Robust half-metallicity at the zincblende CrTe(0 0 1) surfaces and its interface with ZnTe(0 0 1)

ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 322 (2010) 1004–1014

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Robust half-metallicity at the zincblende CrTe(0 0 1) surfaces and its interface with ZnTe(0 0 1) F. Ahmadian a,n, M.R. Abolhassani a,b, S.J. Hashemifar c, M. Elahi a a

Plasma Physics Research Center, Science and Research branch, Islamic Azad University, Tehran, Iran Deparment of Physics, Tarbiat Modares University, Tehran, Iran c Department of Physics, Isfahan University of Technology, 84156-83111 Isfahan, Iran b

a r t i c l e in f o

a b s t r a c t

Article history: Received 26 March 2009 Received in revised form 30 November 2009 Available online 21 December 2009

All electron full potential calculations based on spin density functional theory are performed to study cubic zincblende (ZB) and hexagonal NiAs structures of bulk CrTe, free (0 0 1) surfaces of ZB CrTe, and interface of ZB CrTe with ZnTe(0 0 1). The ferromagnetic NiAs structure is reported to be about 0.26 eV more stable than the ferromagnetic ZB phase while ZB CrTe is found to be a half-metallic ferromagnet with a half-metallic gap of about 2.90 eV. Thermodynamic stability of CrTe(0 0 1) surfaces are studied in the framework of ab-initio thermodynamic. The obtained phase diagram evidences more stability of the Te terminated surface compared with the Cr termination. We discuss that both Te and Cr ideal terminations of CrTe(0 0 1) retain bulk-like half-metallic property but with a reduced half-metallic gap compared with bulk value. The structural, electronic, magnetic, and band alignment properties of the ZB CrTe/ZnTe(0 0 1) interface are computed and a rather large minority valence band offset of about 1.09 eV is observed in this heterojunction. & 2009 Elsevier B.V. All rights reserved.

Keywords: Spintronic Half-metallicity Surface Interface Magnetic properties Electronic properties

1. Introduction Half-metallic (HM) materials, exhibiting complete spin polarization (100%) at the Fermi level, have attracted much attention for the promising applications in the high performance spintronic devices. After de Groot et al. [1] who predicted the half-metallic property of the half-Heusler NiMnSb and PtMnSb alloys, several half-metallic ferromagnets such as rutile structure CrO2[2], double perovskite Sr2FeMoO6[3], spinel Fe3O4[4], pyrite-type CoS2[5,6], and Heusler alloys [7] have been theoretically predicted and/or experimentally synthesized. However, it is highly desirable to explore new half-metallic ferromagnetic materials which are compatible with important III–V and II–VI semiconductors. For this purpose, a new class of half-metallic binary alloys with zincblende (ZB) structure was proposed [8–19]. These materials are increasingly attracting attentions because of rather high Curie temperature, large magnetic moment, and good compatibility with conventional ZB semiconductors. Some active examples of these transition metal alloys are MnAs, MnSb, CrAs, CrSb, CrSe, and CrTe. These materials usually crystallize in the NiAs or MnP type structures but first principle studies show that in the metastable zincblende

structure, they are ferromagnetic (FM) half-metals. In order to stabilize ZB structure, thin films of these alloys have been grown on conventional ZB semiconductors. In this way, ZB phases of MnAs [9], CrAs [10,11], and CrSb [12] have been successfully fabricated as nano dots, ultra thin films and ultra thin layers in multi layers. Recently, Sreenivasan et al. attempted to grow ZB CrTe thin films on GaAs(0 0 1) by using ZnTe buffer layer [20, 21]. To date no theoretical work has been performed on CrTe surfaces and its interface with semiconductors. An ab-initio investigation is helpful to realize the possible surface and interface effects on the half-metallic property of CrTe thin films and provide an outlook on the promising applications of this alloy. In this communication, we present the results of our comprehensive computations on the structural, electronic and magnetic properties of the bulk NiAs and ZB types CrTe, ZB CrTe(0 0 1) surfaces and interfaces with ZnTe(0 0 1). In Section 2, we briefly describe the method of calculations. The structural, electronic and magnetic properties of CrTe in the hexagonal NiAs and ZB structures are presented in Section 3. Following, the surface and interface results will be discussed in two separate sections. Finally, a brief summary is given in Section 6.

2. Computational method n

Corresponding author: Tel: + 98 21 44869627; fax: + 98 21 44869640. E-mail addresses: [email protected], [email protected] (F. Ahmadian). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.12.005

Our calculations have been performed within the framework of density functional theory (DFT), using the local density (LDA)

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[22] and the generalized gradient approximations (GGA) [23]. The computations have being done by using the augmented plane wave plus local orbital (APW+ lo) method implemented in Wien2k package [24]. The Cr and Te atomic sphere radii were set to 2.3 Bohr. The highest orbital momentum for the wave function expansion inside atomic spheres was l = 10 and the plane wave expansion cut off outside spheres was 12.1 Ryd. The Brillouin Zone integrations were performed by using k meshes of 11  11  6, 8  8  8, 8  8  1 k points in the bulk NiAs, bulk ZB bulk, and surface and interface calculations.

