Half-metallicity characteristic at zincblende CrSb(0 0 1) surfaces and its interfaces with GaSb(0 0 1) and InAs(0 0 1)

ARTICLE IN PRESS Physica B 404 (2009) 3684–3693

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Half-metallicity characteristic at zincblende CrSb(0 0 1) surfaces and its interfaces with GaSb(0 0 1) and InAs(0 0 1) F. Ahmadian a,, M.R. Abolhassani a,b, M. Ghoranneviss a, M. Elahi a a b

Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran Department of Physics, Tarbiat Modares University, Tehran, Iran

a r t i c l e in f o

a b s t r a c t

Article history: Received 13 March 2009 Received in revised form 24 May 2009 Accepted 9 June 2009

Electronic and magnetic properties of the zincblende CrSb(0 0 1) surfaces and its interfaces with GaSb(0 0 1) and InAs(0 0 1) semiconductors are studied within the framework of the density-functional theory using the FPLAPW+lo approach. We found that the Cr-terminated surfaces retain the halfmetallic character, while the half-metallicity is destroyed for the Sb-terminated surfaces due to surface states, which originate from p electrons. The phase diagram obtained through the ab-initio atomistic ffi 1:57 eV phase transition has occurred. Also the halfthermodynamics shows that at mCr  mbulk Cr metallicity character is preserved at both CrSb/GaSb and CrSb/InAs interfaces. The conduction band minimum (CBM) of CrSb in the minority spin case lies about 0.63 eV above that of InAs, suggesting that the majority spin can be injected into InAs without being flipped to the conduction bands of the minority spin. On the other hand the CrSb/GaSb interface has a greater valence band offset (VBO) compared with the CrSb/InAs interface and the minority electrons have lower contribution in the injected currents and hence more efficient spin injection into the GaSb semiconductor. Thus the CrSb/GaSb and CrSb/InAs heterojunctions can be useful in the field of spintronics. & 2009 Elsevier B.V. All rights reserved.

PACS: 72.25.Mk 68.35.Md 75.70.i 73.20.r 31.15.E Keywords: Spintronic Half-metallicity Surface Interface Density-functional theory

1. Introduction Half-metallic (HM) ferromagnets are the most desirable and appealing materials for spintronic devices. These materials have one spin channel that is metallic, while the other spin channel has a gap band at the Fermi level, which is known as the half-metallic band gap. Hence, 100% spin polarization of the conducting electrons is expected from these materials. Since de Groot et al. [1] first predicted the HM property in half-Heusler alloys of NiMnSb and PtMnSb, several HM ferromagnets such as rutile structure CrO2 [2], double perovskite Sr2FeMoO6 [3], spinel Fe3O4 [4], pyrite-type CoS2 [5,6], Heusler alloy of Co2MnSi [7], and so on have been theoretically predicted and experimentally synthesized. Recently, many theoretical and experimental attempts have been done on the zinc blende (ZB) compounds such as MAs and MSb (M is a transition-metal element) [8–13], which are compatible with III–V and II–VI semiconductors. It has already

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E-mail addresses: [email protected], [email protected] (F. Ahmadian). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.06.059

been established theoretically that the ZB MnAs phase is a ‘‘nearHM’’ ferromagnet because its HM gap is zero [14,15] and the ZB CrAs [10,16], the ZB MnSb, and ZB MnBi phases [17] are true HM ferromagnets with finite HM gaps. So far only three ZB phases have been fabricated successfully. They are ZB MnAs in nanodots [9], ZB CrAs in thin films and multilayer [10,11], and ZB CrSb in thin films [12]. Later Liu [18] theoretically predicted that the ZB CrSb phase is a robust half-metallic ferromagnet with a magnetic moment of 3.00mB per unit formula and its HM gap reaches 0.774 eV and persists to be nonzero even when it is compressed by 21%. According to the results of B.-G. Lui, the ferromagnetic ZB phase of CrSb is about 1 eV higher in total energy than the antiferromagnetic NiAs phase and therefore ZB CrSb should not exist as bulk crystal, but can be grown as thin films epitaxially on III–V semiconductors [12]. So a practical approach for stabilizing the CrSb compound in the metastable ZB structure is the pseudomorphic growth of CrSb thin films on ZB semiconductors. The lattice parameter of ZB CrSb has been calculated to be equal to 6.14 A˚ [18], which has a negligible difference with the experimental lattice parameters of GaSb (6.1 A˚) and InAs (6.06 A˚) semiconductors. Therefore ZB CrSb might be grown on ZB

