Canted antiferromagnetic order in the kagome material Sr-vesignieite

A. Verrier, F. Bert, J. M. Parent, M. El-Amine, J. C. Orain, D. Boldrin, A. S. Wills, P. Mendels, and J. A. Quilliam

Phys. Rev. B 101, 054425 – Published 18 February 2020

Abstract

We report ${}^{51}V$ NMR, muon spin rotation, and zero-applied-field ${}^{63, 65}{Cu}$ NMR measurements on powder samples of Sr-vesignieite, ${SrCu}_{3} V_{2} O_{8} {(OH)}_{2}$ , a $S = 1 / 2$ nearly kagome Heisenberg antiferromagnet. Our results demonstrate that the ground state is a $q = 0$ magnetic structure with spins canting either in or out of the kagome plane, giving rise to weak ferromagnetism. We determine the size of ordered moments and the angle of canting for different possible $q = 0$ structures and orbital scenarios, thereby providing insight into the role of the Dzyaloshinskii-Moriya interaction in this material.

Received 11 November 2019
Revised 17 January 2020
Accepted 28 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.054425

Physics Subject Headings (PhySH)

Magnetic order Magnetism

Muon spin resonance Nuclear magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Verrier ¹, F. Bert ², J. M. Parent¹, M. El-Amine ¹, J. C. Orain², D. Boldrin^3,*, A. S. Wills³, P. Mendels², and J. A. Quilliam ^1,†

¹Institut Quantique and Département de Physique, Université de Sherbrooke, 2500 boulevard de l'Université, Sherbrooke, Québec, Canada J1K 2R1
²Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
³Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom

^*Present address: School of Physics & Astronomy, University of Glasgow, Glasgow, Scotland G12 8QQ, United Kingdom.
^†jeffrey.quilliam@usherbrooke.ca

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Vol. 101, Iss. 5 — 1 February 2020

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Images

Figure 1
Different coplanar magnetic orders that have been proposed for kagome antiferromagnets and their respective unit cells. PVC, NVC, and SVC are $120^{\circ}$ phases and stand for positive, negative, and staggered vector chirality, respectively, where the vector chirality is defined for every triangle as $κ = \frac{2}{3} (S_{1} \times S_{2} + S_{2} \times S_{3} + S_{3} \times S_{1})$ with labels increasing when turning counterclockwise around the triangle. The SVC order is also referred to as $\sqrt{3} \times \sqrt{3}$ or $q = (1 / 3 1 / 3)$ in other works. The hexagonal triple- $q$ state is described in more detail in Ref. [14].
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Figure 2
(a) Zero-field muon asymmetry in Sr-vesignieite. The silver sample holder background is estimated to be $\sim 0.02 (1)$ from the remaining oscillating asymmetry in low transverse field at 5 K well below $T_{N} ≃ 11 K$ (see inset). (b) Zero-field asymmetry at 1.6 K. Four spontaneous oscillation frequencies are needed to fit the asymmetry in the time domain. They can be readily identified in the Fourier transform of the asymmetry decay (see inset).
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Figure 3
Zero-field NMR spectrum at 3.9 K. Each color corresponds to experiments performed with a particular rf coil. An example simulation using exact diagonalization of Eq. (2) is shown, where the main peaks are in agreement with the data. The NMR intensity is weighted by a factor $f^{- 1} Q^{- 1}$ , where $Q$ is the quality factor of the NMR $R L C$ circuit.
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Figure 4
(a) Reconstruction of the $V$ NMR spectrum at temperature well above the transition (points). A powder simulation of the quadrupolar perturbed Zeeman Hamiltonian (solid line) shows excellent agreement with the data provided two narrow Lorentzian peaks are added at 32.17 and 32.8 MHz. The first additional peak presumably originates from nonmagnetic impurities in the sample, whereas the second is a signal from copper in the rf coil. (b) Reconstructions of the $V$ NMR spectra at varying temperatures. (c) Comparison of two simple models for the 3.8 K spectrum. For each model, two sites are assumed, giving rounded rectangular spectra of different widths (obtained through a convolution of a rectangular spectrum of varying width and a Gaussian function of fixed width). Forcing the spectral weight of the narrow and broad sites to a 1:3 ratio, which would be consistent with the hexagonal triple- $q$ order, yields a poor fit (bottom). In contrast, a good quality fit is obtained with a 3:2 ratio (top).
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Figure 5
$V$ NMR spectrum second moment (red) and $T_{1}^{- 1}$ relaxation rate (blue) at varying temperatures. Sr-vesignieite data [27] (solid circles) are compared with Ba-vesignieite data taken from [19] (open circles).
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Figure 6
Simulation of the dipolar field at the two V sites (blue and red lines) due to PVC and NVC magnetic orders in Sr-vesignieite with a finite number of unit cells, assuming point dipoles of $1 μ_{B}$ . Each line is calculated with a different global rotation of the order. A gray dashed line indicates the magnitude of the magnetic field observed experimentally on the V site. Only Cu sites located at a given distance or closer are included in the simulation. The cumulative field stabilizes at long distances when no canting is included. The magnetic orders are assumed to follow the $3_{1}$ screw axis symmetry.
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