Effects of Na deficiency on spin dynamics in the Mott insulating ${\mathrm{Na}}_{4\ensuremath{-}x}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$

Effects of Na deficiency on spin dynamics in the Mott insulating ${Na}_{4 - x} {Ir}_{3} O_{8}$

Y. S. Choi, C. H. Lee, T. Kihara, H. Zheng, H. Nojiri, J. F. Mitchell, and Kwang-Yong Choi

Phys. Rev. B 109, 144405 – Published 5 April 2024

Abstract

We report on Raman scattering and ${}^{23}{Na}$ nuclear magnetic resonance (NMR) investigations of $j_{eff} = 1 / 2$ hyperkagome antiferromagnet ${Na}_{4 - x} {Ir}_{3} O_{8}$ , which lies in the Mott insulating state. Our Raman scattering experiments unveil remarkable parallels between the magnetic excitations of the pristine ${Na}_{4} {Ir}_{3} O_{8}$ and the Kitaev honeycomb material ${Na}_{2} {IrO}_{3}$ , which are characterized by dominant fractional spinon excitations. In the case of moderate Na-deficient ${Na}_{4 - x} {Ir}_{3} O_{8}$ , however, a substantial suppression of the magnetic excitations is observed, alluding to the notable influence of charge fluctuations on spin dynamics. In addition, our site-specific ${}^{23}{Na}$ NMR measurements offer further insights into the spin dynamics when a minor concentration of holes is introduced into a spin-orbit coupled Mott insulator. Specifically, the spin-lattice relaxation rate $1 / T_{1}$ reveals the emergence of pseudogaplike correlations at the Na(2) site, alongside a critical slowing down behavior at the Na(1) and Na(3) sites. These findings showcase the intricate interplay between itinerant holes and magnetic correlations in a spin-liquid-like background.

Received 14 November 2023
Accepted 22 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.144405

Physics Subject Headings (PhySH)

Spin dynamics

Antiferromagnets Iridates Mott insulators Single crystal materials

Nuclear magnetic resonance Raman spectroscopy Susceptibility measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. S. Choi^1,*, C. H. Lee^2,*, T. Kihara^3,4, H. Zheng⁵, H. Nojiri^3,†, J. F. Mitchell ^5,‡, and Kwang-Yong Choi ^1,§

¹Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Republic of Korea
²Department of Physics, Chung-Ang University, Seoul 06974, Republic of Korea
³Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan
⁴Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
⁵Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

^*These authors contributed equally to this work.
^†nojiri@imr.tohoku.ac.jp
^‡mitchell@anl.gov
^§choisky99@skku.edu

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Vol. 109, Iss. 14 — 1 April 2024

