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

Non-collinear Order and Spin-Orbit Coupling in Sr$_3$ZnIrO$_6$