ARTICLE IN PRESS F. Ahmadian et al. / Physica B 404 (2009) 3684–3693

semiconductors such as GaSb and InAs. But it is important for practical applications whether or not the HM materials preserve the half-metallicity at surfaces and interfaces. In this paper, we have theoretically investigated the HM behaviors on the (0 0 1) surfaces of CrSb and also CrSb/GaSb(0 0 1) and CrSb/InAs(0 0 1) interfaces. The paper is organized as follows. After discussing the computational details in Section 2, the structural, electronic, and magnetic properties of ZB CrSb(0 0 1) surfaces are presented in Section 3. Then we investigate the electronic and magnetic properties of the CrSb/GaSb and CrSb/InAs interfaces. The last section is devoted to the summary and conclusions.

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Table 1 Structural parameters of Cr-terminated and Sb-terminated slabs for both GaSb and InAs lattice constants. Surface

h12

h23

h34

h45

h56

Bulk

Surface energy

aGaSb Cr termination Sb termination

1.47 1.39

1.52 1.49

1.49 1.52

1.50 1.51

– 1.50

1.50 1.50

0.13 0.025

aInAs Cr termination Sb termination

1.49 1.4

1.53 1.49

1.52 1.55

1.52 1.54

– 1.54

1.52 1.52

0.13 0.024

The hij parameter is the interlayer distance of i and j layers in atomic unit (i and j are indexes of layers). The bulk values are given for comparison. Surface energy is in Ry unit.

2. Computational method We used the FPLAPW+lo method implemented in the WIEN2K package [19] within the spin-polarized density-functional theory (DFT), for which the exchange-correlation energy of electrons is described in the generalized gradient approximation (GGA) [20]. Relativistic effects are taken into account within the scalar approximation, neglecting the spin–orbit coupling. Basis functions, charge density, and potential are expanded inside mufin-tin spheres in combination with spherical harmonic functions with a cut-off lmax ¼ 10, and in Fourier series in the interstitial region. Moreover, we used a parameter RMTKmax ¼ 8, which determines the matrix size (convergence), where Kmax is the plane wave cutoff and RMT the smallest of all atomic sphere radii. For all atoms, RMT was chosen as equal to 2.2 a.u. In all calculations we used an 8  8  1 mesh for k-points in the Brillouin zone integration. The self-consistent calculations are considered to be converged only when the integrated charge difference per formula unit, R jrnrn1jdr, between input charge density [rn1(r)] and output charge density [rn(r)] is less than 0.00001.

3. Results and discussions 3.1. Surface results 3.1.1. Structural properties The ZB structure of CrSb in the [0 0 1] direction consists of two different surfaces, Cr and Sb surfaces, with the alternating sequence of ‘‘y/Cr/Sb/Cr/Sb/y’’. Furthermore, there are two possible (0 0 1) terminations for CrSb, one is the Cr termination and the other, the Sb termination surface. In our calculations these surface terminations consist of 9 atomic layers at the Cr termination, 11 atomic layers at the Sb termination, and 20 bohr vacuum thickness. The total energy of all supercells was minimized by accurate relaxation of all atomic positions down to the force value of below 1 mRy/a.u. In the first step we calculated the surface energies of different surfaces in the 2D lattice parameters of InAs (6.19 A˚) and GaSb (6.22 A˚). These values are listed in Table 1. Table 1 values show that for both lattice constants the surface energy at the Sb termination is lower than at the Cr termination and therefore Sb termination surface is more stable than Cr termination surface. In Table 1 we have also listed the interlayer distances for both terminations. The comparison of interlayer distances in the supercells and bulk is a good tool for studying interactions between surface atoms. The values in Table 1 show that the distance between surface and sub-surface layers (h12) at each termination has diminished with respect to bulk values. In both terminations, Cr and Sb atoms on the surface lose two atoms of their four nearest neighbors and approximate to sub-surface

