This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 164.76.102.52

This content was downloaded on 13/11/2014 at 09:20

Please note that terms and conditions apply.

Tailoring ferromagnetism in chromium-doped zinc oxide

View the table of contents for this issue, or go to the journal homepage for more

2014 Mater. Res. Express 1 016108

(http://iopscience.iop.org/2053-1591/1/1/016108)

Home Search Collections Journals About Contact us My IOPscience

Tailoring ferromagnetism in chromium-doped zincoxide

Bakhtiar Ul Haq1, Rashid Ahmed1 and Souraya Goumri-Said2,31 Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, UTM Skudai,81310 Johor, Malaysia2 Physical Sciences and Engineering Division, King Abdullah University of Science andTechnology (KAUST), Thuwal 23955-6900, Saudi ArabiaE-mail: Souraya.Goumri-Said@kaust.edu.sa and rasofi@hotmail.com

Received 18 December 2013, revised 15 January 2014Accepted for publication 15 January 2014Published 11 March 2014

Materials Research Express 1 (2014) 016108

doi:10.1088/2053-1591/1/1/016108

AbstractThe simultaneous manipulation of both charge and spin has made dilutedmagnetic semiconductors (DMS) a potential material for the fabrication ofspintronic devices. We report DMSs based on ZnO doped with Cr in wurtzite(WZ) and zinc-blend (ZB) geometries. The injection of Cr impurities at aconcentration of 6.25% has successfully tuned ferromagnetism in ZnO. Torecognize the nature of magnetic interactions, two spatial configurations areinvestigated, where the impurity atoms are placed at minimum and maximumseparation distances. The material favors the short-range magnetic coupling andhas a tendency towards Cr clustering. The injection of a Cr impurity into ZnOstrongly influences the electronic properties in terms of band structure, depen-dent on the impurity spatial distribution. It is half metallic for both structuralgeometries when impurity atoms have minimum separation and is metallic whenthey are placed far apart. Moreover, replacing Zn with Cr does not show asignificant effect on the structural geometries. Our results endorse that Cr:ZnOcan be efficiently used for spin-polarized transport and other spin-dependentapplications in both hexagonal and cubic phases.

Keywords: ferromagnetic materials, zinc oxide, magnetic impurity interactions,DFT, spintronics

Materials Research Express 1 (2014) 0161082053-1591/14/016108+11$33.00 © 2014 IOP Publishing Ltd

3 Author to whom any correspondence should be addressed.

1. Introduction

The inefficient spin injection across the ferromagnetic-semiconducting interface due to thelarge-impedance mismatching [1] adversely affects the applications of GMRs in spintronics,and demands an alternative spin-polarized material. An alternative approach is to magnetize thesemiconductors by introducing magnetic elements to them, in a dilute range that would makethem DMSs [2]. In DMSs the impurity elements incorporate a magnetic effect into non-magnetic semiconductors by splitting the up and down spin bands. The exploitation of chargeand spin degrees of freedom simultaneously in a single device has made these materialspromising candidates for spintronics [3, 4]. They have attracted enormous attention from boththe industrial and scientific communities due to their potential applications in novel spintronicdevices. A DMS is considered ideal for practical applications if the dopant atoms are distributedhomogenously throughout the host material, and if it shows ferromagnetism at least at roomtemperature. However, the attainment of room temperature ferromagnetism is still challengingin the existing DMSs. Thus, most research is focused on the search for materials showingferromagnetism with Curie temperature (Tc) at least equivalent to room temperature.

Using a theoretical model, Dietl et al [5] investigated the Tc in DMSs based on severalclasses of materials and predicted that GaN and ZnO are the most promising candidates forDMSs. However, some of the positive aspects of ZnO, such as abundant availability, low cost,easy growth, and environmental friendliness, have made it more appropriate over othermaterials for the fabrication of DMSs. Furthermore, the nearly similar ionic radius of Zn to TMshas enabled ZnO to absorb TMs in high concentrations, such as 35% for Mn [6] and 40% forCo [7].

