Brownian Electric Bubble Quasiparticles

Open Access

Brownian Electric Bubble Quasiparticles

Hugo Aramberri and Jorge Íñiguez-González

Phys. Rev. Lett. 132, 136801 – Published 25 March 2024

Abstract

Recent works on electric bubbles (including the experimental demonstration of electric skyrmions) constitute a breakthrough akin to the discovery of magnetic skyrmions some 15 years ago. So far research has focused on obtaining and visualizing these objects, which often appear to be immobile (pinned) in experiments. Thus, critical aspects of magnetic skyrmions—e.g., their quasiparticle nature, Brownian motion—remain unexplored (unproven) for electric bubbles. Here we use predictive atomistic simulations to investigate the basic dynamical properties of these objects in pinning-free model systems. We show that it is possible to find regimes where the electric bubbles can present long lifetimes ( $\sim ns$ ) despite being relatively small (diameter $< 2 nm$ ). Additionally, we find that they can display stochastic dynamics with large and highly tunable diffusion constants. We thus establish the quasiparticle nature of electric bubbles and put them forward for the physical effects and applications (e.g., in token-based probabilistic computing) considered for magnetic skyrmions.

Received 19 September 2023
Accepted 27 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.136801

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Bubble dynamics Domain walls Ferroelectric domains Ferroelectricity Polarization vortices Topological phases of matter

Brownian dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hugo Aramberri ¹ and Jorge Íñiguez-González ^1,2

¹Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), Avenue des Hauts-Fourneaux 5, L-4362 Esch/Alzette, Luxembourg
²Department of Physics and Materials Science, University of Luxembourg, Rue du Brill 41, L-4422 Belvaux, Luxembourg

Article Text

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Supplemental Material

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References

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Issue

Vol. 132, Iss. 13 — 29 March 2024

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Images

Figure 1
Domains in ferroelectric/paraelectric superlattices. Stripe domains (a) “domain liquid” state (b) with spontaneous domain wall motion caused by thermal fluctuations, and e-bubbles (c) resulting from applying an electric field to the stripe phase. Arrows indicate the local polarization in the shown planes; the color code indicates the polarization along the vertical direction (scale to the right).
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Figure 2
Stochastic dynamics of the e-bubbles. Snapshots of molecular dynamics runs at the times indicated above. The first (second) row shows cases with one (two) e-bubble(s) per simulation supercell. We show the dipoles at the middle of the ${PbTiO}_{3}$ layer. We display four periodic images of the simulation supercell. The in-plane simulation supercell ( $16 \times 16$ elemental perovskite units) is marked by black lines. (a)–(c) and (g)–(i) correspond to a $6 / 3$ superlattice at $η = 0 %$ and $T = 150 K$ , under $E = 2.5$ and $2.0 MV {cm}^{- 1}$ , respectively. (d)–(f) and (j)–(l) correspond to a $9 / 3$ superlattice at $η = - 2 %$ and $T = 300 K$ , under $E = 1.4$ and $1.3 MV {cm}^{- 1}$ , respectively. The color scale is that of Fig. 1.
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Figure 3
Activated diffusion of e-bubbles. Left: $6 / 3$ superlattice at $η = 0 %$ and $E = 2.5 MV {cm}^{- 1}$ (a)–(c) Right: $9 / 3$ system at $η = - 2 %$ and $E = 1.4 MV {cm}^{- 1}$ (d)–(f) Mean squared displacement $⟨ r^{2} ⟩$ as a function of time [obtained at 150 K in (a), at 300 K in (d), diffusion coefficient [(b) and (e)] and hopping rates [(c) and (f)] as a function of inverse temperature. In (c) and (f) we show rates corresponding to jumps by 1 (blue) and 2 (green) unit cells. Dashed lines in (b)–(f) indicate Arrhenius fits. Shaded areas (a) and (d) indicate the variance of $r^{2}$ .
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Figure 4
Interbubble interactions. (a) Computed energy map of a two-bubble system, with one bubble at the center and a second at every other possible position of the simulation supercell. (b) Energy profiles between points marked with symbols in (a). (c)–(e) Configurations marked with the corresponding symbols in (a). The central low-energy region inside the dark ring in (a) corresponds to merged e-bubbles. We use a $6 / 3$ superlattice with $η = 0 %$ and $E = 2.1 MV {cm}^{- 1}$ , nominally at 0 K. The in-plane electric dipoles at the bubble walls confer them a Bloch-type skyrmion character (see Supplemental Material [18], note 4 for more). (f)–(g) Similar results for a $9 / 3$ superlattice at $η = - 2 %$ under $E = 1.4 MV {cm}^{- 1}$ .
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