atoms to establish stronger bonds with sub-surface atoms. According to Table 1, by moving toward the center of slabs the interlayer distances tend toward the corresponding value in the bulk case. This shows that at the center of the supercells the structural properties of bulk at each termination are recovered. This result is good evidence for sufficient thickness of the Cr and Sb termination slabs. 3.1.2. Electronic properties In this section we will present the results of lattice parameter of only InAs, because the results of both lattice constants (aGaSb and aInAs) are similar. The spin-resolved density of states (DOS) projected on the atomic orbitals at Cr-terminated surfaces are shown in Fig. 1. The DOS’s of the surface and sub-surface atoms are compared to the bulk-like (the central atoms of supercell) cases. The Cr-terminated surfaces retain the HM nature of bulk CrSb but, however, there are important differences in the DOS of the Cr atom at the surface as compared to the bulk-like case. The peaks at around 2.5 and 1 eV are reduced for the majority and minority spin cases, respectively. The Cr atom at the surface has lost two Sb neighbors and by losing two Sb p orbitals, the local peaks of the bonding states of the Cr atom in these regions have been reduced. But instead the majority peak under the Fermi level has enhanced and compensated the reduced bonding states in both spin directions. These results are completely similar to results obtained for the V surface atom at the (0 0 1) surfaces of VAs [21]. On the other hand, by comparison between the DOS’s of surface and subsurface atoms with bulk-like cases, we observe a relative broadening in the 3.5 to 1.5 eV region for Cr d and Sb p states in the case of surface and sub-surface atoms, respectively. This effect confirms the stronger bonds between sub-surface and surface atoms that was previously mentioned. It is also seen that in the 0 to 2 eV regions the electronic states of the Cr surface atom at the spin majority case slightly shift toward the Fermi level. These effects are mainly due to the surface potential that has been shown in Fig. 2. According to Fig. 2 the potential at the surfaces of both terminations abruptly increases and tends toward a fixed value. The abrupt increasing of the potential at surface causes electronic states of the Cr atom to shift toward the Fermi level. It is clear that the electronic states in the spin minority case have not been shifted by the surface potential and so the half-metallicity character of the surface Cr atom has been preserved. For the Sb-terminated (0 0 1) surfaces the situation is completely different from the Cr-terminated surfaces as can be seen in Fig. 3. The DOS of the surface Sb atoms shows large deviations from that of bulk-like Sb atoms. Such deviations were also observed for As(0 0 1) and P(0 0 1) surfaces in CrAs and CrP, respectively [22,23]. As shown in Fig. 3, for the Sb-terminated surface, the HM character is destroyed due to the surface states

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20

2 Sb tot sub surface

Cr tot surface

DOS (eV/states)

15

Sb tot bulk-like

1

Cr tot bulk-like

10

0

5

-1

-2

0

-3 0.2 Cr s surface

Sb s bulk-like

0.1 DOS (eV/states)

Sb s sub surface

0.04

Cr s bulk-like

0.02

0.0

0.00

-0.02

-0.1

-0.04 -0.2 12

1

10

Sb p bulk-like

Cr d bulk-like

8 DOS (eV/states)

Sb p sub surface

Cr d surface

6

0

4 2 0

-1

-2 -4

-4

-3

-2

-1

0

1

Energy (eV)

2

-4

-3

-2

-1

0

1

2

Energy (eV)

Fig. 1. Spin-resolved total and partial DOS’s of surface Cr and sub-surface Sb atoms at Cr-terminated (0 0 1) surface for InAs lattice constant. The surface DOS’s are compared to those of the bulk-like atoms (dotted lines). Negative and positive numbers on the DOS axis represent the minority and majority spin states, respectively, and the Fermi levels are set to zero.

originating from the Sb surface atom, and are mainly due to Sb p states. The Sb atoms at Sb termination surface lose two of their neighbors; therefore dangling bonds are created. It can be seen from Fig. 3 that these dangling bonds mainly have the character of p orbitals and since the bands derived from p orbitals have a larger bandwidth than the d-bands, the electronic states of the Sb atom at the surface can be extended to the HM band gap. On the other hand, by comparing the total electrostatic potential in both terminations in Fig. 2, it can be clearly seen that the surface potential of the Sb termination is slightly higher than that of Cr termination and so it causes the electronic states of the Sb atom to be extended considerably to the HM band gap.

Comparing the DOS’s of Cr sub-surface and bulk-like atoms at the Sb termination shows that the spin imbalance between the majority and minority states has decreased. A similar phenomenon has been observed for Cr sub-surface atoms at the As termination in the CrAs [22].

