First-principles study on the magnetic and half-metallic properties in bulk and (001) surface of Ti2CoSn Heusler alloy

Thin Solid Films 609 (2016) 19–24

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First-principles study on the magnetic and half-metallic properties in bulk and (001) surface of Ti2CoSn Heusler alloy Peng-Li Yan a, Jian-Min Zhang a,⁎, Ke-Wei Xu b a b

College of Physics and Information Technology, Shaanxi Normal University, Xian 710119, Shaanxi, PR China College of Physics and Mechanical and Electronic Engineering, Xian University of Arts and Science, Xian 710065, Shaanxi, PR China

a r t i c l e

i n f o

Article history: Received 22 July 2015 Received in revised form 24 March 2016 Accepted 20 April 2016 Available online 23 April 2016 Keywords: Heusler alloy Surface Electronic structures Magnetic properties First-principles

a b s t r a c t For the bulk and (001) surface of Ti2CoSn Heusler alloy, the electronic and magnetic properties in bulk and the surface effect on the structural, electronic and magnetic properties of the alloy for different terminations of (001) surface have been studied by using first-principles calculations. The spin-gapless semiconductor (SGS) ferromagnetism with the magnetic moment of 3.00 μ B/f.u. is confirmed in the bulk Ti2CoSn alloy with Hg2CuTi-type structure. For two ideal terminations (TiCo, TiSn) and three modified terminations (CoCo*, TiTi*, SnSn*), the density of states (DOS) indicates that all terminations destroy the SGS character. Furthermore, we find that the atomic magnetic moments (AMM) decrease for the most atoms on the outmost three layers due to structural relaxation of these atoms inward. Both the DOS and AMM of the central layer L9 are similar to the corresponding bulk characters because surface effects fade out at the position of the inner layer, 12 Å below the surface. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Since the half-Heusler compound NiMnSb was firstly confirmed as a promising half-metallic (HM) ferromagnets by Groot et al. in 1983 [1], more and more Heusler alloys have been initially predicted with halfmetallicity by theoretical ab initio calculations and later experimental verifications [2–6]. Half-metals, which have 100% spin polarization at the Fermi level EF, are thus expected to be ideal magnetic electrode candidates [7]. So far, many materials have been found to be half-metallic, for example Heusler compounds [8–11], ferromagnetic metallic oxides [12–14], dilute magnetic semiconductors [15–16] and zincblende (ZB) transition-metal (TM) pnictides and chalcogenides [17–21]. Among these materials, the HM Heusler alloys play a key role in practical applications because they have very high Curie temperatures and structural similarity to widely used binary semiconductors crystallizing in the ZB structure [22–24]. Heusler alloys can be divided in two distinct families: half-Heusler XYZ (crystallize in C1b structure) and full-Heusler X2YZ (crystallize in either Cu2MnAl- or Hg2CuTi-type structure) [9,25,26]. In Hg2CuTi-type structure, two X atoms are located at A (0,0,0) and B (1/ 4,1/4,1/4) sites, whereas Y and Z atoms are located at C (1/2,1/2,1/2) and D (3/4,3/4,3/4) sites, respectively. Recently, the Ti2CoSn Heusler alloy with a Hg2CuTi-type structure has been predicted to be complete half-metal with integer magnetic moment of 3 μ B per formula unit (f.u.) based on the first-principles calculations [27–28].

⁎ Corresponding author. E-mail address: [email protected] (J.-M. Zhang).

http://dx.doi.org/10.1016/j.tsf.2016.04.029 0040-6090/© 2016 Elsevier B.V. All rights reserved.

However, most of the HM ferromagnets are usually used in the form of thin films or multilayers in spintronic devices [29]. Thus it is necessary to study the surface and interface properties in HM ferromagnets due to possible appearance of surface and interface states in minority-spin gap which usually affect and even destroy the half-metallicity, as schematically shown in Fig. 1. For example, for Ti2MnAl [30] and Mn2CoSn [31] Heusler alloys, the half-metallicity in bulk case is destroyed in all terminations of the (001) surface, while the half-metallicity of Co2VAl is only retained in two of the four possible terminations among (111) surfaces [32]. As mentioned above, we know that there are many studies on the surface properties of Heusler alloys, but the Ti2CoSn Heusler alloy has never been investigated theoretically or experimentally in the form of thin films or multilayers. Thus in this paper, we present a comprehensive first-principles study of the electronic and magnetic properties in bulk and the surface effect on the structural, electronic and magnetic properties of the alloy for different terminations of the (001) surface. The paper is organized as follows. Section 2 gives the detail of computational method and the models of different terminations of (001) surface. Section 3 is devoted to the results and discussions, and Section 4 includes the conclusions. 2. Calculation methods and models The calculations were performed by using the Vienna ab-initio simulation package based on the density function theory [33–36]. The electron-ionic core interaction is represented by the projector augmented wave [37] which is more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew–

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Fig. 2. Various atomic terminations of Ti2CoSn (001) surface.

