Successive magnetic phase transitions and multiferroicity in quasi-two-dimensional triangular lattice Heisenberg antiferromagnets Ba$_{3}$CoNb$_{2}$O$_{9}$ and Ba$_{3}$MnNb$_{2}$O$_{9}$*

We have measured magnetic, dielectric and thermodynamic properties of quasi-two-dimensional triangular lattice antiferromagnet (TLAF), Ba$_{3}$CoNb$_{2}$O$_{9}$ (S$=$ 1/2) and Ba$_{3}$MnNb$_{2}$O$_{9}$ (S$=$ 3/2). At zero magnetic field, Ba$_{3}$CoNb$_{2}$O$_{9}$ undergoes a two-step transition at 1.36 K and 1.10 K and enters a 120 degree ordered state. By applying magnetic fields, a series of magnetic phases with fractional saturation magnetization (1/3, 1/2, 2/3 (or $\sqrt 3 $/3Ms) are observed. The collinear spin phase with 1/3 Ms becomes more robust at lower temperatures due to quantum fluctuations. For Ba$_{3}$MnNb$_{2}$O$_{9}$, the 120 degree ordered state is stabilized below 3.10 K at zero field. Under the magnetic field, successive magnetic phase transitions are observed with fractional magnetization 1/3 and 1/2 Ms. The 1/3 Ms phase becomes more stable at higher temperatures due to thermal fluctuations. The ferroelectricity emerges in all spin states in both compounds regardless of the spin chirality. Therefore, Ba$_{3}$CoNb$_{2}$O$_{9}$ and Ba$_{3}$MnNb$_{2}$O$_{9}$ are unique TLAFs exhibiting not only a series of magnetic phase transitions but also multiferroicity.