Many studies have reported room-temperature ferromagnetism (RTFM) in ZnO dopedwith TMs [8, 9] such as Co [10–14], Fe, Ni [15, 16], Mn [17–19], Cr [12, 20], and V [21–23].Among these TMs, several groups [20, 24–34] have preferred Cr as a more appropriate dopantimpurity element because of some of its unique characteristics, for example (1) its ionic radii ofCr (73 pm) is approximately similar to that of Zn (74 pm), (2) the large magnetic moment of Cr(4 μB), and (3) the ferromagnetic precipitate of Cr i.e., CrO2 with Tc of 386 K.

Despite the fact that Cr-doped ZnO has been the subject of several studies, there are stillcertain controversies existing regarding the ferromagnetism mechanism. For instance, somestudies have reported the absence of ferromagnetism in Cr-doped ZnO [12, 35], whereas Liuet al have observed RTFM in it [36]. Similarly, at the level of the first-principles approach, Satoand Katayama [37, 38] have reported Cr:ZnO to be more stable in a ferromagnetic state than ina spin glass state. Robert et al [31] have experimentally reported RTFM in ZnO with a Crconcentration of ∼9.5% and a saturation magnetic moment of magnitude 1.4 μB per Cr ion.Recently, Weng et al have investigated the magnetism in Cr-doped ZnO with intrinsic defectsand report high Tc in p-type Cr:ZnO prepared under an O-rich environment [24]. Chen et alhave reported the spin-polarized state in Cr:ZnO to be the stable one with a total magneticmoment of 7.50 μB [25].

Although several studies are available on Cr:ZnO, in order to productively utilize itspotential for spintronic applications, further comprehensive investigations of its spin-polarizedelectronic structure and magnetic interactions are needed. Moreover, most of the investigationsavailable on Cr:ZnO are focused on the WZ phase. To the best of our knowledge, Cr: ZnO inthe ZB phase has scarcely been studied. In this paper, we report on the effect of Cr doping onthe electronic and magnetic properties of ZnO in a WZ and ZB phase. The present calculations

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

2

have been done in the framework of density functional theory (DFT) using one of the mostefficient approaches, as incorporated in the SIESTA package [39], whose efficiency stems fromusing rigorously localized basis sets together with implementation of linear-scaling algorithms.We focus our attention on the electronic structure and mechanism of ferromagnetism in thepresence of Cr impurity. Our analysis for magnetism reveals a short-range magnetic coupling ina Cr:ZnO system modeled at 6.25% Cr impurity.

2. Computational details

In the present work, we have used the SIESTA package [39]. SIESTA is one of the electronicstructure-modeling methods as well as a software package developed within a density-functional theory (DFT). It makes use of standard norm-conserving pseudopotential (PP) aswell as the application of a flexible linear-numeric combination of an atomic orbitals basis set.In these calculations a DZP basis set was used. To overcome the deficiency of DFT regardingband gap underestimation, the GGA-PBE+U type of exchange correlation functional has beenused [40]. In fact, the GGA+U approach is well recognized to treat localized Zn d and Cr dstates and to incorporate their stronger Coulomb interaction. Here, a typical value of Ueff = 6 eVon the d orbitals of Zn and Cr is adopted. The mesh cutoff was 400 Ry and the ground statevalence configuration of O (2s2, 2p4), Cr (3s2, 3p6, 3d5 4s1), and Zn (3d10 4s2) were used toperform calculations at standard and high pressures. For Brillouin zone (BZ) sampling, a grid of12 × 12 × 12 k-points for the cubic phase, and a grid of 9 × 9 × 2 k-points for the wurtzite phaseis used. The number of k points and the value of the plane wave cutoff energy were chosen byapplying the convergence criteria of total energy.

