SPINTRONIC PROPERTIES OF DILUTE MAGNETIC III-V SEMICONDUCTORS
Leeor Kronik, * Manish Jain, and James R. Chelikowsky
Department of Chemical Engineering and Materials Science, and Minnesota
Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455
Abstract
We present ab initio pseudopotential - density functional calculations for the electronic
structure of the dilute magnetic semiconductors MnxGa1-xAs and MnxGa1-xN, with a realistic
x=0.063, in their ordered ferromagnetic phase. We find that in both materials the introduction of
Mn results in the formation of 100% spin-polarized features that support effective mass transport.
This is primarily due to the hybridization of Mn 3d orbitals with As 4p or N 2p orbitals. In
Mn0.063Ga0.937As, the spin-polarization is ~0.5 eV wide and is due to a spin-split valence band. In
Mn0.063Ga0.937N, it is ~1.5 eV wide and is due to a Mn-related impurity band. Both materials are, in
theory, ideal for spintronic applications, but Mn0.063Ga0.937N appears to offer more design
flexibility.
Introduction
Spintronic devices, i. e., devices that exploit both electron charge and spin, are currently the
focus of an intensive research effort.1 These devices hold the promise of creating a new generation
of electronics with unprecedented functionality. The suggested applications include, e.g., “spin
field effect transistors”,2 which could allow for software re-programming of the microprocessor
hardware during run time, semiconductor-based “spin-valves”,3 which would result in high-density,
non-volatile semiconductor memory chips, and even “spin qubits”,4 to be used as the basic building
block for quantum computing.
An essential ingredient in realizing spintronic devices is the use of dilute magnetic
semiconductors (DMSs) that act as a source for injecting spin-polarized charge carriers into an
underlying conventional semiconductor. DMSs are also semiconductors, but can be ferromagnetic
at the same time, by virtue of incorporation of a magnetic impurity in stoichiometric amounts.5 In
recent years, by far the most studied and used DMS was MnxGa1-xAs (x<~0.1), a material
inherently compatible with the relatively mature GaAs technology, and from which spin-polarized
charge injection to GaAs was successfully demonstrated.6 This material also has two main
drawbacks: First, its Curie temperature is low (~110 K), hindering room temperature operation.
Second, because of a low miscibility limit of Mn in GaAs, MnxGa1-xAs films are usually grown
using low temperature molecular beam epitaxy (MBE) and therefore exhibit a limited electronic
quality. More recently, MnxGa1-xN has attracted considerable interest. The Curie temperature of
this material is close to room temperature,7,8 and Mn is more miscible in GaN than in GaAs.
However, the technology of this material (or, indeed, of GaN in general) is considerably less
developed.
A successful operation of spintronic devices requires more than a ferromagnetic semiconductor.
It requires the support of spin-polarized transport so that spin-polarized charge carriers may be
injected into a non-magnetic semiconductor. Here, we summarize our examinations of the
theoretical limits to spin-polarized transport in both MnxGa1-xAs and MnxGa1-xN, with a realistic
* Current Address: Dept. of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100,
Israel. E-mail: leeor.kronik@weizmann.ac.il
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x=0.063, obtained using first principles calculations.9,10 By comparing the two materials, we draw
technologically relevant conclusions as to their suitability for spintronics applications.
Computational details
All results presented here were obtained using ab initio pseudopotentials within densityfunctional theory, with a plane-wave basis.11 We employed the local-spin-density approximation,
implemented using the Perdew-Wang exchange-correlation functional,12 and used TroullierMartins norm-conserving pseudopotentials.13 Details of pseudopotential and convergence
parameters can be found elsewhere.9,10
All DMS calculations were performed within a 32-atom supercell. For Mn0.063Ga0.937As, we
used 2x2x2 standard unit cells to construct the ideal GaAs lattice as a simple cubic lattice of
supercells containing 64 atoms. We then transformed this lattice into an equivalent body centered
cubic (bcc) lattice of supercells containing 32 atoms. For Mn0.063Ga0.937N, we simply used 2x2x2
standard wurtzite unit cells to obtain a 32-atom supercell. In both cases, we replaced one Ga atom
with a Mn atom, obtaining a DMS with x~6.3%. Because the supercell contains only one Mn atom
and because the infinite crystal is constructed by exact replications of this supercell, all Mn atoms
have the same neighboring atoms and possess the same spin. Therefore, the phase so constructed is
ferromagnetic and ordered by definition. This suffices for establishing the theoretical limits to
spin-polarization, because disorder effects (e. g., alloy disorder, Mn clustering, phase segregation,
etc.), as well as the limited stability of the ferromagnetic phase, will clearly only serve to impede
spin-polarized transport.
