Surface pinning and triggered unwinding of skyrmions in a cubic chiral magnet

Peter Milde, Erik Neuber, Andreas Bauer, Christian Pfleiderer, and Lukas M. Eng

Phys. Rev. B 100, 024408 – Published 8 July 2019

Abstract

In the cubic chiral magnet ${Fe}_{1 - x} {Co}_{x} Si$ a metastable state comprising topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating that surface pinning plays a crucial role. Increasing the magnetic field allows an increasing number of skyrmions to overcome the potential barrier and hence to transform into the ground state. Most notably, we find that the unwinding of individual skyrmions may be triggered by the magnetic tip sample interaction itself, however, only when its magnetization is aligned parallel to the external field. This implies that the stray field of the tip is key for locally overcoming the topological protection. Both the control of the position of topologically nontrivial states and their creation and annihilation on demand pose important challenges in the context of potential skyrmionic applications.

Received 7 January 2019
Revised 23 April 2019

DOI:https://doi.org/10.1103/PhysRevB.100.024408

Physics Subject Headings (PhySH)

Skyrmions

Magnetic force microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Peter Milde ^* and Erik Neuber

Institute of Applied Physics, Technische Universität Dresden, D-01062 Dresden, Germany

Andreas Bauer and Christian Pfleiderer

Physik-Department, Technische Universität München, D-85748 Garching, Germany

Lukas M. Eng

Institute of Applied Physics, Technische Universität Dresden, D-01062 Dresden, Germany and Center of Excellence - Complexity and Topology in Quantum Matter (ct.qmat), Technische Universität Dresden, D-01062 Dresden, Germany

^*peter.milde@tu-dresden.de

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Issue

Vol. 100, Iss. 2 — 1 July 2019

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Images

Figure 1
(a) Magnetic phase diagram and (b) typical magnetic force microscopy data of ${Fe}_{0.5} {Co}_{0.5} Si$ . (a) Schematic magnetic phase diagram as obtained by means of field cooling through the thermodynamically stable pocket of the skyrmion lattice (red shading). When subsequently increasing or decreasing the magnetic field, a metastable skyrmion state (orange shading) survives over a large regime in field and temperature. Dotted lines indicate phase boundaries as observed after zero-field cooling. (b) Typical magnetic force microscopy data as measured after field cooling the skyrmion lattice down to 10 K. The black rectangle marks the area of interest for the analysis described in the following. Note the considerable amount of disorder in the skyrmion state, reflected also in the fast Fourier transform shown on the left-hand side.
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Figure 2
Typical initial magnetic texture after field cooling the sample in an applied field of 16 mT down to 10 K. (a) Magnetic force microscopy image. Blue and red correspond to magnetization components parallel and antiparallel to the line of sight. (b) Black-and-white map of the initial magnetic texture inferred by thresholding the data of (a). White objects correspond to skyrmions. (c) Color map obtained by summing up the black-and-white maps of the nine independent field-cooling cycles. Red indicates positions where a skyrmion was observed after each field cooling.
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Figure 3
Typical magnetic force data as measured after field cooling and subsequently increasing the magnetic field. (a) Initial magnetic texture after field cooling in an applied field of 16 mT down to 10 K. (b) Magnetic texture after increasing the magnetic field to 50 mT. Black squares mark incidences where skyrmions disappears while being scanned. (c) Subsequent MFM image, started 17 min after reaching 50 mT. (d) Final MFM image of the series, started 221 min after reaching 50 mT. (e) Blue-and-orange map, where white circles indicate positions for which a skyrmion is observed throughout the whole series of MFM images (see the text for details). (f) Color map obtained by summing up the black-and-white maps of the nine independent field-cooling cycles. Light green indicates positions where a skyrmion was observed during most experiments.
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Figure 4
Magnetic force microscopy data of the triggered unwinding of single skyrmions. (a)–(i) Three typical examples are shown in the first, second, and third rows. In the left, middle, and right columns the same position on the sample is shown for three consecutive MFM images before, during, and after the collapse of the skyrmion. The position of the collapse is marked by small black arrows. (j) Frequency shift along the $x$ direction, i.e., line scans, around the skyrmion collapse depicted in (h). The line scan across the collapse (red diamonds) is depicted together with the three scans preceding (gray polygons) and following (gray circles) the collapse.
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