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«SMALL QUANTUM DOTS OF DILUTED MAGNETIC III-V SEMICONDACTOR COMPOUNDS Liudmila A. Pozhar PermaNature, Birmingham, AL 35242 Home Address: 149 Essex ...»

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0.001 of the CDD maximum values at the distances about 2 covalent radii of In atoms from the molecular “surfaces” (Fig. 4a). Both molecules exhibit electron charge accumulation near their “surface” regions and nearby space on both “sides” of their surfaces. In the case of the predesigned molecule MEP values at the distances from about 2 covalent radii of In atoms to the “surface” of the molecule as defined by its atomic covalent radii are more negative (Fig. 3a) than those closer to the “surface” of the molecule on its both “sides” (Figs. 3b to 3d), and the electron charge is relatively smoothly distributed in this region. Only well “inside” of the molecule MEP values become more negative than those in the space outside the molecule. Thus, despite of its total charge equal to zero, the pre-designed molecule may be characterized experimentally as a “shell” of delocalized negative charge surrounding the molecule at separations of about 2 covalent radii of In atoms from the “surface” of the molecule, and delocalized positive charge spread near the “surface on its both sides where there are regions of lesser values or zero electron charge. In the case of the vacuum molecule the electron charge is closer to the molecular “surface” on its both “sides”, so the MEP values are more negative in the inner molecular regions, signifying that more electron charge is kept closer to the molecular “surface” and more of it is kept “inside” the molecule.

In the case of the pre-designed molecule the dipole moment is almost twice as large as that of the vacuum molecule (Table 2). Interestingly, the vacuum molecule is a ROHF septet whose uncompensated spin magnetic moment is equal to 7µB (where µB denotes Bohr’s magneton), and uncompensated electron spins delocalized in molecular orbits derived from 3d orbits of In atoms (Fig. 5). At the same time, the pre-designed molecule is a HF singlet with all electron spins compensated and the total spin magnetic moment equal to zero. The spin density distribution (SDD) of the vacuum molecule reaches into the space far outside of the molecule, in TABLE II. Ground State Data for the Studied RHF/ROHF InAs- and GaAs-Based Molecules with One and Two Vanadium Atoms

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agreement with the CDD and MEP data (Fig. 4). Thus, the vacuum molecule In10As3Mn is a nanoscale ferromagnet with the rather large spin magnetic moment brought about by delocalization of electrons of the 3d orbits of In atoms due to d-electrons of the Mn atom. One should note here, that this effect is not only due to Mn atom included in the molecule instead of an As atom. Rather, it is an integrated quantum Coulomb effect that is typical for nanoscale objects composed from a few atoms possessing 3d electrons at conditions where there are no other electrons or atoms to help keep electrons in their octet rule-derived molecular orbits. To stabilize such systems, the octet rule must be violated, and electron charge delocalized throughout the system and even in the space surrounding the system. During this delocalization the electron spin components may or may not be fully compensated giving rise to molecules with the non-zero, and sometimes large, total magnetic moment.

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Fig. 5. Isosurfaces of the spin density distribution (SDD) of the vacuum molecule In10As3Mn corresponding to the fractions (a) 0.0002, (b) 0.001 and (c) 0.005 of the SDD maximum value (not shown). Indium atoms are yellow, As red and Mn blue. In (a) all dimensions are to scale, with atomic sizes roughly corresponding to the atoms’ covalent radii. In (b) and (c) atomic dimensions are reduced to show the SDD surface structure.

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The electronic energy level structure (ELS) of both molecules reflects the loss of tetrahedral symmetry due to the presence of the substitution Mn atom (Fig. 6) with its electronic configuration different from that of As ones. The vacuum molecule features bunches of closely lying orbits both in the region of the highest occupied and that of the lowest unoccupied orbits (HOMO and LUMO, respectively). Nevertheless, the ground states of both molecules correspond

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Fig. 7. (Color online) Pre-designed In10As3Mn molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to the isovalues 0.01 and 0.1 [smaller orbital surfaces in (f) and (i)]. (a) and (b): HOMO 118; (c) HOMO 119; (d) to (f): HOMO 120; (g) to (h): LUMO 122. Indium atoms are yellow, As red and Mn blue. Atomic dimensions are reduced to show the surface structure; other dimensions are to scale. In (b) and (i) MO surfaces are transparent to show contributing atoms.

