Theoretical study of the effective $g$-factor of Cd$_{1-x}$Mn$_x$Te quantum wire under the combined effects of the applied magnetic field, spin-orbit coupling, and exchange effects

In this paper, the energy formula for charge carrier $(e)$ confined in a diluted magnetic semiconductor (DMS) quantum well QW made from Cd$_{1-x}$Mn$_x$Te is generated and utilized to calculate the Density of States (DOS) and the Lande $g$-factor. The Landau levels in a quantum wire that is placed in uniform magnetic field along its axis, taking into account the presence of Rashba spin-orbit interaction and exchange effect, are explored. These effects have altered the DOS and the Landau levels. The electron $g$-factor for the lowest state is explored. Our results show that the $g$-factor is strongly affected by the combined effects of magnetic field and Rashba spin-orbit interaction strengths. The g-factor can vary in a wide range of expands for the bulk value of 2 up to 300, which makes it a good candidate for spintronic applications.