Ni$_2$Mo$_3$O$_8$: zig-zag antiferromagnetic order an integer spin non-centrosymmetric honeycomb lattice

Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with zig-zag antiferromagnetic (AFM) order. Here we report the discovery of zig-zag AFM order in the layered and non-centrosymmetric honeycomb nickelate Ni$_2$Mo$_3$O$_8$ through a combination of magnetization, specific heat, x-ray and neutron diffraction and electron paramagnetic resonance measurements. It is the first example of such order in an integer-spin non-centrosymmetric structure ($P$$_6$3$mc$). Further, each of the two distinct sites of the bipartite honeycomb lattice has a unique crystal field environment, octahedral and tetrahedral Ni$^{2+}$ respectively, enabling independent substitution on each sublattice. Replacement of Ni by Mg on the octahedral site suppresses the long range magnetic order and results in a weakly ferromagnetic state. Conversely, substitution of Fe for Ni enhances the AFM ordering temperature. Thus Ni$_2$Mo$_3$O$_8$ provides a platform on which to explore the rich physics of $S = 1$ on the honeycomb in the presence of competing magnetic interactions with a non-centrosymmetric, formally piezeo-polar, crystal structure.