Theoretical Investigations of Half-Metallicity in Cr-Substituted GaN, GaP, GaAs, GaSb Material Systems

Theoretical Investigations of Half-Metallicity in Cr-SubstitutedGaN, GaP, GaAs, GaSb Material Systems

MUHAMMAD HANEEF,1 SUNEELA ARIF,1,3 JEHAN AKBAR,1

and ATTIYA ABDUL-MALIK2

1.—Material Modeling Laboratory, Department of Physics, Hazara University, Mansehra,Pakistan. 2.—Department of Biochemistry, Hazara University, Mansehra, Pakistan. 3.—e-mail:[email protected]

Theoretical investigations of half-metallicity of Cr-substituted Ga0.875Cr0.125M(M = N, P, As, Sb) material systems are presented in this article The spinpolarized band structures, electronic densities of states, spin splitting aroundthe Fermi level and crystal field splitting energies of these materials areaddressed in their co-relationship with their possible spintronics applications.These materials are found to be half-metallic, that is, metallic in one spin stateand insulator in other.

Key words: Spintronic, half-metals, DMS, DFT, dilute magnetic alloys

INTRODUCTION

The discovery of half-metallicity in III–V dilutedmagnetic semiconductor systems is the biggestaccomplishment for the development of spintronicindustry. The long-range ferromagnetism of semi-conductors with higher Curie temperature is veryimportant for improving the efficiency of spin-baseddevices.

On theoretical grounds, both the model Hamilto-nian approach and parameter-free calculationswithin the density functional theory (DFT) areintensively used to investigate dilute magneticsemiconductors (DMS)1 The most interesting fea-ture of both these theoretical approaches is thestudy of the exchange interaction mechanism andthe magnetism of these compounds at higher tem-perature.2–7

The successful spin injection by Ohno et al.8 haspaved the way for new possibilities of making thesecompounds spintronic components. The discovery offerromagnetism in GaMnAs by Ohno et al.9 andMunekata et al.10 have provided grounds forresearch on diluted magnetic semiconductors. Theincorporation of magnetic ions in the preparationof III–V based DMS is a crucial process.11 There-fore, different techniques have been adopted for

incorporating the magnetic elements into the semi-conductor hetrostructures12 or planner doping.13

GaAs/AlGaAs are flexible hetro-structure materialsfor designing novel spin-based electronic and opto-electronic devices. This justifies our study of Cr-dopedIII–V as a new material system for applications in thespintronic industry. These materials provide a foun-dation for adding new functionalities to state of the artmaterial systems for devices such as light-emittingdiodes, photo detectors, lasers, modulators, integratedcircuits, and filters. The III-As compounds belong tothe common anion III–V semiconductors.

Apart from III-nitrides, these compounds have awide range of energy gap. Under normal conditions,these compounds crystallize in a zincblende struc-ture. Boron Arsenide (BAs) and Aluminum Arsenide(AlAs) are indirect band gap while Gallium Arsenide(GaAs) and Indium Arsenide (InAs) are direct bandgap semiconductor materials. The BAs has resem-blance with silicon in terms of their crystal structureand are a good alternative for alloying with AlAs andGaAs as compared to the wider band gap GaN. Due tothe stronger covalent character, BAs possess apeculiar behavior compared to other III–V com-pounds. There are only a few reports about thetheoretical and experimental work on the structuraland electronic properties of these compounds.

Similarly, GaAs is another member of this cate-gory due to its direct band gap and having a higher(Received February 26, 2013; accepted April 11, 2014)

Journal of ELECTRONIC MATERIALS

DOI: 10.1007/s11664-014-3181-7� 2014 TMS

saturated electron velocity and electron mobility. Ithas a wide range of applications, especially wherethe reliability is a major concern.

In this article, we report on the electronic andmagnetic properties of a Ga0.875Cr0.125 M (M = N, P,As, Sb) materials system. These materials are thebest potential candidates for spintronics applica-tions exhibiting a half-metallic character. Practicalapplications of these materials require a clearunderstanding of the basic properties of materialsalong with proper phenomena.