3.1.3. Magnetic properties The magnetic moments of different atoms in the Cr- and Sbterminated surfaces for both lattice constants are listed in Table 2. For both lattice constants at Cr termination surfaces, it can be seen that the magnetic moments of Cr atoms at the surfaces are

ARTICLE IN PRESS F. Ahmadian et al. / Physica B 404 (2009) 3684–3693

The Gibbs free energy has two important parts: the static total energy that comes out of the DFT calculations and the vibrational energy. It is obtained that at sufficiently low temperatures the vibrational contributions can be neglected [25] and the DFT total energies are enough for surface free energy calculations. Furthermore, the surface free energies of both terminations can be written as follows:

Cr termination Sb termination

0.3

V (Ry)

0.0

-0.3

-0.6

-0.9

0

10

20

30

40

r (a.u.) Fig. 2. Total electrostatic potential profiles of the Cr termination and Sb termination (0 0 1) surfaces. The horizontal axis is the length of supercell in atomic unit.

enhanced compared with those of the corresponding bulk-like values. Due to the reduced coordination number, Cr surface atoms lose electron charge and their magnetic moment increases by approximately 0.7mB. The magnetic moments of Sb sub-surface atoms have decreased by about 0.02mB. In the Sb termination, the enhancement of the magnetic moment in the Sb surface atoms is about 0.03mB, while the magnetic moments of Cr sub-surface atoms have decreased by about 0.4mB. The noticeable reduction of the magnetic moment in the Cr sub-surface atom at the Sb termination shows that the bonds between surface and subsurface atoms are stronger than their similar bonds at Cr termination. These results are completely consistent with the values in Table 1, where the distances between surface and subsurface layers (h12) at Sb termination are smaller than the Cr termination slab. 3.1.4. Phase diagram Our calculations in this section present the relative stability of the different surfaces for the case of the InAs lattice constant within the framework of ab-initio atomistic thermodynamics [24,25]. In this scheme, the surface free energy used to assess the stability of different terminations is defined as follow: , X gðT; P i Þ ¼ ½GðT; P i Þ  N i mi ðT; Pi Þ 2A (1) i

Here G is the Gibbs free energy of the surface, Ni and mi are the number and the chemical potential of the ith element, respectively, 2A is the total surface area of the symmetrical supercell, and g the surface free energy per area. By calculating and comparing the surface free energies of different terminations versus reasonable values of the chemical potentials, we can find the most stable surface having the lowest surface free energy for any given values of chemical potentials. All results of this comparison could be offered as a phase diagram. Clearly two chemical potentials (mCr and mSb) are involved in the CrSb surface free energies (Eq. (1)). The appropriate thickness of the supercells shows that the surfaces are in thermodynamic equilibrium with the central bulk layers and imposes the following equilibrium condition to the chemical potentials:

mCr þ mSb ¼ g CrSb bulk g CrSb bulk

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(2)

is the Gibbs free energy of the bulk CrSb. This where equation reduces the number of independent chemical potentials of Eq. (1) to one.

2AgCr-termination ¼ 0:05 Ry  mCr

(3)

2AgSb-termination ¼ 0:36 Ry þ mCr

(4)

In Fig. 4 the surface free energies for both terminations are plotted versus the chemical potential of the Cr atom. As expected, in the small values of mCr the Sb termination surface is stable; by increasing mCr, the energy difference of the two terminations is reduced and finally with the occurrence of phase transition at mCr  mbulk ffi 1:57 eV, Cr termination is stabled. Cr In practice, the phase diagram obtained from the surface free energies is valid only within a limited range of the chemical potentials because over-increasing or -decreasing these parameters may lead to the decomposition of the alloy. For example if mCr becomes too low then the Cr atoms prefer to leave the sample and bulk Sb (at rhombohedral structure) will form. Hence the lower limit of mCr is determined by the Gibbs free energy of bulk Sb: Sb CrSb mmin Cr þ g bulk ¼ g bulk

g Sb bulk

(5)

g CrSb bulk are

and the Gibs free energies of bulk Sb and CrSb, where respectively. The maximum value of mCr can be obtained from the Gibs free energy of Cr bulk (in the bcc structure): max g Cr bulk ¼ mCr

(6)