3. Results and discussion

To obtain our desired defective Cr:ZnO systems, we constructed a 2 × 2 × 2 supercell based onthe unit cell of ZnO. A supercell with such a configuration contains 64 atoms. To introduce Crimpurity into the supercell cell at concentration of 6.25%, we replaced two host cations with Cr,namely Zn30Cr2O32. Cr atoms are set in even numbers to investigate antiferromagentic mode bytuning antiparallel spin of Cr atoms. To analyze the stability of the material as a function ofimpurity distribution, two different spatial arrangements, C1 and C2, are investigated as shownin figure 1 and defined in the literature [25, 41]. In C1 configuration the Cr atoms are located ata minimum distance from each other and separated by an oxygen atom such as Cr-O-Cr,whereas in C2 configuration, the Cr atoms are placed at the maximum possible distance fromthe other Cr atoms and separated by two oxygen atoms and one Zn atom such that Cr-O-Zn-O-Cr.

To explore the effect of Cr impurities on the lattice constant of ZnO on the structuralgeometries, we calculated the lattice constant of Cr:ZnO in the ZB phase. The calculated latticeconstants of magnitude 4.589 Å are in good agreement with the experimental, and with ourpreviously calculated value of ZnO (ZB) [42–44]. This shows that our modeled supercellsystem is reasonably accurate. The injection of Cr into the host material was found to somewhatreduce the value of a. This decrease is because of slight mismatching in the ionic radii of thecation (Zn∼ 74 pm) and dopant (Cr∼ 73 pm). However, no significant distortion was found in

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

3

the symmetry of the cubic crystal system. This shows that ZnO in the ZB phase can absorb Crimpurities up to a high concentration.

Before investigating the electronic and magnetic properties of all the consideredconfigurations, it is important to check their stability in FM order. To achieve this target, thetotal energy is calculated for the spin of the two Cr atoms set parallel or antiparallel,representing ferromagnetism (FM) or antiferromagnetism (AFM). For checking the FM or AFMground state magnetic stability, the difference in the energies of FM and AFM spin states(ΔE=EAFM −EFM) is used as an indicator. Our analysis for magnetic state stability suggests thatFM coupling is the ground state for both (near and far) spatial arrangements. The energydifference ΔE=EAFM−EFM for the considered configuration is presented in graphical

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

4

Figure 1. The simulated supercell of Cr:ZnO in WZ and ZB geometries. In C1arrangement the impurity atoms are located at a minimum distance separated by an O-atom. In C2 arrangement, the two impurity atoms are separated by two O atoms and oneZn atom.

Figure 2. Stability investigation of FM toward AFM order in Cr:ZnO in cubic andhexagonal phases.

comparison in figure 2. The calculated total energies of the supercell for both FM and AFM spinmodes were found to be lower in the C1 configuration than in the corresponding C2configuration. This shows that Cr:ZnO-based DMS favors short-range Cr–Cr magnetic couplingand shows a tendency to cluster together.

The injection of Cr impurity into ZnO has significantly influenced its electronic structure,which strongly depends on the distribution of impurity atoms in the matrix of ZnO. We observedsome interesting features of its electronic structure that depend on the structural geometry, as wellas the spatial arrangements of Cr impurity at C1 and C2, as shown in figures 3 and 4. For C1configuration in the WZ phase, the electronic structures of Cr:ZnO show an overlapping of themajority spin states at the Fermi level. For a minority spin, there exists a marginal gap in V.B. andC.B. This displays the half-metallic nature of Cr:ZnO which is in agreement with the findings ofWang et al [45]. In C2 arrangement, the transport of charges has been shown for both majorityand minority spins at Γ-point which reflects the metallic nature of Cr:ZnO, when the Cr atoms are

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

5

Figure 3. Spin-polarized electronic band-structures of Cr:ZnO in C1 and C2 spatialarrangements with wurtzite geometry. The black lines show the majority spincomponents and the red lines show the minority spin components.

