Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic ${\mathrm{TbB}}_{4}$

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Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic ${TbB}_{4}$

R. Misawa, K. Arakawa, T. Yoshioka, H. Ueda, F. Iga, K. Tamasaku, Y. Tanaka, and T. Kimura

Phys. Rev. B 108, 134433 – Published 24 October 2023

Abstract

Resonant x-ray diffraction (RXD) measurements at the Tb $L_{3}$ and the $M_{5}$ edges were carried out on a single crystal of a rare-earth tetraboride, ${TbB}_{4}$ , which exhibits antiferromagnetic (AFM) order breaking both space-inversion and time-reversal symmetries. Considering its crystallographic and magnetic symmetries, both the anisotropic tensor of susceptibility (ATS) scattering and the magnetic scattering contribute to space-group-forbidden odd00 reflections under the resonant conditions in the AFM phase. We found that the RXD intensity of odd00 reflections depends on the helicity of the circularly polarized incident x rays, which is reasonably explained in terms of the interference effect between the ATS and the magnetic scatterings. Furthermore, the circular dichroic RXD showed a sample-position dependence, which reflects spatial distributions of AFM domains in ${TbB}_{4}$ . Our study reveals that RXD using circularly polarized x rays is a powerful technique to probe not only the magnitude but also the sign of AFM order parameters and to spatially resolve AFM domains in materials breaking both space-inversion and time-reversal symmetries.

Received 21 August 2023
Accepted 4 October 2023

DOI:https://doi.org/10.1103/PhysRevB.108.134433

Physics Subject Headings (PhySH)

Magnetism

Antiferromagnets Rare-earth magnetic materials

X-ray diffraction X-ray imaging

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. Misawa¹, K. Arakawa¹, T. Yoshioka¹, H. Ueda ², F. Iga ³, K. Tamasaku ⁴, Y. Tanaka⁴, and T. Kimura ^1,5

¹Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
²SwissFEL, Paul Scherrer Institute, Forschungsstrasse 111, 5232 Villigen, Switzerland
³Graduate School of Science and Engineering, Ibaraki University, Mito 310-8512, Japan
⁴RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japan
⁵Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan

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Vol. 108, Iss. 13 — 1 October 2023

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Figure 1
Magnetic structures of ${TbB}_{4}$ . (a) In the AFM1 phase ( $T_{N 2} < T < T_{N 1}$ ), Tb moments are aligned along the $〈 110 〉$ directions, and fourfold symmetry is preserved. There are two domain states which are converted into each other by either the time-reversal operation or the space-inversion operation. (b) In the AFM2 phase ( $T < T_{N 2}$ ), the fourfold symmetry is broken, and four domain states are present. Magnetic point groups of the respective phases are also shown.
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Figure 2
Photon energy profiles in the vicinity of the Tb $L_{3}$ edge in ${TbB}_{4}$ . (a) X-ray absorption spectrum (XAS). (b) Integrated intensity of the 200 Bragg reflection. (c) Integrated intensity of the 300 forbidden reflection for the $σ^{'} - π$ and the $π^{'} - π$ channels at $ψ = - 90^{\circ}$ . These data were taken at temperatures below $T_{N 1}$ . The dashed line indicates the photon energy ( $E_{ph} = 7.5175 keV$ ) used for the experiments of Figs. 3 and 4. Inset: The scattering geometry of our resonant x-ray diffraction measurements. Here θ denotes the Bragg angle. The origin of azimuthal angle $(ψ = 0$ ) is defined as the condition that the $c$ axis is perpendicular to the scattering plane.
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Figure 3
Azimuthal angle ( $ψ$ ) dependence of the integrated intensity obtained from the 300 forbidden reflection at 30 K $(< T_{N 1})$ and 60 K $(> T_{N 1})$ . The data were taken for the $σ^{'} - π$ channel at $E_{ph} = 7.5175 keV$ . The solid curves for 30 and 60 K are fits to the experimental data with Eqs. (9) and (11), respectively.
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Figure 4
(a)–(d) Temperature evolution of the 300 forbidden reflection obtained for the $σ^{'} - π$ (blue) and the $π^{'} - π$ channels at $ψ = - 90^{\circ}$ . The data were taken at $E_{ph} = 7.5175 keV$ during warming. (a), (c) Peak profiles of the 300 reflection at selected temperatures for the $σ^{'} - π$ (a) and the $π^{'} - π$ (c) channels. Solid curves are fits to Gaussian functions. (b), (d) Integrated intensity of the 300 reflection as a function of temperature for the $σ^{'} - π$ (b) and the $π^{'} - π$ (d) channels. (e), (f) Temperature evolution of the 300 forbidden reflection obtained at $ψ = - 90^{\circ}$ using LCP and RCP incident x rays. (e) Peak profiles at 30 K $(< T_{N 1})$ . (f) Integrated intensity of the 300 reflection as a function of temperature.
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Figure 5
(a), (b) Photon energy profiles near the Tb $M_{4, 5}$ edges in ${TbB}_{4}$ . (a) X-ray absorption spectrum (XAS) obtained by measuring the fluorescence yield at room temperature. (b) Integrated intensity of the 100 forbidden reflection. Spectrum at 50 K is multiplied by 100 for ease of eyes. The vertical broken line in (a) and (b) denote the photon energy used for the measurement of panels (c) and (d). (c), (d) Temperature evolution of the 100 forbidden reflection obtained using LCP incident x rays with $E_{ph} = 1237.5 eV$ . (c) Integrated intensity of the 100 reflection as a function of temperature. (d) Rocking curves of the 100 reflection at 13, 30, and 49 K.
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Figure 6
Time-reversal antiferromagnetic domains in the AFM1 phase of ${TbB}_{4}$ . (a), (b) Two-dimensional maps of the intensity of the 100 forbidden reflection. These measurements were performed at 30 K using (a) RCP and (b) LCP x rays with $E_{ph} = 1237.5 eV$ . (c), (d) Line profiles of the intensity obtained with RCP and LCP incident x rays at red lines Z (// $b$ ) and Y (// $c$ ) in panels (a) and (b).
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Physical Review B

covering condensed matter and materials physics

Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic ${TbB}_{4}$

R. Misawa, K. Arakawa, T. Yoshioka, H. Ueda, F. Iga, K. Tamasaku, Y. Tanaka, and T. Kimura

Phys. Rev. B 108, 134433 – Published 24 October 2023

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Physical Review B

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Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic TbB4

R. Misawa, K. Arakawa, T. Yoshioka, H. Ueda, F. Iga, K. Tamasaku, Y. Tanaka, and T. Kimura

Phys. Rev. B 108, 134433 – Published 24 October 2023

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Resonant x-ray diffraction study using circularly polarized x rays on antiferromagnetic ${TbB}_{4}$