3. Bulk CrTe The ground state properties of ZB and NiAs structures of CrTe with ferromagnetic (FM), antiferromagnetic(AFM), and nonmagnetic (NM) states were obtained by calculating the total energy of these systems as a function of volume and then fitting the calculated values by the Murnaghan equation of state [25]. In the case of NiAs type structures, first we set the c/a ratio to the experimental value and found the equilibrium volume. Then, volume of the unit cell was fixed at the obtained equilibrium volume and the c/a ratio was optimized. The final volume optimization, performed at the optimized c/a ratio, was used for characterization of NiAs type structures. In order to select the appropriate approximation to the exchange–correlation energy, we have calculated the bulk properties of CrTe both in the local density (LDA) and generalized gradient approximations (GGA). Our results shows that at low volumes the NiAs phase is more stable than the ZB phase in the FM, AFM, and NM states whereas increasing volume favors stability of the ZB structure. The transition pressure from NiAs to ZB in the FM state was determined from the common tangents of the energy–volume curves and is found to be  6.0 and 3.1 GPa within LDA and GGA, respectively. The obtained equilibrium structural parameters including lattice constant, bulk modulus, cohesive energy, and magnetic energy per formula unit are listed in Table 1. The magnetic energy is defined as the difference between the minima of the FM and NM energy–volume curves. According to Table 1 values the cohesive energy of the NiAs structure within LDA (GGA) is about 0.8 eV (0.26 eV) less than ZB in the FM state, implying more stability of the FM NiAs phase. Our calculated lattice parameters are in good agreement with the experimental and other computational data. It is observed that in the NiAs (FM) structure, GGA (LDA) overestimates (underestimates) the value of lattice parameters a and c by about 3% (1%) and 0.2% (8%), respectively, compared with experiment. The obtained c/a ratio in our calculations is 1.52 (1.46) within GGA (LDA) hence GGA gives better value with respect to the measured value of 1.56. The rather large underestimation of c/a ratio is due to the significant underestimation of c lattice parameter in LDA. The lack of gradient terms in LDA, leads to a more uniform electron density in the system compared to real systems and then bonds with in LDA are usually stronger. Hence LDA tends to over bind crystals and shrink lattice constants. Presence of gradient corrections in GGA improves this deficiency and usually gives rise to better structural properties compared with LDA. Therefore we use GGA for the rest of our calculations. In Fig. 1 we present the band structure and total density of states (DOS) of CrTe in the FM NiAs phase. The bands around – 12 eV are mainly due to the semicore Te s states being well separated from the valence bands. The lower parts of the valence band are mainly contributed by Cr s and p states while the upper parts close to the Fermi level are hybridized Te p and Cr d states. Comparing the DOS of majority and minority channels indicates

1005

Table 1 The structural parameters of hexagonal NiAs type and cubic ZB type CrTe in FM, ˚ lattice parameters, B (GPa): bulk module, EC (Ryd): AFM and NM states, a and c (A): cohesive energy per formula unit, EM (Ryd): magnetic energy per formula unit. Structure

Reference

a

c

B

EC

EM

NiAs(FM-GGA) NiAs(FM-LDA)

Present work Present work Other works

4.12 3.95 3.85a 3.98b 4.00c 4.01d

6.26 5.77 6.02a 6.22b 6.25c 6.25d

45 67 46a 44e

 0.50  0.63

 0.08  0.006

4.13 3.96 4.23 4.14 6.27 6.09 6.23 6.01 5.92 5.77 6.29f 6.07g 6.44h 6.21i 6.10i

6.03 5.70 4.86 4.72

54 70 116 143 45 53 40 52 70 78 46f

 0.49  0.62  0.46  0.6  0.48  0.57  0.46  0.56  0.37  0.51

– – – –  0.10  0.06 – – – –

Experiment NiAs(AFM-GGA) NiAs(AFM-LDA) NiAs(NM-GGA) NiAs(NM-LDA) ZB(FM-GGA) ZB(FM-LDA) ZB(AFM-GGA) ZB(AFM-LDA) ZB(NM-GGA) ZB(NM-LDA)

Present work Present work Present work Present work Present work Present work Present work Present work Present work Present work Other works

Experiment

a

Ref. [26]. Ref. [27]. Ref. [29, 30]. d Ref. [31]. e Ref. [28]. f Ref. [19]. g Ref. [32]. h Ref. [33]. i Ref. [21]. b c

an exchange splitting of about 4 eV in the system. Although, within GGA, CrTe in the FM NiAs phase does not show halfmetallic property but we observe that in the spin down channel the Fermi level crosses a conduction band which is not hybridized with the valence bands. Therefore, we speculate that a more appropriate exchange–correlation energy functionals such as LDA+U may lead to the half-metallic property by shifting up the minority conduction band and thus opening up a gap at the Fermi level of the minority channel. Turning to the magnetic properties, we calculated the CrTe spin moment in the FM NiAs phase as a function of primitive cell volume (Fig. 2). The total magnetization Ms at equilibrium volume is about 3.90 mB and atomic magnetic moments of Cr and Te are 3.55 and  0.09 mB, respectively. The results indicate that by increasing volume, the CrTe spin moment increases to saturate to the value of 4 mB at volumes larger than 328 a.u.3. The saturation of the magnetization to 4 mB can be explained by considering charge transfer from Cr to Te atom. Two electrons are transferred from each Cr to the neighboring Te atoms to fill completely Te 5p shell. This leads to a Cr electronic configuration with four electrons in the valence band, which arrange themselves following Hund’s rules and produce a magnetic moment of 4 mB. The same magnetic behavior is reported for MnAs [34]. Fig. 3 shows the band structure of the FM zincblende CrTe phase at equilibrium volume. In order to be able to compare the equilibrium and matched ZB lattices, the tetragonal representation of equilibrium ZB lattice, including two atomic basis points, is used for band structure calculation. The obtained results clearly evidence the half-metallic behavior of the system with a large half-metallic gap of about 2.90 eV. The spin-flip gap (the energy difference between Fermi level and the conduction band