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Figure 1
(a) Crystal structure of ${Na}_{4} {Ir}_{3} O_{8}$ with three different Na sites. The blue, yellow, red, and gray spheres represent Ir, Na(1), Na(2), and Na(3) atoms, respectively. The oxygen atoms are omitted for clarity. Na(1) is connected to three Ir to form the Ir3Na tetrahedra. Na(2) and Na(3) also constitute a network of corner-shared tetrahedra, each having a 75% occupancy. XRD pattern of the ground single crystals of (b) ${Na}_{4} {Ir}_{3} O_{8}$ and (c) ${Na}_{4 - x} {Ir}_{3} O_{8}$ . The observed, calculated, and difference patterns are denoted by the red circles and black and blue lines, respectively. The diffraction peaks for ${Na}_{4} {Ir}_{3} O_{8}$ and ${Na}_{2} {IrO}_{3}$ are marked with the respective green and purple bars beneath the XRD patterns.
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Figure 2
Temperature dependence of the magnetic susceptibility $χ (T)$ for ${Na}_{4} {Ir}_{3} O_{8}$ (blue line), ${Na}_{4 - x} {Ir}_{3} O_{8}$ (pink circles; $crystal 1)$ , and ${Na}_{2} {IrO}_{3}$ (emerald squares) measured under a magnetic field of $μ_{0} H = 0.1 T$ . The inset zooms in on the low-temperature magnetic susceptibility, indicative of a spin-frozen transition at $T_{f} = 6 K$ .
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Figure 3
Comparison of the Raman spectra between ${Na}_{2} {IrO}_{3}$ (upper), ${Na}_{4} {Ir}_{3} O_{8}$ (middle), and ${Na}_{4 - x} {Ir}_{3} O_{8}$ (lower panel; $crystal 2)$ in (xx) polarization at temperatures of $T = 5$ and 280 K. The color shadings denote magnetic excitations.
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Figure 4
Temperature dependence of the Raman spectra for (a) ${Na}_{2} {IrO}_{3}$ , (b) ${Na}_{4} {Ir}_{3} O_{8}$ , and (c) ${Na}_{4 - x} {Ir}_{3} O_{8}$ ( $crystal 2)$ . Thermal evolution of magnetic excitations obtained by subtracting phonon peaks for (d) ${Na}_{2} {IrO}_{3}$ , (e) ${Na}_{4} {Ir}_{3} O_{8}$ , and (f) ${Na}_{4 - x} {Ir}_{3} O_{8}$ ( $crystal 2)$ . Temperature dependence of the low- and high-energy magnetic scattering intensity integrated over the frequency range (g) $ω = 28 - 300 {cm}^{- 1}$ and (h) $ω = 300 - 800 {cm}^{- 1}$ for ${Na}_{2} {IrO}_{3}$ (red squares), ${Na}_{4} {Ir}_{3} O_{8}$ (blue circles), and ${Na}_{4 - x} {Ir}_{3} O_{8}$ (green triangles; $crystal 2)$ . The intensities are normalized to the $T = 400 K$ data. (i) Spin-orbit excitons of ${Na}_{2} {IrO}_{3}, {Na}_{4} {Ir}_{3} O_{8}$ , and ${Na}_{4 - x} {Ir}_{3} O_{8}$ ( $crystal 2)$ measured at room temperature.
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Figure 5
(a) Temperature dependence of ${}^{23}{Na}$ NMR spectra for ${Na}_{4 - x} {Ir}_{3} O_{8}$ measured at an external field of $μ_{0} H = 8.5 T$ . (b) The color contour plot of the histogram $P (1 / T_{1})$ in the temperature- $1 / T_{1}$ plane. (c) Distribution function $P (1 / T_{1})$ as selected temperatures. The symbols mark two components of $1 / T_{1}^{slow}$ (pink circles) and $1 / T_{1}^{fast}$ (green squares). The red dotted and green solid lines are representative of two Gaussian fits. (d) Log-log plot of the ${}^{23}{Na}$ spin-lattice relaxation rates: $1 / T_{1}^{fast}$ (pink circles), $1 / T_{1}^{slow}$ (azure squares), $1 / T_{1}^{*}$ (open triangles), and $1 / T_{1}$ for Na(2) (green diamonds). The blue line represents $1 / T_{1}$ of ${Na}_{2} {IrO}_{3}$ taken from Ref. [51]. The dashed lines are fits to the power-law dependence $1 / T_{1} \sim T^{n}$ . (e) Comparison of $1 / T_{1}$ between ${Na}_{4 - x} {Ir}_{3} O_{8}$ [for Na(2)] and ${Na}_{3} {Ir}_{3} O_{8}$ .
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Physical Review B

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Effects of Na deficiency on spin dynamics in the Mott insulating ${Na}_{4 - x} {Ir}_{3} O_{8}$

Y. S. Choi, C. H. Lee, T. Kihara, H. Zheng, H. Nojiri, J. F. Mitchell, and Kwang-Yong Choi

Phys. Rev. B 109, 144405 – Published 5 April 2024

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Effects of Na deficiency on spin dynamics in the Mott insulating Na4−xIr3O8

Y. S. Choi, C. H. Lee, T. Kihara, H. Zheng, H. Nojiri, J. F. Mitchell, and Kwang-Yong Choi

Phys. Rev. B 109, 144405 – Published 5 April 2024

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Effects of Na deficiency on spin dynamics in the Mott insulating ${Na}_{4 - x} {Ir}_{3} O_{8}$