The formation energy of ZB CrSb was found to be positive (about 0.1 Ry); therefore ZB CrSb is an unstable structure, which is not formed in equilibrium conditions. This result is in agreement with a recent report [18]. This implies that the lower limit of mCr is larger than the higher limit of mCr, leaving no thermodynamically accessible region in our phase diagram. These observations indicate that both Cr and Sb terminations are not stable in equilibrium conditions and non-equilibrium growth techniques are required for realizing these surface terminations. 3.2. Interface results As previously implied, InAs and GaSb semiconductors with ZB stable structure are promising candidates for CrSb growth because of their close lattice matching to ZB CrSb. However, there are small mismatches between ZB CrSb and both GaSb and InAs semiconductors and a small strain is imposed at the interface when CrSb is deposited to InAs(0 0 1) and GaSb(0 0 1) substrates. To find out the optimized structure of CrSb on each GaSb and InAs substrates we fixed the 2D (in plane) lattice constant of CrSb equal to the calculated lattice constants of GaSb and InAs semiconductors and by establishing the tetragonal unit cell we relaxed the lattice parameter in the growth direction to minimize the total energy. The obtained lattice parameters (in the growth direction) of CrSb are 6 and 6.08 A˚ for GaSb and InAs substrates, respectively. In order to construct the interface between CrSb and both GaSb and InAs semiconductors, we used the supercell approach; in particular, tests performed as a function of the cell dimensions have shown that bulk conditions at both sides of the interface were well recovered using two slabs with 7 and 9 layers, one 7-layer slab for CrSb(0 0 1) and a 9-layer slab for each of the GaSb(0 0 1) and InAs(0 0 1) substrates. We have also optimized the interfacial distance parameter (the spacing between substrate and

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2

8 Cr tot sub surface Sb tot surface Sb tot bulk-like

1 DOS (states/eV)

6

Cr tot bulk-like

4 0

2 0

-1

-2 -2 0.3 0.04

Cr s sub surface

Sb s surface 0.2

DOS (states/eV)

Sb s bulk-like 0.02

Cr s bulk-like

0.1

0.0

0.00

-0.1 -0.02 -0.2 8

1 Sb p surface

DOS (states/eV)

Sb p bulk-like

Cr d sub surface

6

0

Cr d bulk-like

4 2

-1

0 -2

-2

-4

-3

-2

-1 Energy (eV)

0

1

2

-4

-3

-2

-1

0

1

2

Energy (eV)

Fig. 3. Spin-resolved total and partial DOS’s of surface Sb and sub-surface Cr atoms at Sb-terminated (0 0 1) surfaces for InAs lattice constant. The surface DOS’s are compared to those of the bulk-like atoms (dotted lines). Negative and positive numbers on the DOS axis represent the minority and majority spin states, respectively, and the Fermi levels are set to zero.

film) by testing different values of this parameter and letting the atoms move along the [0 0 1] direction to minimize simultaneously the forces on the atoms and the total energy. For constructing the type of junction we were encountered with different selections, but here we have presented only the most stable junctions. The investigated junctions for CrSb/GaSb and CrSb/InAs heterojunctions are ‘‘y/Ga/Sb/Cr/y’’ and ‘‘y/In/As/ Cr/y’’, respectively. In order to study and compare the stability of both interfaces, we initially calculated the formation energies by comparing the

fully minimized total energies of the interface supercells with bulk GaSb, InAs, and CrSb energies. For the remaining nonstoichiometric atoms in the supercells, the bulk energies of As, Sb, and Cr crystals were used (corresponding to mAs ¼ mbulk As , bulk mSb ¼ mbulk Sb , and mCr ¼ mCr ). The obtained formation energies are 0.1 and 0.42 Ry for CrSb/GaSb and CrSb/InAs supercells, respectively. So, the CrSb/GaSb interface is more stable than the CrSb/InAs interface. In the following, electronic and magnetic properties of both interfaces have been separately investigated.

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Table 2 Spin magnetic moments in mB for the surface and sub-surface layers in the case of Cr- and Sb-terminated (0 0 1) surfaces for both GaSb and InAs lattice constants.

6

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Cr d ( top interface) Cr d (film center)

Cr (surface) aGaSb aInAs

3.8 3.8

Sb (sub-surface)

Cr (bulk-like)

Sb (bulk-like)

0.2 0.2

3.1 3.1

0.22 0.22

Cr (sub-surface)

Cr (bulk-like)

Sb (bulk-like)

3.08 3.08

0.22 0.22

Sb terminated Sb (surface) aGaSb aInAs

2.7 2.7

0.25 0.25

DOS (states/eV)

Cr terminated

-2 1.0

Cr termination Sb termination

DOS (states/eV)

0.5

phase transition

γ (Ry)

2

0

The bulk-like (the central atoms of supercell) values are given for comparison.

0.4

4

0.2

0.0

-0.5

Sb p (interface)

0.0

Sb p (film center) Sb p (substrate center)

-1.0 -0.2 -0.40

-0.35

-0.30

-0.25

-0.20

0.2

-0.15

Fig. 4. Phase diagram of the two ideal terminations of CrSb(0 0 1).

