Magnetic properties of a spin-orbit entangled ${J}_{\mathrm{eff}}$ = $\frac{1}{2}$ honeycomb lattice

Magnetic properties of a spin-orbit entangled $J_{eff}$ = $\frac{1}{2}$ honeycomb lattice

J. Khatua, Q. P. Ding, M. S. Ramachandra Rao, K. Y. Choi, A. Zorko, Y. Furukawa, and P. Khuntia

Phys. Rev. B 108, 054442 – Published 30 August 2023

Abstract

The interplay between spin-orbit coupling, anisotropic magnetic interaction, frustration-induced quantum fluctuations, and spin correlations can lead to novel quantum states with exotic excitations in rare-earth-based quantum magnets. Herein, we present the crystal structure, magnetization, electron spin resonance (ESR), specific heat, and nuclear magnetic resonance (NMR) experiments on the polycrystalline samples of ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ , in which ${Yb}^{3 +}$ ions form a perfect honeycomb lattice without detectable antisite disorder. The magnetization data reveal antiferromagnetically coupled spin-orbit entangled $J_{eff} = \frac{1}{2}$ degrees of freedom of ${Yb}^{3 +}$ ions in the Kramers doublet state. The ESR measurements reveal that the first excited Kramers doublet is 32.3(7) meV above the ground state. The specific heat results suggest the absence of any long-range magnetic order in the measured temperature range. Furthermore, the ${}^{29}{Si}$ NMR results do not indicate any signature of magnetic ordering down to 1.6 K, and the spin-lattice relaxation rate reveals the presence of a field-induced gap that is attributed to the Zeeman splitting of the Kramers doublet state in this quantum material. Our experiments detect neither spin freezing nor long-range magnetic ordering down to 1.6 K. The current results suggest the presence of short-range spin correlations in this spin-orbit entangled $J_{eff} = \frac{1}{2}$ rare-earth magnet on a honeycomb lattice.

Received 21 April 2023
Revised 28 July 2023
Accepted 18 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.054442

Physics Subject Headings (PhySH)

Magnetic susceptibility Magnetism

Strongly correlated systems

Nuclear magnetic resonance Specific heat measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Khatua¹, Q. P. Ding ², M. S. Ramachandra Rao^3,4, K. Y. Choi⁵, A. Zorko^6,7, Y. Furukawa², and P. Khuntia ^1,4,*

¹Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
²Ames National Laboratory, U.S. DOE, and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
³Department of Physics, Nano Functional Materials Technology Centre and Materials Science Research Centre, Indian Institute of Technology Madras, Chennai-600036, India
⁴Quantum Centre of Excellence for Diamond and Emergent Materials, Indian Institute of Technology Madras, Chennai 600036, India
⁵Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea
⁶Jožef Stefan Institute, Jamova c. 39, SI-1000 Ljubljana, Slovenia
⁷Faculty of Mathematics and Physics, University of Ljubljana, Jadranska u. 19, SI-1000 Ljubljana, Slovenia

^*pkhuntia@iitm.ac.in

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Vol. 108, Iss. 5 — 1 August 2023