Fig. 1. The schematic representations for the total density of states (DOS) (black lines) of a half-metallic (HM) material, and possible appearance of the surface state (red lines) in minority-spin gap which destroys the HM character of the material. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Burke–Ernzerhof [38] formulation of the generalized gradient approximation. A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 × 10−4 eV/atom and 0.02 eV/Å, respectively. The cutoff energy for the plane-waves is chosen to be 300 eV. The Brillouin zone is sampled with Monkhorst–Pack scheme using (3 × 3 × 3) and (9 × 9 × 1) k-meshes for bulk and surface structures of alloy, together with a Methfessel–Paxton method (ISMEAR = 1) for structural optimization and a tetrahedron method with Blöchl corrections (ISMEAR = −5) for density of states (DOS) of 0.1 eV smearing broadening. The spin polarization P is calculated using the following formula: P¼

N↑ ðE F Þ−N↓ ðE F Þ  100% N ↑ ðE F Þ þ N↓ ðE F Þ

ð1Þ

where N↑(EF) and N↓(EF) are the DOS of spin-up and spin-down electrons at the Fermi level EF. Then the Ti2CoSn Heusler alloy with Hg2CuTi-type structure cleaved parallel to (001) plane can create two ideal terminated structures: TiCo and TiSn terminations. The modified CoCo*, TiTi* and SnSn* terminations are created by substituting surface atoms Ti with Co on the first TiCo layer, Sn with Ti on the first TiSn layer and Ti with Sn on the first TiSn layer in the ideal terminations, respectively. The (001) surface is simulated using a slab containing 17 atom layers and in order to avoid the interactions of nearby slabs, we add a 12 Å vacuum on top of these surfaces, as shown in Fig. 2. To obtain the optimized structures, we allow all atoms to relax. 3. Results and discussions 3.1. Bulk Ti2CoSn Heusler alloy There are no available experimental lattice constants for Ti2CoSn Heusler alloy. Consequently, the cubic lattice parameters for the alloy

are optimized by minimizing the total energy with respect to the lattice parameter. As shown in Table 1, the optimized lattice constant a of Ti2CoSn is 6.341 Å, which is in agreement with the previous firstprinciples calculations [27–28]. It is also found that the Ti2CoSn is ferromagnetic with total magnetic moment of 3.000 μ B/f.u., following the Slater–Pauling rules μ t = Zt − 18 [39–42] where Zt denoting the accumulated number of valence electrons in the unit cell containing four atoms. The atomic magnetic moments (AMM) of TiA, TiB, Co and Sn are also listed in Table 1. It can be seen that due to different surroundings, the AMM of TiA is much larger than that of TiB. The magnetic moment of Co atom is parallel to those of two neighbor TiA and TiB atoms, so there is a ferromagnetic coupling relation between Ti and Co atoms. The sp atom Sn exhibits a very small induced magnetic moment and couples ferromagnetically with both Ti and Co atoms. In order to understand the bulk electronic structure, the calculated total and partial DOS for the bulk Ti2CoSn Heusler alloy is presented in Fig. 3. The partial DOS projected onto the completely filled s orbital of each atom with two electrons are not plotted here because they are located at an energy of − 8 eV below EF. In total DOS plot, the spin-up channel has almost zero width energy gap, while the spin-down channel has a semiconductor character with a band gap of about 0.763 eV, showing the bulk Ti2CoSn Heusler alloy is a spin-gapless semiconductor (SGS) which is different from the previous first-principles calculations [27–28]. Since the Sn-p state is located in −5.5 to −2.5 eV energy region for both spin channels, so the formation of the spin-down gap is mainly contributed by the d–d hybridization of the TiA-d, TiB-d and Co-d states. The occupied states in both spin channels from − 3 to about −1 eV, the Co-d states are dominated due to Co-d orbital having seven valence electrons. Around the Fermi level EF, the zero width energy gap in the spin-up channel is determined by the TiA-d and TiB-d states below and above the EF, respectively. For unoccupied states of both spin channels above the EF, the Co-d states are less than TiA-d or

Table 1 Optimized lattice constant a(Å), the atomic magnetic moments μ i(μ B), and total magnetic moments μ tot(μ B) in bulk Ti2CoSn. Structure

a

μ TiA

μ TiB

μ Co

μ Sn

μ tot

Ti2CoSn

6.341 6.36 [27] 6.34 [28]