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Fig. 8. (Color online) Vacuum In10As3Mn molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to several isovalues. (a) and (b): HOMO 121, isovalue 0.005; (c) and (d): HOMO 122, isovalue 0.005; (e) and (f): HOMO 123, isovalue 0.01; (g), (h) and (i): LUMO 124, 125 and 126, respectively, isovalue 0.015. In atoms are yellow, As red and Mn blue. Atomic dimensions are reduced to show the isosurface structure; other dimensions are to scale.

to deep minimum of the total energy, and their ELSs exhibit large OTEs (Table 2). The octet rule is violated, as about 240 electrons - many more than the number of usual “valence” ones contribute to formation of the molecular orbitals (MOs) of these molecules. The nature of the MOs confirms the violation of the octet rule, and some of the MOs are similar to those introduced and studied in Ref. 122 for small non-stoichiometric atomic clusters. In the case of the pre-designed molecule, the bonding HOMO 118, which is the third occupied MO counting from the uppermost HOMO 120, is a pd-type MO derived from several major contributions: (1) 5p atomic orbits (AOs) of In atoms hybridized with 3d AOs of Mn, (2) 4p AOs of As atoms hybridized with 5p AOs of In atoms and 3d AOs of Mn atom, and (3) large pp- and small pdligand bonding of In atoms between themselves (Figs. 7a and 7b). These AOs also contribute to the rest of MOs in the near HOMO – LUMO region, including HOMO 119 and the proper HOMO 120 (Figs. 7c to 7e). In the latter case, contributions from 4d AOs of In atoms are significant. Ligand (In - In) bonding, primarily of pp-type and similar to that of π-type studied in Ref. 122, can be observed in all cases. The ligand bonding is mediated by As and Mn atoms. All three HOMOs in Figs. 7a to 7f are bonding MOs, which is a further illustration of stability of the pre-designed singlet. The LUMO 122 is also a bonding MO similar in nature to those of the HOMOs, but contributions from 4d AOs of In atoms here are negligibly small. In all cased In atoms bond to Mn via hybridization of their 5p AOs and 3d AOs of Mn, in agreement with Zener’s assumption (34). However, in the pre-designed In10As3Mn molecules, Mn and As atoms do not bond directly: their bonding is always mediated by 5p AOs of In atoms, in contrast to MnAs 4p- bonding suggestion of Ref. 79.

Several MOs in the HOMO – LUMO region of the vacuum molecule are depicted in Fig.

8. In this case, all MOs in the immediate HOMO – LUMO region are essentially shaped by hybridization of 3d AOs of the Mn atom and 4p AOs of As atoms, in agreement with suggestion of Ref. (79). The lower HOMO 121 (Figs. 8a and 8b) bonds In atoms through As atoms in two equal parts of the molecule, while there is no bonding between those two parts. The HOMO 122 (Figs. 8c and 8d) is a bonding MO with the major contributions from the 3dz2 AO of the Mn atom and 4p AOs of As atoms, and very samll contributions from 4d AOs of In atoms. In contrast, the proper HOMO 123 (Figs. 8e and 8f) has significant contributions from 4d orbits of two In atoms, in addition to the major contributions from 3dxy AOs of the Mn atom and 4p AOs of As atoms.

Similar to HOMO 121 and 122, HOMO 123 is a bonding MO. The lower LUMOs 124, 125 and 126 (Figs. 8g to 8i) are also derived from the above mentioned AOs of In, As and Mn atoms, but these MOs feature significant ligand (In atoms) bonding contributions. In particular, the major contribution to LUMO 124 (Fig. 8g) comes from bonding of 4 In atoms between themselves through their 5p AOs (a “sandwich” in the lower left part of Fig. 8g that consists of a large negative “football” surface in the lower left part of Fig. 8g and the corresponding positive “lid” on the top), and with 3 other In atoms whose bonding is mediated by 3d AOs of Mn and 4p AOs of As atoms. The two higher MOs in the LUMO region, LUMO 125 and LUMO 126, are also bonding MOs, but ligand bonding there is realized through bonding with Mn and As atoms. The discussed MO properties of In10As3Mn molecules manifest violation of the octet rule of the standard valence theory, in agreement with other available observations (122, 119 – 121) and indicate that there may exist a wide range of non-stoichiometric molecules that are stable either on their own, or can be stabilized by their environment, such as quantum confinement.

