Magnetic anisotropies of quantum dots*

Magnetic anisotropies in quantum dots (QDs) doped by magnetic ions are discussed in terms of two frameworks: anisotropic g-factors and magnetocrystalline anisotropy energy [1]. Two examples, related to zinc-blende $p$-doped materials, are given of how these frameworks are utilized: four-level Hamiltonian of a flat QD and a cuboid infinite-well QD containing a single hole. The latter model, despite being an idealization of a real QD, displays a rich phenomenology of anisotropies. We quantify the anisotropy constants for ZnSe and CdTe QDs, confirming that the Ising-like effective Hamiltonians apply to magnetic QDs [2]. Compared to bulk systems, confinement tuning offers a new way to control easy axes in magnetic QDs. [1] K. Vyborny et al., preprint (2011). [2] C. Le Gall et al., Phys. Rev. Lett. 107, 057401 (2011).