Effects of internal exchange fields on magnetization steps in diluted magnetic semiconductors

Abstract

We present a new model of the high-field magnetization in dilute (x≤0.05) $A_{1\mathrm{-}x}^{\mathrm{II}}$ ${\mathrm{Mn}}_{\mathrm{x}}$ ${\mathrm{B}}^{\mathrm{VI}}$ alloys ($A^{\mathrm{\Pi }}$=Zn, Cd, Hg; $B^{\mathrm{VI}}$=S, Se, Te) which includes the effects of internal effective fields due to distant-neighbor exchange interactions. The model represents an extension of a nearest-neighbor-only cluster model used previously for these materials to explain the observation of ‘‘magnetization steps’’ associated with Mn nearest-neighbor pairs. The presence of internal fields causes a broadening and shift of these steps, in agreement with experiment. The distributions of such fields for fcc and hcp magnetic sublattices are modeled by considering exchange interactions out to third and fourth neighbors, respectively. Published data for ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te and ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se are reinterpreted using this approach to provide a more accurate determination of nearest-neighbor exchange constants as well as approximate values of more-distant interactions. All are found to be antiferromagnetic. The internal-field corrections reduce the magnitude of the nearest-neighbor exchange constant by 18% in the telluride and 9% in the selenide. The more-distant exchange is found to be larger than previously assumed but consistent with other known magnetic properties.