3.2.1. Electronic and magnetic properties 3.2.1.1. The CrSb/GaSb junction. Fig. 5 shows the spin-resolved density of states (DOS) projected on the atomic orbitals for the Cr atom at the top interface, the Sb atom at the interface, and the Ga atom at the sub-interface in the CrSb/GaSb heterojunction. All DOS’s have been compared with the bulk-like cases. As observed, there is 100% spin polarization in the interface region and HM behavior of interface has been preserved. Our calculations show that the DOS of the Cr s atom at the top interface (not shown here), about 3 eV in the spin minority case, has slightly moved away from the Fermi level and the exchange splitting effect in the electronic states of Cr s has decreased. This is consistent with the magnetic moment of the Cr atom (at top interface) in Table 3, which with respect to the Cr atom at film center (bulk-like case) has slightly decreased. According to Fig. 5 it is seen that the electronic states in the spin minority case of Cr d have shifted toward the Fermi level and the HM band gap with respect to the bulk-like case has decreased. In Fig. 5, we also show the DOS of the Sb p atom at CrSb/ GaSb(0 0 1) interface. As seen, the interface Sb atom has a medium behavior between that of Sb atoms in the center of the film (bulk-like CrSb) and center of substrate (bulk-like GaSb). This behavior is completely consistent with reported magnetic moments in Table 3. The magnetic moment of Sb in the bulklike region of ZB CrSb is about 0.21mB, while for the Sb atom in the center of the substrate it is zero. Thus, it is clear that the magnetic moment of the interface Sb atom (about 0.11mB) is approximately equal to the average of the corresponding bulk-like

DOS (states/eV)

μCr (Ry)

0.1 0.0 -0.1 Ga p (sub interface)

-0.2

Ga p (substrate center)

-4

-3

-2

-1 Energy (eV)

0

1

2

Fig. 5. Spin-resolved partial DOS’s of Cr (at top interface), Sb (at interface), and Ga (at sub-interface) atoms in the CrSb/GaSb heterojunction. The majority and minority states are plotted upward and downward, respectively. Dotted lines correspond to bulk-like (film center or substrate center) partial DOS. The Fermi energy is set to zero.

values in the two sides of the interface, consistent with the aforementioned intermediate character of the interface Sb atom. Recently, similar behavior has also been observed in the interface Se atom at the CrSe(0 0 1)/ZnSe(0 0 1) heterojunction [26]. There are two mechanisms that are relevant for the variations of DOS in the interface regions with respect to the bulk. The first one is the potential line up due to the interface dipole, which leads to the interface potential barriers and shifts the corresponding DOS toward higher energies. Comparing the DOS of the Sb p atom at the interface with the Sb p atom at the center of the film shows a slight shift toward the Fermi level and more broadening of the interface Sb p states. This small shift is attributed to the potential

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Table 3 Spin magnetic moments in mB for top interface, interface, and sub-interface atoms at CrSb/GaSb (0 0 1) and CrSb/InAs (0 0 1) heterojunctions. CrSb/GaSb

CrSb/InAs

Atom

Position

Magnetic moment

Atom

Position

Magnetic moment

Cr Cr Sb Sb Sb Ga Ga

Top interface Film center Interface Substrate center Film center Sub-interface Substrate center

3.05 3.11 0.11 0 0.21 0 0

In In As As Cr Cr –

Sub-interface Substrate center Interface Substrate center Top interface Film center –

0.01 0 0.13 0 3 3.16 –

The bulk-like (film center or substrate center) values are given for comparison.

CrSb/InAs

CrSb/GaSb

InAs

GaSb

-1.2

CrSb

-1.2

V (Ry)

CrSb

-1.4 -1.4 -1.6

0

5

10

15

20

r (a.u.)

25

-1.6

5

10

15

20

25

r (a.u.)

Fig. 6. Total electrostatic potential profiles of the CrSb/GaSb(0 0 1) and CrSb/InAs(0 0 1) heterojunctions. The horizontal axis is the length of supercell in atomic unit.

raise-up at the interface, which is shown in Fig. 6. It is clear from Fig. 6 that the total electrostatic potential around the interface has abruptly increased. The second one is the exchange splitting effect, which is relative to the splitting between the minority and majority DOS’s. As seen from Fig. 5 the exchange splitting in the DOS of the Sb p atom at interface with respect to central atoms of the film and the substrate has decreased and increased, respectively. These changes in the exchange splitting of the interface Sb atom are expectable, because the p states of the interface Sb atom hybridize with neighboring Cr d states on one side (accompanied by observed exchange splitting in the bulk CrSb [18]) and with neighboring Ga s and p states on the other side (without exchange splitting similar to bulk GaSb). Finally, by generally looking at the DOS of the Ga p atom at sub-interface, it is clearly observed that the potential raise-up has affected the electronic states of Ga p and slightly moved them toward the Fermi level. Also, the presence of significant electronic states in the spin majority case at the Fermi level shows that the HM character of interface Sb atom has been transferred to the Ga atom at the sub-interface.

