Semicond. Sci. Technol. zyxwvutsrq 7 (1992) zyxwvuts 364-367. Printed in zyxwvutsr the UK The influence of composition fluctuations on the spin transition spectra of shallow donors in semimagnetic semiconductors Yu G Semenov and V A Stephanovich Institute zyxwvutsr d Semiconductors, 252650 Kiev, Ukraine Received 14 May 1991, accepted for publication 23 September 1991 Abstract. An otiginal approach has been developed to describe shallowdonor spin-transition spectra in semimagnetic semiconductors for arbitrary impurity content. The approach is based zyxwvuts on the statistical theory of the magnetic resonance line shape. With this tool, the lower limit of the magnetic impurity concentration nl zz 0.%;3 is found at which the position of the resonance maximum Em may still be calculated in the mean exchange field approximation (a, is the radius of the shallow donor ground state). The upper limit, at which the nearest-neighbour model is consistent for description of E,. is found to be n, z 0.03a;'. A simple functional approximation of computed E, values is proposed in the impurity concentration range nl 2 0.03a;3. A quantitative description is offered for earlier experimental results on the spin-flip Raman scattering by shallow donors in Cd,-,Mn,S and EPR d shallow donors in ZnS:Mn 1. Introduction There are two reasons why in semimagnetic semicon- ductors (SMS) the band states of electrons undergoing the exchange interaction with the subsystem of mag- netic ions split: the direct action of magnetic field on the electron spin (Zeeman splitting, gepB H), and the molecular exchange field G. proportional to the spin polarization (Si) of the localized spin momenta (see zyxwvu [l] and the references therein). Since the typical SMS At-,Mn,B6 (z is the mole fraction of cation A2 re- placed by the impurity Mn) are good paramagnets, (SLz) is close to its maximum Si in relatively small magnetic fields H 11 zyxwvutsrqponmlkjihgfedcba Z at low temperatures zyxwvutsr T. In the wide-gap SMS the exchange contribution to the spin-splitting of the conduction band Ge = zyxwvut -Jez(Sz) ( 1) (J, is the carrier-ion exchange constant; for A~-,Mn,B6 its value is 0.24.3 eV) may exceed that of the Zeeman splitting by one or two orders of magnitude (giant spin splitting effect [I]). When the large-radius electron centres effectively interact with a large number N of magnetic ions, the spin splitting is not determined by the mean field (1) but ~2681242/92/030364+04$04SO @ 1992 IOP Publishing Ud by thc local exchange field G,. Thc latter may eithcr be of the stochastic nature or governed by the polaron effect [2]. Quite a number of experiments applying the spin- flip Raman scattering (SFRS) method have been made to study these phenomena. The measured shifts of the SFRS line maxima have been adequately described in terms of the local exchange field model: E,,, zz IG, + gepLgHI. Nonetheless, it was noted in [3] that the exchange contribution to the shift of the SFRS line maximum A E,,, = E,,, - gepB H may disagree with the value G, even in rather large fields H (in the absence of polaron or spin-fluctuation contribution to Gi), if N is not large enough. The disagreement was related to fluctuations of the SMS composition at the scale of the electron state radius ao. It was shown that the calculated maximum of SFRS line, which is determined by the most probable configurations of magnetic ions, does not coincide with the gravity centre of the line if the fluctuations are taken into account. zy Tb illustrate this situation, figure 1 presents the computed shape of the spin transition corresponding to several Values Of the magnetic component concentration ni. However, in the model proposed in [3] the exchange interaction of an electron with the donor is considered with regard to its effect on the nearest magnetic ion. Therefore, the