1.691

0.919

0.368

0.013

3.000

P.-L. Yan et al. / Thin Solid Films 609 (2016) 19–24

21

Fig. 3. The calculated total and partial density of states (DOS) for the Ti2CoSn Heusler alloy. The black and red solid lines represent the spin-up and spin-down channels, respectively. The zero energy value corresponds to the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

TiB-d states because there are seven and two valence electrons on Co-3d and Ti-3d orbitals, respectively.

rumpling R occurs on the L1 of TiCo termination and no relaxation and thus no rumpling is found on the central L9 as expected. 3.2.2. Surface magnetic properties Motivated by quantifying the surface effect on the magnetic properties, we have calculated the magnetic moments of each atom on L1, L2, L3 and L9 of the five different terminations for Ti2CoSn (001) surface and the results are listed in Table 3. We can see that, similar to the bulk case, the AMM on the Sn atom is neglectably small due to the lack d electrons. As expected, the AMM on central L9 of the five different terminations is close to those of the corresponding atom in bulk case (see Table 1). Except TiB atom on L1 of TiSn termination, Co* and Co atoms on L1 of CoCo* termination and Co atom on L2 of SnSn* termination with enhanced moments, the AMM on the most other TiA, TiB and Co atoms on the outmost three layers is decreased compared to the values of the corresponding atoms in bulk case due to shrinkage of these atoms inwards and thus enhancing hybridization. On the contrary, the Sn* atom on L1 of SnSn* termination moves toward vacuum region and presents more delocalization, the largest AMM for Sn is 0.056 μ B.

3.2. Ti2CoSn (001) surface 3.2.1. Surface atomic relaxation The (001) surface of Ti2CoSn Heusler alloy is modeled with five different terminations TiCo, TiSn, CoCo*, TiTi* and SnSn*. In Fig. 2, various atomic terminations of Ti2CoSn (001) surface have been displayed. Considering that the relaxation of the atoms is limited to the outermost layers, we list the optimized fractional coordinate Z perpendicular to (001) surface for atoms on the layer 1 (L1), layer 2 (L2), layer 3 (L3) and the central layer 9 (L9) as well as the relaxed fractional rumpling R of the corresponding layer in Table 2 for the five terminations of Ti2CoSn (001) surface. The initial fractional coordinate Z0 is also given for the corresponding layer. It can be seen that, due to the different atomic relaxations, all terminations exhibit roughness in varying degrees. Comparing with initial fractional coordinate Z0, we found that all atoms on L1, L2 and L3 of the five terminations of the Ti2CoSn (001) surface are relaxed inward (toward the central layer) except for the substituted Sn* atom on L1 of the SnSn* termination which is relaxed outward (toward the vacuum region). In addition, the maximum

3.2.3. Surface electronic properties To understand the surface electronic properties, Fig. 4 depicts the total DOS of the Ti2CoSn (001) surface with TiCo, TiSn, CoCo*, TiTi*

Table 2 The optimized fractional coordinate Z perpendicular to (001) surface for atoms on layer 1 (L1), layer 2 (L2), layer 3 (L3) and the central layer 9 (L9) as well as the relaxed fractional rumpling R of the corresponding layer for five different terminations of Ti2CoSn (001) surface. The initial fractional coordinate Z0 is also given for the corresponding layer. Layer

Z0

L1

0.1708

L2

0.2120

L3

0.2531

L9

0.5000

TiCo

TiSn

CoCo*

TiTi*

SnSn*

A

Z

R

A

Z

R

A

Z

R

A

Z

R

A

Z

R

TiA Co Sn TiB TiA Co TiA Co

0.1733 0.1883 0.2178 0.2174 0.2574 0.2593 0.5000 0.5000

0.0150

Sn TiB TiA Co Sn TiB Sn TiB

0.1741 0.1793 0.2155 0.2187 0.2577 0.2576 0.5000 0.5000

0.0052

Co* Co Sn TiB TiA Co TiA Co

0.1863 0.1894 0.2171 0.2163 0.2570 0.2602 0.5000 0.5000

0.0031

Ti* TiB TiA Co Sn TiB Sn TiB

0.1838 0.1837 0.2121 0.2163 0.2573 0.2568 0.5000 0.5000

0.0001

Sn* Sn TiA Co Sn TiB Sn TiB

0.1653 0.1761 0.2136 0.2239 0.2583 0.2568 0.5000 0.5000

0.0108

0.0004 0.0019 0

0.0032 0.0001 0

0.0008 0.0032 0

0.0042 0.0005 0

0.0103 0.0015 0

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Table 3 The calculated magnetic moments μ i (μ B) of each atom on layer 1 (L1), layer 2 (L2), layer 3 (L3) and the central layer 9 (L 9) for five different terminations of Ti2CoSn (001) surface. The atom with star symbol (*) represents the corresponding substituted atom. TiCo

