Honeycomb lattice with a kagome superstructure of nearest-neighbour bonds is what we term as the kagome-honeycomb lattice. It has been realized in materials exhibiting quantum paramagnetic behaviour.
I will discuss two examples of interacting spins on the kagome-honeycomb lattice. One of these concerns an old family of spin-1 kagome compounds, and the other is about a recently reported distorted honeycomb antiferromagnet exhibiting magnetisation plateaus. I will present an understanding of their quantum paramagnetic phases, and also describe the mechanism for magnetisation plateaus. I will also briefly allude to other problems studied on this lattice.
