${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$: A spin-$\frac{1}{2}$ triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit

The perovskite ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ comprises equilateral effective spin-$\frac{1}{2} {\mathrm{Co}}^{2+}$ triangular layers separated by six nonmagnetic layers. Susceptibility, specific heat, and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ is basically a two-dimensional magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ is very close to be a realization of the paradigmatic spin-$\frac{1}{2}$ triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperatures according to the Mermin and Wagner theorem.

Figure 1

(a) Stacked layer structure of ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ with ${\mathrm{Co}}^{2+}$ ions sitting on a triangular lattice. (b) Rietveld refinement of the neutron powder diffraction pattern measured at $T=0.3$ K with $\lambda =1.54$ Å. (c) Temperature dependence of the inverse dc magnetic susceptibility and corresponding Curie-Weiss fits. (d) Isothermal dc magnetization measured at $T=1.8$ K and extrapolation of the saturated magnetization from the linear dependence above the saturation field (blue solid line).

Figure 2

(a) Temperature dependence of the magnetic ac susceptibility of ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ and corresponding high-temperature series expansion simulations for the 2D spin-$\frac{1}{2}$ triangular-lattice antiferromagnet with $XXZ$ exchange anisotropy. Values of $\mathrm{\Delta }=0.9$, 1.0, and 1.1 are used and simulations run down to a temperature of 0.5 K using Padé approximants of order [6,6]. The measurements are obtained with an ac excitation field of amplitude 0.5 Oe and frequency 300 Hz, and matched to the dc susceptibility below $T=15$ K by an overall $T$-independent rescaling factor [31]. (b) Temperature dependence of the magnetic part of the specific heat of ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ and matching simulations. Inset: Comparison to the magnetic specific heat of ${\mathrm{Ba}}_3{\mathrm{CoNb}}_2{\mathrm{O}}_9$.

Figure 3

(a) Powder-averaged inelastic NS spectra of ${\mathrm{Ba}}_8{\mathrm{CoNb}}_6{\mathrm{O}}_{24}$ at $T=0.3\text{K}$. Data collected at $T=10\text{K}$ are used as the background. (b), (c) NS intensity calculated for $J=\text{0.144}\text{meV}$ using nonlinear SWT with $1/S$ corrections and linear SWT, respectively. Calculated intensities have been convoluted by Gaussian profiles of full width at half maximum $\mathrm{\Delta }E=0.025$ meV and $\mathrm{\Delta }Q=0.015$ Å${}^{-1}$ to approximate the effects of instrumental resolution. (d), (e) Comparisons between experiment (red dots), $1/S$-SWT (solid black line), and linear SWT (dashed blue line) as energy-integrated ($0.05\le E\le 0.52$ meV) and momentum-integrated ($0.6\le Q\le 0.9$ Å${}^{-1}$) cuts, respectively. The shaded (gray) area corresponds to the longitudinal (two-magnon) contribution to the NS intensity in $1/S$-SWT. The high-energy bump around $E=0.45$ meV in (e) is an artifact of our $1/S$ approximation [5]. (f) Temperature dependence of the energy-integrated intensity of (d) and the graphs of different temperatures have been displaced each time by an intensity of 0.6. Error bars correspond to one standard error.