Thermoelectric Signature of Individual Skyrmions

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Thermoelectric Signature of Individual Skyrmions

Alexander Fernández Scarioni, Craig Barton, Héctor Corte-León, Sibylle Sievers, Xiukun Hu, Fernando Ajejas, William Legrand, Nicolas Reyren, Vincent Cros, Olga Kazakova, and Hans W. Schumacher

Phys. Rev. Lett. 126, 077202 – Published 16 February 2021

Abstract

We experimentally study the thermoelectrical signature of individual skyrmions in chiral $Pt / Co / Ru$ multilayers. Using a combination of controlled nucleation, single skyrmion annihilation, and magnetic field dependent measurements the thermoelectric signature of individual skyrmions is characterized. The observed signature is explained by the anomalous Nernst effect of the skyrmion’s spin structure. Possible topological contributions to the observed thermoelectrical signature are discussed. Such thermoelectrical characterization allows for noninvasive detection and counting of skyrmions and enables fundamental studies of topological thermoelectric effects on the nanoscale.

Received 7 April 2020
Revised 26 June 2020
Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.077202

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)

Magnetism Nernst effect Skyrmions Thermomagnetic effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Alexander Fernández Scarioni ¹, Craig Barton ², Héctor Corte-León ², Sibylle Sievers ¹, Xiukun Hu ¹, Fernando Ajejas ³, William Legrand ³, Nicolas Reyren ³, Vincent Cros³, Olga Kazakova², and Hans W. Schumacher¹

¹Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
²National Physical Laboratory, Teddington TW110LW, United Kingdom
³Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France

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Issue

Vol. 126, Iss. 7 — 19 February 2021

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Images

Figure 1
(a) Scanning electron micrograph of the device. (b) ANE voltage as a function of the applied out-of-plane field. The black arrows mark the corresponding domain states imaged by MFM shown in (c)–(e). The inset shows an MFM image of the film before patterning in zero field. (c)–(e) MFM images of the microstripe for increasingly negative values of the total out-of-plane magnetic field. Here, the stated field is the sum of the applied field and the tip stray field at the sample surface. The white arrow indicates a skyrmion. (f) Simulated temperature distribution for $I_{heater} = 4.3 mA$ . (g) Simulated temperature profile along the dashed line in (f). (h) Measured temperature rise (black circles) as a function of applied current and ANE amplitude (red squares) in the microstripe vs. $I_{heater}$ .
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Figure 2
(a)–(d) MFM measurements of the microstripe before and after application of single 200-ns-long current pulses. (a) Current density $j = 3.55 \times 10^{11} A / m^{2}$ , magnetic field $μ_{0} H_{z} = 11.28 mT$ . (b) $j = 3.76 \times 10^{11} A / m^{2}$ , $μ_{0} H_{z} = 11.28 mT$ . (c) $j = 3.86 \times 10^{11} A / m^{2}$ , $μ_{0} H_{z} = 17.16 mT$ . (d) $j = 3.97 \times 10^{11} A / m^{2}$ , $μ_{0} H_{z} = 23.05 mT$ . (e) Nucleation phase diagram for skyrmion generation. The parameter range suitable for skyrmion nucleation is indicated by the dotted black line.
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Figure 3
Two independent sequences of MFM images, (a)–(c) and (d)–(f), demonstrating the probe induced annihilation process of individual skyrmions. (g) $Δ V_{ANE}$ as function of the number of skyrmions in the sensing area corresponding to the skyrmion configurations (a)–(f). The red dots correspond to (a)–(c); the blue triangles correspond to (d)–(f). The green line is a linear fit, yielding an average Nernst voltage of $4.6 \pm 0.2 nV$ per skyrmion.
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Figure 4
(a) ANE signal as a function of the total effective reversed area. The different symbols correspond to three nucleation/annihilation sequences [same in (c)]. The orange line represents the calculated ANE voltage for the given reversed magnetization area [same in (c) and (d)]. Left inset: MFM image of a single skyrmion with the derived $A_{sky}$ . Right inset: section through the MFM phase signal (black) of the same skyrmion and Gaussian-fit data (red). (b) MFM images showing the field dependence of a single skyrmion. (c) ANE voltage as a function of total skyrmion area $A_{sky}$ at different magnetic fields. (d) Differential ANE voltages ${δ V}_{ANE}$ plotted against the difference in reversed area. The red line is a linear fit of the data allowing for a nonzero intercept.
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