Phys. Rev. Materials 4, 114419 (2020) - Skyrmion generation from irreversible fission of stripes in chiral multilayer films

Skyrmion generation from irreversible fission of stripes in chiral multilayer films

Anthony K. C. Tan, James Lourembam, Xiaoye Chen, Pin Ho, Hang Khume Tan, and Anjan Soumyanarayanan

Phys. Rev. Materials 4, 114419 – Published 30 November 2020

Abstract

Competing interactions produce finite-size textures in myriad condensed matter systems, typically forming elongated stripe or round bubble domains. Transitions between stripe and bubble phases, driven by field or temperature, are expected to be reversible in nature. Here we report on the distinct character of the analogous transition for nanoscale spin textures in chiral Co/Pt-based multilayer films, known to host Néel skyrmions, using microscopy, magnetometry, and micromagnetic simulations. Upon increasing field, individual stripes fission into multiple skyrmions, and this transition exhibits a macroscopic signature of irreversibility. Crucially, upon field reversal, the skyrmions do not fuse back into stripes, with many skyrmions retaining their morphology down to zero field. Both the macroscopic irreversibility and the microscopic zero-field skyrmion density are governed by the thermodynamic material parameter determining chiral domain stability. These results establish the thermodynamic and microscopic framework underlying ambient skyrmion generation and stability in chiral multilayer films and provide immediate directions for their functionalization in devices.

Received 31 March 2020
Accepted 7 October 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.114419

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Skyrmions Spin texture

Chiral magnets Multilayer thin films

Magnetic force microscopy Magnetization measurements Micromagnetic modeling Sputtering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Anthony K. C. Tan ¹, James Lourembam ^1,2,*, Xiaoye Chen ^1,2,*, Pin Ho ^1,2, Hang Khume Tan ^1,2, and Anjan Soumyanarayanan ^1,2,3,†

¹Data Storage Institute, Agency for Science, Technology and Research, 138634 Singapore
²Institute of Materials Research and Engineering, Agency for Science, Technology and Research, 138634 Singapore
³Physics Department, National University of Singapore, 117551 Singapore

^*These authors contributed equally to this work.
^†anjan@imre.a-star.edu.sg

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Vol. 4, Iss. 11 — November 2020

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Figure 1
(a) Set of first-order reversal curves (gray lines) of sample Fe(4)/Co(6), acquired by sweeping the field from $- H_{s}$ to the reversal field $H_{r}$ (white circles) and back to $- H_{s}$ . Arrows indicate FORC field sweep protocol up to $H_{r}$ (black) and the reversal path for representative major (purple, $H_{r} > H_{s}$ ) and minor (red, $H_{r} < H_{s}$ ) loops. Also shown are MFM images for two selected FORCs [red and purple dots in (a)], showing in (b) and (d) the in-field (IF) and in (c) and (e) the zero-field (ZF) configurations. The two cases shown represent for (b) and (c) a minor loop ( $H_{r} = 220$ mT $< H_{s}$ ), corresponding to an IF skyrmion phase, and for (d) and (e) a major loop ( $H_{r} = 310$ mT $> H_{s}$ ), i.e., a uniformly magnetized IF phase.
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Figure 2
Experimental FORC irreversibility and ZF textures for Fe(4)/Co(6) stacks. (a) Color plot of the measured $ρ (H, H_{r})$ [defined in Eq. (2)] and (b) the switching field distribution [SFD, defined in Eq. (4)] obtained from a set of FORCs on Fe(4)/Co(6) (full FORCs in [29]). The two prominent irreversible processes ( $ρ \neq 0$ ), marked by black and orange lines, are denoted by $F$ and $A$ , respectively. The $F$ and $A$ indicators are also shown within imaging results for direct comparison with FORC. (c) Skyrmion density plots from MFM imaging of IF ( $n_{S}$ ) and ZF ( $n_{S}^{Z}$ ) morphology with varying $H$ and $H_{r}$ respectively. Also shown are representative MFM images of (d)–(f) IF and (g)–(i) ZF morphology for selected $(H, H_{r})$ pairs [enlarged data markers in (c)].
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Figure 3
Simulated FORC irreversibility and ZF textures for Fe(4)/Co(6) stacks. (a) Color plot of simulated FORC irreversibility $ρ (H, H_{r})$ and (b) the corresponding SFD obtained from micromagnetic simulations of FORCs for Fe(4)/Co(6) parameters. As in Fig. 2, the two most prominent features are labeled as $A$ and $F$ , respectively. (c) Corresponding plots of skyrmion densities of simulated IF and ZF magnetization with varying $H$ and $H_{r}$ respectively. The $A$ and $F$ lines from (a) and (b) are overlaid for comparison. Also shown are representative simulated magnetization images of (d)–(f) IF and (g)–(i) ZF morphology for selected $(H, H_{r})$ pairs [corresponding to data markers in (c)].
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Figure 4
Microscopic analysis of the simulated Fe(4)/Co(6) FORC loop with $H_{r} = 0.7 H_{s}$ to elucidate the irreversibility of the stripe - skyrmion transition. The field evolution of the density of skyrmions $n_{S}$ (red), stripes $n_{R}$ (black), and their sum total $n_{tot}$ (shaded yellow) is shown on (a) the FORC upsweep ( $0 \to 0.7 H_{s}$ ) and (b) down-sweep ( $0.7 H_{s} \to 0$ ) following negative saturation. A sharp change is seen at the guide line corresponding to $F$ [from Figs. 3 and 3]. The field evolution of a prototypical stripe is shown along the FORC (c) upsweep and (d) downsweep, after its separation from the LS state (colorscale indicates field magnitude). The texture is identified and isolated for each field slice and stacked horizontally for direct comparison with (a) and (b). (e) Schematic depiction of the energetics of textures along the FORC loop. On the upsweep, stripes fission into skyrmions near $H_{F}$ ( $F$ peak). Upon field reversal, the enhanced metastability of skyrmions enables their persistence to ZF (details in text).
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Figure 5
Experimentally measured variation of FORC irreversibility and ZF textures is shown for the five $Fe (x) / Co (y)$ samples investigated here, wherein $κ$ varies over 0.3–4.1. (a)–(d) Color plots of FORC irreversibility $ρ (H, H_{r})$ [cf., Fig. 2] for four samples corresponding to $κ$ values shown in (e). Dashed black and orange lines indicate $F$ and $A$ peaks, which diverge with increasing $κ$ . (e) Normalized distance $δ H_{r} / H_{s}$ between $A$ and $F$ peaks plotted against $κ$ , showing a monotonic increase. (f)–(i) MFM field evolution of skyrmion densities for IF $[n_{S} (H)]$ and ZF $[n_{S}^{Z} (H_{r})]$ configurations for the four samples examined in (a)–(d), showing dome-shaped field trends. Top right inset for each panel shows the ZF MFM image corresponding to the maximum in $n_{S}^{Z}$ [green circle in $n_{S}^{Z} (H_{r})]$ . Left insets in (f) and (i) illustrate the expected ZF energy landscape for samples with high and low $κ$ , respectively. (j) Maximum ZF skyrmion density $n_{S, \max}^{Z}$ for all five samples plotted against $κ$ .
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Physical Review Materials

Skyrmion generation from irreversible fission of stripes in chiral multilayer films

Anthony K. C. Tan, James Lourembam, Xiaoye Chen, Pin Ho, Hang Khume Tan, and Anjan Soumyanarayanan

Phys. Rev. Materials 4, 114419 – Published 30 November 2020

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