  Sr$_{3}$ZnIrO$_{6}$ is an effective spin one-half Mott insulating iridate
belonging to a family of magnets which includes a number of quasi-one
dimensional systems as well as materials exhibiting three dimensional order.
Here we present the results of an extensive investigation into the magnetism
including heat capacity, a.c. susceptibility, muon spin rotation ($\mu$SR),
neutron diffraction and inelastic neutron scattering on the same sample. It is
established that the material exhibits a transition at about $17$ K into a
three-dimensional antiferromagnetic structure with propagation vector
$\boldsymbol{k}=(0,\frac{1}{2},1)$ in the hexagonal setting of R$\bar{3}$c and
non-collinear moments of $0.87$$\mu_B$ on Ir$^{4+}$ ions. Further we have
observed a well defined powder averaged spin wave spectrum with zone boundary
energy of $\sim 5$ meV at $5$ K. We stress that a theoretical analysis shows
that the observed non-collinear magnetic structure arises from anisotropic
inter- and intra- chain exchange which has its origin in significant spin-orbit
coupling. The model can satisfactorily explain the observed spin wave
excitations.