TiSn

CoCo*

TiTi*

SnSn*

Atom

μi

Atom

μi

Atom

μi

Atom

μi

Atom

μi

TiA(L1) Co(L1) TiB(L2) Sn(L2) TiA(L3) Co(L3) TiA(L 9) Co(L 9)

1.408 0.030 0.383 −0.006 1.353 0.190 1.681 0.362

TiB(L1) Sn(L1) TiA(L2) Co(L2) TiB(L3) Sn(L3) TiB(L 9) Sn(L 9)

1.103 −0.051 1.369 0.177 0.799 −0.004 0.918 0.013

Co*(L1) Co(L1) TiB(L2) Sn(L2) TiA(L3) Co(L3) TiA(L 9) Co(L 9)

1.127 0.653 −0.156 −0.026 1.224 0.191 1.680 0.326

TiB(L1) Ti*(L1) TiA(L2) Co(L2) TiB(L3) Sn(L3) TiB(L 9) Sn(L 9)

−0.001 −0.005 0.073 0.147 0.566 0.006 0.921 0.012

Sn*(L1) Sn(L1) TiA(L2) Co(L2) TiB(L3) Sn(L3) TiB(L 9) Sn(L 9)

0.056 −0.046 0.701 0.432 0.497 −0.011 0.924 0.012

and SnSn* terminations. Firstly, from Fig. 4 we can see that all terminations of the Ti2CoSn (001) surface destroy the SGS character of the bulk Ti2CoSn with spin polarizations P of 73.2%, 94.2%, 79.2%, 48.1% and 63.4% for TiCo, TiSn, CoCo*, TiTi* and SnSn* terminations, respectively. We investigate CoCo*. TiTi* and SnSn* modified terminations to explore possible thin films with high polarization. But from calculated spin polarization, we find that the two modified terminations TiTi* and SnSn* terminations have lower spin polarizations compared with two ideal terminations even the TiTi* termination with the lowest spin polarization P of 48.1%. The CoCo* termination has a little bigger spin polarization compared with the TiCo termination. Thus Fig. 5 only depicts the local DOS projected onto the d orbital of the TM Ti and Co atoms as well as p orbital of the Sn atom on L1, L2, L3 and L9 of the two ideal terminations TiCo (a) and TiSn (b) for Ti2CoSn (001) surface together with the corresponding atomic partial DOS in bulk case for comparison. From Fig. 5, we can see that the atomic partial DOS on the central L9 of all configurations is matched well with that in the bulk structure, which indicates that the thickness for slab model is sufficient to study the properties of surface. However, for atoms on the outmost three layers of both TiCo and TiSn terminations of the Ti2CoSn (001) surface, the spin-down gap of the bulk Ti2CoSn is filled mainly by both Ti-d and Co-d states hybridized weakly with the Sn-p states. This phenomenon is known as an

effect of surface originating from the surface potential [43–44]. In addition, comparing to the corresponding atomic partial DOS, we also find the partial DOS of the atoms on outmost three layers not only shift toward the higher energy region but also driving up in higher energy region and driving down in lower energy region for both spin channels. Such a tendency increases from inner layer to surface layer due to both change of coordination and structural relaxation. 4. Conclusions The structural, electronic and magnetic properties of the bulk and five different terminations of (001) surface of Ti2CoSn Heusler alloy have been studied by using first-principles calculations. The spin polarization calculation exhibits that the bulk Ti2CoSn alloy is SGS with magnetic moment of 3 μ B/f.u.. In addition, we find that all terminations of Ti2CoSn (001) surface destroy the SGS property of the bulk phase. And all terminations exhibit corrugations due to different relaxations of the atoms. Our work also indicates that the AMM of the outmost three layers atoms is decreased compared to the corresponding bulk values due to shrinkage of these atoms inwards. Moreover, we can see that not only the magnetic moments but also DOS of atoms on central layer L9 are close to the corresponding bulk value. We expect the present work will stimulate further experimental efforts to fabricate and

Fig. 4. The calculated total density of states (DOS) of the Ti2CoSn (001) surface with TiCo, TiSn, CoCo*, TiTi* and SnSn* terminations. The black and red solid lines represent the spin-up and spin-down states. The zero energy value corresponds to the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 5. The calculated atomic partial density of states (DOS) of (001) surface of Ti2CoSn Heusler alloy with two ideal terminations: (a) TiCo and (b) TiSn terminations. The corresponding atomic DOS (red dashed lines) in bulk Ti2CoSn are also presented for comparison. The zero energy value corresponds to the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

investigate the electronic and magnetic properties of Heusler alloy Ti2CoSn thin films and multilayers. Acknowledgments The authors would like to acknowledge the National Natural Science Foundation of China (Grant No. 51071098) for providing financial support for this research.

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