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4 NiAs structure 2 EF

0 Energy (eV)

-2 -4 -6 -8 -10 -12 majority spin

-14 4 2

Energy (eV)

0

EF

-2 -4 -6 -8 -10 -12

minority spin

-14 Γ

Σ

M

Λ

K

Γ

Δ A

1

3

5

7

9

DOS (eV/states)

Magnetization (μB /formula unit)

Fig. 1. The majority and minority electronic band structure and density of states of bulk CrTe in hexagonal NiAs type structure. The Fermi energy is set to zero.

4

3

NiAs phase ZB phase equilibrium Volume (ZB) equilibrium Volume (NiAs)

2

150

200

250

300

350

400

450

500

550

Volume (a.u3 /formula unit) Fig. 2. The variation of the total magnetic moment as a function of primitive cell volume in the ZB and NiAs structures of bulk CrTe. The equilibrium volumes are shown by vertical dashed and solid lines.

minimum) of CrTe is found to be about 0.8 eV which is larger than the CrSe spin-flip gap (0.59 eV) [35]. The minority valence band is composed of six states which are mainly from the Te p electrons

while the lower part of the minority conduction band is mainly due to the Cr eg states. In the majority channel, the six bands below the valence band from 4.5 to  2.5 eV mainly originate from the Te p orbital, the four lowest valence bands around  1.5 eV mainly are the Cr eg states, and the three valence bands crossing the Fermi level mainly have Cr t2g character. For considering hybridizations and interactions in the system, we calculated the partial DOS of FM ZB–CrTe, shown in Fig. 4. Obviously, there is a strong hybridization between minority Cr t2g and Te p states which is responsible for the formation of the half-metallic gap in ZB half-metallic compounds [36]. As a result, the half-metallic gap is between Te p states and Cr t2g states. It will be explained that this fact has significant impact in the half-metallic behavior of CrTe(0 0 1) surfaces. Although bulk ZB CrTe shows half-metallic behavior, but similar to some other half-metals, surface or interface effects may destroy half-metallicity and substantially reduce the Fermi level spin polarization from the ideal 100% value. The interface effects originate from the lattice and chemical mismatches at the junction of two compounds. In order to decrease the interface effects and also obtain an epitaxial interface, the alloy should be grown on a substrate with a close lattice constant to the alloy. The ˚ and CrTe (6.27 A) ˚ calculated lattice parameters of ZnTe (6.18 A) are very close together, indicating suitability of this ZB semiconductor to be used as a substrate for growing ZB CrTe thin films.

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Equilibrium ZB CrTe Lattice

1007

Distorted ZB CrTe Lattice

4 majority spin

majority spin

Energy (eV)

2

EF

0

-2

-4 4

Energy (eV)

2

EF

0

-2

-4 minority spin R

Λ

Γ

minority spin Δ

X

Z

M

Σ

Γ R

Λ

Γ

Δ

X

Z

Σ

M

Γ

Fig. 3. The spin polarized electronic band structure of bulk CrTe in the tetragonal representation of the equilibrium ZB (left column) and tetragonally deformed ZB (right column) structures. The Fermi energy is set to zero.

Cr t2g Te p

DOS (states/eV)

2

GGA GGA+SO

8

1 4 0 0 -1 -4

-2 -6

-4

-2

0

2

4

Energy (eV)

-6

-4

-2

0

2

4

Energy (eV)

Fig. 4. Left: The spin polarized partial DOS of the Cr t2g and Te p orbitals in the ZB structure. Right: The spin polarized total DOS of the ZB CrTe in the presence (GGA +SO) and absence (GGA) of spin–orbit interaction. Positive and negative DOS correspond to majority and minority spins. The Fermi energy is set to zero.

It explains why Sreenivasan et al. [20] used a ZnTe buffer layer on GaAs (0 0 1) to grow thin ZB CrTe layers. The very small lattice mismatch between CrTe and ZnTe should be harmless and the grown ZB CrTe thin films on ZnTe(0 0 1) are expected to keep their half-metallic character. Moreover, since these compounds have common anion, the CrTe(0 0 1)/ZnTe(0 0 1) interface is expected

to be coherent without strong chemical mismatch effect. Compared to the HM ferromagnetic Heusler compounds, the binary ZB HM ferromagnets are expected to form more smooth interfaces with ZB semiconductors, which lead to suppression of interface states in the energy gap of the minority spin and maintain the half-metallicity.