Figure 4. Spin-polarized electronic band-structures of zinc-blend Cr:ZnO in C1 and C2spatial arrangements. The black lines show the majority spin components and the redlines show the minority spin components.

placed far apart. In contrast to the WZ phase, the electronic structure in the ZB phase shows acomparatively large energy gap for the majority spin components of magnitude 0.715 eV. Forminority spins, the electronic states overlap with the Fermi level. Thus, as in the WZ phase, theelectronic structure of a Cr: no system in the ZB phase holds the half metallicity in a C1 spatialarrangement. For the C2 case, the electronic structures show an overlapping of states with theFermi level at Γ-point for both the majority and minority spin states, showing zero energy bandgaps. The overlapping of states with the Fermi level is mainly caused by the Cr impurity band nearthe Fermi level that has been fused into CB states. This shows that Cr dopants act as donors inZnO. We also observe splitting states near the Fermi level for both WZ and ZB geometries thatreveal tuning of magnetism in Cr:ZnO due to Cr impurities.

In the WZ phase, the electrons defining the VB maximum for majority and minority spincarry out a minor difference in energies and thus result in the spliting of the VB edge. Thecomputed VB edge-splitting energy is of magnitude 0.027 eV, which is the difference of energiesof the mentioned electrons. In ZB, the electrons defining the VB maxima for the majority spin aresignificantly higher in energy than those of the minority spin and result in a comparatively highVB edge-spin splitting energy of 0.902 eV. We observed the same band-edge spin-splitting energyfor both the C1 and C2 arrangements. For C.B., the majority spin carriers that define the C.B.minimum carry lower energy than minority spin carriers. The computed differences in theirenergies for C1 and C2 are 0.018 eV and 0.27 eV, respectively, in the WZ phase. The computeddifference in energies for the ZB phase is 0.105 eV for C1 and 0.106 eV for C2.

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

6

Figure 5. Spin-polarized total and partial DOS of Cr:ZnO in hexagonal phase for C1and C2 spatial arrangements.

To further investigate the interactions of atoms in terms of orbitals and exchange interactionmechanisms, we plotted the total and partial DOS of Cr-contaminated systems in figures 5 and 6,respectively, and compared them to those of the pure ZnO (from literature, [42, 46]). The DOSprofile of the Cr:ZnO system shows that the presence of Cr impurity atoms considerably influencethe map of DOS in terms of states arrangement. The spin-polarized d-electrons exhibit mirrorsymmetry in both majority and minority spins, and show almost zero effective Zn d-bandexchange splitting. Compared to pure ZnO, the binding energies of Zn-d electrons aresignificantly increased in the presence of Cr impurity. However, the shape of the Zn-d band is notsignificantly changed. The calculated binding energies of Zn-d electrons in WZ and ZBgeometries are −4.9 eV and −6.17 eV, respectively. The O-p and Cr-p electrons have a marginalcontribution in V.B. and are localized in C.B. Cr up-spin d-electrons mostly appear in V.B. andthe down-spin d-electrons are dominant in the C.B. Cr d-bands carry a large effective exchangesplitting of magnitude 16.09 eV, with 14.07 eV in the C1 and C2 arrangements for the WZ phase.In ZB this effective exchange splitting was 16.35 eV for C1 and 14.84 eV for C2. The DOSprofiles for majority spin carriers show a hump at the Fermi level defined by the Cr-d electronsthat confirms the half metallicity of Cr:ZnO system. For both hexagonal and cubic phases, thestates in appearance near the Fermi level originate from Cr 3d-electrons that possess a largesplitting, leading to a complete spin polarization of d-electrons in the vicinity of the Fermi level.These highly spin-polarized conduction carriers suggest that Cr:ZnO in the WZ and ZB phases arepotential materials for spintronic devices where spin-dependent currents are needed.

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

7

Figure 6. Spin-polarized total and partial DOS of Cr:ZnO in cubic phase for C1 and C2spatial arrangements.

