Bound magnetic polaron in Cr-based diluted magnetic semiconductors

The theory of a donor bound magnetic polaron (BMP) in Cr-based diluted magnetic semiconductors is presented. The Cr BMP generalizes the physical situation for Mn-based and Fe-based BMP due to particular energy structure of ${\mathrm{Cr}}^{2+}$ ions, exhibiting features typical for both ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{2+}$ ions. The ground state of the ${\mathrm{Cr}}^{2+}$ ion is a semidoublet, yielding a permanent magnetic moment of the ion, similarly as for ${\mathrm{Mn}}^{2+}$ or ${\mathrm{Co}}^{2+}$ ions. On the other hand the ground state is followed by closely lying excited states, analogously to the situation for ${\mathrm{Fe}}^{2+}$ ions. The developed Cr BMP model recovers characteristic behavior of both Mn BMP and Fe BMP: zero-field spin-flip energy (a fingerprint of Mn BMP) and anticrossings of BMP states (typical for Fe BMP). The model provides a perfect description of the BMP energy structure recently observed in a spin-flip Raman scattering experiment of ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}\mathrm{S}.$ Additionally, from this analysis the ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}\mathrm{S}$ conduction band exchange integral is evaluated as ${N}_{0}\ensuremath{\alpha}=+0.22\mathrm{eV}.$