Structural, electronic and magnetic properties of Fe ...

Physica B 440 (2014) 1–9

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Structural, electronic and magnetic properties of Fe, Co, Mn-doped GaN and ZnO diluted magnetic semiconductors A. Alsaad n Jordan University of Science and Technology, Department of Physical Sciences, PO Box 3030, Irbid 22110, Jordan

art ic l e i nf o

a b s t r a c t

Article history: Received 30 December 2013 Received in revised form 13 January 2014 Accepted 21 January 2014 Available online 29 January 2014

We performed first-principles spin polarized computations to study the structural, electronic, and magnetic properties of diluted magnetic semiconductors (DMSs) based on wide band-gap wurtzite ZnO and GaN semiconductors doped with transition magnetic metals. The main feature of the resulting DMSs is the strong ferromagnetic spin–spin interaction. We characterzie the gaint Zeeman effect observed experimentally upon applying an external magnetic field using pure quantum mechanical based technique. We found that this effect increases substantially with Fe content in GaN:Fe3 þ DMS system at an external magnetic field of 10 T. We found that the magnetization of ZnO and GaN doped with Mn3 þ , Mn2 þ , Co2 þ and Fe3 þ is well described by the Brillouin function. The p–d exchange integrals α and β for these transition magnetic ions doped wide band-gap DMSs have been determined accurately. They exhibit positive value for Ga1 xMnxN and Ga1 xFexN and Zn1 xCoxO indicating ferromagnetic interaction. Furthermore, Magnetocrystalline anistropy energy (MAE) and perpinduclar magnetocrystalline anistropy (PMCA) of ZnO:Mn3 þ , GaN:Fe3 þ , and ZnO: Co2 þ diluted systems for transition ion concentration fixed at x ¼0.125 have been calculated and discussed based on spin-dependent band structure and density of states calculations. We found a robustness of PMCA with respect to lattice strain is remarakable for all the three DMSs systems studied. We found that ZnO:Mn3 þ DMS is a good spin injector. & 2014 Elsevier B.V. All rights reserved.

Keywords: Diluted magnetic semiconductors Wide band-gap semiconductors Giant Zeeman splitting Anisotropic ions system Spin–orbit interaction P–d exchange integrals

1. Introduction Diluted magnetic semiconductors (DMSs) based on wide band gap GaN and ZnO compound semiconductors are potential candidates for high Curie temperature spintronics. Diluted magnetic semiconductors (DMSs) obtained by substituting small contents of transition and rare-earth magnetic ions in coordinated relaxed positions of GaN and ZnO have attracted much attention due to its prospective material and device applications. Transition metals that have partially filled d states have the electronic configurations Fe (4s23d6), Co (4s23d7) and Mn (4s23d5) have been extensively used as magnetic impurities in DMSs for spintronic based devices. The incompletely filled d states contain unpaired electrons, thus, they exhibit magnetic ordering. Several techniques have been proposed to account for magnetic ordering in DMS systems. First-principles calculations can be used to study these techniques theoretically. In ZnO- and GaN-DMSs doped with transition magnetic atoms, the charge carriers in host semiconductors couple with magnetic moments accompanying the transition magnetic atoms. In particular, 3d orbitals of the transition metal ions are

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hybridized with p orbitals of the cations of the host semiconductor. This hybridization magnetically couples the localized 3d spins of magnetic ions with the spin of charge carriers in the host semiconductor [1]. Most importantly, for device applications, we should seek the production of DMS materials of magnetic properties that can be utilized at Curie temperature Tc equals to or greater than the room temperature. The spintronics based on II–VI compounds (such as CdTe, ZnSe, CdSe, CdS, etc.) doped with d-block transition ions substituting their original cations sites were the most individual DMSs examined [1] using theoretical and experimental methods. The industry of doped II–VI encountered several hurdles due to the difficulty of obtaining critical temperatures close to the room temperatures and the complexity of doping II–VI systems with n-type and p-type dopants. On the other hand, III–V semiconductors offer the alternative due to the possibility of obtaining critical temperatures above room temperature and the easiness of doping III–V systems with both n-type and p-type dopants which make such systems potential candidates for high speed electronic, magnetoelectronic, and optoelectronic devices. The GaN and ZnO compounds have attracted extreme consideration in searching for high Tc ferromagnetic DMS materials since Dietl et al. [2] projected that GaN- and ZnO-based DMSs could display ferromagnetism above room temperature upon doping with small fraction of transition elements such as Mn or

