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

Abstract

We consider a classical Heisenberg model on
the kagom'{e} and the square kagom'{e} 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 field $H$ by both numerical and analytical methods.
We find some universal properties that are present in all models.
The magnetization curve $M(H)$ usually contains only non-linear components
and there is at least one magnetic field driven phase transition.
Details of the $M(H)$ 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.