Results and discussion
Structural optimization is a prerequisite to a successful computation of electronic structure. This
is because relaxation around the Mn impurity could, in principle, change the electronic structure
substantially. We have explicitly allowed for structural relaxation by displacing each atom from its
equilibrium position in a symmetry-breaking fashion and allowing each atom to move under the
forces exerted by the electrons and the other atoms. We found that the introduction of Mn had a
non-negligible effect only on the position of the first shell of N neighbors, where the Mn-As and
Mn-N bond lengths were elongated by a small 1.6% and 3%, respectively, in agreement with
experiment.14 The tetrahedral symmetry was not destroyed, and subsequent atomic shells around
the Mn impurity were left unperturbed. We note that a reduced coordination number consistent
with Mn clustering was found experimentally in both materials, but is absent in our simulations of
the ideally ordered alloy. Importantly, we found that the structural relaxation effects are small and
have negligible consequences on electronic and magnetic properties.
For both materials, we found a global magnetic moment of 4 Bohr-magnetons (b) per supercell. This value is in agreement with the magnetic moment of 5 b for the free Mn atom, which is
reduced to 4 b in the lattice because the Mn impurity acts as an acceptor.
Calculations for the density of states of the two alloys are presented in Fig. 1. Clearly, both
majority and minority spin components of either alloy display a band-gap, indicating that the
introduction of Mn did not destroy the semiconducting nature of the material. The band-gap of both
materials is underestimated with respect to the experimental value – a well-known effect of density
functional theory, resulting from it being a ground state theory not suited for the computation of
excited state properties.11
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(a) MnGaAs
(b) MnGaN
Figure 1. Density-of-states curves for:
(a) zincblende Mn0.063Ga0.937As; (b) wurtzite Mn0.063Ga0.937N.
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The most striking result of the introduction of Mn is the formation of Mn-related, ideally spinpolarized features, with a width of ~0.5 eV in Mn0.063Ga0.937As and ~1.5 eV in Mn0.063Ga0.937N.
Orbital analysis of the spin-polarized features indicates that they are due to significant
hybridization of the Mn 3d states with As 4p or N 2p states.
Importantly, the Fermi level is within the spin-polarized feature in both cases. This means that
both materials are half-metallic, i. e., that their majority spin density of states is metallic, but their
minority spin density of states is semiconducting. Because transported charge carriers come from
the vicinity of the Fermi level, they will have a well-defined (majority) spin. Therefore, the
theoretical limit to spin-polarized transport is an ideal 100%.
In practice, the position of the Fermi level is determined by “unintentional doping” of defects
and residual impurities. If these effects are significant, “Fermi level engineering”, performed by
adding a different donor or acceptor species (in trace amounts, such that the band structure is not
affected) may be required for bringing the Fermi level to within the ideally spin-polarized energy
range. Such engineering need be done with care, as it would also affect the free carrier density and
therefore the Curie temperature.7 We stress that particular attention must be paid to appropriate
design of the interface, where the Fermi level position may be significantly altered due to interface
states.
The presence of a spin-polarized band per se is not, however, a sufficient condition for efficient
spin-polarized transport. An additional requirement is that charge carriers within the spin-polarized
feature are sufficiently mobile. To assess this, we calculated the band structure diagrams for both
materials. These are given in Fig. 2, where the bands are plotted for several high-symmetry
directions in the Brillouin zone. (Note that in light of our choice of a bcc super-cell for
Mn0.063Ga0.937As, the Brillouin zone must correspond to a bcc real-space lattice, even though the
local atomic configuration is that of a slightly perturbed zincblende lattice).