2

A. Alsaad / Physica B 440 (2014) 1–9

Cr. This can be justified by the forceful p–d hybridization between the p-orbitals of the valence band of the host semiconductor and the d-orbitals of the magnetic impurity ions. Das et al. [3] reported first-principles calculations on Cr-doped GaN that they are ferromagnetic regardless whether the host GaN is of the form of loose or collects. A number of experimental methods have been investigated to produce single-phase (Ga, Mn) N, among which are ion implantation [4], epitaxial growth [5–10], CVD growth of Mn doped GaN nanowires [11], and diffusion of Mn into GaN stencils [12]. Room temperature ferromagnetism has been observed in (Ga, Mn) N, and assigned to positive spin-charge double exchange interaction. This interaction might be the major factor in determining the total magnetic moment of (Ga, Mn) N samples. Furthermore, doping with other transition metal ions in IIInitride materials, such as Mn-doped AIN [13], Cr-doped GaN [14–16], Cr-doped AIN [14,17], Al in AsN alloys [18], Co-doped GaN [19], Fe-implanted p type GaN epilayer [20], Gd-doped GaN films [21], and Vanadium (V)-doped GaN [19]. The solubility of transition metals in GaN is about 10% to form single phase solid solution. On the other hand, this could be 35% in ZnO. Although, room temperature ferromagnetism has evidently been observed for p-type (Zn, Mn) O, experimental observations has indicated ferromagnetism in n-type (Zn, Mn) O [22,23]. Curie temperatures of values above room temperature have been published for insulating Co-doped ZnO films [24]. Ga1 xMnxN thin film has a paramagnetic behavior when incorporated in superconducting quantum interference devices (SQUID) [25]. Above room temperature ferromagnetism with Tc 4300 K was also observed in Zn1 x (Co0.5Fe0.5) xO thin films made by magnetron co-sputtering and post annealing in vacuum [26]. The mechanisms responsible for ferromagnetism in such systems are yet to be clarified. Recently, several theoretical research teams have been proposed theoretical models based on mean-field theory to explain the detailed exchange mechanisms to account for the magnetic properties observed experimentally in different DMS systems. The Mn d levels are below the valence band minimum of GaAs, but are deeply located in the GaN wide band gap and since the nature of the p–d hybridization intensely depends on their comparative positions in the electronic band structure. This would need significant amendments to current simple models to ensure successful explanation of ferromagnetism in GaN- and ZnObased DMS and (Ga, Mn) N system. A universal theory explaining ferromagnetism in ZnO- and GaN-based DMSs and the wide range of Tc in (Ga, Mn) N has not been fairly understood. The state of ferromagnetism in transition metal-doped GaN and ZnO systems is yet to be explored. The optical and magnetic properties of these DMSs such as photoluminescence, excitons formation, and transition energies are strongly affected by the giant Zeeman splitting. We devote the major part of this work for studying the structural, electronic, and magnetic properties including giant Zeeman splitting of ZnO-and GaN-based DMSs using first-principles methods. Therefore leads to a deeper theoretical understanding of these DMSs systems.

2. Theoretical method The band structure, density of states, and ferromagnetism of GaN and ZnO-based DMSs depend on fabrication conditions. The controversy of reported results among different groups working on these systems highlighted the lack of theoretical models dealing with the structural, magnetic and optical properties of GaN and ZnO-based DMSs. First-principles density functional theory [27,28] simulations are used in our study. The electronic structure was calculated using the Projector augmented wave (PAW) method [29] as implemented in the Vienna ab initio simulation

