Electron hopping in Fe1?xCuxCr2S4 (0<x<0.5)

A theoretical expression for the line shape of the Mössbauer spectra in the presence of electron hopping between Fe²⁺ and Fe³⁺ is obtained by using a simple stochastic model. Analyses based upon this expression show that the origin of the complicated Mössbauer spectra observed in the magnetic semiconductors Fe_1?xCu_xCr₂S₄ (0<x<0.5) at 77 K is electron hopping between Fe⁺² and Fe³⁺ This hopping occurs at a rate of a few MHz. Quantitative estimates are given for some parameters; the isomer shifts, the internal magnetic fields, the quadrupole splittings and the proportions of Fe²⁺ and Fe³⁺. The valence distribution in this system is determined from the results. For example, the distribution Fe²⁺_0.69Fe³+_0.29Cu¹⁺_0.02Cr³⁺_1.72Cr²⁺_0.28S^2?₄ is obtained for x = 0.02. The existence of Cr²⁺ is concluded.