Publikationsserver der RWTH Aachen University
Ab-initio calculations for dilute magnetic semiconductors
Abstract
dc:descriptionThis thesis focusses on ab-initio calculations for the electronic structure and the magnetic properties of dilute magnetic semiconductors (DMS). In particular we aim at the understanding of the complex exchange interactions in these systems. Our calculations are based on density functional theory, being ideally suited for a description of the material specific properties of the considered DMS. Moreover we use the KKR Green function method in connection with the coherent potential approximation (CPA), which allows to include the random substitutional disorder in a mean field-like approximation for the electronic structure. Finally we calculate the exchange coupling constants Jij between two impurities in a CPA medium by using the Lichtenstein formula and from this calculate the Curie temperature by a numerically exact Monte Carlo method. The understanding of exchange interactions is a difficult problem, since in magnetism no elementary magnetic interactions exist. We use here the "magnetic force theorem" or "frozen potential approximation", which assumes that the sizes of the magnetic moments do not change due to rotations of the moments. Then for frozen potentials the change of the total energy due to rotations can be well approximated by the single particle energies alone. This results to the simpler problem of understanding the density of states, in particular those features in the spin dependent local density of states resulting from the hybridization with the orbitals of neighboring impurities. Based on this analysis we found and investigated four different exchange mechanisms being of importance in DMS systems: Double exchange: favors the ferromagnetic alignment and arises from the hybridization of partially occupied impurity states, resulting in occupied bonding and empty antibonding states. In the disordered DMS systems this effect leads to a broadening of the impurity band, with the halfwidth scaling as the square root of the concentration c. This coupling is very strong, but short ranged. It is typical for wide-band-gap semiconductors with partially filled impurity bands, such as e.g. (Ga,Mn)N. However, the resulting Curie temperatures are very small, since in the dilute limit the strong NN coupling cannot lead to a ferromagnetic cluster percolating through the whole system. Thus these DMS with wide band gaps, which were considered as great hope for room-temperature DMS, have in fact very low Curie temperatures, being determined by the very weak longer ranged coupling. p-dexchange: This ferromagnetism occurs in DMS systems, in which the majority d-states of the magnetic impurity are located below the center of the valence p-bands. This situation is only occurs for Mn-impurities in III-V systems with heavier anions such as (X,Mn)As and (X,Mn)Sb, with X = Al, Ga, In. Due to p-d hybridization, the majority p-band is pushed to higher energies and is partially emptied, leading to hole mediated ferromagnetism. The coupling constants Jij are relatively weak, but longer ranged. Therefore the Curie temperatures are only moderately reduced by the percolation effect. Antiferromagnetic superexchange: arises from the hybridization between occupied majority states and empty minority states. It is a rather strong interaction and short ranged. Typical for this interaction is that it is largest, if the Fermi level lies in a gap; thus it does not require carriers, i.e. a finite density of states at EF, which is the case for the above two mechanisms. Prototype examples for this super exchange is (Ga,Fe)As and (Cd,Mn)Te. Ferromagnetic superexchange: arises from the hybridization between occupied and empty majority (minority) states. It is weaker and very short ranged. The prototype example, which we found, is (Ga,V)As where the eg and t2g-majority states hybridize. This is in contrast to the apriori belief that the eg-states are very localized and always constitute non-bonding states. Based on realistic ab-initio calculations and model calculations with simple shifts of the Fermi level, we demonstrate that the coupling constants Jij(EF) of the nearest neighbors show a very systematic and universal behavior of the exchange interactions, being the same in all DMS with zinc-blende or wurtzite structure. A second topic we have investigated in this thesis is the pressure dependence of the exchange interactions and the Curie temperatures in (Ga,Mn)As and (In,Mn)As, using the LDA and the LDA+U approximations. In both systems we find similar trends, which we believe are typical for DMS. At normal pressure the exchange mechanisms in Ga0.95Mn0.05As is a mixture between double and p-d exchange, if the LDA is used, while in LDA+U Zener's p-d exchange dominates the behavior. However upon compression the antiferromagnetic superexchange becomes of increasing importance. The superexchange varies as |tdd|^2/Delta_xs, where tdd is the hopping matrix element between the majority d-states and the minority d-states, which strongly increases with pressure, while Delta_xs, the exchange splitting, is reduced with pressure due to the hybridization induced reduction of the local moments. On the other hand for larger lattice constants only double and p-d exchange are important, which however decrease with increasing lattice constants. Thus in the mean-field approximation, the Curie temperature is largest at about the equilibrium lattice constant. In LDA+U this maximum is shifted to a 6% compressed lattice constant, since due to the Hubbard U the superexchange is reduced. In In0.95Mn0.05As the behavior is similar. However, compared to Ga0.95Mn0.05As the maximum in Curie temperature (Tc) is shifted to much stronger compressed lattices. Exact calculations of Tc by Monte Carlo simulations show a somehow different behavior. In both systems the critical temperatures stay relatively constant in a large volume interval. This is related to the fact, that the nearest neighbor couplings, being particularly strong for the superexchange, are not relevant for Tc due to the percolation effect.
Degree
thesis:*- Grantor dc:publisher
- Publikationsserver der RWTH Aachen University
- Year dc:date
- 2008
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Belhadji, Brahim
- Contributors dc:contributor
-
- Meyr, Heinrich
Subjects
dc:subject × 6Rights
dc:rights- Statement dc:rights
-
- info:eu-repo/semantics/openAccess
- Language dc:language
- eng