package VASP [30]. The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) form [31] was used for the exchange-correlation functional. We set the plane-wave-cut-off energy to 400 eV. We used a 4 4 4 Monkhorst-Pack grid to minimize the computation time. Instead of the all-electron electron-ion potential norm-conserving pseudopotentials were used. The relaxed atomic positions were followed by minimizing the total energy (i.e., as small as 10 6 eV), and the Hellmann–Faynmann forces. These forces were as small as 0.003 eV/Å at convergence in the unit cell of all different electronic structure relaxations that has been performed. The controversy of reported results among different groups working on these systems highlighted the lack of theoretical models dealing with the structural, magnetic and optical properties of GaN and ZnO-based DMSs. For magnetic properties of GaN and ZnO based DMSs, spin-polarized density functional calculations were performed with DFT based DMol3 package developed by ACCELRYS [32]. DMol3 allows structural optimization with and without geometry constraints, as well as computation of a variety of structural and electronic properties of DMS systems. Both VASP and DMo13 computational packages yield similar results when employed for the computation of electronic structures of our DMS systems. Several doped models and the pure ZnO were modeled in 3 3 2 supercells consisting of 72 atoms, using our calculated lattice constants of the wurtzite ZnO (a ¼3.25 Å and c¼ 5.05 Å) host semiconductors. In order to investigate the electronic structures of wurtzite GaN crystals, we consider a 72-atom supercell composed of 18 GaN primitive cells using the calculated parameters (a ¼3.189 Å and c ¼5.196 Å) of wurtzite GaN. The doping of transition ions in GaN and ZnO host semiconductors can be presented in the following simple picture. In GaN and ZnO-based a substantial portion of atoms (40% of Mn in ZnO) is randomly replaced by transition-metal (TM) elements, resulting in the formation of localized magnetic moments in the semiconductor matrix. The presence of magnetic ions affects the free carrier behavior through the sp–d exchange interaction between the localized magnetic moments and the spins of the carriers in host semiconductors. Mn, Co, Fe elements have valence electrons corresponding to the 4s orbital, and have partially filled 3d shells (i.e. Mn (4s2 3d5), Fe (4s2 3d6), Co (4s2 3d7)). Both GaN and ZnO are of wurtzite structure which is formed by tetrahedral (s–p3) bonding. Basically, 3d transition-metal ions substitute for the cations of the host semiconductors, i.e., Zn sites in ZnO and Ga sites in GaN. In ZnO, the particular TM, for example, Mn, contributes its 4s2 electrons to the s–p3 bonding, and can substitutionally replace the Zn in the tetrahedral bonding to form a Mn2 þ charge state. In GaN, the bonding configuration requires 3 electrons which can be satisfied with the TM contributing three electrons and form Mn3 þ charge states. However, depending on the position of the Fermi level, which is close to the conduction band in GaN, the third electron may be obtained from a donor site resulting in a large binding energy without leaving any corresponding hole in the valence band. This means that both Mn2 þ (3d5 for Mn) and Mn3 þ (3d4 for Mn) states might be possible and coexist in GaN. The 3d band of the Mn2 þ ion is exactly half-filled, with an energy gap between the up-spin (↑) occupied states and empty downspin (↓) states. Thus, for instance, in doping Mn ions in ZnO and GaN hosts, the expected oxidation and charge state is Mn2 þ in ZnO and Mn3 þ in GaN. The TM d bands of the transition metal hybridize with the host valence bands (O p bands in ZnO and N p bands in GaN) to form the tetrahedral bonding. This hybridization gives rise to the exchange interaction between the localized 3d spins and the carriers in the host valence band. In this simple picture, the s band of the conduction band does not mix with the TM d bands, but it is still influenced by the magnetic ion. For other transition metals, such as Fe, Co, one of the bands is usually partially filled (up or down). Tables 1 and 2 show the oxidation


and charge states of different TM ions in ZnO and GaN hosts. The room temperature ferromagnetism in wide band gap DMSs is not well understood. The magnetization of an isolated ion system oMz 4 is related to the average spin oSz 4 by the relation (Table 3). oM z 4 ¼ gμB N 0 x o Sz 4

ð1Þ

where g is the g-factor, μB is the Bohr magneton. N0 is the cation density; x is the magnetic ion concentration. Since the magnetization o MZ 4 and mean spin value oSZ 4 have the same magnetic field trend, they are usually discussed simultaneously. The signs of the two quantities are opposite, so o SZ 4 is positive and is used in our study [33]. The magnetization of a system of isotropic ions with spins S can be expressed in terms of the Brillouin function 2S þ 1 2S þ 1 1 1 BS ðξÞ ¼ coth ξ coth ξ ð2Þ 2S 2S 2S 2S The average spin of the system of isotropic spins (Mn and Co based DMSs with zinc-blende structure) can be expressed in terms of Brillouin function [33] gμB SB o S 4 ¼ SBS ð3Þ kB T KB Is the Boltzmann constant and T is the absolute temperature. In the wide band gap DMSs that crystallize in wurtzite structure, the Table 1 Parameters appearing in Eq. (4) that characterize the anisotropy of magnetic ion impurities in host wurtzite wide band gap ZnO and GaN semiconductors. Magnetic ion

Semiconductor host

Spin state

g||

g?

Co2 þ Co2 þ Co2 þ Mn3 þ Mn2 þ Fe3 þ Fe3 þ

ZnO ZnO ZnO GaN ZnO ZnO GaN

3/2 3/2 3/2 2 5/2 5/2 5/2

2.2384 2.2380 2.2800 1.9100 2.0016 2.0062 1.9900

2.2768 0.3410 2.2755 0.3420 0.3450 1.9800 0.2700 2.0016 0.0027 2.0062 0.0074 1.9970 0.0093

D (meV)

References

Magnetic ion

Semiconductor host

ΔC (meV)

Δ|| (meV)

Δ? (meV)

Shpα (eV)

Shpβ (eV)