For both hexagonal and cubic phases, Cr:ZnO shows a high magnetic moment of 7.11 μBand 7.35 μB for spatial arrangements C1 and C2, respectively, in the ZB phase, whereas for theWZ phase, our calculations give a higher magnetic moment of 7.29 μB and 7.41 μB. It is worthnoting that the magnetic moment in Cr:ZnO at the rate of 12.5% Cr impurity has been reportedas 3.70 μB and 3.82 μB for WZ and ZB geometries [28]. This suggests that the observedmagnetization in Cr:ZnO is inversely dependent on the dopant concentration. The observedferromagnetism is mainly contributed by Cr ions that carry local magnetic moments of 2.88 μBand 2.94 μB, corresponding to C1 and C2 arrangements in ZB, and 2.92 μB and 2.98 μBcorresponding to C1 and C2 of the hexagonal phase. In all the considered configurations, themechanism of magnetization is the same. In fact, the magnetized Cr atoms strongly influencethe associated nearest neighboring O-ions by inducing the magnetic moment to them. Thisphenomenon was observed in both spatial arrangements. Also, the affected O-ions carry almostthe same local magnetic moment of 0.20 μB in C1 and 0.21 μB in C2 for both the hexagonal andcubic phases. In response, the magnetized O-ions further extend the magnetization to Zn andother O-ions. In this way the ferromagnetism has been homogenously distributed throughoutthe supercell. Zn atoms and the remaining far-apart O-ions in the supercell have variant localmagnetic moments less than 0.15 μB.

There are several models presented to define the origin of ferromagnetism in DMSs, forinstance, bound magnetic polarons, double exchange and super exchange, phenomenologicalZener/Ruderman–Kittel–Kasuya–Yoshida, and the spin-split donor impurity model. Our resultson the electronic structure suggest the FM to be defined by the double exchange mechanism,which explains the ferromagnetism if the impurity bands are lying at the band gap. The V.B.edge and C.B. edge spin-splitting are computed along the high-symmetry Γ point in theBrillouin zone and reported in table 1. Our analysis shows that both the V.B. and C.B. spin-splitting are strongly dependent on the local magnetic moment of Cr. Furthermore, theexchange constants (Nα, Nβ) are calculated in the way defined by Sanvito et al [47]. for half-metallic materials. Nα and Nβ are directly calculated from V.B. edge spin-splitting Δ υE and C.B.edge spin-splitting ΔE ,c such as:

Δ= ⟨ ⟩αN E x/ Sc

Δ= ⟨ ⟩βυN E x/ S

where Δ = −↓ ↑E E Ec cc and Δ = −υ υ υ↓ ↑E E E . The up and down arrows are used for up and down

spin states. x is the concentration of Cr impurity and ⟨S⟩ represents the half of the localmagnetic moment per Cr atom.

In order to complete the discussion on the polarization of the ZnO induced by Cr atomsdoping, we display the spin-density isosurface contours for both configurations C1 and C2 incubic and hexagonal structures (figure 7). These contour plots indicate a strong spin polarization

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

8

Table 1. The calculated V.B. and C.B. edge-splitting energies and exchange constantsof Cr:ZnO in C1 and C2 spatial arrangements.

Zn30Cr2O32C1 C2

ΔE c Δ υE Nα Nβ ΔEc Δ υE Nα Nβ

WZ −0.061 −0.017 −0.266 −0.055 0.234 0.041 1.011 0.180ZB −0.170 −0.876 −0.765 −3.942 −0.648 −0.899 −2.821 −3.914

by Cr atoms in the Cr:ZnO system. Consequently, it has influenced the neighbor atoms; as aresult their spin density deviates from a spherical distribution. The polarization of spin densityis dependent on the location of the impurity atoms within the lattice. For instance, in C1configuration with a WZ structure, the polarization of spin density distribution of Cr atomsoccurs in the direction of the nearest linking atoms. In C2 configuration, the density isdistributed in quadruple. In ZB structure, the spin density distribution is more important in thedirection of approaching atoms for C1 configuration, whereas for C2 configuration, the spindensity is distributed in the form of a dipole. In C1 configuration, the spin is located in thebonding region compared to C2.