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In order to verify the lattice mismatch effect, we studied the tetragonally distorted ZB structure of CrTe by fixing the in-plane lattice constants of CrTe to that of ZnTe and relaxing the vertical lattice constant of CrTe in the growth direction. The relaxed value ˚ The of c in the tetragonal structure is found to be about 6.43 A. band structure of the tetragonally distorted ZB CrTe is shown in Fig. 3. By comparing the band structure of the equilibrium and distorted ZB structures, we observe that in the G-M direction and in G point, tetragonal distortion remove the degeneracy of some bands and slightly split them. Such behavior is due to the fact that the tetragonal distortion distinguishes the z-axis from the x and y axes and reduces symmetry of crystal. The same behavior has been observed in the tetragonal ZB CrSb structure [36]. It is evident from Fig. 3 that the half-metallic property is preserved in the tetragonal structure of CrTe. We calculated and plotted in Fig. 2 the magnetic moment of CrTe in the ideal zincblende structure at different unit cell volumes. It is observed that the magnetic moment is fixed at 4 mB in a wide range of volumes, pointing the half-metallicity of the system. The existence of a band gap at the Fermi level of the spin minority states lead to an integer number of spin down electrons in the system. Consequently the spin magnetic moment is also an integer number in a half-metal. This leads to a simple ‘‘rule of 8’’ [32]: Mtot ¼ ðZtot 8ÞmB

ð1Þ

where 8 electrons contribute to bonding p–d bands and Ztot is the total number of valence electrons. CrTe has 12 valence electrons in formula unit and so the total magnetic moment (Mtot) according to Eq. (1) should be 4 mB. Reduction of the magnetic moment from integer value of 4 at low volumes indicates destroying the half-metallicity under high pressure. Finally, since there are some experimental evidences for strong magnetic anisotropy in ZB CrTe thin films [21], we considered full relativistic effects on our results by applying spin–orbit corrections to bulk ZB CrTe. In Fig. 4, we have compared the total DOS of ZB CrTe in the presence and absence of spin–orbit correction. Visibly, the spin–orbit correction does not influence significantly the electronic DOS (especially around the Fermi level) and halfmetallic features. The computed cohesive energies within GGA and GGA+ SO are 0.476 and  0.484 Ryd, respectively. Due to the negligible contribution of spin–orbit interaction to the halfmetallic and cohesive energy properties of ZB CrTe we ignore this effect in the surface and interface calculations.

layers (d0TeCr ) is substantially smaller than the bulk value. Surface atoms move toward subsurface atoms to make stronger bonds and compensate the lack of neighbors at the surfaces. The value of d0TeCr at the Te termination is smaller than the Cr termination, implying stronger surface bonding at the Te termination. These statements about surface bonding are well confirmed by calculated valence electron density diagrams presented in Fig. 5. Comparing the electron density contours of surface atoms with bulk-like atoms evidences the stronger surface Cr–Te bonds at Cr and (specially) Te termination. In both supercells sufficiently far below surfaces and in the center of slab, interlayer distances are close to the bulk value. This shows that the selected slabs are thick enough to recover bulk behavior in the central layers. The obtained surface energies indicate more stability of Te surface than Cr surface. It may be qualitatively explained by comparing the cohesive energy of bulk Cr and Te. We computed these two systems and found that the cohesive energy of bulk Cr (  0.32 Ryd/atom) is about twice bulk Te ( 0.15 Ryd/atom). Therefore the required energy cost for creating Cr termination is

Table 2 The relaxed interlayer distances and surface energies of the ideal terminations of CrTe(0 0 1) surface. diTeCr ðBohrÞ : The ith Te–Cr interlayer distance from the surface, the index i measures the distance from the surface, i =0 indicates the distance between surface and subsurface layers. The bulk value of interlayer distance is given for comparison.

Cr termination Te termination

d0TeCr

d1TeCr

d2TeCr

d3TeCr

dTeCr bulk

Surface energy (Ryd)

2.83 2.57

3.16 3.02

3.03 3.12

3.04 3.06

3.04 3.04

0.14 0.01

4. Surface results In this section, we present the magnetic, electronic, and structural properties of CrTe(0 0 1) surfaces. There are two possible (0 0 1) terminations for ZB CrTe, Cr, and Te terminations. These surfaces have been computed in the slab supercells consisting of 17 atomic layers for both Cr and Te terminations and 20 Bohr vacuum thicknesses. The in-plane lattice constants of ˚ Except few central CrTe slab were set to that of ZnTe (6.18 A). layers, all atomic positions were relaxed accurately down to the forces of about 1 mRy/a.u. 4.1. Structural properties The calculated structural properties of the relaxed terminations of CrTe (0 0 1) are reported in Table 2 along with bulk values for comparison. The analysis of the interlayer distances in the surface supercells is helpful for understanding the surface interactions in the system. We observe that in both terminations the distance between surface and subsurface

Fig. 5. The calculated electron density contour plots on the crystallographic (1 0 0) side view planes of the ideal Cr and Te surface terminations of CrTe(0 0 1).

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DOS (states/eV)

DOS (states/eV)

Cr termination

Te termination

Cr d surface Cr d bulk-like

8

0

0

-1

Te p subsurface Te p bulk-like

Te p surface Te p bulk-like

1

4

1

1009

8

Cr d subsurface Cr d bulk-like

4

0

0

-1 -4

-2 0 Energy (eV)

2

-4

-2 0 Energy (eV)

2

Fig. 6. The spin polarized partial DOS of Cr d and Te p orbitals at the surface and subsurface layers of the ideal CrTe(0 0 1) terminations. Negative DOS corresponds to minority spin. The Fermi energy is set to zero. The corresponding bulk DOS are given for comparison.

more than Te termination, in qualitative agreement with the obtained surface energies.