Mn3 þ Co2 þ Mn2 þ Fe3 þ Fe3 þ

GaN ZnO ZnO ZnO GaN

60 17 52 70 80

5.1 2.8 3.5 9.4 11

8.0 6.3 5.1 8.3 8.4

0.60 0.70 0.62 0.75 0.68

0.40 0.30 0.48 0.25 0.32

Table 3 Spin–orbit coupling ΔESO and magnetocrystalline anisotropy energy MAE's for bcc Fe, hcp Co, and bcc Mn transition elements. The MAE is given in μ eV/atom. Experimental MAE's are those given Refs. [55,63,64]. All energies, given relative to self-consistent results with no spin–orbit coupling. MAE

Mn

Co

Fe

Direction and ΔESO

(0 0 1) – 9080.74 (1 1 1) – 9082.24

(0 0 0 1) – 7830.82

(0 0 1) – 6020.68 (1 1 1)–6018.65

a b c

Ref. [55]. Ref. [63]. Ref. [64].

1.50 2.70a

coupling between the crystal field and the spin–orbit interaction enhances a strong magnetic anisotropy. Magnetic ions such as Mn2 þ or Fe3 þ (with S ¼5/2) doped in wide band gap semiconductors such as GaN and ZnO can be described using Brillouin function. The ground state of magnetic ions under the effect of external magnetic field can be described by spin Hamiltonian [34], H z ¼ μB g jj Bz Sz þ μB g ? ðBz Sz þ By Sy Þ þDS2z

ð4Þ

where S is the spin, D is the zero field splitting. The factors g|| and g ? are the g factors for the magnetic field oriented parallel and perpendicular to c-axis, respectively. The mean spin o Sz 4 for magnetic ion impurity with S ¼2 (Co3 þ , Fe2 þ , Cr2 þ , Mn3 þ ) can be written as o Sz 4 ¼

e d sinhðδÞ þ 2e 4d sinhð2δÞ 1=2 þ e d coshðδÞ þ e 4d coshð2δÞ

ð5Þ

For magnetic ions with S ¼3/2 (V2 þ , Cr3 þ , Co2 þ ) o Sz 4 ¼

ð1=2Þsinhð1=2 δÞ þ 3=2e 2d sinhð3=2δÞ coshð1=2δÞ þ e 2d coshð3=2δÞ

ð6Þ

For magnetic ions with spin S¼ 1 (Co þ ) o Sz 4 ¼

e d sinhðδÞ 1=2 þ e d coshðδÞ

ð7Þ

where d ¼ D=kB T and δ ¼ g jj μB B =kB T . For magnetic ions with z spin S¼ 5/2, the magnetization can be written as o Sz 4 ¼

1=2 sinhð1=2δÞ þ 3=2e 2d sinhð3=2δÞ þ 5=2e 6d sinhð5=2δÞ coshð1=2δÞ þe 2d coshð3=2δÞ þe 6d coshð5=2δÞ ð8Þ

[35] [36] [37] [38] [39] [40] [41]

Table 2 The parameters appearing in Eqs. (10), (11) and (12) for different magnetic ions doped in wurtzite GaN and ZnO host semiconductors. The magnitude of the magnetic field used is 10 T.

This work (MAE) Experimental

3

ð1 0 1 0Þ – 7832.72 1.90 1.30b–1.60c

2.03 1.4a

It should be noted that, for the easy magnetization, the deviation from Brillouin function is neglected. For higher temperatures, the magnetization of a system of isotropic ions can be written as gμB SB ð9Þ o M z 4 ¼ gμB N 0 xS0 BS kB T

3. Results and discussions 3.1. Calculation of the giant Zeeman effect: the case of GaN:Fe DMS As indicated by Table 1, the g-factors for S ¼5/2 spin configurations are almost the same for both magnetic field directions. Magnetic ions with S¼ 5/2 have five electrons in the d shell. Thus, the spin–orbit interaction provides the major contribution to anisotropy. In addition, such isotropic magnetic ions remain so even upon doping in anisotropic host semiconductor, as a result, they can be well understood using Brillouin function. However, for the cases of S ¼3/2 and S¼ 2 spin configurations (Mn3 þ in GaN), the field splitting D is comparable to the thermal energy kBT which indicates that anisotropy is very critical for the determination of the magnetization of these spin configurations in wide band gap wurtzite host semiconductors. The excitonic model is used to compute the exchange integrals between different magnetic ions and the free carriers in the ZnO and GaN host semiconductors. In wurtzite GaN and ZnO, the crystal field and the spin–orbit coupling split the valence band into three fragments each of which has an exciton. This causes these semiconductors to have a large optical anisotropy. In order to characterize the giant Zeeman effect quantatively, we formulate the 6 6 effective Hamiltonian for the valence band of wurtzite GaN semiconductor using crystal field splitting ΔC, spin–orbit coupling parallel and perpendicular

4


(Δ||andΔ ? ) to the c-axis of the wurtzite can be written as ! H 3V 0 ¼ H ð0Þ val 0 H 3V where 0 H 3V

ΔJ B ¼ @ ΔJ Δ?

