All-electrical detection of skyrmion lattice state and chiral surface twists

Letter

All-electrical detection of skyrmion lattice state and chiral surface twists

A. Aqeel, M. Azhar, N. Vlietstra, A. Pozzi, J. Sahliger, H. Huebl, T. T. M. Palstra, C. H. Back, and M. Mostovoy

Phys. Rev. B 103, L100410 – Published 19 March 2021

Abstract

We study the high-temperature phase diagram of the chiral magnetic insulator ${Cu}_{2} O Se O_{3}$ by measuring the spin-Hall magnetoresistance (SMR) in a thin Pt electrode. We find distinct changes in the phase and amplitude of the SMR signal at critical lines separating different magnetic phases of bulk ${Cu}_{2} O Se O_{3}$ . The skyrmion lattice state appears as a strong dip in the SMR phase. A strong enhancement of the SMR amplitude is observed in the conical spiral state, which we explain by an additional symmetry-allowed contribution to the SMR present in noncollinear magnets. We demonstrate that the SMR can be used as an all-electrical probe of chiral surface twists and skyrmions in magnetic insulators.

Received 30 April 2020
Revised 30 November 2020
Accepted 5 March 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L100410

Physics Subject Headings (PhySH)

Magnetic texture Magnetism Magnetotransport

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Aqeel ¹, M. Azhar ², N. Vlietstra^1,3, A. Pozzi ², J. Sahliger¹, H. Huebl ^3,1,4, T. T. M. Palstra², C. H. Back ^1,4, and M. Mostovoy²

¹Department of Physics, Technical University Munich, 85748 Garching, Germany
²Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
³Walther-Meißner-Institute, 85748 Garching, Germany
⁴Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany

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Issue

Vol. 103, Iss. 10 — 1 March 2021

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Images

Figure 1
(a) Schematic representation of the device configuration used to measure the spin-Hall magnetoresistance in the $Pt | CSO$ bilayer system, with an applied magnetic field $H$ at an angle $α$ to $x$ , the direction of the current. The skyrmion tubes are represented by color-coding the magnetization projection along the applied magnetic field direction (red to blue). Top (b) and cross-sectional (c) view of the surface twists in the field-polarized state. The increase in the twist angle between the magnetization and the applied field near the surface is indicated by color (red to green).
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Figure 2
(a) Angular dependence of the SMR signal, $V_{SMR}$ , measured at $μ_{0} H = 600$ mT in a planar-Hall geometry shown in Fig. 1. $V_{SMR}^{ampl}$ and $ϕ$ are the amplitude and phase of $V_{SMR}$ , respectively. The solid lines show the $V_{SMR}^{ampl} sin (2 (α - ϕ)$ ) fit with $ϕ = 0^{\circ}$ (black) and $ϕ = 90^{\circ}$ (red). (b), (c) Temperature dependence of $V_{SMR}^{ampl}$ and $ϕ$ , respectively. Here, the shaded area corresponds to the skyrmion lattice state. (d) Contour map of phase $ϕ$ versus magnetic field and temperature combined with the results of broadband ferromagnetic resonance. The hollow and solid circles represent the phase boundaries extracted from the magnetic resonance data measured by applying $H$ along the [1 –1 1] and [–2 –1 1] crystallographic directions of CSO, respectively. The magnetic phase boundaries are highlighted by dashed lines. We identify helical (H), conical (C) ( $H_{c 1}$ is the low field boundary), field-polarized ferrimagnetic state (FP) ( $H_{c 2}$ is the low-field boundary), and the skyrmion lattice state (SkL) ( $H_{A 1}$ and $H_{A 2}$ are low- and high-field boundaries). (e) Line scans of $ϕ$ as function of applied field $H$ at two different temperatures.
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Figure 3
Field dependence of the spin-Hall magnetoresistance (a) amplitude $V_{SMR}^{ampl}$ , and (b) phase $ϕ$ , in the conical spiral (C) and collinear field-polarized (FP) states calculated for each of the three terms in Eq. (3) separately: blue ( $A_{1}$ and $ϕ_{1}$ , due to the first term), magenta ( $A_{2}$ and $ϕ_{2}$ , due to the second term) and green lines ( $A_{3}$ and $ϕ_{3}$ , due to the third term). Field dependence of (c) $V_{SMR}^{ampl}$ and (d) $ϕ$ in the C and FP states calculated numerically using Eq. (3) with $b Q / a = - 1.59$ and $c / a = 0$ (solid blue lines). The dashed line shows the effect of the interfacial DMI, for $D_{int} = - 0.30 J$ . The dotted blue line is obtained by considering only the first term in Eq. (3). Open circles are the experimental data taken at 51 K. Here, the critical field, $H_{c 2} = 56$ mT. Field dependence of (e) $V_{SMR}^{ampl}$ and (f) $ϕ$ calculated numerically using Eq. (3) with $b Q / a = - 1.84$ and $c / a = 0$ for the C and FP states (blue solid lines) and for the skyrmion lattice (SkL) state (red sold lines). The dashed blue lines show the effect of the interfacial DMI of strength $D_{int} = - 0.40 J$ for the C state. Open circles are results of experimental measurements at 55 K. The color bars at the $x$ axes of the figures indicate the magnetic phases, deduced from FMR measurements for the experimental data: the C, SkL, and FP state are indicated by yellow, red, and white color, respectively. The critical fields determined from FMR measurements at 55 K are: $H_{c 2} = 40$ mT, and the boundaries of the SkL, $H_{A 1}$ and $H_{A 2}$ , are 15 mT and 23 mT, respectively.
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