Suppressed incommensurate order in swedenborgite ${\mathrm{Ca}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{BaCo}}_{4}{\mathrm{O}}_{7}$

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Suppressed incommensurate order in swedenborgite ${Ca}_{0.5} Y_{0.5} {BaCo}_{4} O_{7}$

Shang Gao, Vilmos Kocsis, Minoru Soda, Feng Ye, Yaohua Liu, Andrew F. May, Yasujiro Taguchi, Yoshinori Tokura, Taka-hisa Arima, Werner Schweika, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 104, L140408 – Published 18 October 2021

Abstract

Swedenborgite ${Ca}_{0.5} Y_{0.5} {BaCo}_{4} O_{7}$ (CYBCO) with geometrically frustrated kagome and triangular lattices exhibits a disordered ground state in spite of strong antiferromagnetic couplings between the Co spins. The character of the disordered state has been debated due to ambiguous Co states in the triangular layers. Here, we perform single-crystal diffuse neutron scattering experiments to fully characterize the short-range spin correlations in CYBCO. Through reverse Monte Carlo and self-consistent Gaussian approximation analyses, we confirm that the Co ions in both the kagome and triangular layers are magnetic, and the interlayer couplings, together with the lattice distortion, promote an incommensurate magnetic order that is suppressed possibly by exchange disorder. Our work clarifies the short-range spin correlations in CYBCO and establishes a general correspondence between unequal interactions and incommensurate spin correlations on the swedenborgite lattice.

Received 10 July 2021
Accepted 30 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L140408

Physics Subject Headings (PhySH)

Frustrated magnetism

Kagome lattice

Quasi elastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shang Gao^1,2,3,*, Vilmos Kocsis^3,†, Minoru Soda^3,4, Feng Ye ¹, Yaohua Liu¹, Andrew F. May², Yasujiro Taguchi ³, Yoshinori Tokura^3,5, Taka-hisa Arima^3,6, Werner Schweika ^7,8, Andrew D. Christianson², and Matthew B. Stone¹

¹Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
⁴Department of Physics, Advanced Sciences, GSHS, Ochanomizu University, Tokyo 112-8610, Japan
⁵Department of Applied Physics and Tokyo College, University of Tokyo, Tokyo 113-8656, Japan
⁶Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8561, Japan
⁷Jülich Center for Neutron Science JCNS and Peter Grünberg Institute PGI, JARA-FIT, Forschungszentrum Jülich, Jülich 52425, Germany
⁸European Spallation Source ESS ERIC, Lund 22100, Sweden

^*gaos2@ornl.gov
^†Present address: Institut für Festkörperforschung, Leibniz IFW Dresden, 01069 Dresden, Germany.

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Vol. 104, Iss. 14 — 1 October 2021

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Figure 1
(a) The Co ions in CYBCO form a lattice of alternating triangular (Co1) and kagome (Co2) layers in the $a b$ plane. The crystal structure is shown in the hexagonal unit cell. $J_{1}$ ( $J_{2}$ ) denotes the couplings within the kagome layers (between the kagome and triangular layers). (b) Refinement results of the XRD data measured at room temperature for pulverized CYBCO crystals. Data points are shown as red circles. The calculated pattern is shown as the black solid line. The vertical bars show the positions of the Bragg peaks for CYBCO with space group $P n a 2_{1}$ . The blue line at the bottom shows the difference of measured and calculated intensities.
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Figure 2
Short-range spin correlations in CYBCO in the (a) $(h k 0)$ , (b) $(h k 2)$ , and (c) $(h 0 l)$ planes. In each panel, the upper half is the experimental data collected on CORELLI at 2 K, and the lower half is the calculated spin correlations from the RMC simulations. In (a) and (b), the solid line indicates the periodicity of the diffuse scattering pattern in the $(h k 0)$ and $(h k 2)$ planes. In (a), the dashed line outlines the first Brillouin zone boundary with the $K (\frac{1}{3} \frac{1}{3} 0)$ point indicated. The additional ringlike scattering in the experimental data arises from the sample environment.
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Figure 3
(a) Spin correlations $〈 S (0) \cdot S (r) 〉$ as a function of distance $r$ calculated through RMC. Gray squares (red circles) are the correlations for the Co1 (Co2) spins along the $c$ ( $a$ ) axis. For the first-neighbor Co2 spins at $r \sim 3.2$ Å, correlations within the bipyramids (intra-bp) and out of the bipyramids (inter-bp) are calculated separately. Error bars representing the standard deviations are smaller than the size of the symbol. (b) Total moment of the spin bipyramid as a function of $J_{2} / J_{1}$ . Insets are representative ground states for infinitely small $J_{2} / J_{1}$ (left) and $J_{2} / J_{1} \geq 1.5$ (right).
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Figure 4
The diffuse neutron scattering pattern in the $(h k 0)$ plane calculated through the SCGA method for $J_{2} / J_{1} = 0.5$ at reversed temperature $β = 100$ (a) and in $(h k 0)$ and $(h k 2)$ planes calculated for $J_{2} / J_{1} = 1.0$ at $β = 4.5$ (b). The hexagon outlines the same region as the solid hexagon in Fig. 2. Pinch points arising from the flat eigenbands disappear at $J_{2} / J_{1} > \sqrt{2} / 2$ , giving rise to a pattern that is similar to the experimental results.
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Figure 5
Diffuse neutron scattering pattern in the $(h k 2)$ plane (a) and $(h k 0)$ plane (e) calculated by the SCGA method using a $J_{1 a} - J_{1 b} - J_{1 c} - J_{2}$ model at $β = 3.2$ , where $J_{1 a} = 0.9, J_{1 b} = 1.0$ , and $J_{1 c} = 1.1$ are the distinctive first-neighbor couplings in the kagome layer due to lattice distortion. The calculated intensities are averaged over equally populated domains. Zoomed-in plot for the experimental diffuse scattering patterns in the $(h k 2)$ plane (b)–(d) and $(h k 0)$ plane (f)–(h). Data were collected at (b), (f) 2 K, (c), (g) 50 K, and (d), (h) 100 K. The dashed line in (d) outlines the first Brillouin zone boundary.
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Physical Review B

covering condensed matter and materials physics

Suppressed incommensurate order in swedenborgite ${Ca}_{0.5} Y_{0.5} {BaCo}_{4} O_{7}$

Shang Gao, Vilmos Kocsis, Minoru Soda, Feng Ye, Yaohua Liu, Andrew F. May, Yasujiro Taguchi, Yoshinori Tokura, Taka-hisa Arima, Werner Schweika, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 104, L140408 – Published 18 October 2021

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Physical Review B

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Suppressed incommensurate order in swedenborgite Ca0.5Y0.5BaCo4O7

Shang Gao, Vilmos Kocsis, Minoru Soda, Feng Ye, Yaohua Liu, Andrew F. May, Yasujiro Taguchi, Yoshinori Tokura, Taka-hisa Arima, Werner Schweika, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 104, L140408 – Published 18 October 2021

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Suppressed incommensurate order in swedenborgite ${Ca}_{0.5} Y_{0.5} {BaCo}_{4} O_{7}$