ΔJ

Δ?

ΔJ

Δ?

Δ ?

ΔC Δ J

ð10Þ

1 C A

By applying a magnetic field parallel to c-axis of the wurtzite structure, the magnetic ions possess spin–orbit interactions that can be included in a 6 6 diagonal Hamiltonian Hso The total Hamiltonian becomes 1 ð0Þ H V ¼ H ð0Þ þ H SO ¼ H val þ Shp αx o Sz 4 val 2 0 1 1 0 0 0 0 0 B0 1 0 0 0 0 C B C B C B 0 0 1 0 0 0 C C B B0 0 0 1 0 0 C B C B C @0 0 0 0 1 0 A 0

0

0

0

0

ð11Þ

1

where Shpα parameter is the hole-spin carrier exchange, o SZ 4 is the mean spin along c-axis and x is the magnetic ions concentration [42]. A similar mean field Hamiltonian can be defined for the conduction band ! 1 0 1 H C ¼ H ð0Þ S þ βx o S 4 ð12Þ z C 0 1 2 hp It has been shown that Zeeman shift of excitons is strongly enhanced in the presence of a substantial content of magnetic ions impurities in host semiconductors [43–46]. Fig. 1 shows the crystal-field ΔC, spin–orbit splitting (Δ|| and Δ ? ) as a function of Fe3 þ content in GaN. The figures indicate a significant enhancement of giant Zeeman splitting with the increase in Fe3 þ magnetic ion content. Thus, this enhancement is expected to be even more significant in Ga1 xFexN alloys for larger Fe3 þ magnetic ion contents. This behavior would be expected also for other alloys produced by inserting large content of transition magnetic ions in GaN and ZnO host semiconductors. 3.2. Structural properties of transition magnetic ions-doped GaN and ZnO DMSs In this section, we study the behavior of GaMnN, GaFeN, and ZnCoO systems as a function of transition ions concentrations. In particular, we investigated the mean cation–cation distance as a function of the transition ion concentration for the whole compositional range in each of the systems. Fig. 2 indicates that the cation–cation distances for different systems are linear extrapolations between those of the binary parent compounds. These parameters are very critical in determining the spin–orbit interaction and in the formation of excitons so they need to be calculated very accurately. A precise calculation of those parameters for the entire compositional range is necessary to compute the different interactions involve in determining the magnetic properties and giant Zeeman splitting in ZnO and GaN based DMSs. 3.3. Magnetocrystalline anisotropy energy in bcc Fe, bcc Mn, and hcp Co The magnetic anisotropy which is determined by the dependence of the energy of a magnetic system on the orientation of its

Fig. 1. (1) Crystal field splitting energy as a function of the Fe3 þ magnetic ion content in GaN at a magnetic field of 10 T. (2) Spin–orbit splitting Δ J as a function of Fe3 þ magnetic ion content in GaN at a magnetic field of 10 T. (3) Spin–orbit splitting Δ ? as a function of Fe3 þ magnetic ion content in GaN at a magnetic field of 10 T.

magnetization is a quantity of great interest for spintronic applications. The orientation of the easy axis corresponding to the minimum of energy determines the magnetization direction at low temperature. The origin of magnetocrystalline anisotropy is twofold: magnetostatic interaction and spin–orbit coupling [47]. The first one determines the so-called shape anisotropy, while the second is responsible for the overall magnetocrystalline anisotropy energy (MAE). Due to the smallness of the energy differences between two magnetic orientations, the determination of MAE still remains numerically difficult and requires an elaborate technique. However, several works have been proposed to the calculations of MAE in monolayers [48], multilayers [49] thin films [50], cluster [51,52] or nanowires [53] systems with ab-initio as well as tight-binding electronic structure methods. The problem of the magnetocrystalline anisotropy energy (MAE) in the ferromagnetic 3d metals Fe, Co, and Mn is still inadequately solved problems in the field of spintronics [54–58]. The MAE, which is


5

direction. However, the energy cost per atom to align the magnetization along some other direction can be abnormally small. For example, the measured magneto crystalline anisotropy (MCA) energy EMCA ¼ Eð0001Þ Eð1010Þ is only 60 μeV per atom atom for hcp Co. The corresponding quantity for bcc Fe and MN is even smaller [62], EMCA ¼ Eð001Þ Eð111Þ 1 μ eV per atom

3.4. The perpendicular magnetocrystalline anisotropy of GaN:Mn, GaN:Fe, ZnO:Co and the (0 0 1), (0 0 0 1)-terminated Mn, Fe, and Co surfaces.

