  Inelastic neutron scattering on the spin-chain compound Sr$_3$NiIrO$_6$
reveals gapped quasi-1D magnetic excitations. The observed one-magnon band
between 29.5 and 39 meV consists of two dispersive modes. The spin wave
spectrum could be well fitted with an antiferromagnetic anisotropic exchange
model and single ion anisotropy on the Ni site. The extracted dominant
anisotropic antiferromagnetic intra-chain exchange interaction between Ir and
Ni ions are $J_z=19.5$ meV and $J_{xy}=12.1$ meV. These values justify previous
electronic structure calculations, showing the importance of Ir spin orbit
coupling on the electron correlations. The magnetic excitations survive up to
200 K well above the magnetic ordering temperature of $T_N \sim 70$ K, also
indicating a quasi-1D nature of the magnetic interactions in Sr$_3$NiIrO$_6$.
Our results not only support the idea of the existence of a new temperature
scale well above $T_N$, but also emphasize the need to consider new exchange
paths complicated by the SOC, resulting in additional characteristic
temperatures in such spin-chain systems.
