Observation of the skyrmion side-face state in a chiral magnet

Letter

Observation of the skyrmion side-face state in a chiral magnet

Xiaodong Xie, Kejing Ran, Yizhou Liu, Raymond Fan, Wancong Tan, Haonan Jin, Manuel Valvidares, Nicolas Jaouen, Haifeng Du, Gerrit van der Laan, Thorsten Hesjedal, and Shilei Zhang

Phys. Rev. B 107, L060405 – Published 7 February 2023

Abstract

We identify a three-dimensional skyrmion side-face state in chiral magnets that consists of a thin layer of modulated surface spirals and an array of phase-locked skyrmion screws. Such chiral spin structures lead to a characteristic X-shaped magnetic diffraction pattern in resonant elastic x-ray scattering, reminiscent of Photo 51 of the DNA double-helix diffraction. By measuring both thin plates and bulk ${Cu}_{2} {OSeO}_{3}$ crystals in the field-in-plane geometry, we unambiguously identify the modulated skyrmion strings by retrieving their chirality and helix angle. The breaking of the translational symmetry along the side faces suppresses the bulk-favored conical state, providing a stabilization mechanism for the skyrmion lattice phase that has been overlooked so far.

Received 15 May 2022
Revised 28 November 2022
Accepted 24 January 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L060405

Physics Subject Headings (PhySH)

Skyrmions

Chiral magnets Helimagnets

Resonant elastic x-ray scattering X-ray resonant magnetic scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaodong Xie^1,*, Kejing Ran^1,*, Yizhou Liu², Raymond Fan ³, Wancong Tan¹, Haonan Jin ¹, Manuel Valvidares⁴, Nicolas Jaouen ⁵, Haifeng Du^6,†, Gerrit van der Laan ³, Thorsten Hesjedal ⁷, and Shilei Zhang ^1,‡

¹School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China; and ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
²RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
³Diamond Light Source, Harwell Science and Innovation Campus, Didcot OX11 0DE, United Kingdom
⁴ALBA Synchrotron Light Source, Barcelona, E-08290, Spain
⁵Synchrotron SOLEIL, Gif-sur-Yvette, France
⁶The Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory and University of Science and Technology of China, Chinese Academy of Science (CAS), Hefei, Anhui Province, China
⁷Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

^*These authors contributed equally to this work.
^†duhf@hmfl.ac.cn
^‡shilei.zhang@shanghaitech.edu.cn

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Issue

Vol. 107, Iss. 6 — 1 February 2023

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Images

Figure 1
(a) SFS at the side of a chiral bulk magnet. The color scale represents the $m_{y}$ component of the magnetization. (b) Preimage representation of a skyrmion screw. (c) In the isosurface plot for $m_{y} = 0.9$ , the definition of the screw parameters $α$ (helix angle), $λ_{s}$ (thread spacing), and $λ_{p}$ (pitch) is given. (d) Thickness-field phase diagram for the side-face region, obtained from simulations. The green area only hosts the spiral side-face state, while the gray regions correspond to a mixed state of the two neighboring phases. For details, see Sec. S6 in Ref. [55]. The numbers on the top indicate the maximum number of skyrmion rows that can be supported. The dotted line at $t / λ_{h} = 1.83$ indicates the phase boundaries for a $t = 110$ nm system. (e) Plot of the helix angle $α$ and the cone angle $ξ$ as a function of field for a $t = 110$ nm system. The inset shows the field dependence of $L_{p}$ .
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Figure 2
(a) Schematics of the REXS setup. The coordinate system refers to the sample coordinates. (b)–(d) REXS patterns in transmission geometry of 110-nm-thick ${Cu}_{2} {OSeO}_{3}$ measured at 54 K for increasing applied field from 0 to 28 mT. (e) Magnetic scattering wave vector–magnetic field $(| q | - B)$ REXS intensity map measured at 54 K. (f) Magnetic phase diagram derived from REXS data. The phase boundaries (at low temperature) can be compared with the simulated data (“bulk” region) shown in Fig. 1.
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Figure 3
(a)–(c) CD-REXS patterns of the magnetic phases characteristic for the side face of bulk ${Cu}_{2} {OSeO}_{3}$ , i.e., (a) the SFS [labeled (i)], (b) the SFS with axiosymmetric skyrmion string modulations embedded in the conical phase [labeled (ii)], and (c) the in-plane skyrmion phase [labeled (iii)]. The insets to the panels illustrate the modulation mode of the magnetic states. (d) SFS phase diagram. The small black dots along lines of constant $T$ represent the data points in the field-temperature space at which REXS measurements were carried out (between 8 and 30 mT and 25 and 58 K). Each point is colored depending on the measured $α$ of the SFS [outside the SFS phase pocket, $α$ is not defined and the point is left blank, see panel (c)]. A finite $α$ (of up to $\sim 40^{\circ})$ is found in the red region (i) of the phase diagram, corresponding to the SFS shown panel (a). In contrast, the blue region $(α = 0^{\circ})$ corresponds to the SFS phase (ii) with axiosymmetric skyrmion string modulations embedded in the conical phase [see panel (b)]. Below the SFS phase, the helical phase dominates. The pink area at high temperatures just below the transition temperature represents the bulk skyrmion lattice phase (iii) as obtained by superconducting quantum interference device (SQUID) measurements.
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