4.2. Electronic properties In this part we discuss the spin polarized electronic band structures of CrTe(0 0 1) terminations. The spin majority band structures of both terminations have a metallic character while in the spin down channel a gap is observed at the Fermi level, indicating the half-metallic character of both surface terminations. The half-metallic band gaps of Cr and Te surfaces are 2.31 and 1.47 eV, respectively. These values are smaller than the corresponding bulk value (2.90 eV). In order to understand why CrTe surfaces have smaller half-metallic gap than bulk we inspect the valence partial DOS of surface atoms, presented in Fig. 6. For comparison, the corresponding bulk partial DOS are also plotted in this figure. Although, similar to the bulk, the surfaces have 100% spin polarization at the Fermi level, but there are obvious differences between the bulk and surface partial DOS. In the surface Cr partial DOS (Cr termination), the peaks below 2 eV in both spin channels are substantially reduced with respect to the bulk DOS. The localized part of the Cr d partial DOS (below 2 eV) in the bulk CrTe is highly hybridized with Te p orbital. The surface Cr atom loses two Te nearest neighbors. Hence the p–d hybridization is weakened at the surface and consequently the local weight of the Cr d states is reduced. On the other hand, the majority peak in the valence band is enhanced by acquiring the lost weight of the local p–d hybridized states from both spin channels. The same trend was observed at the V termination of VAs (0 0 1) [32]. Moreover, we observe that the partial DOS of surface Cr and subsurface Te atoms are more broadened than the bulk partial DOS. This effect is attributed to the strong bonding between subsurface and surface atoms stated in the structural properties discussions. We observe that the half-metallic gap at Cr surface is close to the bulk value. It is due to the fact that the lower edge of the halfmetallic gap in CrTe is controlled by Te p states and since these

states are not considerably shifted by surface effects, the halfmetallic gap remains almost unchanged. In the case of the Te terminated (0 0 1) surface, as can be seen in Fig. 6, the surface effects are more pronounced than the Cr surface and the half-metallic gap is substantially reduced with respect to the bulk value. It is mainly due to the minority surface states originated from the surface Te p orbital. The surface Te atom has two broken bonds which rehybridize and participate in the enhanced surface Te–Cr bond, mentioned in the structural properties. This rehybridization is evident in the more broadened surface Te and subsurface Cr partial DOS compared with corresponding bulk DOS. Moreover the rehybridized surface Te partial DOS is obviously shifted toward the Fermi energy. This shift may be attributed to the surface potential. The bulk crystal potential should rise up at the surface to join the zero level vacuum potential. This potential rise up enhances the energy of the surface electrons and consequently shifts surface DOS toward higher energies, resulting in a reduced half-metallic gap at the surface. In similar studies on CrAs(0 0 1) and CrP(0 0 1) surfaces, it was observed that the surface effects in the Cr terminations are substantially different to the As and P terminated surfaces [37,38]. The advantage of CrTe is the fact that both ideal (0 0 1) terminations of this alloy keep their half-metallic property while in the case of ZB CrP and CrAs alloys, only Cr(0 0 1) surface has half-metallic character. It is not reported whether the Cr termination is the stable termination of ZB CrAs(0 0 1) and CrP(0 0 1) surfaces.

4.3. Magnetic properties The magnetic moments of all atoms in both Cr and Te terminations are listed in Table 3 along with bulk values for comparison. It is seen that the magnetic moments of surface Cr and Te atoms are considerably enhanced with respect to the bulk values. The origin of these exchange enhancements is the lower coordination number of atoms at surfaces. The noticeable

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Table 3 The calculated Cr and Te atomic magnetic moments (mB) at different distances to the CrTe(0 0 1) surface layer. The superscript indices on atomic names indicate the distance from the surface (the index zero and c stand for the surface layer and central layers). The bulk values are given for comparison. Cr termination

Cr0 4.00

Te1  0.12

Cr2 3.69

Te3  0.13

Cr4 3.62

Te5  0.14

Cr6 3.62

Te7  0.14

CrC 3.62

Te termination

Te0  0.26

Cr1 3.21

Te2  0.16

Cr3 3.63

Te4  0.14

Cr5 3.63

Te6  0.14

Cr7 3.62

TeC  0.14

Bulk

Cr 3.62

Te  0.14

reduction of the magnetic moments of the subsurface Cr and Te atoms is due to the intensified Cr–Te bonds at surfaces, being mentioned in the previous discussions. The magnetic moments of central atoms are found to be very close to the bulk values, reconfirming the sufficient thickness of the applied supercell.

In order to address stability of CrTe(0 0 1) terminations in more realistic conditions, we apply ab-initio atomistic thermodynamics scheme [39,40] and define the surface free energy g as follows:

gi ¼ ðGslab mCr NCr mTe NTe Þ=2A

ð2Þ

slab

is the Gibbs free energy of the slab, NX and mX are Here, G the number and the chemical potential of the X element, and gi is the surface free energy per unit of surface area of ith terminations (i=Cr or Te). Since surfaces are in thermodynamic equilibrium with central bulk-like layers, the following equilibrium condition is imposed to atomic chemical potentials: bulk mCr þ mTe ¼ gCrTe

0.2

accessible region

0.1 Phase Transition 0.0 -0.33

-0.30

-0.27

-0.24

-0.21

-0.18

-0.15

μCr (Ryd) Fig. 7. The variation of the ideal Te and Cr surface terminations free energy g (times 2A) versus the Cr chemical potential. The vertical dashed lines show the low and high limits of the Cr chemical potential.