Fig. 2. (1)The Mean cation–cation distance as a function of Mn composition x for Zn1 xMnxO DMS. The binary parent compounds ZnO and MnO crystallize in wurtzite structure. The line is a guide for eye. (2) The Mean cation–cation distance as a function of Mn composition x for Ga1 xFexO DMS. The binary parent compounds GaN crystallizes in wurtzite structure, whereas FeN crystallizes in zinc-blende structure. The line is a guide for eye. (3) The Mean cation–cation distance as a function of Co composition x for Zn1 xCoxO DMS. The binary parent compounds ZnO and CoO crystallize in wurtzite structure.

the energy required to orient the magnetization along a certain crystallographic axis, called the easy axis, and is in the cubic 3d transition metals a very small quantity of only a few meV/atom [59–61]. Nevertheless, the MAE is the source of the permanent ferromagnetism in Fe, Co, and Mn. In addition, the MAE causes the (0 0 1) axis to be the preferential magnetization axis in bcc Fe and Mn. The main complication is the smallness of the MAE of only a few meV/atom, a value which is defined as the difference of two total energies for different magnetization directions. The energy of a ferromagnetic crystal is typically smallest when its magnetization is directed along a specific, high symmetry, crystallographic

In this section, we focus on perpendicular magnetocrystalline anisotropy (PMCA) in the GaN:Mn, GaN:Fe, and ZnO:Co DMS systems with transition ion concentration in each is fixed at x¼ 0.125. Fig. 3 below demonstrates the surface termination for the bulk and (0 0 1) surfaces in GaN:Mn DMS system. Structures of bulk and surfaces with both terminations are presented in Fig. 3. Bulk MnGa is depicted with one Mn and Ga atoms, the other with only Mn atoms, where the Mn of each plane is denoted by MnI and MnII, respectively. In surface calculations, we used a single-slab approach for two possible terminations, MnGa-terminated and Mn-terminated, as depicted in Fig. 3(b) and (c), respectively. In our study, MnGa- and Mn-terminated surfaces are modeled with 12 and 16 layers, respectively. The lattice constants of bulk MnGa were determined to be (a ¼3.31 Å and c/ a¼ 1.82). The perpendicular magnetocrystalline anistropy (PMCA) of GaN:Mn, ZnO:Co, GaN:Fe, the Fe and Mn-terminated (0 0 1) surfaces, and (0 0 0 1) co-terminated surface have been studied as illustrated in Figs. 4–6. We found that PMCA is robust with respect to in-plane strain in each of the three DMS systems. This robustness of PMCA with respect to lattice strain ranging between ( 10% and 10%) is remarakable for all the three DMSs systems studied considering that the change of lattice constant for the γ-Fe surface resulted in the reversal of the spin-orientation [65]. Furthermore, the enhancement of PMCA in surfaces over the bulk has a great application potential for the design and fabrication spintronicbased devices. Fig. 7–9 show density of states (DOS) of Mn d-bands at MnGa- and Mn-terminated (0 0 1) surfaces, Co d-bands at ZnCoand co-terminated (0 0 0 1) surfaces, and Fe d-bands at FeGa- and Fe-terminated (0 0 1) surfaces summed up together summed up together. This DOS has been clipped in the energy window that shows those states that contribute to the enhanced MCA. For the GaN:Mn system, we found that 40% of the manganese ions primarily substitute Ga ions in the GaN lattice, and part of them are ferromagnetically coupled up to room temperature even in isolated non-interacting nanocrystals. The rest of the ions are magnetically disordered or uncoupled. Surprisingly, these small Ga1 xMnxN nanocrystals possess relatively large low-temperature magnetic coercivity and relatively high blocking temperature in the isolated form, which indicate large magnetic anisotropy [66]. For the ZnO:Co system, we found that 36% of Co ions primarily replace zinc ions in the ZnO lattice, and part of them are ferromagnetically coupled even in isolated non-interacting nanocrystals. The rest of the ions are magnetically disordered or uncoupled. Remarkably, these small Zn1 xCoxO nanocrystals possess relatively large low-temperature magnetic coercivity which indicates large magnetic anisotropy in this system. For the GaN:Fe system, we found that 50% of Co ions primarily replace Ga ions in the GaN lattice, and large portion of them are ferromagnetically coupled even in isolated non-interacting nanocrystals. The rest of the ions are magnetically disordered or uncoupled. Interestingly, these small Ga1 xFexN nanocrystals possess relatively large low-temperature magnetic coercivity

6


Fig. 3. Structure of MnGa sublattice of GaMnN system (a) bulk, (b) MnGa-, and (c) Mn-terminated (0 0 1) surfaces, where MnI, MnII, and Ga are denoted in white, orange, and blue spheres, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. EMCA of GaMnN and Mn-terminated (0 0 1) surfaces as a function of the difference in-plane lattice constants. Zero percentage indicates the lattice constant of bulk (3.31 Å).

