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We report the results of low-temperature thermal and magnetic measurements onBa$_3$CoNb$_2$O$_9$ powder, described as a uniform triangular-latticeantiferromagnet (TLAF) with a fictitious spin-1/2. Ba$_3$CoNb$_2$O$_9$ is foundto undergo two-step antiferromagnetic transitions at $T_{\rm N1}=1.39~{\rm K}$and $T_{\rm N2}=1.13~{\rm K}$. As the magnetic field is increased, both $T_{\rmN1}$ and $T_{\rm N2}$ monotonically decrease. The magnetic field vs temperaturephase diagram indicates that the exchange interactions are nearly of theHeisenberg type with weak easy-axis anisotropy and that the exchangeinteraction between triangular lattices is crucial, in contrast to the case ofthe quasi-two-dimensional TLAF Ba$_3$CoSb$_2$O$_9$ [Susuki {\it et al}., Phys.Rev. Lett. \textbf{110}, 267201 (2013)].

Magnetic Phase Diagram of the S=1/2 Triangular-Lattice Heisenberg Antiferromagnet Ba3CoNb2O9