Thermal Evolution of Skyrmion Formation Mechanism in Chiral Multilayer Films

Xiaoye Chen, Edwin Chue, Jian Feng Kong, Hui Ru Tan, Hang Khume Tan, and Anjan Soumyanarayanan

Phys. Rev. Applied 17, 044039 – Published 20 April 2022

Abstract

Magnetic skyrmions form in chiral multilayers from the shrinking or fission of elongated stripe textures. Here we report an experimental and theoretical study of the temperature dependence of this stripe-to-skyrmion transition in $Co$ / $Pt$ -based multilayers. Field-reversal magnetometry and Lorentz microscopy experiments over 100–350 K establish the increased efficacy of stripe-to-skyrmion fission at higher temperatures—driven primarily by the thermal evolution of key magnetic interactions—which enhances the resulting skyrmion density. Atomistic calculations elucidate that the energy barrier to fission governs the thermodynamics of skyrmion formation. Our results establish a mechanistic picture of the stripe-to-skyrmion transition and advance the use of thermal knobs for efficient skyrmion generation.

Received 23 July 2021
Revised 20 February 2022
Accepted 21 March 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.044039

Physics Subject Headings (PhySH)

Skyrmions Spintronics Temperature

Magnetic multilayers

Chiral symmetry

Lorentz microscopy Magnetization measurements Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaoye Chen ^1,*,‡, Edwin Chue^2,‡, Jian Feng Kong ³, Hui Ru Tan ¹, Hang Khume Tan ¹, and Anjan Soumyanarayanan ^2,1,†

¹Institute of Materials Research & Engineering, Agency for Science, Technology & Research (A*STAR), 138634, Singapore
²Physics Department, National University of Singapore (NUS), 117551, Singapore
³Institute of High Performance Computing, Agency for Science, Technology & Research (A*STAR), 138632, Singapore

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

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 17, Iss. 4 — April 2022

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
FORC magnetometry and irreversibility. OP magnetization FORCs for samples Fe(0)/Co(10) (a) and Fe(3)/Co(7) (b) at 300 K. Field is swept from $- H_{s}$ to the reversal field $H_{r}$ (circles) and back to $- H_{s}$ . Arrows show sweep protocol for major (blue, $H_{r} > H_{s}$ ) and minor (red, $H_{r} < H_{s}$ ) loops. Dotted box is the region of interest for FORC analysis. (c),(d) Set of FORCs at 300 K for both samples for selected $H_{r}$ (circles, major loop in black). Enlarged insets show the approximately $0.9 H_{s}$ convergence-divergence (c) and intermediate field convergence (d) of proximate FORCs (green, orange). (e),(f) Color plot of FORC irreversibility $ρ (H, H_{r})$ [Eq. (1)] for both samples. Irreversible processes, e.g., domain annihilation [ $A$ , (e) inset] and fission [ $F$ , (f) inset], present as nonzero $ρ$ features.
Reuse & Permissions
Figure 2
Thermal evolution of FORC irreversibility. (a)–(d) Enlargements of Fe(3)/Co(7) $M (H)$ loops at 100, 200, 300, and 350 K, respectively. $H_{s}$ (red, unpolarized) and $H_{s}^{'}$ (black, polarized) indicate saturation fields, and dotted blue arrow indicates their difference ( $H_{s} - H_{s}^{'}$ ). (e)–(h) Color plots of FORC irreversibility $ρ (H, H_{r})$ at the respective temperatures. Red arrow indicates $Δ H_{F A}$ , the separation between $A$ and $F$ features [defined in (h)], and dotted blue arrow indicates [ $H_{s} - H_{s}^{'}$ , as in (a)]. (i) Evolution of $Δ H_{F A}$ , normalized to $H_{s}$ , with temperature $T$ . Error bars represent the total peak fit uncertainty [31]. The line is a guide to the eye.
Reuse & Permissions
Figure 3
LTEM-imaged texture density evolution. (a),(c),(f),(h) LTEM images of textural field evolution of Fe(3)/Co(7) at 100 K (a), 200 K (c), 300 K (f), and 350 K (h). Dashed white lines highlight individual stripe-to-skyrmion transitions. (b),(d),(e),(g) Field dependence of measured skyrmion ( $n_{S}$ , blue) and stripe ( $n_{R}$ , red) densities. Stars represent maximum densities [ $n_{S}^{\max}$ and $n_{R}^{\max}$ , see (d)]. Error bars represent confidence in texture identification [31]. (i) Average number of skyrmions formed per stripe, $η_{R S} \equiv n_{S}^{\max}$ / $n_{R}^{\max}$ , plotted against temperature. Lines in (b),(d),(e),(g),(i) are guides to the eye.
Reuse & Permissions
Figure 4
Thermodynamic evolution of stripe-to-skyrmion transition. Temperature dependence of (a) saturation magnetization $M_{s}$ and (b) estimated $κ$ (see text) for the three studied samples. In (a), the data for Fe(3)/Co(7) (by 0.05 A/m) and Fe(4)/Co(6) (by 0.1 A/m) are vertically offset for clarity, and dotted curves represent Bloch $T^{3 / 2}$ fits. (c),(d) Compiled variation of $Δ H_{F A}$ [from FORC $ρ (H, H_{r})$ ] and $η_{R S}$ ( $\equiv n_{S}^{\max} / n_{R}^{\max}$ , from LTEM) with $κ_{est}$ across samples and temperatures. Schematic insets show definitions of $Δ H_{F A}$ (c) and $n_{S}^{\max}$ , $n_{R}^{\max}$ (d). Lines in (b)–(d) are guides to the eye.
Reuse & Permissions
Figure 5
Atomistic calculations of stripe-to-skyrmion transition energetics. (a) Schematic energy surface, showing the minimum energy path (red arrows) between two quasiequilibrium states (green dots). White dots show intermediate states. (b) GNEB-simulated magnetization images of stripe-to-skyrmion fission for Fe(3)/Co(7) parameters at $T = 200$ K, showing initial (1), intermediate (2 and 3), and final (4) magnetization states. (c) Energy profile for the transition in (b), with positions of states (1)–(4) overlaid. The energy barrier $E_{b}$ (red arrow) and net energy difference $Δ E$ (blue arrow) are indicated. Plots of (d) $Δ E (T)$ , (e) $E_{b} (T)$ , and (f) transition lifetime $τ_{R S} (T)$ [from Eq. (2)] against temperature for stripe-to-skyrmion fission for Fe(3)/Co(7) parameters. Solid lines in (d)–(f) are guides to the eye.
Reuse & Permissions

Physical Review Applied