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Figure 1
(a) Rietveld refinement profile of the room-temperature x-ray diffraction data of ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ . The black circle represents the experimentally observed data points and the orange solid line is the calculated data. The rows of vertical bars are the Bragg reflection positions for ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ (olive bars), ${Ba}_{2} {SiO}_{4}$ (violet bars), and ${Yb}_{2} O_{3}$ (pink bars). The blue line is the difference between observed and calculated intensities. (b) A single unit cell of the trigonal crystal structure of ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ . The nearest-neighbor oxygen atom of ${Yb}^{3 +}$ ions form a ${YbO}_{6}$ octahedra. The possible in-plane nearest-neighbor and interplane exchange interactions through the bridges Yb-O-Si-O-Yb and Yb-O-Si-O-Si-O-Yb are shown, respectively. (c) Structure depicting nearest-neighbor (5.79 Å) ${Yb}^{3 +}$ ions which form honeycomb planes. There are three such consecutive honeycomb planes in the unit cell of ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ .
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Figure 2
(a) Temperature dependence of magnetic susceptibility in several magnetic fields. The inset (left bottom corner) shows the comparison of the zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility as a function of temperature in a magnetic field $μ_{0} H = 0.01$ T. (b) Temperature dependence of inverse magnetic susceptibility in a magnetic field $μ_{0} H = 1$ T with Curie-Weiss fit in the high-temperature (red line) and the low-temperature (orange line) regions. The top inset shows the Curie-Weiss fit of inverse magnetic susceptibility in the low-temperature region. The bottom inset shows the estimated Curie-Weiss temperature as a function of the upper limit of temperature range in the Curie-Weiss fit where the constant value of Curie-Weiss temperature at low temperatures is shown by a dotted orange line. (c) Isotherm magnetization as a function of magnetic field at several temperatures where the solid line represents the Brillouin function fit for paramagnetic ${Yb}^{3 +}$ spins with $J_{eff} = \frac{1}{2}$ moment.
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Figure 3
(a) The ESR spectra of ${Ba}_{9} {Yb}_{2} {Si}_{6} O_{24}$ at various temperatures (circles), with corresponding best fits with isotropic Lorentzian line shape (solid lines) above 70 K. The spectra are shifted vertically for clarity. (b) The temperature dependence of the ESR linewidth (circles), with the solid line representing the fit to the Orbach model, yielding the energy gap of $Δ = 32.3 (7)$ meV (see text for details).
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Figure 4
Temperature dependence of zero-field specific heat divided by temperature, $C_{p} / T$ , where the red line is the fitting curve by the Debye model (see text) which accounts for phonon contributions. (b) Temperature dependence of $C_{p} / T$ in several magnetic fields. The anomaly at $\sim T = 2.26$ K in zero field corresponds to the transition temperature of the minor impurity phase of ${Yb}_{2} O_{3}$ in BYSO. (c) Temperature dependence of magnetic specific heat in several magnetic fields where the solid line depicts the fit using Eq. (1).
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Figure 5
The field-swept ${}^{29}{Si}$ -NMR spectra measured at a constant frequency $ν = 61$ MHz at various temperatures. The blue dashed vertical line corresponds to the zero-shift reference position of 7.2123 T. The blue curve at the bottom shows the calculated asymmetric NMR spectrum due to hyperfine anisotropy ( $K_{iso}$ and $K_{ax}$ ) with nearly zero inhomogeneous magnetic broadening at $T = 1.6$ K. The red curves are calculated spectra by taking into consideration the inhomogeneous magnetic broadening introduced by convoluting the Lorentzian function with the full width at half maximum defined as a parameter $Δ ν$ . The slightly asymmetric shape in the spectra at higher temperatures above $\sim 60$ K is probably due to the ${}^{29}{Si}$ NMR signal at the zero-shift position from the nonmagnetic impurity of ${Ba}_{2} {SiO}_{4}$ [85]. (b) Temperature dependence of $K_{iso}$ and $K_{ax}$ . The inset shows $K_{iso}$ and $K_{ax}$ versus magnetic susceptibility $χ$ . The solid and dashed lines are linear fits, $K_{iso} = 0.45 χ + 0.032$ and $K_{ax} = 0.95 χ - 0.012$ , respectively, with units of percent for NMR shifts and ${cm}^{3}$ /mol for magnetic susceptibility. (c) The temperature dependence of $Δ ν$ (inhomogeneous magnetic broadening) determined by the simulation of the NMR spectra measured at different frequencies (i.e., different magnetic field). (d) The temperature dependence of the ${}^{29}{Si}$ NMR spin-lattice relaxation rate (1/ $T_{1}$ ) measured at five different fields on a log-log scale. The inset shows the 1/ $T_{1}$ as a function of inverse temperature (1/ $T$ ) for different magnetic fields on a semilogarithmic scale. The black lines in the inset represent the fits with a phenomenological model valid for thermally activated behavior of 1/ $T_{1}$ as discussed in the text. (e) Magnetic field dependence of the magnitude of the field-induced gap estimated from the 1/ $T_{1}$ and heat capacity measurements.
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Magnetic properties of a spin-orbit entangled $J_{eff}$ = $\frac{1}{2}$ honeycomb lattice

J. Khatua, Q. P. Ding, M. S. Ramachandra Rao, K. Y. Choi, A. Zorko, Y. Furukawa, and P. Khuntia

Phys. Rev. B 108, 054442 – Published 30 August 2023

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Magnetic properties of a spin-orbit entangled Jeff = 12 honeycomb lattice

J. Khatua, Q. P. Ding, M. S. Ramachandra Rao, K. Y. Choi, A. Zorko, Y. Furukawa, and P. Khuntia

Phys. Rev. B 108, 054442 – Published 30 August 2023

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Magnetic properties of a spin-orbit entangled $J_{eff}$ = $\frac{1}{2}$ honeycomb lattice