In the geometrically frustrated materials with the low-dimensional and small spin moment, the quantum fluctuation could interfere with the complicated interplay of the spin, electron, lattice and orbital interactions, and host exotic ground states such as nematic spin-state and chiral liquid phase. While the quantum phases of the one-dimensional chain and S - 1/2 two-dimensional triangular-lattice antiferromagnet (TLAF) had been more thoroughly investigated by both theorists and experimentalists, the work on S = 1 TLAF has been limited. We induced the lattice distortion into the TLAFs, A3NiNb2O9 (A = Ba, Sr, and Ca) with S (Ni2+) = 1, and applied the thermodynamic, magnetic and neutron scattering measurements. Although A3NiNb2O9 kept the non-collinear 120{\deg} antiferromagnetic phase as the ground state, the Ni2+-lattice changed from the equilateral triangle (A = Ba) into isosceles triangle (A = Sr and Ca). The inelastic neutron scattering data were simulated by the linear spin-wave theory, and the competition between the single-ion anisotropy and the exchange anisotropy from the distorted lattice was discussed.
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