The HF and ROHF MOs are not very accurate, and the corresponding OTEs of the two In-based molecules are rather large (Table 2), which is typical for HF approximation (see a discussion in Chapter 2). However, the obtained results hint at the existing opportunities to manipulate electronic and magnetic properties of small molecules composed of semiconductor compound atoms using the synthesis environment, such as quantum confinement, and adjusting the composition. The studied case demonstrates rich prospects opened by the use of quantum confinement as an element of molecular synthesis conditions. In particular, the pre-designed In10As3Mn molecule virtually synthesized at conditions mimicking quantum confinement is a HF singlet (“antiferromagnetic” electron spin arrangement in the molecule) with the total magnetic moment equal to zero and HF OTE about 3.9 eV. At the same time, in the absence of spatial constraints (quantum confinement) the same atoms self-assemble into a different molecule with a relatively large magnetic moment and ROHF OTE about 1.24 eV.

While hardware restrictions do not allow virtual synthesis of much larger atomic systems (see Chapter 3 for more information), the discussed results in the case of small In10As3Mn molecules lead to several important conclusions concerning electronic and magnetic properties of thin films of, and possibly bulk, InAsMn. [Note, that the composition of the studied molecules correspond to about 7% of Mn in the zincblende InAs structure, that is, to the upper limit of the case of “diluted magnetic semiconductors”.] Based on the analysis of CDDs and SDDs of the In10As3Mn molecules and those of In10As4 molecules analyzed in Chapter 4, one can conclude that electron charge deficit in the immediate vicinity of the “surface” and “inside” of the In10As3Mn molecules (that is, regions of positive MEP somewhat below 1 nm in linear dimensions) is, to a degree, orchestrated by the Mn atom. In the language of the semiphenomenological theory of semiconductors this charge deficit is called “hole”. While average linear dimensions of a system are orders of magnitude larger than 1 nm (the case of bulk solids, thick films, large QDs and QWs, etc.) such a “hole” may be considered localized in the vicinity of a Mn atom. However, in the case of nanometer-thin films that are widely investigated at present (see Sec. I) such a hole cannot be treated as a localized object, because its “localization dimensions” are of the order of the thickness of the film. Therefore, in the case of thin films, small QDs and QWs of InAsMn with a few percent of Mn and characteristic dimensions of several nanometers, one must consider such a hole as a region of electron charge deficit delocalized over the outer “surface” of the pyramidal element of the InAs zincblende lattice composed of 10 to 14 In and As atoms containing a Mn atom as an As-substitution defect.

Moreover, even in the pre-designed case (that is, the case reflecting conditions of the InAs zinkblende lattice) that region of electron charge deficit is not uniform, and is not centered on Mn atom. Instead, that region is composed of a system of sub-regions of electron charge deficit with centered near the geometrical center of the pyramids. This conclusion is further supported by data on the SDDs of the studied molecules (Fig. 5). In particular, for both molecules one can observe a large spin density values in the region including the pyramid geometrical center where there is no atoms in the InAs zincblende lattice.

Using the virtual synthesis data discussed above one can finally answer the question concerning “the place of residence” of the “holes”. In particular, in the case when a nanometerthick InAsMn film/system is sandwiched between some other films/systems (such systems are widely studied at present, see Sec. I) the holes do not reside exclusively inside of the InAsMn film/system. Rather, they include portions of the confining systems.

Further on, the ELS of the studied In10As3Mn molecules differs significantly, especially in the HOMO-LUMO regions. This means, that for systems with one or more linear dimensions in the range of a few nanometers, the “band” structure (if such a structure still can be properly identified) is not derived directly from InAs or Mn “valence bands”. Instead, it should be treated as a new band structure originating from quantum confinement and Coulomb effects governing quantum motion of strongly correlated electrons in broken symmetry systems. Thus, reasoning about the “impurity band” and its position related to the “valence band” of the host lattice is meaningless for small systems with one or more linear dimensions in the range of a few nanometers.

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