4. Conclusion

In the present work, we used a DFT-based PPs method with a DZP basis set to study the effectof Cr doping on the physical properties of ZnO in WZ and ZB phases. These phases are found

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

9

spin density0.88

0.73

0.59

0.44

0.29

0.15

0

spin density

0 0.17 0.33 0.55 0.66 0.83

Figure 7. Spin density contours showing the magnetization of Cr:ZnO systems in (a)hexagonal and (b) cubic phases for both configurations C1 and C2 spatial arrangements.

to be stable in FM order, which makes them potentially interesting for spintronic applications.Moreover, injection of Cr into ZnO induced a strong magnetic moment without any distortionin the geometrical symmetry and reveals that the FM coupling is defined by a double exchangemechanism. Overall, both phases (WZ and ZB) are found to be half metallic when the Cr ionsare injected. The magnetization mechanism is found to be similar to the recently studied DMSbased on ZnO.

Acknowledgement

The first two authors would like to thank the MOHE of Malaysia and UTM for financial supportof this research through Grant No. R.J130000.7826.4F113.

References

[1] Schmidt G, Ferrand D, Molenkamp L, Filip A and Van Wees B 2000 Phys. Rev. B 62 R4790[2] Fiederling R, Keim M, Reuscher G, Ossau W, Schmidt G, Waag A and Molenkamp L 1999 Nature 402 787[3] Furdyna J 1982 J. Appl. Phys. 53 7637[4] Ohno Y, Young D, Beschoten B, Matsukura F, Ohno H and Awschalom D 1999 Nature 402 790[5] Dai L, Deng H, Chen J and Wei M 2007 Solid State Commun. 143 378[6] Fukumura T, Jin Z, Ohtomo A, Koinuma H and Kawasaki M 1999 Appl. Phys. Lett. 75 3366[7] Kim J H, Lee J B, Kim H, Kim D, Ihm Y and Choo W K 2002 IEEE Trans. Magn. 38 2880[8] Wang Y, Hou T, Tian S, Lee S-T and Li Y 2011 J. Phys. Chem. C 115 7706[9] Wu L, Hou T, Wang Y, Zhao Y, Guo Z, Li Y and Lee S-T 2012 J. Alloys Comp. 541 250

[10] Lee H-J, Jeong S-Y, Cho C R and Park C H 2002 Appl. Phys. Lett. 81 4020[11] Biegger E, Fonin M, Rudiger U, Jan Ben N, Beyer M, Thomay T, Bratschitsch R and Dedkov Y S 2007

J. Appl. Phys. 101 073904[12] Venkatesan M, Fitzgerald C, Lunney J and Coey J 2004 Phys. Rev. Lett. 93 177206[13] Song C, Geng K, Zeng F, Wang X, Shen Y, Pan F, Xie Y, Liu T, Zhou H and Fan Z 2006 Phys. Rev. B 73

024405[14] Huang H-H, Yang C-A, Huang P-H, Lai C-H, Chin T, Huang H, Bor H and Huang R 2007 J. Appl. Phys. 101

09H116[15] Cong C, Hong J, Liu Q, Liao L and Zhang K 2006 Solid State Commun. 138 511[16] Zhou S, Potzger K, Zhang G, Eichhorn F, Skorupa W, Helm M and Fassbender J 2006 J. Appl. Phys. 100

114304[17] Mofor A C, El-Shaer A, Bakin A, Waag A, Ahlers H, Siegner U, Sievers S, Albrecht M, Schoch W and

Izyumskaya N 2005 Appl. Phys. Lett. 87 062501[18] Xu H, Liu Y, Xu C, Liu Y, Shao C and Mu R 2006 J. Chem. Phys. 124 074707[19] Deng R, Zhou H, Li Y-F, Wu T, Yao B, Qin J-M, Wan Y-C, Jiang D-Y, Liang Q-C and Liu L 2013 J. Appl.

