In most of semimagnetic semiconductors (SMSC) on the basis polar A²B⁶ compounds that have wide technical significance, there realizes polaron of large radius. The band structure of SMSC compared with ordinary semiconductors are more sensitive to external magnetic field due to the presence of the exchange interaction between conduction electrons and localized electrons of magnetic ions. In particular, the exchange interaction have an influence on the parameters of energy band and a result, energy spectrum of charge carriers in the SMSC becomes anisotropic, which leads to the appearance of new physical effects in these materials.
The principal objective of this work is theoretical study of the effect of the exchange interaction due to the presence of magnetic impurities on the basic characteristics of the optical polaron (such as ground state energy of polaron, longitudinal and transverse polaron masses of the electron) in the narrow gap SMSC. SMC on the basis A²B⁶ semiconductors possess in mostly one-walley cubic crystal structure. For this, first the solution of problem about anisotropic bulk optical polaron is generalized for the case of weak coupling in one-valley cubic crystal structure. It is assumed that the energy spectrum of band electrons have form an ellipsoid of rotation in this structure. The anisotropy of the phonon spectrum was not considered taking into account that phonon with any wave vector qr is divided into longitudinal and transverse.Contribution to the energy of a conduction electron is calculated in the framework of the perturbation theory in the second order due to the weak interaction with optical phonons at low temperatures. That conduction electron is considered in the one-electron approximation. It is assumed that the weak coupling conduction electrons are moving quite slowly.
Then, on basis of obtained results the expressions for the polaron binding energy, longitudinal and transverse polaron masses of the electron are given for the SMSC which possess an anisotropic energy spectrum in the magnetic field. The anisotropic electron energy spectrum for the SMSC takes into account the influence of non-quantizing magnetic field through the exchange interaction between spins of conduction electrons and paramagnetic ions.
Further it is considered so called nonresonant polaron restricting ourselves with weak magnetic field. This approach means that the at low temperatures virtual transitions of an electron interacting with phonons within the lower conduction sub-band are taken into account. However, such approach solving the problem of non-quantizing magnetic field requires the realization of condition: formula; where w_c is the cyclotron frequency, 6A is the distance between the lowest conduction bands of spin ¯ and spin¯ . Discovered of threshold mechanism in this case occurs in the range of magnetic fields, where the splitting on spin of lowest subbands of the conduction zone do not overlap with the temperature increasing.The such overlap for the sample formula with x = 0.066 takes place at temperature higher than 3.5 K.
Based on numerical calculations of the polaron effective mass carried out for the formula with x = 0.066( which has the structure of zinc blend-sphalerite up to х = 0.37) it is found that the transverse and longitudinal polaron mass, renormalized due to electron-phonon interaction, increases compared with corresponding band values. However, polaron mass of electrons decreases owing to exchange interaction with increasing magnetic field. Also it has been established that ground-state energy of polaron decreases as to standard case owing to exchange interaction with increasing magnetic field.
From an analysis of calculating results it has been established that the exchange interaction decreases the polaron binding energy in comparison with standard case in weak magnetic field.