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Next-gen memory: How skyrmions behave at surfaces

Related publications: Zhang S. L., van der Laan G., Wang W. W., Haghighirad A. A. & Hesjedal T. Direct Observation of Twisted Surface skyrmions in Bulk Crystals. Phys. Rev. Lett. 120, 227202 (2018). DOI: 10.1103/PhysRevLett.120.227202; Zhang S., van der Laan G., Müller J., Heinen L., Garst M., Bauer A., Berger H., Pfleiderer C. & Hesjedal T. Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet. Proc. Natl. Acad. Sci. 115, 6386–6391 (2018). DOI: 10.1073/pnas.1803367115

Publication keywords: Resonant elastic X-ray scattering (REXS); Magnetic skyrmions; Surface reconstruction

Magnetic skyrmions are promising candidates for the next generation of memory devices as they allow increased storage density, and require less energy. The established methods for studying skyrmions, e.g. neutron diffraction and electron microscopy, are not sensitive to the near-surface region of a sample, which is the area most relevant for applications.

In order to characterise the 3D structure of the skyrmion lattice for the first time, an international team of researchers established a new X-ray technique for the direct measurement of the helicity angle – a quantity that is characteristic for the different types of skyrmions. They then made use of the uniquely tunable surface-sensitivity of soft X-rays, tuning the energy of the incident X-rays across the absorption edge, while carrying out circular dichroism of resonant elastic X-ray scattering peak technique. This allowed them to fully reconstruct the detailed structure of the skyrmion lattice as a function of depth, information crucial for enabling future skyrmion-based devices.

The soft X-ray diffractometer RASOR on the Beamline for Advanced Dichroism (I10) is extremely well-suited for characterising skyrmion structures. It offers ultra-high reciprocal space resolution, allowing clear observation of magnetic signals, with an advanced sample environment (ultra-high vacuum (UHV), high temperature stability, magnetic vector field, and multi-axis goniometer).

$Figure 1: It’s skyrmion time! Look-up ‘clock’ illustrating the one-to-one correspondence of the extinction direction (red arrow) and the skyrmion helicity angle. The circular dichroism (CD) of the diffraction peaks is obtained by taking the difference of the diffraction intensities with leftand right-circularly polarised incident light. The CD-REXS pattern for a skyrmion lattice state exhibits positive and negative peaks (yellow and blue spots), separated by the indicated extinction direction at which the CD intensity vanishes. Adapted from Phys. Rev. Lett. 120, 227202 (2018).$: Figure 1: It’s skyrmion time! Look-up ‘clock’ illustrating the one-to-one
correspondence of the extinction direction (red arrow) and the skyrmion
helicity angle. The circular dichroism (CD) of the diffraction peaks is
obtained by taking the difference of the diffraction intensities with leftand
right-circularly polarised incident light. The CD-REXS pattern for a
skyrmion lattice state exhibits positive and negative peaks (yellow and
blue spots), separated by the indicated extinction direction at which the
CD intensity vanishes. Adapted from Phys. Rev. Lett. 120, 227202 (2018).

The discovery of skyrmions in chiral magnets, featuring non-trivial topological winding described by a highly unusual emergent electrodynamics, has inspired tremendous efforts to read, write, and manipulate individual skyrmion bubbles, as well as skyrmionic textures in tailored nano-systems amenable for data storage, transmission, and processing¹. So far, skyrmions have been mostly treated as two-dimensional objects that extend into the third dimension forming tubular structures. However, it is well-known that the abrupt change of boundary conditions (truncated crystal) can lead to a shift in atomic positions in order to lower energy, commonly known as a (structural) surface reconstruction. Similarly, magnetic structures at or in the vicinity of a surface may be fundamentally different from the bulk, resulting from broken symmetry or non-continuous properties. Different mechanisms have been discussed as the underlying cause of magnetic surface effects, which depend on the intrinsic and extrinsic properties of the system, and which may be present at the same time, leading to a magnetic surface reconstruction. Their presence has far-reaching implications for the creation of skyrmions in surface-dominated systems. More generally, it identifies surface-induced magnetic effects as an unchartered scientific territory, in particular due to the lack of experimental tools allowing for their study.

Magnetic skyrmions are characterised by the topological winding number N, radial profile, polarity, and helicity angle χ. Prior to our work, only two types of N = 1 skyrmions with different helicity angles were experimentally confirmed, i.e., Néel-type skyrmions (χ = 0° or 180°) that exist at the surface/interface of thin film systems with strong spin-orbit coupling, and Bloch-type chiral skyrmions which are found in chiral magnets, such as MnSi and Cu₂OSeO₃ (χ = ±90°). We recently developed a set of new resonant elastic X-ray scattering (REXS) based methods² with which the winding number N³, and the exact value of the helicity angle χ, can be unambiguously determined, making use of circular dichroism. The hexagonally long-range ordered skyrmion lattice phase gives rise to a six-fold-symmetric diffraction pattern in REXS² (see Fig. 1).

