  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.