Method of Calculation

The Kohn–Sham equation14 was solved by usingthe full potential linearized augmented plane-wavemethod (FP-LAPW) with the generalized gradientapproximation (GGA)15 to calculate the robustnessof half-metallicity of Ga0.875Cr0.125 M (M = N, P, As,Sb) with the lattice compression. In the generalizedgradient scheme, the exchange–correlation energyExc is a function of the local electron spin densitiesq(r) and their gradient:

EGGAxc ðq"; q#Þ ¼

Zexcðq"ð~rÞ; q#ð~rÞ;rqð~rÞÞqð~rÞd3r (1)

where q› and qfl are electron densities for spin-upand spin-down states, respectively, and exc is theexchange correlation energy per particle. Details ofthe spin-polarized FP-LAPW method, formulae, andwien2k software used for the present calculationsare reported in Refs. 16 and 17.

In the full potential scheme, the whole crystal wasdivided into two different parts: (1) atomic spheres,and (2) interstitial region (region outside the atomicspheres). The wave function for the system wasexpanded into two different basis sets. Within eachatomic sphere, the wave function was expanded inspherical harmonics, while in the interstitial regionit was expanded in a plane wave basis. In the samemanner, the potential was expanded as:

VðrÞ ¼

Xlm

VlmðrÞYlmðrÞ � � � � � � � ðaÞX

K

VKeiKr � � � � � � � � � � � � � �ðbÞ

8>><>>:

(2)

Equation 2a represents the potential inside thesphere and Eq. 2b represents the potential for theinterstitial region. The wave function was expandedin terms of spherical harmonics up to l = 9. Fur-thermore, inside the muffin tin sphere, the potentialwas spherically symmetric and constant elsewhere.The core electrons (inside the muffin tin sphere)were treated fully relativistically and the valenceelectrons were treated semi-relativistically.18 Inorder to ensure that no electron leakage was takingplace while the results were well converged andaccurate, 120 k points and RMT 9 Kmax = 8.00 basisfunctions were used.

RESULTS AND DISCUSSION

Electronic Band Structure and Densitiesof States

The electronic properties of Ga0.875Cr0.125M(M = N, P, As, Sb) were investigated by analyzingthe spin-dependent densities of the states and bandstructures of these compounds. In contradiction torare-earth elements where 4f electrons are partiallyshielded by the 5s and 5p electrons, TM-3d electronswere directly exposed to the environment. Thematerial properties in these compounds stronglydepend on the interaction of these electrons with theneighboring atoms.

Substitution of transition metals into the semi-conductors creates an impurity band in the forbid-den energy gap along with the permissible states.The ferromagnetic nature of Cr-doped III–V dilutemagnetic semiconductors at low concentrations hasbeen reported by Kaminska et al.19 and Frazieret al.20 in their experimental study. Our theoreticalcalculation confirmed the ferromagnetic nature ofthese compounds at higher concentrations. Alonghigh symmetry directions in the first Brillouinzones, the calculated spin polarized band structuresfor Ga0.875Cr0.125M (M = N, P, As, Sb) are presentedin Figs. 1, 2, 3, and 4, respectively. The spin-polar-ized band structure of these compounds depict thatthese compounds are metallic in spin-up state andinsulator in spin-down state. It is clear from thespin-polarized band structure that Ga0.875Cr0.125Nis a degenerate semiconductor, while Ga0.875Cr0.125P,Ga0.875Cr0.125As and Ga0.875Cr0.125Sb exhibit half-metallic characters.

The local strain and local electric field due to Cr(12.5%) substitution decreases the band gap of pureGaN from 3.44 eV to 2.88 eV, for GaP from 2.26 eVto 1.00 eV, for GaAs from 1.43 eV to 0.6 eV, and forGaSb from 0.726 eV to 0.4 eV.

The top of the valence band and the bottom of theconduction band around the C symmetry pointconfirms the wide band gap nature of these mate-rials. The overall band structure results depict thatGa0.875Cr0.125M (M = P, As and Sb) are half-metallicin nature, i.e. metallic in the majority spin state andinsulators in the minority spin states, whileGa0.875Cr0.125N is metallic for both spin states. Boththe conduction band and valence band states over-lap with each other due to the overlapping of Cr-3dand N–P states.

