Reminiscence of a magnetization plateau in a magnetization processes of toy-model triangular and tetrahedral clusters

We discuss magnetization curves of a toy-model trigonal and tetrahedral clusters. Nonlinearity of magnetization with local minimum of differential susceptibility resembling known magnetization plateaus of triangular-lattice and pyrochlore lattice antiferromagnets is observed at intermediate temperature range $ J\lesssim T\lesssim\Theta$ (here $J$ is the exchange coupling constant and $\Theta$ is a Curie-Weiss temperature). This behavior is due to increased statistical weight of the states with intermediate total spin of the cluster, which is related to the `order-by-disorder' mechanism of plateau stabilization of a macroscopic frustrated magnet.