: Figure 2: Depth-dependent probing and model of the skyrmion surface state in Cu2OSeO3. (a) Depth-dependence of the averaged helicity angle (χprobed) and fit to the data (red curve) using the model
in (b). At the top surface, the skyrmions are Néel-type with χ = 180°. The helicity angle continuously decreases when probing deeper into the crystal, eventually reaching the well-characterised
bulk skyrmion state with χ = 90°. (b) Illustration of the skyrmion crystal with its surface state. In (c), the corresponding skyrmion magnetisation patterns for the indicated helicity angles are shown.
Adapted from PNAS 115, 6386-6391 (2018).

Circular dichroism (CD), the difference between the intensities obtained using left- and right-circularly polarised incident light, is known to be sensitive to the chirality of a material. In our experiment, the CD-REXS was obtained by integrating a series of reciprocal-space-map scans for each polarisation separately, followed by normalisation and subsequent subtraction of the left- and right-circularly polarised patterns⁴. The direct CD-REXS pattern shows six magnetic peaks with varying CD intensities, and a distinct boundary that separates the positive and negative halves. Each χ corresponds to a characteristic CD-REXS pattern, in which a dichroism extinction vector can be defined as illustrated by the red arrows in Fig. 1. Consequently, the orientation of the dichroism extinction vector exclusively reveals the helicity angle, which is a unique characteristic of a skyrmion.

The RASOR diffractometer on beamline I10 is uniquely suited for soft X-ray resonant magnetic diffraction experiments of the skyrmion lattice state. RASOR has ultra-high reciprocal space resolution – a necessary condition for the observation of these magnetic structures – and its large UHV chamber allows for the incorporation of a magnetic vector field setup, which is essential for stabilising the skyrmion lattice state.

Furthermore, by tuning the energy of the incident X-rays, it is possible to systematically vary the probing depth to perform a depth-dependent mapping of the magnetic state. At the 2p absorption edge of a 3d transition metal, the soft X-rays are particularly surface-sensitive as the absorption is large, whereas away from the absorption maximum, increasingly deeper layers are probed as well. In the case of the investigated material, Cu₂OSeO₃, the probing depth was tuned from ∼31 nm (at Cu L₃ resonance at 931.25 eV) to ∼77 nm at 932.45 eV. In a CD-REXS experiment, the spectroscopic measurement therefore provides a strategy to obtain the helicity angle as a function of depth in a three-dimensional skyrmion crystal. From measurements as a function of the photon energy, we obtain the probed helicity angle as a function of depth (see Fig. 2a). Very much in contrast to the expected Bloch-type skyrmion (c = 90°), c(z) shows a smooth variation of the skyrmion type with depth (Fig. 2b). Most interestingly, on the top surface of Cu₂OSeO₃, the skyrmions have χ ≈ 180°, which is not expected for a chiral magnet in any existing theoretical framework. Deep below the surface in the bulk, Bloch-type skyrmions are found as expected, however, pushed an order of magnitude further down than predicted by recent models.

In conclusion, we present the observation of a new topological surface state, and a new form of skyrmion ordering. By using a novel X-ray diffraction technique (CD-REXS), we were able to determine the skyrmion helicity angle as a function of depth along the skyrmion tubes. Our study surprisingly reveals Néel-type surface skyrmions, and a continuous transformation into the well-established Bloch-type bulk state with increasing depth. The recently developed theoretical 3D skyrmion models, which have predicted minute surface effects, greatly underestimate its magnitude, emphasising the unexpected significance of the surface. Our findings further highlight the fact that the helicity angle is a degree of freedom for magnetic skyrmions, which can take different values. A detailed knowledge of surface effects will allow us to tailor nanostructures⁵, thereby unlocking the door for the engineering of new skyrmion devices.

References:

Fert A. et al. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017). DOI: 10.1038/ natrevmats.2017.31
Zhang S. L. et al. Resonant elastic x-ray scattering from the skyrmion lattice in Cu2OSeO3. Phys. Rev. B 93, 214420 (2016). DOI: 10.1103/ PhysRevB.93.214420
Zhang S. L. et al. Topological Winding Number of Skyrmions. Nat. Commun. 8, 14619 (2017). DOI: 10.1038/ncomms14619
Zhang S. L. et al. Direct experimental determination of spiral spin structures via the dichroism extinction effect in resonant elastic soft x-ray scattering. Phys. Rev. B 96, 94401 (2017). DOI: 10.1103/PhysRevB.96.094401
Zhang S. et al. Real-Space Observation of Skyrmionium in a Ferromagnet- Magnetic Topological Insulator Heterostructure. Nano Lett. 18, 1057–1063 (2018). DOI: 10.1021/acs.nanolett.7b04537

Funding acknowledgement:

We acknowledge financial support by the Semiconductor Research Corporation (SRC), and the Engineering and Physical Sciences Research Council under grant EP/N032128/1.

Corresponding author:

Dr Shilei Zhang, University of Oxford, [email protected]

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Next-gen memory: How skyrmions behave at surfaces