Phys. 114 033910[20] Hong N H, Sakai J, Huong N T, Poirot N and Ruyter A 2005 Phys. Rev. B 72 045336[21] Saeki H, Tabata H and Kawai T 2001 Solid State Commun. 120 439[22] Ramachandran S, Tiwari A, Narayan J and Prater J 2005 Appl. Phys. Lett. 87 172502[23] Hong N H, Sakai J and Hassini A 2005 J. Appl. Phys. 97 10D312[24] Weng Z, Huang Z and Lin W 2012 J. Appl. Phys. 111 113915[25] Chen Y, Zhou F, Song Q, Yan H, Yang X and Wei T 2012 Phys. B 407 464

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

10

[26] Mamouni N, El Kenz A, Ez-Zahraouy H, Loulidi M, Benyoussef A and Bououdina M 2013 J. Magn. Magn.Mater. 340 86

[27] Liu Y, Yang Y, Yang J, Guan Q, Liu H, Yang L, Zhang Y, Wang Y, Wei M and Liu X 2011 J. Solid StateChem. 184 1273

[28] Jia X, Qin M and Yang W 2011 J. Magn. Magn. Mater. 323 1423[29] Duan L, Zhao X, Liu J, Wang T and Rao G 2010 Appl. Phys. A 99 679[30] Shah L R, Zhu H, Wang W, Ali B, Zhu T, Fan X, Song Y, Wen Q, Zhang H and Shah S I 2010 J. Phys. D:

Appl. Phys. 43 035002[31] Roberts B K, Pakhomov A B, Shutthanandan V S and Krishnan K M 2005 J. Appl. Phys. 97 10D310[32] Yang Y, Zhong C, Wang X, He B, Wei S, Zeng F and Pan F 2008 J. Appl. Phys. 104 064102[33] Gupta M K, Sinha N and Kumar B 2012 J. Appl. Phys. 112 014303[34] Fu C, Han L, Liu C and Gao Y 2013 Phys. Status Solidi a 210 1358[35] Ueda K, Tabata H and Kawai T 2001 Appl. Phys. Lett. 79 988[36] Liu H, Zhang X, Li L, Wang Y, Gao K, Li Z, Zheng R, Ringer S, Zhang B and Zhang X 2007 Appl. Phys.

Lett. 91 072511[37] Sato K and Katayama-Yoshida H 2001 Phys. B 308 904[38] Sato K and Katayama-Yoshida H 2002 Semicond. Sci. Technol. 17 367[39] Soler J M, Artacho E, Gale J D, García A, Junquera J, Ordejón P and Sánchez-Portal D 2002 J. Phys.:

Condens. Matter. 14 2745[40] Chai G, Lin C, Wang J, Zhang M, Wei J and Cheng W 2011 J Phys. Chem. C 115 2907[41] Gopal P and Spaldin N A 2006 Phys. Rev. B 74 094418[42] Ul Haq B, Ahmed R, Goumri-Said S, Shaari A and Afaq A 2013 Phase Transit. 86 1167[43] Zhou S-M, Gong H-C, Zhang B, Du Z-L, Zhang X-T and Wu S-X 2008 Nanotechnology 19 175303[44] Ul Haq B, Afaq A, Ahmed R and Naseem S 2012 Int. J. Mod. Phys. C 23 1250043[45] Wang F, Pang Z, Lin L, Fang S, Dai Y and Han S 2009 J. Magn. Magn. Mater. 321 3067[46] Haq B U, Ahmed R, Khenata R, Ahmed M and Hussain R 2013 Mater. Sci. Semicond. Proc. 169 1162[47] Sanvito S, Ordejón P and Hill N A 2001 Phys. Rev. B 63 165206

Mater. Res. Express 1 (2014) 016108 B Ul Haq et al

11