We carried out inelastic neutron scattering experiments on a buckled honeycomb lattice antiferromagnet Ba$_{2}$NiTeO$_{6}$ exhibiting a stripe structure at a low temperature. Magnetic excitations are observed in the energy range of $hbar omega lesssim 10$ meV having an anisotropy gap of 2 meV at 2 K. We perform spin-wave calculations to identify the spin model. The obtained microscopic parameters are consistent with the location of the stripe structure in the classical phase diagram. Furthermore, the Weiss temperature independently estimated from a bulk magnetic susceptibility is consistent with the microscopic parameters. The results reveal that a competition between the NN and NNN interactions that together with a relatively large single ion magnetic anisotropy stabilize the stripe magnetic structure.
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