Using Fig. 2a, it is apparent that the above-discussed spin-polarized feature in the majority spin
of Mn0.063Ga0.937As results from a Mn-induced spin-splitting of the valence band, where the valence
band maximum of the majority spin is ~0.5 eV above that of the minority spin. This prediction is in
qualitative agreement with experiment.15 Quantitatively, a smaller split of ~0.1 eV is found
experimentally, for two reasons. First, the samples used in experiments had a degree of disorder,
decreasing the degree of splitting. Second, density functional theory is likely to overestimate the
splitting.16 The combination of theory and experiment therefore provides an upper and lower
bound, respectively, for the width of the spin-polarized energy range at the top of the valence band.
Analysis of the curvature at the top of the valence band indicates that the effective mass of the spinpolarized holes is similar to that found in pure GaAs. We therefore find that spin-polarized
transport in Mn0.063Ga0.937As can be explained within a simple effective mass transport picture.
Using Fig. 2b, we conclude that the spin-polarized feature in Mn0.063Ga0.937N has a different
physical origin. The valence band remains essentially unpolarized. Instead, an independent, spinpolarized impurity band arises. This band features a significant dispersion along some directions of
the Brillouin zone. This is again an ideal situation for spin-injection, as 100% spin-polarized carrier
injection may proceed by simple effective-mass transport in the impurity band.
We note that the practical attainment of “pure” band-like transport also depends on the degree
of order in the material, with hopping conductivity increasing in significance at the expense of
band-like transport with increasing disorder.17 As both defect and disorder effects are strongly
growth and sample dependent, and do not affect our discussion of the ultimate performance limits,
they are not pursued further here.
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(a)
(b)
Figure 2. Band structure diagram along selected high symmetry directions of:
(a) zincblende Mn0.063Ga0.937As; (b) wurtzite Mn0.063Ga0.937N.
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Physically, the sharp difference in the nature of the Mn-related spin-polarized feature in
Mn0.063Ga0.937As and Mn0.063Ga0.937N is due to the nature of the Mn impurity in the host material. In
GaAs, Mn is a shallow acceptor, situated ~0.1 eV above the valence band maximum in the isolated
impurity limit.18 It hybridizes primarily with the valence band, and completely merges with it for a
few percent of Mn. In contrast, Mn is a deep acceptor in GaN - forming a level that is well over 1
eV above the valence band maximum.19 Its interaction with the valence band is therefore much
smaller, and the introduction of Mn barely polarizes the valence band. For x=0.063, the impurity
band does not hybridize to an extent sufficient for merging with the valence band.
The greater width of the spin-polarized in Mn0.063Ga0.937N, with respect to Mn0.063Ga0.937As,
should result in an enhanced immunity to both defect effects on the Fermi level position and
disorder effects on the band structure. Thus, we find that GaN is superior to GaAs not only in
having an elevated Curie temperature, but also in having an electronic structure that is much more
suitable for spin-polarized charge transport and potentially much more tolerant to technological
limitations.
Conclusions
In conclusion, we have used density-functional theory based pseudopotential calculations to
elucidate the electronic structure of ordered, ferromagnetic MnxGa1-xAs and MnxGa1-xN with an
experimentally realistic Mn content of x=0.063. We find that both materials possess an energy
region possessing a well-defined spin, derived from hybridization of Mn 3d orbitals with As 4p or
N 2p orbitals. In Mn0.063Ga0.937As, this feature is only several tenths of an eV wide, and is due to a
spin-split valence band. In Mn0.063Ga0.937N, it is ~1.5 eV wide and is due to an independent
impurity band. By stringent material and device design, including Fermi level engineering, and
assuming a sufficiently high degree of order and a sufficiently low temperature, both
Mn0.063Ga0.937As and Mn0.063Ga0.937N emerge as a theoretically ideal source of spin-polarized
carriers that would be compatible with existing GaAs and GaN technology, respectively.
Theoretically, Mn0.063Ga0.937N allow greater design flexibility. GaN-based technology is
considerably less mature than GaAs-based technology, so that practical spintronic devices based on
MnxGa1-xN have yet to be demonstrated. We hope that this works provides further motivation for
experimental work in that direction.
Acknowledgments
This work was supported in part by the National Science Foundation, the MRSEC Program of
the National Science Foundation under Award Number DMR-9809364, and the Minnesota
Supercomputing Institute.
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