitude, the system is allowed to evolve dynamically, eventually reaching the state shown in [Fig. 4(b), state (0)]. All 180° DWs in the simulation space have a $− m y$ component set by B_y,¹⁴ resulting in the magnetic charge distribution, once again represented by the “+” and “−” signs.

As DW of opposite charge get closer promoted by the growth of the inverted domain, the intensity of the demagnetizing field (⁠ $B → d$⁠) associated to the magnetic charges begins to increase [Fig. 4(b), state (1)]. The varying $B → d$ in combination with the constant $B →$ eventually reaches the sufficient field magnitude for overcoming the anisotropy dominated nucleation field, as a consequence locally inverting the magnetization. This allows for the formation of a new pair of 180° DWs during the reversal, with their core magnetization pointing along $+ m y$⁠, given that the $y ̂$ component of $B → d$ in this case is opposite and larger in magnitude than the original set by $B →$⁠, i.e., $B d y$ > −B_y. This is exemplified in the crop shown in [Fig. 4(b), state (2)]; the new 180° DW forms next to the original $→ ↓ ←$ from [Fig. 4(b), state (1)], resulting in a 360° DW with $← ↑ → ↓ ←$ configuration. Thus, for the formation of 360° DW and the forthcoming rings, it is key for the $y ̂$ component of $B → d$ to be opposite in sign and greater in magnitude than B_y. In the hypothetical case where either $B →$ and/or $B → d$ were purely along $x ̂$⁠, it would not have lead to the formation of the rings, as the existence of non-zero transverse field components is crucial.

From this point on, a ring is finally formed after the red domains shrink due to the opposing $B →$ [Fig. 4(b), states (3)–(5)]. The key role of an alternating B_y field [Fig. 4(b), states (0)–(1)] for the formation of 360° DW rings in a system with m_x domains is similar to previous works in nanowires with injection pads,¹⁴ where 360° DW were stabilized via the application of alternating external magnetic fields. Here, instead, the net magnetic field is dominated by $B → ext$ or $B → d$⁠, for different steps of formation.

In this ideal simulation space, the ring eventually annihilates [Fig. 4(b), state (6)], in contrast with the experimental results where rings remain stable. This can be readily explained due to the presence of pinning sites, defects, and imperfections in the real sample that locally alter the magnetic energy landscape, leading to their meta-stability.⁴² 

The mechanism for the formation and stabilization of rings described here is applicable to a single film subject to a demagnetizing sequence with a nonzero constant offset field. This type of procedure is more likely to happen in films with an intrinsic bias field, which explains the larger number of works reporting the observance of rings in exchanged bias bilayers.

In conclusion, we have observed 360° DW rings via XMCD-PEEM magnetic vector reconstruction, forming in a SAF exhibiting exchange bias due to IL-DMI. These textures are observed at remanence after applying IP demagnetizing field sequences where a global offset in field is added. A combination of XMCD-PEEM and XRMS shows how the rings are only found when the field offset does not perfectly compensate for the IL-DMI exchange bias field present in the SAF. We propose a mechanism for the formation and stability of the rings, based on analyzing their magnetic charge distribution and topology, in combination with micromagnetic simulations. First, a non-zero net IP field parallel to the easy axis, result of external and IL-DMI fields, is key for their stability at remanence. This net field in combination with pinning sites prevents their relaxation and annihilation due to their trivial topology. Secondly, a non-zero component of the net field perpendicular to the easy axis is required for their formation. This component sets the initial direction of two 180° walls at the start of the reversal process, which subsequently combine with two other 180° walls that form afterward. The wall component of this second set of 180° walls is opposite to the original ones, set by the strong demagnetizing field in between domains that dominate as these become closer to each other. The combination of the two sets of consecutive 180° walls results in two 360° walls of opposite chirality, leading to a 360° wall ring. A deep understanding of the effect of IL-DMI on the magnetic reversal process and domain structure of SAFs is crucial for the potential exploitation of this effect in spintronic devices.

See the supplementary material for comparison between XMCD-PEEM images taken at Co and Fe edges (Fig. S1), evidencing identical magnetic textures in both cases.

This work was supported by UKRI through an EPSRC studentship, Nos. EP/N509668/1 and EP/R513222/1, the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (No. PRTR-C17.I1), and the Aragon Government through the Project Q-MAD.

A.H.-R. acknowledges the support by Spanish MICIN under Grant No. PID2019-104604RB/AEI/10.13039/501100011033 and by Asturias FICYT under Grant No. AYUD/2021/51185 with the support of FEDER funds. S.R.-G. acknowledges the financial support of the Alexander von Humboldt foundation. L.S. acknowledges support from the EPSRC Cambridge NanoDTC No. EP/L015978/1. C.D. acknowledges funding from the Max Planck Society Lise Meitner Excellence Program. The ALBA Synchrotron is funded by the Ministry of Research and Innovation of Spain, by the Generalitat de Catalunya and by European FEDER funds. We acknowledge Synchrotron SOLEIL for providing the synchrotron radiation facilities (Proposal No. 20191674). S.M. acknowledges support from EPSRC Project No. EP/T006811/1. M.A.N. and M.F. acknowledge support from MICIN project PID2021-122980OB-C54. For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC-BY) licence to any Author Accepted Manuscript version arising from this submission.

The author have no conflicts to disclose.

Miguel A. Cascales Sandoval: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Aurelio Hierro-Rodríguez: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Sandra Ruiz-Gómez: Data curation (lead); Investigation (equal); Writing – review & editing (equal). Luka Skoric: Investigation (equal); Software (supporting); Writing – review & editing (equal). Claire Donnelly: Investigation (equal); Writing – review & editing (equal). Miguel Angel Niño: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Elena Vedmedenko: Investigation (equal); Writing – review & editing (equal). Damien McGrouther: Investigation (equal); Writing – review & editing (equal). Stephen McVitie: Investigation (equal); Writing – review & editing (equal). Samuel Flewett: Investigation (equal); Writing – review & editing (equal). Nicolas Jaouen: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Michael Foerster: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (supporting); Writing – review & editing (equal). Amalio Fernández-Pacheco: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data utilized to generate the figures shown in the text can be found at the Enlighten repository of the University of Glasgow: https://doi.org/10.5525/gla.researchdata.1511.