Three-dimensional structure of hybrid magnetic skyrmions determined by neutron scattering

W. L. N. C. Liyanage, Nan Tang, Lizabeth Quigley, Julie A. Borchers, Alexander J. Grutter, Brian B. Maranville, Sunil K. Sinha, Nicolas Reyren, Sergio A. Montoya, Eric E. Fullerton, Lisa DeBeer-Schmitt, and Dustin A. Gilbert

Phys. Rev. B 107, 184412 – Published 5 May 2023

Abstract

Magnetic skyrmions are topologically protected chiral spin textures which present opportunities for next-generation magnetic data storage and logic information technologies. The topology of these structures originates in the geometric configuration of the magnetic spins, more generally described as the structure. While the skyrmion structure is most often depicted using a two-dimensional projection of the three-dimensional (3D) structure, recent works have emphasized the role of all three dimensions in determining the topology and their response to external stimuli. In this paper, grazing-incidence small-angle neutron scattering and polarized neutron reflectometry are used to determine the 3D structure of hybrid skyrmions. The structure of the hybrid skyrmions, which includes a combination of Néel-like and Bloch-like components along their length, is expected to significantly contribute to their notable stability, which includes ambient conditions. To interpret the neutron scattering data, micromagnetic simulations of the hybrid skyrmions were performed, and the corresponding diffraction patterns were determined using a Born approximation transformation. The converged magnetic profile reveals the magnetic structure along with the skyrmion depth profile, including the thickness of the Bloch and Néel segments and the diameter of the core.

Received 6 October 2022
Revised 17 March 2023
Accepted 17 April 2023

DOI:https://doi.org/10.1103/PhysRevB.107.184412

Physics Subject Headings (PhySH)

Micromagnetism Skyrmions

Multilayer thin films

Neutron reflectometry Small angle neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

W. L. N. C. Liyanage¹, Nan Tang², Lizabeth Quigley², Julie A. Borchers³, Alexander J. Grutter³, Brian B. Maranville ³, Sunil K. Sinha⁴, Nicolas Reyren⁵, Sergio A. Montoya⁴, Eric E. Fullerton⁴, Lisa DeBeer-Schmitt⁶, and Dustin A. Gilbert^1,2,*

¹Department of Physics and Astronomy, University of Tennessee, Tennessee, USA
²Materials Science and Engineering Department, University of Tennessee, Tennessee, USA
³NIST Center for Neutron Research, National Institute for Standards and Technology, Gaithersburg, Maryland, USA
⁴Center for Memory and Recording Research, University of California, San Diego, California, USA
⁵Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, Palaiseau 91767, France
⁶Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, USA

^*dagilbert@utk.edu

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Issue

Vol. 107, Iss. 18 — 1 May 2023

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Images

Figure 1
Measured small-angle neutron scattering (SANS) signal in (a) the stripe state and (b) the skyrmion state, both taken in a small residual field, aligned with the neutron beam along the film normal direction. The $z$ contrast uses a logarithmic scale. (c) Diagram of the grazing-incidence SANS (GISANS) configuration, with the red arrow indicating the specular reflection and orange arrows indicating the off-specular (GISANS) peaks. Coordinates for the GISANS results are defined relative to the center of the direct beam. For GISANS measurements, the sample is rotated around its $y$ axis.
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Figure 2
(a) Specular reflectivity measurement and (b) converged depth profile for the Gd/Fe multilayer in the saturated state (in-plane saturation, 500 mT). The neutron polarization axis is in-plane and parallel to the saturating field in this scattering configuration. Only the non-spin-flip data are shown since there is no appreciable spin-flip signal in saturation. (c) Specular reflectometry and (d) converged depth profile measured in a 1-mT field, in the skyrmion state with the magnetic surface state emphasized in (e). For (a), the neutron polarization axis is in the plane of the film, while for (c), the neutron polarization axis is out-of-plane and parallel to the small guide field.
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Figure 3
Grazing-incidence small-angle neutron scattering (GISANS) data in (a) the stripe state, (b) skyrmion state, and (c) saturated state. The $z$ contrast uses a logarithmic scale. For all three measurements, the specular peak appears at $Q_{y} = 0$ , while the off-specular peaks appear at $Q_{y} = \pm 0.00338 Å^{- 1}$ and $\pm 0.00250 Å^{- 1}$ for the stripe and skyrmion states, respectively. (d) Integrated intensity of the specular reflection from GISANS for the skyrmion (triangle), out-of-plane saturated states (circle), and theory from the Refl1d model (line). (e) Integrated intensity from the off-specular diffraction peak from GISANS (circle) and theoretical results from micromagnetic modeling (line).
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Figure 4
(a) Plane view image of the simulated skyrmion lattice. (b)–(f) Slices of the magnetic configuration taken along the length of the skyrmion tube, with (b) $Z = 16$ nm corresponding to the top surface and an inward wrapping Néel cap, (d) $Z = 59$ nm corresponding to the middle and a clockwise Bloch type, and (f) $Z = 101$ nm corresponding to the bottom surface and an outward wrapping Néel cap. (g) The in-plane width of the skyrmion boundary region. (h) The total in-plane magnetization from oommf integrated vs depth and compared with the magnetic scattering length density (SLD) profile from the polarized neutron reflectometry (PNR) results. (i) The in-plane angle of the skyrmion boundary region vs depth, with $+ 90^{\circ} / 0 / - 90^{\circ}$ corresponding to inward Néel, clockwise Bloch, and outward Néel, respectively. Note that $0^{\circ}$ is defined as the azimuthal direction.
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Figure 5
Calculated two-dimensional (2D) (a) transmission small-angle neutron scattering (SANS), (b) grazing-incidence SANS (GISANS) measurements simulated at $Q_{z} = - 0.031 Å^{- 1}$ , and (c) cumulative GISANS pattern from the oommf simulations of the skyrmion state. The $z$ contrast uses a logarithmic scale. The cumulative GISANS pattern is the sum of all measured θ angles (i.e., all measured $Q_{z}$ values), while the experimental results are measured at sequential angles, analogous to (b) and Fig. 3. (d) Average non-spin-flip specular reflectivity $〈 R^{+ +}, R^{- -} 〉$ and spin-flip reflectivity $〈 R^{+ -}, R^{- +} 〉$ from polarized neutron reflectometry (PNR), REFL 1D [one-dimensional (1D) depth profile] and three-dimensional (3D) micromagnetic simulation (oommf, shown in Fig. 4) at $Q_{y} = 0$ . A constant background was added to the 3D oommf model.
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