Spin-Dependent Transport in Heavily Mn-Doped GaAs

Abstract

The theory of magnetotransport in heavily Mn-doped GaAs, a p-type ferromagnetic semiconductor, is developed in the weak coupling limit by calculating the temperature and magnetic field dependences of the spin disorder scattering-limited hole mobility. The theory is based on the exchange interaction between the itinerant holes and the localized 3d spins of the Mn ions, and it is developed by using Zubarev's double-time Green's functions. The relaxation time of the charge carriers is calculated from the imaginary part of the self-energy appearing in the derived hole propagator. Adding a contribution from impurity scattering the total hole mobility is estimated. Comparison to the experimental resistivity data shows that a good agreement with the measured results is obtained only if the short-range order and the consequent T dependence of the critical scattering are taken into account in the paramagnetic region. The measured resistivity peak near Curie temperature is broader than the calculated one, which together with the estimated large exchange parameter J pd ¼ 2:3 eV calls for an extension of the present theory to the intermediate or strong coupling cases.

Spin-Dependent Transport in Heavily Mn-Doped GaAs II: Effect of Collisional Broadening

“…The average spin polarization hS z i of the magnetic ions can be caluclated by using the standard mean-field theory [8,12]. The higher order Green's function G ps 0 ðRÞ in (2) is defined in the vector form as…”

“…The equation of motion (2) can be solved, if the three components of the higher order Green's function (5) are estimated by using the single particle propagator G ks , as it was shwon in our previous paper [8]. However, in order to include the collisional broadening effects due to Mn ions we now have to keep the terms that depend on the dopant potential in the equation of motion for the Green's function (5).…”

“…The perturbed Green's function is obtainable from (1) and the equation of motion [8,11] for the hole propagator G ks ¼ hha ks ; a y hs 0 ii…”

“…There are various advanced methods to take into account the CB effects in the transport theory [9,10]. Here we apply Zubarev's double-time Green's functions [11], which also were used in our previous paper [8], to add the CB effects in the theory of spin disorder and impurity scatterings.…”

“…Typically, in the theory of spin disorder scattering for metallic materials (metals or heavily doped semiconductors) the short range order is neglected in a temperature independent resistivity above the Curie temperature. However, in a recent paper [8] we have shown that in the case of heavily Mn-doped GaAs, which is a ferromagnetic semiconductor, also the short range order must be taken into account in order to explain the measured temperature dependence of the resistivity in the paramagnetic region. We considered the spin disorder scattering together with the strong impurity scattering, and showed that both the measured resistivity peak and the magnetoresistance can be explained well by the theory.…”