Stability of magnetic polarons in magnetic semiconductor single electron transistors: The effect of Coulomb interaction and external magnetic field

Abstract

In a magnetic single electron transistor (SET), which consists of a magnetic quantum dot (QD) coupled electrically to nonmagnetic source, drain, and gate electrodes, a magnetic polaron (MP) formation may occur, that is, the charge carrier spin may spin‐polarize the magnetic atoms of the QD and simultaneously the carrier becomes more tightly bound to the QD. We have studied theoretically the effect of the Coulomb interaction and magnetic field on the stability of the MPs in ferromagnetic SETs in the Coulomb blockade regime. The calculated results show that the temperature range, where MP is stable can be controlled by the gate voltage of the SET. At temperatures below the Curie temperature the stability decreases with magnetic field, whereas at higher temperatures the opposite is true. The Coulomb repulsion between two charge carriers separates the spin‐up and spin‐down energy levels, which stabilizes the MP further.

Magnetic ordering in quantum dots: Open versus closed shells

“…Unlike many studies of magnetic QDs that do not go beyond mean field theory, 8,60,[72][73][74] we will utilize two methods which include spin fluctuations. The first is a coarse-grained approach 9 in which we discretize the QD space into a number of cells, N c with N k being the number of Mn spins belonging to each grid point where N k j=1 S jz is the projection of the total spin onto the zaxis of the Mn contained at the k th grid point.…”

Magnetic polaron formation in graphene-based single-electron transistor

“…Then, using LMFT the average spin polarization is a continuous function of position, and it is given by where B S is the Brillouin function for a magnetic atom with the total spin quantum number S . The magnetic part of the free energy F m in can be calculated in the usual way , and the MP binding energy is defined as the energy difference …”

“…where B S is the Brillouin function for a magnetic atom with the total spin quantum number S. The magnetic part of the free energy F m in (11) can be calculated in the usual way [44,45,56,57], and the MP binding energy is defined as the energy difference…”

“…Now, we can treat the electrons inside the disk‐like graphene QD with a radius R 0 as ordinary charge carriers, as we did in our previous paper in the case of magnetic semiconductor QDs . In our simple model, we neglect the effect of the surface polar phonons arising from polar substrate (SiC) on the temperature dependence of the magnetic properties of our model system .…”

“…The MP formation has been studied intensively, both theoretically [42][43][44][45][46][47][48][49] and experimentally [50][51][52][53][54][55] in the case of anti-or paramagnetic II-VI compound semiconductors. Recently, we have extended the theoretical treatment to ferromagnetic III-V compound semiconductor QDs and SETs [56,57]. In the present paper, we properly modify our previous model and apply it to graphene/FMI QDs and SETs.…”