ð3Þ

bulk gCrTe

is the Gibbs free energy of bulk CrTe. The main where remained task is relating the Gibbs free energy to obtained abinitio data. There are three contributions to the Gibbs free energy: G=Etot + Fvib+PV which Etot is the ground state internal energy and Fvib is vibrational free energy. A simple dimensional speculation indicates that the PV contribution is negligible in normal conditions. Although the vibrational free energy is not a trivial contribution, but it is argued that since energy differences control stability issues, vibrational contributions cancel out each other and the Gibbs free energy differences could be approximated by DFT total energy differences [40]. Following this approach we calculated the surface free energy of Cr and Te terminations and plotted the results in Fig. 7. It is observed that at small values of mCr the Te termination is stable while increasing mCr to values larger than  0.18 Ryd favors formation of Cr termination. In practice, the obtained ab-initio phase diagram is valid within a limited range of the chemical potentials because overincreasing or -decreasing these parameters may lead to decomposition of the system. For example if mCr becomes too low then the Cr atoms prefer to leave the sample and bulk Te (hexagonal structure) will form. Therefore, the lower limit of mCr is calculated from the Gibbs free energy of bulk hexagonal Te: bulk bulk mmin Cr þgTe ¼ gCrTe

γ2A (Ryd)

4.4. Phase diagram

Cr termination Te termination

0.3

ð4Þ

bulk bulk and gCrTe are the Gibbs free energies of bulk Te and Where gTe CrTe, respectively. The higher limit of mCr corresponds to bulk ¼ mmax formation of bulk Cr (gCr Cr ). We calculated the ground state energy of bulk Cr and Te to determine the low and high limits of the Cr chemical potential. It is seen that whole accessible region of the phase diagram (Fig. 7.) is occupied by the Te termination and the Cr termination is not achievable in equilibrium thermodynamic conditions.

5. CrTe/ZnTe (0 0 1) interface 5.1. Structural properties As previously mentioned, ZnTe is an appropriate substrate for growing very thin films of ZB CrTe. In order to establish the interface between CrTe and ZnTe, we used the supercell approach; in particular, tests performed as a function of the cell dimensions have shown that the bulk conditions at both sides of the interface were well recovered by using interface slabs composed of 8 CrTe and 8 ZnTe monolayers. Two interface terminations are realizable for CrTe/ ZnTe(0 0 1) heterojunction, Te, and Cr–Zn terminations. In the Te terminated interface, the Te terminated CrTe(0 0 1) and ZnTe(0 0 1) surfaces join at the interface (–Te–Cr–Te–Zn–Te–) and Cr atoms continue the fcc Zn sublattice of the substrate. While in the Cr–Zn termination (–Cr–Te–Cr–Zn–Te–Zn–) the Cr atoms follow the fcc Te sublattice of the substrate. In the Te termination the interface atomic bonds are similar to the bulk CrTe and ZnTe bonds and the bonding character changes coherently at the interface. In similar studies on CrSe/ZnSe(0 0 1) interface [35] it was shown that the Se terminated interface is much more stable than the Cr–Zn termination. Therefore we adopt the Te termination of the CrTe/ZnTe(0 0 1) interface as the more stable structure and in the rest of the paper we focus on this terminated junction. The fact that there is no famous Cr–Zn bond in natural materials provides extra argument for our selection. All structural parameters of the interface supercell, including interlayer and interface distances and atomic positions were accurately relaxed and optimized. In Table 4 we have listed several interlayer distances in the relaxed Te terminated ZnTe/CrTe(0 0 1) interface. The obtained data indicate that the Zn–Te interlayer distance at the interface is

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Table 4 The relaxed interlayer distances at the stable Te termination of CrTe/ZnTe(0 0 1) interface. diTeX ðBohrÞ : The interlayer distance between X and Te layers, the index i measures from both sides the distance from the interface, i=0 indicates the distance between the interface Te and subinterface Cr or Zn layers. The bulk values are given for comparison. d2ZnTe

d1TeZn

d0ZnTe

d0TeCr

d1CrTe

d2TeCr

dbulk TeCr

2.92

2.92

2.91

2.94

3.01

3.02

3.03

3.04

DOS (states/eV)

dbulk ZnTe

Te 4

0.5

1011

slightly increased with respect to the bulk value while the interface Te–Cr interlayer distance is somewhat decreased. In other words, the interface Te atom is slightly displaced toward neighboring Cr atom, indicating further tendency of Cr atom (compared with Zn) to make bond with Te. In order to verify this statement, we determined the Cr–Te and Zn–Te bonding energies by calculating the CrTe and ZnTe bulk cohesive energies per formula unit. The obtained values are about 0.48 Ryd for Cr–Te and  0.35 Ryd for Zn–Te bonds, confirming the larger strength of

4

Cr 9

2 0.0 0 -0.5

-2

subinterface

1 DOS (states/eV)

Zn 5

Te 10

0.5 0 0.0 -1 -0.5

DOS (states/eV)

-2 Te 6

0.5

Cr 11

6 3

0.0

0 -0.5 -3

DOS (states/eV)

2 Zn 7

0.5

Te 12 0

0.0 -2

-0.5

DOS (states/eV)

subinterface

Te 8

0.5

Cr 13

6 3

0.0

0 -0.5 -3

interface -6

-4

-2

0

Energy (eV)

2

4

-6

-4

-2

0

2

4

Energy (eV)

Fig. 8. The spin polarized atomic resolved DOS of various layers of the CrTe/ZnTe(0 0 1) interface supercell. Te8 is the interface Te atom, Te4 is the central atom in ZnTe slab, Cr13 is the central layer in CrTe slab, and other atoms are in between in order of the indices. Negative DOS corresponds to minority spin. The Fermi energy is set to zero. The atomic DOS of central atoms (Te4 and Cr13) are compared with corresponding bulk values (dotted lines).

