Experimental Realization of a Spin-$1/2$ Triangular-Lattice Heisenberg Antiferromagnet

We report the results of magnetization and specific heat measurements on ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$, in which the magnetic ${\mathrm{Co}}^{2+}$ ion has a fictitious spin $1/2$, and provide evidence that a spin-$1/2$ Heisenberg antiferromagnet on a regular triangular lattice is actually realized in ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Sb}}_2{\mathrm{O}}_9$. We found that the entire magnetization curve including the one-third quantum magnetization plateau is in excellent quantitative agreement with the results of theoretical calculations. We also found that ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ undergoes a three-step transition within a narrow temperature range.

Figure 1

Crystal structure of ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$. The blue single octahedron is a ${\mathrm{CoO}}_6$ octahedron with a ${\mathrm{Co}}^{2+}$ ion at the center, and the face-sharing ${\mathrm{Sb}}_2{\mathrm{O}}_9$ double octahedron is shaded ochre. Magnetic ${\mathrm{Co}}^{2+}$ ions form a regular triangular lattice in the $ab$ plane. Dotted lines denote the chemical unit cell.

Figure 2

(a) Raw magnetization curve of ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ powder measured at 1.3 K and derivative susceptibility $dM/dH$ vs magnetic field $H$. Dashed lines denote the Van Vleck paramagnetism evaluated from the magnetization slope above the saturation field $H_s=31.9\mathrm{T}$. (b) Magnetization curve corrected for Van Vleck paramagnetism. Thick dashed and solid lines denote the theoretical magnetization curves calculated by the higher order coupled cluster method (CCM) [13] and by exact diagonalization (ED) for a 39-site rhombic cluster [16], respectively. Thin dotted lines denote classical magnetization curves.

Figure 3

Temperature dependence of magnetic susceptibilities for ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ obtained before and after correction of Van Vleck paramagnetism. The solid line denotes the theoretical susceptibility calculated by series expansion [29] with $J/k_{\mathrm{B}}=18.2\mathrm{K}$ and $g=3.82$.

Figure 4

Low-temperature specific heat of ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ measured at zero magnetic field. The inset shows an expansion of the graph around 3.8 K.