«SMALL QUANTUM DOTS OF DILUTED MAGNETIC III-V SEMICONDACTOR COMPOUNDS Liudmila A. Pozhar PermaNature, Birmingham, AL 35242 Home Address: 149 Essex ...»
experimentally realized in quantum confinement. Indeed, this molecule has a deep ground state energy minimum (Table II) that is about 720 H deeper than that of the vacuum In10As3Mn molecule, which is the only other relatively stable molecule with a large uncompensated magnetic moment 7µB. At the same time, the vacuum In10As3Mn molecule has been computationally synthesized in the absence of any spatial constraints applied to its atoms, and such conditions are not exactly realizable in experiment. Moreover, the pre-designed In10As3Mn molecule is “antiferromagnetic” with zero total uncompensated magnetic moment. Thus, it seems likely that application of spatial constraints to positions of atoms in In10As3Mn cluster atoms in the process of experimental synthesis of In10As3Mn molecules (let alone films) may lead to a molecule with a smaller uncompensated magnetic moment than that of the vacuum In10As3Mn one analyzed above. Thus, among InAs- and GaAs-based molecules with two V substitution atoms only the pre-designed Ga10As2V2 may be of interest for DMS applications.
Indeed, as already noted, the pre-designed In10As2V2 molecule is a ROHF singlet, while the vacuum In10As2V2 (Figs. 28a and 28b) and Ga10As2V2 (Figs. 28e and 28f) molecules may not be realizable experimentally.
In this Chapter first-principle, quantum statistical mechanical methods, RHF and ROHF, were used to synthesize virtually 10 molecules optimized from In, Ga and As atoms in arrangements that reflect tetrahedral symmetries of the zincblende InAs and GaAs bulk lattices, or are derivable from such arrangements by the total energy minimization. The above discussion follows initial steps toward realization of a program of virtual studies of semiconductor atomic
Fig. 28. Isosurfaces of the spin density distributions (SDDs) of the pre-designed In10As2V2 [(a) and (b)] and Ga10As2V2 [(c) and (d)] molecules, and the vacuum molecule Ga10As2V2 [(e) and (f)],.
corresponding to the fractions (isovalues): (a) 0.001, (b) 0.004, (c) 0.002, (d) 0.003, (e) 0.002 and (f)
0.002 of the respective SDD maximum values (not shown). In (a) and (b) indium atoms are yellow, As red and Mn blue. In (c) to (f) Ga atoms are blue, As brown and V yellow. In (b) to (f) all atomic dimensions are reduced to show the SDD surface structure. In (a) atomic dimensions are roughly correspond to those defined by the atoms’ covalent radii.
clusters and nanoscale systems introduced in Refs. 119 – 121, 123, 124 and related publications.
It is necessary to underline here that much more research is needed before any final quantitative conclusions concerning the systems discussed here are reached. It is well known (see Chapter 3) that RHF and ROHF methods overestimate OTE values and do not provide accurate molecular orbitals for atomic clusters so optimized. However, it is also known that these methods permit to obtain important information and data to enable further theoretical studies and to guide experimental developments. In particular, CI, MCSCF, MP-2 and other subsequent and progressively more accurate, first principle approximation methods use RHF or ROHF MOs as input, and the RHF/ROHF ground state energy, CDD and SDD data provide important information and ideas for prospective applications.
Several questions important for DMS applications concern the nature of magnetism and band structure the band structure exhibited by DMS, and the location of the holes mediated by impurity atoms (see Sec. 1 for references). Analysis of RHF/ROHF data discussed in this Chapter provides some important insights that may answer the above questions posed by experimentalists studying DMS systems.
1. In the case of nanoscale InAs- and GaAs-based DMS systems (such as thin films, small QD and QWs, etc.) with at least one linear dimension in the range of a few nanometers the ELS structure is defined by quantum confinement and Coulomb interaction effects, and cannot be described in terms of impurity-driven modification of the band systems of the parent InAs and GaAs bulk lattices. Moreover, such ELSs may only remotely remind a band structure, especially in the case of small QDs. Rather, ELS in such cases is similar to that of molecules and is formed by all participating atoms. Perturbation theory-based approaches no not work for such strongly correlated electron systems.
2. Magnetism in DMS systems is derived from electron charge and spin re-distribution in a broad vicinity of impurity atoms that may include over 10 lattice atoms surrounding the impurity atoms (and not necessarily centered at the impurity atoms). This electron charge and spin re-distribution is a response of the nearby lattice atoms to the impurity-based disturbance of the electron charge of the lattice atoms. In the majority of the studied cases, the non-zero total spin magnetic moment arises from uncompensated electron spins of 4d In or Ga electrons in the process of such electron charge re-distribution.