Fig. 5. EMCA of GaFeN and Fe-terminated (0 0 1) surfaces as a function of the difference in-plane lattice constants. Zero percentage indicates the lattice constant of bulk (3.81 Å).

which indicates remarkably large magnetic anisotropy in this system. Electronic properties of transition magnetic ions-doped GaN and ZnO DMSs 1- ZnO:Mn system: a ¼3.38 Å, c/a ¼1.598, Mn concentration x ¼0.125.

Fig. 6. EMCA of ZnOCo and Co-terminated (0 0 0 1) surfaces as a function of the difference in-plane lattice constants. Zero percentage indicates the lattice constant of bulk (3.38 Å).

Fig. 10 shows the electronic properties of Mn0.125Zn0.875O DMSs in its ordered ferromagnetic phase. The material is found to be half-metallic in the sense that the majority spin does not posses a Fermi surface (i.e., the Fermi level falls within the bandgap) whereas minority spin posses a Fermi surface. This is useful for spintronic applications. Electrons injected from the vacinity of Fermi level would have a well-defined spin. The spin polarized is wide and corresponds to a hybridized impurity band. Therefore, this DMS could be considered as an excellent spin injector. The inplane and out-plane energy electronic structure is shown in Fig. 11. 2- ZnO:Co system: a¼ 3.38 Å, c/a ¼1.598, Co concentration x¼ 0.125. Fig. 12 shows the electronic properties of Co0.125Zn0.875O DMSs in its ordered ferromagnetic phase. It has been found that both majority spin and minority spin do not posses a Fermi surface Electrons injected from the vacinity of Fermi level would not have a well-defined spin. The spin polarized is narrow. In this case, the spin-polarized feature is narrow and corresponds to a spin-split valence band. As a result, the level of Co magnetic ions dopants should be increased in order for this material to be used as a good spin injector. The in-plane and out-plane energy electronic structure is shown in Fig. 13. 3- GaN:Fe system a¼ 3.81 Å, c/a ¼ 1.630, Fe ion concentration x¼ 0.125


Mn 3d

7

Fe 3d

Spin up

Spin down

DOS (states/eV f.u.)

DOS (states/eV f.u.)

Spin up

Spin down

E - EF (eV)

E - EF (eV) Fig. 7. Density of states (DOS) of Mn d-bands at MnGa- and Mn-terminated (0 0 1) surfaces summed up together. This DOS has been clipped in the energy window that shows those states that contribute to the enhanced MCA.

Fig. 9. Density of states (DOS) of Fe d-bands at FeGa- and Fe-terminated (0 0 1) surfaces summed up together. This DOS has been clipped in the energy window that shows those states that contribute to the enhanced MCA.

Co 3d

DOS(states/eV f.u.)

Spin up

Spin down

Fig. 10. The spin-dependent band structure that shows the spin-split of the s, p, and d bands of wurtzite ZnO:Mn DMS obtained for Mn concentration x ¼ 0.125 along selected high symmetry directions in the Brillouin zone. Solid and dotted lines are for majority and minority spin states, respectively. The zero of energy is set to the Fermi level EF.

E - EF (eV) Fig. 8. Density of states (DOS) of Co d-bands at ZnCo- and Co-terminated (0 0 0 1) surfaces summed up together. This DOS has been clipped in the energy window that shows those states that contribute to the enhanced MCA.

Fig. 14 shows the electronic properties of Fe0.125Ga0.875N DMSs in its ordered ferromagnetic phase. It has been found that both majority spin and minority spin do not posses a Fermi surface Electrons injected from the vacinity of Fermi level would not have a well-defined spin. The spin polarized is narrow. In this case, the spin-polarized feature is narrow and corresponds to a spin-split valence band. As a result, the level of Fe magnetic ions dopants

should be increased in order for this material to be used as a good spin injector. The in-plane and out-plane energy electronic structure is shown in Fig. 15. Figs. 13–15 show tha in-plane and out-of-plane electronic band structures for the three DMS systems considered in this work. The MCA is calculated based on band structure calculations. The main contribution to the change of MCA of each othe systems comes from the bands that cross the Fermi surface. Bands with minimal distance from the Fermi surface do not contribute to the change in MCA. On the other bands that are close to the Fermi surface contribute the most to the change in MCA. However, there is no systematic correlation. And the bands in the vicinity of Fermi surface should be added together near the Fermi surface to have significant effect on the change of MCA.