3.2.1.2. The CrSb/InAs junction. Our results on the local DOS of three atoms around CrSb/InAs junction have been presented in Fig. 7. According to Fig. 7 no interface states are formed within the HM gap at the CrSb/InAs interface and the half-metallicity character is conserved throughout. Comparing the DOS of the In p atom at sub-interface with the In p atom at the center of the substrate (bulk-like case) shows that

the spin majority states at the Fermi level have increased and destroyed the balance between the spin majority and minority states of the In atom in the bulk-like case. This result confirms the reported magnetic moment value in Table 3 of the In atom in the sub-interface to be about 0.01mB. The DOS of the As p atom in the interface of CrSb/InAs shows that the exchange splitting effect is more dominant with respect to the interface potential raise-up effect (the total electrostatic potential is shown in Fig. 6). In the CrSb/InAs heterojunction each interface As atom has two In neighbors on one side, and two Cr neighbors on the other side. The p–d hybridization between Cr and As on one side (similar to CrAs bulk [22]), preserves the spin minority gap at the Fermi level, and the exchange splitting is still present. The magnetic moment of about 0.13mB attributed to the As atom in Table 3 is smaller than that of the bulk case (about 0.38mB). The considerable reduction of magnetic moment of the interface As atom with respect to the bulk case is due to its having an intermediate role between film and substrate. This behavior is similar to the interface Sb atom in the CrSb/GaSb supercell. The DOS of the Cr d atom at top interface shows that the exchange splitting effect has slightly decreased with respect to the Cr d atom in the center of the film and this result confirms the presented magnetic moment of the Cr atom in Table 3, which is about 0.16 smaller than that of the Cr atom at the film center.

3.2.1.3. Band alignment. Finally we extracted the spin-resolved band alignments as a technologically relevant quantity for the electronic and spintronic properties of layered devices. In general

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combined with a potential line-up parameter obtained from interface slab calculations. The potential line-up at CrSb/GaSb and CrSb/InAs heterojunctions is determined by comparing the electronic structure of the core electrons in the bulk and interface central layers. According to this procedure, the  DEslab , where potential line-up parameter is defined as DEbulk s s slab DEbulk and D E are the energy differences of Cr 1s and Ga 1s (or s s Cr 1s and In 1s) core electrons in the bulk compounds and slab central layers, respectively. A similar approach has been employed for the calculation of valence band offset (VBO) in GaAs/AlAs [27]. The obtained potential line-ups for CrSb/GaSb and CrSb/InAs supercells are 0.08 and 0.07 eV, respectively. By applying these potential line-ups, we aligned and separately matched the calculated bulk band structures of CrSb with GaSb and that of CrSb with InAs, to determine the band diagram of the CrSb/GaSb and CrSb/InAs heterojunctions. The band alignment profiles are schematically shown in Fig. 8. Since GGA approximation underestimates the band gaps of semiconductors, we shifted up the conduction bands (CBs) of GaSb and InAs to match the experimental band gaps (0.726 and 0.354 eV, respectively) in the band alignments. The obtained band alignment parameters in the CrSb/GaSb(0 0 1) and CrSb/InAs(0 0 1) heterojunctions are listed in Table 4. The calculated value of Fn for CrSb/GaSb(0 0 1) is in good agreement with the reported value in recent work (0.89 eV) [28]. As observed of Fig. 8, in both interfaces the Fermi level of CrSb lies below the CBM of GaSb and InAs semiconductors. This suggests that a Schottky barrier can be formed for n-GaSb or n-InAs and a reverse bias should be applied to allow majority spin to tunnel into GaSb or InAs semiconductors. In the CrSb/InAs interface the CBM of minority spin in the CrSb lies at about 0.63 eV above the CBM of InAs and so the majority spin electrons can be directly injected to n-InAs with less probability of being flipped to the CBs of the minority spin under the applied reverse bias. This suggests the possibility of highly efficient spin injection. On the other hand the CrSb/GaSb heterojunction has a greater VBO compared with the CrSb/InAs heterojunction. This may be evidence for the lower contribution of minority electrons in the injected currents and hence more efficient spin injection into the GaSb semiconductor. Therefore both GaSb and InAs semiconductors are promising and suitable substrates for the injection of efficient spin polarization current of ZB CrSb.

