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We report the results of low-temperature thermal and magnetic measurements on Ba$_3$CoNb$_2$O$_9$ powder, described as a uniform triangular-lattice antiferromagnet (TLAF) with a fictitious spin-1/2. Ba$_3$CoNb$_2$O$_9$ is found to 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 $T_{\rm N1}$ and …