In-plane N\'eel wall chirality and orientation of interfacial Dzyaloshinskii-Moriya vector in magnetic films

In-plane Néel wall chirality and orientation of interfacial Dzyaloshinskii-Moriya vector in magnetic films

MacCallum Robertson, Christopher J. Agostino, Gong Chen, Sang Pyo Kang, Arantzazu Mascaraque, Enrique Garcia Michel, Changyeon Won, Yizheng Wu, Andreas K. Schmid, and Kai Liu

Phys. Rev. B 102, 024417 – Published 14 July 2020

Abstract

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is of great interest as it can stabilize chiral spin structures in thin films. Experiments verifying the orientation of the interfacial DMI vector remain rare, in part due to the difficulty of separating vector components of DMI. In this study, Fe/Ni bilayers and Co/Ni multilayers were deposited epitaxially onto Cu(001) and Pt(111) substrates, respectively. By tailoring the effective anisotropy, spin reorientation transitions (SRTs) are employed to probe the orientation of the DMI vector by measuring the spin structure of domain walls on both sides of the SRTs. The interfacial DMI is found to be sufficiently strong to stabilize chiral Néel walls in the out-of-plane magnetized regimes, while achiral Néel walls are observed in the in-plane magnetized regimes. These findings experimentally confirm that the out-of-plane component of the DMI vector is insignificant in these fcc(001) and fcc(111) oriented interfaces, even in the presence of atomic steps.

Received 14 February 2020
Revised 3 June 2020
Accepted 23 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.024417

Physics Subject Headings (PhySH)

Domain walls Magnetic domains

Thin films

Electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

MacCallum Robertson ¹, Christopher J. Agostino ^2,3,4, Gong Chen^1,*, Sang Pyo Kang⁵, Arantzazu Mascaraque ^6,7, Enrique Garcia Michel ⁸, Changyeon Won⁵, Yizheng Wu ⁹, Andreas K. Schmid², and Kai Liu ^1,10,†

¹Department of Physics, University of California, Davis, California 95616, USA
²NCEM, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Physics Department, University of California, Berkeley, California 94720, USA
⁴Department of Astronomy, Indiana University, Bloomington, Indiana 47405, USA
⁵Department of Physics, Kyung Hee University, Seoul 02447, Korea
⁶Dpto. de Física de Materiales, Universidad Complutense de Madrid, 28040 Madrid, Spain
⁷Unidad Asociada IQFR(CSIC)-UCM, Madrid E-28040, Spain
⁸Dept. Condensed Matter Physics, and IFIMAC-Condensed Matter Physics Center, Universidad Autonoma de Madrid, 28049 Madrid, Spain
⁹Department of Physics, State Key Laboratory of Surface Physics, and Advanced Materials Laboratory, Fudan University, Shanghai 200433, China
¹⁰Physics Department, Georgetown University, Washington, DC 20057, USA

^*Correspondence author: gchenncem@gmail.com
^†Kai.Liu@georgetown.edu

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Vol. 102, Iss. 2 — 1 July 2020

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Figure 1
(a), (b) Sketches of sample structures and colorized SPLEEM images for two Fe/Ni/Cu(001) bilayer films, showing the orientation of the local magnetization vector based on the corresponding color wheel in the inset. White arrows additionally highlight domain wall magnetization orientation. (c) Histogram corresponding to (a) showing the normalized counts (each dot representing counts after binning) of the angle α, defined as the angle between the DW magnetization vector $m$ and the DW normal vector $n$ , as shown in the inset. A single peak at $α = 0^{\circ}$ demonstrates left-handed Néel DW structure. (d) Histogram corresponding to (b) showing the normalized count of the angle χ, defined as the angle between the DW magnetization vector $m$ and the domain magnetization $m_{d}$ , as shown in the inset; Peaks at $χ = \pm 90^{\circ}$ and 270° indicate achiral Néel DW structure.
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Figure 2
(a), (b) Sketches of sample structures and colorized SPLEEM images for the ${[Co / Ni]}_{n}$ on Pt(111) system, showing the orientation of the local magnetization vector based on the corresponding color wheel in the inset. White arrows additionally highlight domain wall magnetization orientation. (c) Histogram corresponding to (a) showing the normalized counts (each dot representing counts after binning) of the angle α, defined as the angle between the DW magnetization vector $m$ and the DW normal vector $n$ , as shown in the inset. A single peak at $α = 0^{\circ}$ demonstrates left-handed Néel DW structure. (d) Histogram corresponding to (b) showing the normalized count of the angle χ, defined as the angle between the DW magnetization vector $m$ and the domain magnetization $m_{d}$ , as shown in the inset; Peaks at $χ = \pm 90^{\circ}$ and 270° indicate achiral Néel DW structure.
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Figure 3
Monte Carlo simulations for (a) out-of-plane magnetized and (b) in-plane magnetized thin film systems with equally strong DMI, showing chiral Néel domain walls in (a) and achiral Néel domain walls in (b). Local magnetization directions are rendered in color according to the color wheel in the inset. In addition, arrows highlight magnetization directions in domains and domain walls.
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Figure 4
(a), (b) DMI vector (teal) for fcc(001) and fcc(111), respectively. Red spin sites denote selected nearest neighbors to a central site between which the DMI vector ( $D_{i j}$ ) is shown in teal. The dotted circles facilitate comparison between fcc(001) and fcc(111), showing the same relative orientation of the DMI vector with respect to neighboring spin sites. (c), (d) Neighboring spin sites $S_{i}$ and $S_{j}$ (red) in right-handed chiral (c) out-of-plane and (d) in-plane magnetized Néel walls. The magnetization vector, DMI vector ( $D_{i j}$ ), and cross product ( $S_{i} \times S_{j})$ are denoted by the black, teal, and yellow arrows, respectively.
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Figure 5
(a) LEEM image showing atomic steps (dark lines) of Cu(001), over an 8 µm area [42]. (b) The possible DMI vector $D_{i j}$ at an atomic double step is represented by teal arrows. (c) The cross product ( $S_{i} \times S_{j})$ between neighboring spin sites at an atomic double step (where $S_{i}$ is always the central spin and $S_{j}$ is always the neighbor), shown by yellow arrows, that will contribute to a nonzero $E_{DM}$ .
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Physical Review B

covering condensed matter and materials physics

In-plane Néel wall chirality and orientation of interfacial Dzyaloshinskii-Moriya vector in magnetic films

MacCallum Robertson, Christopher J. Agostino, Gong Chen, Sang Pyo Kang, Arantzazu Mascaraque, Enrique Garcia Michel, Changyeon Won, Yizheng Wu, Andreas K. Schmid, and Kai Liu

Phys. Rev. B 102, 024417 – Published 14 July 2020

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Physical Review B

covering condensed matter and materials physics

In-plane Néel wall chirality and orientation of interfacial Dzyaloshinskii-Moriya vector in magnetic films

MacCallum Robertson, Christopher J. Agostino, Gong Chen, Sang Pyo Kang, Arantzazu Mascaraque, Enrique Garcia Michel, Changyeon Won, Yizheng Wu, Andreas K. Schmid, and Kai Liu

Phys. Rev. B 102, 024417 – Published 14 July 2020

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