8


Fig. 11. In-plane and out of plane band structures of ZnO:Mn DMS obtained for Mn concentration x ¼0.125 along selected high symmetry directions in the Brillouin zone. The zero of energy is set to the Fermi level EF.

Fig. 12. The spin-dependent band structure that shows the spin-split of the s, p, and d bands of ZnO:Co DMS obtained for Co concentration x ¼0.125 along selected high symmetry directions in the Brillouin zone. Solid and dotted lines are for majority and minority spin states, respectively. The zero of energy is set to the Fermi level EF.

Fig. 13. In-plane and out-of-plane band structures of ZnO:Co DMS obtained for Co concentration x ¼0.125 along selected high symmetry directions in the Brillouin zone. The zero of energy is set to the Fermi level EF.

4. Conclusions In summary, we used ab initio first-principles calculations to compute structural, electronic and magnetic properties of the transition metals doped ZnO and GaN DMSs. We found that the

Fig. 14. The spin-dependent band structure that shows the spin-split of the s, p, and d bands of GaN:Fe DMS obtained for Fe concentration x¼ 0.125 along selected high symmetry directions in the Brillouin zone. Solid and dotted lines are for majority and minority spin states, respectively. The zero of energy is set to the Fermi level EF.

Fig. 15. In-plane and out-of-plane band structure of GaN:Fe DMS obtained for Fe concentration x ¼0.125 along selected high symmetry directions in the Brillouin zone. The zero of energy is set to the Fermi level EF.

mean cation–cation distances in ZnO:Mn3 þ , GaN:Fe3 þ , and ZnO: Co2 þ DMS systems exhibit linear behavior for the entire compositional range. The mean cation–cation distance for a given composition can be calculated as a linear extrapolation between those in the binary parent compounds. We found that an excitonic quantum mechanical model that takes into account the splitting of the valence band into three components due to crystal-field, spin– orbit coupling and electron–hole interaction can be used to describe the giant Zeeman splitting quantatively in the three DMSs systems investigated. Our results show a strong ferromagnetic interaction between the magnetic ions impurities and the free holes of the host semiconductors. We found that the contribution to the giant Zeeman splitting from the crystal field component follows the trend ΔC (Fe3 þ in GaN)4 ΔC (Fe3 þ in ZnO)4 ΔC (Mn3 þ in GaN) 4ΔC (Mn2 þ in ZnO) 4ΔC (Co2 þ in ZnO). The spin–orbit contribution parallel to the c-axis (the axis at which magnetic field is applied) exhibits the ascending order Δ|| (Fe3 þ in GaN) 4Δ|| (Fe3 þ in ZnO) 4Δ|| (Mn3 þ in GaN) 4Δ||(Mn2 þ in ZnO)4Δ|| (Co2 þ in ZnO). Similarly, the spin–orbit contribution perpendicular to the magnetic field follows the descending trend Δ ? (Co2 þ in ZnO) oΔ ? (Mn2 þ in ZnOo Δ ? (Mn3 þ in GaN)oΔ ? (Fe3 þ in ZnO) oΔ ? (Fe3 þ in GaN). Upon applying an external magnetic field of 10 T on GaN:Fe DMS resulted from doping GaN with a 12.5% of Fe, our results show a substantial enhancement of the crystal-field ΔC,


spin–orbit splitting (Δ||andΔ ? ) as a function of Fe3 þ concentration. This ascending trend indicates a substantial increase in the giant Zeeman splitting in GaN:Fe3 þ DMS. This in agreement with previous experimental results obtained for a smaller concentration of magnetic ions in GaN and ZnO based DMSs. Our results indicate that such DMSs systems could lead to materials that exhibit room temperature ferromagnetism, we computed MAE's of bcc Mn, bcc Fe and hcp Co. Our refined results show a better agreement with experimental results than previous theoretical results. However, the disagreement with experimental results is due to smallness of MAE in bulk and the difficulty of calculating this small physical quantity. Based on spin-dependent electronic band structure and density of states calculations, we computed the perpendicular magnetocrystalline anisotropy (PMCA) in a strained lattice of each of the three DMS systems studied in this work. We found a robustness of PMCA with respect to lattice strain ranging between ( 10% and 10%) that is remarakable for all the three DMSs systems studied. The analysis of band structure show that the bands close to the Fermi surface have to the major contribution to the magnetocrystalline anistropy and the ZnO:Mn DMS is a potential candidate to be an excellent spin injector in spintronic-based applications. Acknowledgments The Author would like to thank Jordan university of Science and Technology at Irbid, Jordan for providing me with the financial support to come to University of Nebraska at Omaha (UNO), USA to spend my sabbatical year to work on transition and rare-earth magnetic ions doped in semiconductor host. I would like to thank UNO for providing me with technical support. References [1] [2] [3] [4] [5]

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