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the Cr–Te bond. As it is clearly visible in Table 4, by moving away from the interface layer, the interlayer distances approach the corresponding bulk values, revealing the bulk behavior of the central layers and enough thickness of the applied slab supercell. 5.2. Electronic properties For investigation of the electronic structure of the CrTe/ZnTe(0 0 1) interface, the atomic partial DOS of several layers from center of the ZnTe substrate toward center of the CrTe film were calculated and presented in Fig. 8. We observe that the ZnTe central layers (Te4 and Zn5) have a bulk ZnTe like nonmagnetic DOS with a clear band gap at the Fermi level. By approaching the interface the nonmagnetic partial DOS continuously change toward the ferromagnetic half-metallic behavior in such a way that the interface Te atom (Te8) exhibits a moderate exchange splitting. This atom connects the nonmagnetic ZnTe slab to the ferromagnetic CrTe layers. The p–d hybridization between Te8 and Cr9 enhance exchange interactions in Te8 while the s–p hybridization between Te8 and Zn7 weakens this interaction. Therefore the interface Te

atom (Te8) has a medium behavior between Te atoms in the bulk CrTe (Te12) and ZnTe (Te4). We observe that the central CrTe layers (Te12 and Cr13) reveal a bulk CrTe like half-metallic behavior. Notably, it is seen that the partial DOS of the interface Te8 and Cr9 are more broadened than the central Te12 and Cr13 partial DOS, providing another evidence for the stronger Cr–Te interaction at interface. The behavior of interface Te atom is completely similar to interface Se atom in CrSe(0 0 1)/ZnSe(0 0 1) [35]. For further consideration of the interface effects on electronic structure, we calculated and presented the orbital partial DOS (PDOS) of the interface Te8 and subinterface Zn7 and Cr9 atoms in Fig. 9. In part (a) of this figure, it is visible that the interface Zn d PDOS in both majority and minority channels are shifted away from the Fermi level compared with the bulk-like Zn states. This is due to the electrostatic potential difference between the semiconductor and metal sides of the interface, clearly visible in the calculated and presented electrostatic potential diagram in Fig. 9. This potential difference effect is also detectable in the PDOS of the interface Te (Fig. 9c) and subinterface Cr atoms (Fig. 9b). The interface Te PDOS, compared with Te atom in bulk

Zn d subinterface Zn d (bulk ZnTe)

0.10

Cr d subinterface Cr d (bulk CrTe)

8

DOS (states/eV)

0.05 4 0.00 0

-0.05

-0.10 -6

-4

-2

0

2

4

-6

-4

-2

2

4

Te p interface Te p (bulk ZnTe) Te p (bulk CrTe)

1 DOS (states/eV)

0

0

-1

-2 -6

-4

-2

0

2

4

Energy (eV) 0.0

V (Ryd)

Interface position

-0.1

-0.2 Zn

Te

Zn

Te

Zn

Te

Zn

Te

Cr

Te

Cr

Te

Cr

Te

Cr

Te

Fig. 9. Top: The spin polarized orbital partial DOS of (a) the subinterface Zn, (b) the subinterface Cr, and (c) the interface Te atoms. The central bulk-like DOS are given for comparison. The interface Te p partial DOS is compared with both central Te atoms in ZnTe and CrTe slabs. Negative DOS corresponds to minority spin. The Fermi energy is set to zero. Bottom: The total electrostatic potential profile at CrTe/ZnTe(0 0 1) heterojunction. The interface Te layer is shown by the solid line

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Te

Zn

Te

Zn

Te

Cr

Te

Cr

Te

Cr

0.02 3.62 0.01 3.60

0.00 Cr

Zn

3.58

Magnetic moment (μB )

-0.01

Magnetic moment (μB )

Magnetic moment (μB )

Zn

1013

0.00 -0.04 -0.08 -0.12

Te

-0.16 Zn

Te

Zn

Te

Zn

Te

Cr

Te

Cr

Te

Cr

Fig. 10. The local atomic magnetic moments plotted as a function of layer distance to the interface. The interface Te layer is shown by the dashed line.

ZnTe, is shifted away from the Fermi level while, compared with Te atom in bulk CrTe, is shifted toward the Fermi level. A slight shift toward the Fermi level is also visible in the subinterface Cr PDOS.

In Fig. 10 we have plotted the magnetic moments of the different atomic species in the CrTe/ZnTe(0 0 1) junction as a function of the distance from the interface. Notably, sufficiently far from the junction, the bulk magnetic moments are recovered. The bulk values for Cr and Te atoms in the strained CrTe compound are 3.62 and  0.14 mB while ZnTe is a nonmagnetic semiconductor with zero atomic magnetic moments. The magnetic moment of the interface Te atom is equal to the average of the corresponding bulk values in two sides of the interface, consistent with the intermediate character of the interface Te atom observed in the DOS plots. By approaching to the interface, the magnetic moment of Cr decreases while that of Zn atom slightly increases. Obviously the origin of this behavior is the hybridization of the ferromagnetic CrTe layers with nonmagnetic ZnTe layers at the interface.