The spin-polarized densities of states of thesematerials give the micro-details of atomic and orbi-tal origin of these band structures, which is pre-sented in Figs. 5, 6 and 7, respectively. It is clearfrom these figures that Cr-t2g states hybridizedstrongly with the anion p-states and created largebonding and anti-bonding hybrids, while the e.g.state is usually of a non bonding character. Bondinghybrids lie within the valence band while the anti-bonding is shifted to the higher energy states due tothe hybridization. Bonding hybrids mostly of

Haneef, Arif, Akbar, and Abdul-Malik

p-character is around the host material whilehigher anti-bonding exhibiting the d-characterresides around the 3d atom. In minority spin states,anion-P states and Cr-3d states are pulled by the

conduction band thus creating a gap at the Fermi-level. The presence of a forbidden energy gaparound the Fermi level in minority spin (fl) suggeststhat these materials are insulator in this spin state.

Fig. 1. Spin-polarized band structure of Ga0.875Cr0.125N in (a) majority spin state and (b) minority spin state.

Fig. 2. Spin-polarized total density of state (DOS) and partial DOS 0f Ga0.875Cr0.125P in zinc-blende-phase.

Theoretical Investigations of Half-Metallicity in Cr-Substituted GaN, GaP,GaAs, GaSb Material Systems

Fig. 3. Spin-polarized total density of state (DOS) and partial DOS of Ga0.875Cr0.125As in zinc-blende phase.

Fig. 4. Spin-polarized total density of state (DOS) and partial DOS of Ga0.875Cr0.125Sb in zinc-blende phase.


Half-metallic energy gaps of Ga0.875Cr01.25P,Ga0.875Cr0.125As, and Ga0.875Cr0.125 Sb preventthese materials from the activation of the majorityspin state (›).

The exchange interaction lies at the heart of long-range ferromagnetic order. The dominant spd-ex-change interactions for these compounds confirmthat the mechanism of ferromagnetism is doubleexchange.

The value of spd-exchange splitting can be foundby calculating EV

› , EVfl, EC

› , and ECfl values, and their

differences are DEC and DEV (values are given inTable I). The minima of the conduction band edgeand maxima of the valence band edge at C symme-try point can be written (for spin-up and spin-downstates) as:

DEC ¼ E#CBMIn � E"CBMin (3a)

DEV ¼ E#VBMax � E"VBMax (3b)

where ECBMinfl , ECBMin

› represent the conductionband minima in the spin-down and spin-up states,whereas EVBMax

fl and EVBMin› represent the valence

band maxima in the spin-down and spin-up states,respectively. These values indicate that potential ismore effective for minority spin state than themajority spin state. The value of the exchangesplitting is the maximum for Ga0.875Cr01.25Sb and

minimum for Ga0.875Cr01.25N. The difference in thevalue of the exchange splitting is related to thedifference in magnetization and values of the bandgap of the materials.

Another proof of the half-metallicity in this com-pound is the crystal field splitting energy. ForGa0.875Cr0.125Neg/t2g centered at (16.37/16.98)eVand their difference is (DE = t2g � eg) 0.61 eV, forGa0.875Cr0.125Aseg/t2g centered at (16.37/16.74) eV(DE = 0.37) for Ga0.875Cr0.125Peg/t2g centered at(16.18/16.65) eV ((DE = 0.47) and for Ga0.875Cr0.125

Sbeg/t2g centered at (16.46/16.65) eV (DE = 0.19).From these values, it is clear that there is adecrease in the crystal field splitting as we go fromGa0.875Cr0.125N to Ga0.875Cr0.125Sb. This decrease isdue to the increase in atomic volume by the additionof more electrons. This will result in an increase inthe shielding effect and hence a decrease in thesplitting energy.

Magnetic Properties

The main source of ferromagnetism in thesematerials is unfilled 3d states. On further analysisof d-state, it is found that the partially filled t2g

state causes ferromagnetism in these compounds.Ferromagnetism in III–V DMS is dominated by thedouble exchange interaction, which is a conse-quence of the large band width and well-localizedwave function in the impurity state in the gap. Thesubstitution of Cr atom in GaN, GaP, GaAs, and

Fig. 5. Spin-polarized total density of state (DOS) and partial DOS of Ga0.875Cr0.125N in zinc-blende phase.


