Revealing the Absolute Direction of the Dzyaloshinskii-Moriya Interaction in Prototypical Weak Ferromagnets by Polarized Neutrons

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Revealing the Absolute Direction of the Dzyaloshinskii-Moriya Interaction in Prototypical Weak Ferromagnets by Polarized Neutrons

H. Thoma, V. Hutanu, H. Deng, V. E. Dmitrienko, P. J. Brown, A. Gukasov, G. Roth, and M. Angst

Phys. Rev. X 11, 011060 – Published 25 March 2021

Abstract

Polarized neutron diffraction (PND) is a powerful technique to distinguish a weak magnetic contribution from the total scattering intensity. It can provide a detailed insight into the microscopic spin ordering at the unit cell level, but also into the mesoscopic magnetic ordering, like different types of domain populations. Here we report on the application of this technique to the long-standing problem of determining the absolute direction of the Dzyaloshinskii-Moriya vector in relation to the crystal structure. The proposed PND method, based on the measurement of one representative reflection, is easy to perform and straightforward to interpret. The absolute sign of the Dzyaloshinskii-Moriya interaction (DMI) in ${MnCO}_{3}$ has been independently determined by PND and found to be in agreement with recent results obtained by resonant magnetic synchrotron scattering. This validates the method. In addition, the absolute DMI vector direction in the prototypical room-temperature weak ferromagnet $α − {Fe}_{2} O_{3}$ (hematite) has been determined for the first time. To demonstrate the generality of our method, further examples with different symmetries are also presented. Ab initio calculations of the resulting weak noncollinear magnetization using the quantum espresso package, considering DMI in addition to the symmetric magnetic exchange interaction, were also conducted and found to be in agreement with the experimental results from PND.

Received 9 June 2020
Revised 29 November 2020
Accepted 14 January 2021

DOI:https://doi.org/10.1103/PhysRevX.11.011060

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)

Antiferromagnetism Dzyaloshinskii-Moriya interaction Magnetic domains

Antiferromagnets Single crystal materials

Density functional calculations Neutron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Thoma ^1,*, V. Hutanu ^2,†, H. Deng ^2,‡, V. E. Dmitrienko³, P. J. Brown⁴, A. Gukasov ⁵, G. Roth⁶, and M. Angst ^7,§

¹Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, 85748 Garching, Germany
²Institute of Crystallography, RWTH Aachen University and Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), 85748 Garching, Germany
³A. V. Shubnikov Institute of Crystallography, FRSC “Crystallography and Photonics,” RAS, Moscow 119333, Russia
⁴12 Little St Marys Lane, Cambridge, CB2 1RR, United Kingdom
⁵Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gif-sur-Yvette, France
⁶Institute of Crystallography, RWTH Aachen University, 52056 Aachen, Germany
⁷Jülich Centre for Neutron Science JCNS and Peter Grünberg Institut PGI, JARA-FIT, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

^*h.thoma@fz-juelich.de
^†vladimir.hutanu@frm2.tum.de
^‡hao.deng@frm2.tum.de
^§m.angst@fz-juelich.de

Popular Summary

Identifying, understanding, and predicting fundamental magnetic interactions in materials is an essential step toward their utilization in novel devices. One of these basic interactions is the Dzyaloshinskii-Moriya interaction (DMI), a type of coupling between neighboring spins that sightly tilts them when they would otherwise tend to align. Although this DMI-induced canting is usually small, it can lead to small net magnetic moments in “weak ferromagnets” and its direction has a significant impact on spintronic applications and topological materials. Here, we establish polarized neutron diffraction (PND) as an efficient technique for determining the absolute direction of the DMI in bulk materials.

In PND, a beam of neutrons, filtered through a device that transmits only one spin state, scatters off a material, and the resulting diffraction pattern reveals information about the material’s magnetic structure at the atomic level. In this work, we show how to relate measured PND data to the absolute DMI direction. With this approach, we unambiguously answer a long-standing question about the absolute sign of the DMI in various weak ferromagnetic systems with a wide range of crystal symmetries. We support our findings with ab initio calculations, which reproduce our experimental results.

We believe this technique will form the basis for future DMI studies in weak ferromagnets and encourage further PND experiments to reveal the DMI direction in many more compounds.

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Vol. 11, Iss. 1 — January - March 2021

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Figure 1
The local environment of the manganese atom in the $z = 0$ layer (green sphere) in the hexagonal unit cell of ${MnCO}_{3}$ . The six nearest-neighbor manganese atoms are shown as blue spheres, with the light blue atoms above ( $z = 1 / 6$ ) and the dark blue atoms below ( $z = - 1 / 6$ ) the central atom. The oxygen atoms ( $z = \pm 1 / 12$ ) between these manganese layers are shown as yellow spheres. The carbon atoms are omitted for clarity. Panels (a) and (b) show the two possible magnetic moment configurations which stabilize depending on the sign of the DMI by applying an external magnetic field $H$ along the $[110]$ direction and, thus, aligning the WFM moment along $H$ . The definition of $D_{z}$ is given in the text.
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Figure 2
The local environment of the iron atoms of the $z = 0$ layer (light and dark green spheres) in the hexagonal unit cell of $α − {Fe}_{2} O_{3}$ . The three nearest-neighbor iron atoms of the $z = \pm 1 / 6$ layer are shown as blue spheres, with the light blue atoms above ( $z = + 1 / 6 - Δ z_{Fe}$ ) and the dark blue atoms below ( $z = - 1 / 6 + Δ z_{Fe}$ ) the central layer. The oxygen atoms ( $z = \pm 1 / 12$ ) between these iron layers are shown as yellow spheres. Panels (a)–(d) show the two possible magnetic moment configurations (a),(b) and their 180° domains (c),(d), which could stabilize depending on the sign of the DMI by applying an external magnetic field $H$ along the $[120]$ direction. By aligning the WFM moment along $H$ , configurations (a) and (b) are energetically favored to their 180° domains. The definition of $D_{z}$ is given in the text.
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Figure 3
Visualized results of the symmetry restricted magnetic moment refinement in ${MnCO}_{3}$ from Table 1. The left-hand side shows the projection of the exact field direction (orange arrow) and the resulting magnetic moment configuration (red arrows) on the $a b$ plane. The magnetic field has a small out-of-plane component of 1.2(5)° toward the $c$ axis. All angles are drawn exaggerated to be visible. Additionally, the orthogonal $x$ , $y$ , and $z$ directions used in the text are defined. The right-hand side shows the comparison between the observed and calculated asymmetry values for the refinement.
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Figure 4
Visualized results of the symmetry restricted magnetic moment refinement in $α − {Fe}_{2} O_{3}$ from Table 2. The left-hand side shows the projection of the exact field direction (orange arrow) and the resulting magnetic moment configuration (red arrows) on the $a b$ plane. The magnetic field has a small out-of-plane component of $- 0.7 (1) °$ toward the $c$ axis. All angles are drawn exaggerated to be visible. Additionally, the orthogonal $x$ , $y$ , and $z$ directions used in the text are defined. The right-hand side shows the comparison between the observed and calculated asymmetry values for the refinement.
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