5.4. Band alignment The spin resolved band alignment parameters are technologically relevant quantities in the electronic transport properties of layered devices. In general a half-metal/semiconductor heterojunction for the majority spin resembles a metal/semiconductor contact with a p- or n-type Schottky barrier (FP, Fn) while in the minority channel this interface acts as a semiconductor/semiconductor heterojunction and the band discontinuities are defined as the valence and conduction band offsets (VBO, CBO). FP (Fn) are defined as the difference between semiconductor valence band maximum, VBM (conduction band minimum, CBM) and metal Fermi level while VBO (CBO) is the difference between minority half-metal VBM (CBM) and semiconductor VBM (CBM).

1 Energy (eV)

5.3. Magnetic properties

2

CBO = 0.7 eV Φn

= 1.49 eV Fermi level of CrTe

0 ΦP

= 0.9 eV

-1 VBO = 1.09 eV -2

-3 ZnTe

growth direction

CrTe

Fig. 11. The Schematic band diagram at CrTe/ZnTe(0 0 1) heterojunction. VB and CB stand for valence and conduction bands. The CrTe Fermi energy is set to zero.

In order to calculate the band alignment parameters we follow the well established ‘‘bulk plus line up’’ procedure in which the bulk band structures are combined with a potential line up parameter obtained from interface slab calculations. The potential line up at ZnTe/CrTe heterojunction is determined by comparing the electronic structure of the core electrons in the bulk and interface central layers. The 1s core electrons are selected for this purpose as they are well shielded from the interface effects. The DEslab where potential line up parameter is defined as DEbulk s s DEbulk and DEslab are the energy differences of Cr 1s and Zn 1s core s s electrons in the bulk compounds and slab central layers, respectively. In this way a potential line up of about 0.16 eV was obtained for the Te terminated ZnTe/CrTe(0 0 1) interface. By applying this potential line up, we aligned and matched separately calculated bulk band structures of CrTe with ZnTe to determine the band diagram of ZnTe/CrTe heterojunction, presented in Fig. 11. In order to verify the reliability of the obtained band alignment parameters, we recalculated them by

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Table 5 The majority Schottky barriers (eV) and minority band offsets (eV) at CrTe/ ZnTe(0 0 1) heterojunction. Our results are compared with the band alignment parameters of some other half-metal/semiconductor heterojunction.

higher minority valence band offset compared with Heusler based heterojunctions.

Heterojunction

Fn

Fp

VBO

CBO

Acknowledgment

CrTe/ZnTe (present work) CrSe/ZnSea VAs/GaAsb Co2MnSi/GaAsc Co2Cr0.5Fe0.5Al/GaAsd

1.49 1.84 1.19 1.20 2.20

0.90 0.88 0.23 0.18  0.78

1.09 1.94 1.03 0.03 0.32

0.7 1.28 0.93 0.50 1.93

The authors would like to thank the Computational Nanotechnology Supercomputing Centre, Institute for research in fundamental sciences (IPM), P.O.Box. 19395-5531, Tehran, Iran, for their support and the supercomputing facilities.

a

Ref. [35]. Ref. [42]. Ref. [43]. d Ref. [44]. b

References

c

applying the supercell Fermi energy. In this procedure, the eigen energy of the Cr 1s deep core state in the bulk and supercell central layer was used as the reference energy. The observed changes in the results were negligible (about 0.002 Ryd) indicating the reliable thickness of our thin film supercells for band alignment studies. Following Peressi et al. [41], we emphasize the necessity of many body corrections to the single-particle eigenvalues obtained from the LDA/GGA calculations and used to evaluate the bulk band structures and the interface line ups. Since these corrections are normally much less important for the valence bands than they are for the conduction bands in semiconductors, many body corrections mainly influence the CBO and Fn parameters. In order to improve the reliability of these parameters, we shifted up the ZnTe CBM to recover the experimental band gap value (2.39 eV). The minority band gap of ZB CrTe is the calculated one, since we are not aware of any experimental measurement and many body corrections in this system. The final estimate of band alignment parameters in CrTe/ ZnTe(0 0 1) interface are listed in Table 5 accompanied by corresponding reported data for other interfaces. Notably, CrTe/ ZnTe interface similar to CrSe/ZnSe and VAs/GaAs interfaces has a higher minority VBO compared with Heusler alloys. It may be an evidence for lower contribution of minority electrons of binary zincblende half-metals in the injected currents and so more efficient spin injection into semiconductors. Moreover, the n type Schottky barrier height of CrTe/ZnTe interface is about 0.35 eV less than that of CrSe/ZnSe, suggesting the higher rate of majority electrons injection into semiconductor in CrTe/ZnTe junction.

6. Summary and conclusions Density functional–full potential computations were employed to investigate the structural, electronic, and magnetic properties of bulk CrTe in ZB and NiAs structures, ZB CrTe(0 0 1) surfaces, and ZB CrTe/ZnTe(0 0 1) interfaces. It was found that the FM NiAs structure is the stable state of bulk CrTe and ZB CrTe could be stabilized by applying a negative pressure (expansion) of about 3.1 GPa. The obtained ab-initio phase diagram indicate that the Te terminated CrTe(0 0 1) surface is the only thermodynamically achievable ideal terminations. We discussed that both Te and Cr ideal terminations keep 100% Fermi level spin polarization while the minority p surface states substantially reduce the halfmetallic gap of the stable Te surface termination. It was argued that at the CrTe/ZnTe(0 0 1) interface, the electronic and magnetic properties of atomic layers change coherently from nonmagnetic semiconductor substrate to ferromagnetic half-metallic film. The interface band alignment parameters were determined and it was found that the CrTe/ZnTe(0 0 1) heterojunction has a substantially

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