3. In the studied cases, the process of the electron charge re-distribution leads to charge delocalization about up to 13 atoms neighboring the substitution impurity atom(s). The redistributed charge sets in highly hybridized, bonding molecular orbits that possess three major types of contributions. In the majority of the studied cases, one of two major contributions come from pd-type hybrid bonding between of Mn or V atoms, and 3 to 4 ligand atoms (In or Ga): Mn or V contribute through their 3d AOs, and In or Ga atoms through their hybridized 4p AOs that develop in response to the presence of 3d AOs of Mn or V atoms. The other major contribution to bonding MOs comes from hybrid p-bonding of Ga or In with As atoms. This later contribution also mediates ligand bonding between up to 4 In or Ga atoms. These results confirm and enrich the major idea of the p-d Zener model. Also, the obtained results do not reveal any significant 4p-bonding between Mn and As atoms in InAs-based molecules, in contrast to suggestion of Ref. 79. Instead, there are some contributions to bonding MOs from 5p-4d bonding between different In atoms in such molecules (pd ligand bonding).
4. The total uncompensated magnetic moment is delocalized over the entire molecules, but is at maximum in the vicinity of In or Ga atoms. Because RHF/ROHF MOs may not be quite accurate, especially in the case where many-electron atoms, such as In, Ga and As, are involved, further detailed studies of the considered systems by CI, MCSCF and MP-2 methods are necessary to identify quantitatively mechanisms of “generation” of the uncompensated magnetic moment in the studied molecules. At this stage, it is clear that uncompensated total magnetic moment appears in response to charge disturbance introduced by 3d electrons of Mn or V atoms. However, only in two of the studied cases the uncompensated magnetic moment is spread about the geometrical centers of the molecular structures (but not in the vicinity of Mn or V atoms). In the other 8 studied cases the total magnetic moment is delocalized further including all In or Ga atoms. It is also clear that quantitatively, the total magnetic moment is not equal to what could have been contributed by 3d electrons of V or Mn atoms alone, as their contributions are small. The spin multiplicity of the virtually synthesized molecules range from 1 to 11, which signifies that many more electron spins residing on Ga or In atoms are involved. Indeed, calculations of each of the topmost occupied RHF/ROHF MOs for the studied molecules involves about 120 electrons of the parent atoms, instead of involving only “valence” electrons of the atoms.
5. The electron charge delocalization about many atoms surrounding an impurity atom creates regions of electron charge deficit with the major portion surrounding the “surfaces” of the studied molecule on outside of and inside the molecule structures. Although the total charge of the molecules is zero, such “shells” of the electron charge deficit behave as delocalized and polarized positive charge when external electromagnetic fields ate applied. They separate the electron charge localized deeper inside the molecular structure from that pushed outside the molecular “surface”. The electron charge deficit “shells” are physical realization of idealized, positively charged “holes” of the semi-phenomenological band theory of semiconductors. Such “shells” – holes – embrace from about 8 to 14 atoms in the studied cases, and are larger in size for In-based molecules, exceeding 1 nm in linear dimensions.
Due to the total non-zero magnetic moment of such molecules, the holes are spin-polarized, as they are regions of deficit if the spin-polarized electron charge.
6. Considering that linear dimensions of the holes mediated by substitution impurity atoms in the studied cases exceed 1 nm, in thin DMS films and other nanosystems with at least one linear dimension in the range of a few nanometers such holes may include atoms of other systems spatially confining a DMS nanosystem. Moreover, if a suitably directed electromagnetic field gradient is applied, these “shells” of electron charge deficit will move in response to the electron motion, and may leave the DMS nanosystem of their origin.
7. With a change in thermodynamic conditions, such as temperature or pressure applied to a DMS nanosystem, structural changes may provoke another electron charge re-distribution that will affect the shape of the holes, and thus affest the impurity-mediated magnetic moment. Among the studied molecules only two (Ga10As3V) ones did not change their spin multiplicity in response to a change in conditions of their synthesis. The rest of the studied molecules changed values of their total uncompensated magnetic moments in response to a change in synthesis conditions, and two molecules (In10As3Mn and In10As2V2) became “antiferromagnetic” RHF singlets with the total magnetic moment equal to zero. These results identify a mechanism behind transitions from a ferromagnetic state to a non-magnetic state in some DMS thin film systems observed in recent experiments (see Sec. 1 for references and a further discussion of these experimental observations).
8. All calculations of this chapter are done for systems at zero absolute temperature. However, the OTE of all virtually synthesized, stable molecules (including even septets, Table II) are much larger than any temperature-derived contributions at room temperature. Thus, the obtained results are likely to be relevant, in some cases even quantitatively, to the studied systems at room temperature.
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