GaSb provides localized spin. These localized spinsacts as an accepters centre and generate a hole forthe mediation of ferromagnetic coupling betweenTM atoms, which causes a double exchange inter-action among the localized magnetic moments ofthese compounds.21–24

The data presented in Table I show that totalmagnetic moments of Ga0.875Cr0.125N, Ga0.875

Cr0.125P, Ga0.875Cr0.125As, and Ga0.875Cr0.125Sb area consequence of Cr, Ga, N/P/As/Sb and interstialsites. The main contribution comes from the unfilledCr-3d states and anion p-states with a small con-tribution from cation and interstial sites. Table Ishows that local the magnetic moment of Cr reducesfrom its free space value of 3.000 lB to 2.46579 lB

for Ga0.875Cr0.125N, to 2.76951 lB for Ga0.875Cr0.125P,

Fig. 6. Spin-polarized band structure of Ga0.875Cr0.125As in (a) majority spin state and (b) minority spin state (zinc-blende phase).

Fig. 7. Spin-polarized band structure of Ga0.875Cr0.125Sb in (a) majority spin state and (b) minority spin state.


to 2.97261 lB for Ga0.875Cr0.125As, and for Ga0.875

Cr0.125Sb increases to 3.16871 lB. This rearrangementof magnetic moments on the transition metal (TM)site is due to the inducing of magnetic moments onnonmagnetic sites. The negative value of magneticmoments on Ga, N, P, As, and Sb show that theirspins are aligned anti-parallel to TM spins. The netinteger magnetic moments for the Ga0.875Cr0.125P,Ga0.875Cr0.125As, and Ga0.875Cr0.125Sb are the evi-dence of their half-metallic nature.

The contribution of the valence and conductionbands in the process of exchange splitting can bediscovered by calculating the value of the exchangeconstants Noa and Nob. The spd-splitting greatlyaffects the band structure of the host material andthese effects are discussed in Ref. 25.

The values of Noa and Nob are calculated directlyfrom the conduction band-edge (DEC = ECBMIn

fl �ECBMin

› ) spin splitting and valence band edge (DEV =EVBMax

fl � EVBMax› ) spin splitting using the following

equation

Noa ¼DEC

x Mh i (4a)

Nob ¼DEV

x Mh i (4b)

The calculated values of Noa and Nob forGa0.875Cr0.125M (M = N, P, As, Sb) are presented inTable I. The values vary for all the three com-pounds, which confirm their magnetic nature. Thevariations are more important for No a than for Nob.

CONCLUSIONS

In summary, we found that the magnetic prop-erties of Ga0.875Cr0.125N, Ga0.875Cr0.125P, Ga0.875-

Cr0.125As, and Ga0.875Cr0.125Sb change by 12.5% Crsubstitution. The spin-polarized band structuresand the densities of states plots represent 100% spinpolarization around the Fermi level for Ga0.875

Cr0.125P, Ga0.875Cr0.125As, and Ga0.875Cr0.125Sbmaterial systems. These compounds are found to beideal half-metals for spintronics devices.

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Table I. Total magnet moments and partial magnetic moments in the unit of Bohar magneton (lB) and latticeconstants (A) exchange splitting energies and crystal field splitting energies of Ga0.875Cr0.125M (M = N, P, Asand Sb)

Sites (lB) Ga0.875Cr0.125N Ga0.875Cr0.125P Ga0.875Cr0.125As Ga0.875Cr0.125Sb

Lattice constant 4.56 5.43 5.65 6.08MTotal 3.011 3.000 3.000 3.000Mint 0.55418 0.36777 0.3806 0.11052M� 2.46579 2.76951 2.97261 3.16871MGa 0.0074 0.00028 �0.00083 �0.00275MN �0.2957 – – –MP – �0.05492 – –MAs – – �0.6711 –MSb – – – �0.07076EC

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Theoretical Investigations of Half-Metallicity in Cr-Substituted GaN, GaP, GaAs, GaSb Material Systems