The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states

We consider a classical Heisenberg model on the kagomé and the square kagomé lattice, where at zero magnetic field non-coplanar cuboctahedral ground states with twelve sublattices exist if suitable exchange couplings are introduced between the other neighbors. Such 'cuboc ground states' are remarkable because they allow for chiral ordering. For these models, we discuss the magnetization process in an applied magnetic fieldHby both numerical and analytical methods. We find some universal properties that are present in all models. The magnetization curveM(H) usually contains only non-linear components and there is at least one magnetic field driven phase transition. Details of theM(H) curve such as the number and characteristics (continuous or discontinuous) of the phase transitions depend on the lattice and the details of the exchange between the further neighbors. Typical features of these magnetization processes can already be derived for a paradigmatic 12-spin model that we define in this work.