Magnetic properties of the triangular-lattice antiferromagnets <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ba</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>R</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mn>9</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>18</mml:mn></mml:msub></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mi>Yb</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>Er</mml:mi><mml:mo>)</mml:mo></mml:math>

Abstract

Frustration-induced strong quantum fluctuations, spin correlations, and interplay between competing degrees of freedom are some of the key ingredients that underlie exotic states with fractional excitations in quantum materials. Rare-earth-based two-dimensional magnetic lattices possessing a crystal electric field, spin-orbit coupling, anisotropy, and electron correlation between rare-earth moments offer a new paradigm in this context. Herein, we present crystal structure, magnetic susceptibility, and specific heat results accompanied by crystal electric field calculations on polycrystalline samples of ${\mathrm{Ba}}_{3}{R\mathrm{B}}_{9}{\mathrm{O}}_{18}$ $(R=\mathrm{Yb}, \mathrm{Er})$, in which ${R}^{3+}$ ions form a perfect triangular lattice. The localized ${R}^{3+}$ spins show neither long-range magnetic order nor spin-glass behavior down to 1.9 K in ${\mathrm{Ba}}_{3}{R\mathrm{B}}_{9}{\mathrm{O}}_{18}$. Magnetization data reveal pseudospin ${J}_{\mathrm{eff}}=1/2$ $({\mathrm{Yb}}^{3+})$ degrees of freedom in the Kramers doublet state and a weak antiferromagnetic interaction between ${J}_{\mathrm{eff}}=1/2$ moments in the Yb variant. On the other hand, the effective moment ${\ensuremath{\mu}}_{\mathrm{eff}}=8.8\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ was obtained from the Curie-Weiss fit of the low-temperature susceptibility data in ${\mathrm{Ba}}_{3}{\mathrm{ErB}}_{9}{\mathrm{O}}_{18}$, which suggests the admixture of higher-crystal-electric-field states with the ground state. The Curie-Weiss fit of low-temperature susceptibility data for the Er system unveils the presence of a bit stronger antiferromagnetic interaction between ${\mathrm{Er}}^{3+}$ moments compared with its ${\mathrm{Yb}}^{3+}$ analog. ${\mathrm{Ba}}_{3}{\mathrm{ErB}}_{9}{\mathrm{O}}_{18}$ does not show long-range magnetic order down to 500 mK. Furthermore, our crystal electric field calculations based on the thermodynamic data suggest the presence of a small gap between the ground and first excited Kramers doublets. The broad maximum around 4 K in the specific heat at zero field is attributed to the thermal population of the first crystal electric field excited state in ${\mathrm{Ba}}_{3}{\mathrm{ErB}}_{9}{\mathrm{O}}_{18}$.

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