In p (sub interface)

DOS (states/eV)

0.1

In p (substrate center)

0.0

-0.1

DOS (states/eV)

0.3

0.0

-0.3 As p (interface) As p (substrate center)

-0.6 Cr d (top interface) Cr d (film center)

DOS (states/eV)

6

3691

3

0

4. Conclusion

-6

-4

-2 Energy (eV)

0

2

Fig. 7. Spin-resolved partial DOS’s of Cr (at top interface), As (at interface), and In (at sub-interface) atoms in the CrSb/InAs heterojunction. The majority and minority states are plotted upward and downward, respectively. Dotted lines correspond to bulk-like (film center or substrate center) partial DOS. The Fermi energy is set to zero.

the 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 the interface acts as a semiconductor/semiconductor heterojunction and the band discontinuities are defined as valence and conduction band offsets (VBO, CBO). As indicated in Fig. 8 Fp (Fn) is 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). 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

We employed density-functional calculations to investigate the structural, electronic, and magnetic properties of ZB CrSb (0 0 1) surfaces and ZB CrSb(0 0 1) interfaces with GaAs(0 0 1) and InAs(0 0 1) semiconductors. The results show that the Sb termination surface of CrSb(0 0 1) is more stable than the Cr termination surface while the CrSb/GaSb interface was found to be more stable than the CrSb/InAs interface. It was found that Cr-terminated surfaces are HM, whereas the HM nature is destroyed for the Sbterminated surface due to surface states in the minority band. The magnetic moments of the surface Cr (Sb) atoms were found to be enhanced by 0.7mB (0.03mB) at the Cr termination (Sb termination), whereas the magnetic moments of the sub-surface Cr (Sb) atoms were reduced by 0.3mB (0.02mB) at the Sb termination (Cr termination). The obtained phase diagram shows that the Cr and Sb termination surfaces are not theoretically stable and probably such surfaces can be grown using non-equilibrium growth methods. Results of our calculations confirm that CrSb retains HM behavior at the CrSb/GaSb and CrSb/InAs interfaces. The DOS of Sb and As interface atoms in the CrSb/GaSb and CrSb/InAs heterojunctions, respectively, show an intermediate behavior in comparison with central atoms of film and substrate.

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F. Ahmadian et al. / Physica B 404 (2009) 3684–3693

1 CBO

GaSb-CBM

CrSb-CBM

Energy (eV)

Φn Φp

0

Fermi level of CrSb

GaSb-VBM

VBO

-1

CrSb-VBM

GaSb

growth direction

CrSb

1 CrSb-CBM

Energy (eV)

CBO InAs-CBM Φn

0

Fermi level of CrSb

Φp InAs-VBM VBO

-1

CrSb-VBM

growth direction

InAs

CrSb

Fig. 8. Schematic band diagram in the CrSb/GaSb(0 0 1) and CrSb/InAs(0 0 1) heterojunctions. The Fermi energy of CrSb is set to zero.

Table 4 Calculated band offsets and Schottky barrier heights in [0 0 1] direction of CrSb/ GaSb(0 0 1) and CrSb/InAs(0 0 1) heterojunctions. Heterojunction

Fn

Fp

VBO

CBO

CrSb/GaSb CrSb/InAs

0.76 0.14

0.04 0.35

0.96 0.54

0.002 0.63

Acknowledgments The authors would like to thank the Computational Nanotechnology Supercomputing Center, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran, for their support and supercomputing facilities. F. Ahmadian gratefully appreciates Dr. S.J. Hashemifar for helpful discussions.

All parameters are in eV unit.

References The calculated band alignment at CrSb/InAs heterojunction shows the possibility of directly injecting majority spins into the semiconductor with less possibility of being flipped to the CBs of the minority spin of CrSb. Also CrSb/GaSb heterojunction has a greater VBO compared with CrSb/InAs heterojunction and the probability of injecting the minority spins of CrSb into GaSb is less than the probability of their being injected into InAs. These results suggest that the CrSb/GaSb and CrSb/InAs heterojunctions are suitable candidates in the field of spintronics.

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