Prediction of half-metallic properties for the AMnSe2 (A=Rb, Cs) compounds from first-principle calculations

Journal of Magnetism and Magnetic Materials 399 (2016) 179–184

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Prediction of half-metallic properties for the AMnSe2 (A ¼Rb, Cs) compounds from first-principle calculations A. Benmakhlouf a,b,n, A. Bentabet c, A. Bouhemadou d,e, A. Benghia b a

Département de Physique, Faculté des Sciences Exactes, Université Abderrahmane Mira, Bejaia 06000, Algeria Laboratoire de Physique des Matériaux, Université Amar Telidji, BP 37G, Laghouat 03000, Algeria c Laboratoire de Recherche: Caractérisation et Valorisation des Ressources Naturelles, Université de Bordj Bou Arreridj, 34000, Algeria d Laboratory for Developing New Materials and their Characterization, University of Setif 1, Setif 19000, Algeria e Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia b

art ic l e i nf o

a b s t r a c t

Article history: Received 18 July 2015 Received in revised form 22 September 2015 Accepted 24 September 2015 Available online 28 September 2015

Using first-principle calculations method based on spin-polarized density functional theory, we have predicted the half-metallic character of the AMnSe2 (A¼Rb, Cs) layered compounds. The structural, electronic, magnetic and elastic properties of these ternary chalcogenides crystals have been investigated. The electronic exchange-correlation energy has been described by the generalized gradient approximation GGA and the GGAþU (U is the Hubbard correction). Our calculated structural parameters are in good agreement with the available experimental data. The calculated total magnetic moment is equal to 4.00 μB for both studied compounds. Architecture of the electronic states near the Fermi level has been explored and the origin of the gap in the considered half-metallic alloys has been determined. Single-crystals and polycrystals elastic moduli and related properties for both investigated materials have been examined. & 2015 Elsevier B.V. All rights reserved.

Keywords: First-principle calculations GGA and GGA þ U Spin-polarized Half-metallic Ternary chalcogenides Elastic constants

1. Introduction Initially predicted by de Groot and collaborators [1] and verified by other authors [2–6], the half-metallic ferromagnets (HMF) alloys are amongst the most promising materials for possible application in magnetism and spin electronic devices [7–9]. At the Fermi level EF of the HMF, the majority-spin band is of metallic character and the minority-spin band is semiconducting, resulting in 100% spin polarization, which maximizes the efficiency of spintronic devices [7,10]. As described by de Groot and M Mueller [1], the half metallic behavior in a material is closely related to the crystal structure, valence-electron count, covalent bonding and large splitting of the d-electron band states. Many material classes are half-metallic. Besides half- and fullHeusler alloys, there are other families of materials which are halfmetallic systems, e.g., some metallic oxides like CrO2 and Fe3O4, zinc-blende compounds like CrAs and CrSb and some manganite like La0.7Sr0.3MnO3[11–18]. An intensive scientific effort has been devoted to the investigation of the ternary manganese chalcogenides A–Mn–Q, where A ¼alkali metal and Q¼ chalcogenides n Corresponding author at: Département de Physique, Faculté des Sciences Exactes, Université Abderrahmane Mira, Bejaia 06000, Algeria. E-mail address: [email protected] (A. Benmakhlouf).

http://dx.doi.org/10.1016/j.jmmm.2015.09.078 0304-8853/& 2015 Elsevier B.V. All rights reserved.

[19–25]. In 1999, Kim and Hughbanks [26] reported the synthesis, structural characterization and magnetic properties of the ternary metal chalcogenides RbMnSe2 and CsMnSe2. To the best of our knowledge, this is the only study that was devoted to these two compounds. The understanding of the electronic and magnetic properties of RbMnSe2 and CsMnSe2 may give an insight related to their performance in the field of magnetic and spintronic applications. Therefore, a detailed study of the title compounds is necessary to get a more complete picture of their physical properties. In this work, we aim to provide a detailed study of the structural, elastic, electronic and magnetic properties of the RbMnSe2 and CsMnSe2 compounds. The present study was carried out by using first-principle plane-wave pseudo-potential total energy calculations. This paper is organized as follows. We briefly describe the used calculational methods in Section 2. The obtained results are reported and discussed in Section 3. The most important conclusions and remarks drawn from our present theoretical study are given in Section 4.

2. Method of calculations All present calculations were carried out using pseudo-potential total energy method with plane-wave basis as implemented in the CASTEP Package [27]. The tightly bound core electrons were

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represented by the Vanderbilt-type ultrasoft pseudo-potential [28]. In all performed calculations, the Rb: 4s2 4p6 5s1, Cs: 5s2 5p6 6s1 Mn: 3d5 4s2 and Se: 4s2 4p4 were treated as valence states. The exchange and correlation energies were described by the generalized gradient approximation (GGA) as parameterized by Perdew-Burk-Ernzerhof, the so-called GGA-PBE [29] as well as the GGA together with the Hubbard correction (GGA þU) to account for the nonlocal effect in the exchange-correlation functional [30]. Only the 3d orbitals of the manganese atoms were treated using the GGA þU approach with U¼2.5 eV. Spin-polarized calculations were considered. The integrations over the Brillouin zone were replaced by a discrete summation on special set of k-points using Monkhorst-Pack scheme [31]. To ensure highly converged and precise results, the plane-wave basis set was defined by an energy cut-off of 500 eV and the Brillouin-zone (BZ) integration was performed over a 6 × 6 × 2 grid. The structural parameters were determined using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization technique [32]. The tolerance for geometry optimization was set as the difference of total energy was within 5 × 10−6 eV/atom , maximum ionic Hellmann–Feynman force was within 0.01 eV/Å , maximum stress was within 0.02 eV/Å and maximum displacement was within 5 × 10−4Å

Table 1 Calculated lattice parameters a and c, conventional-cell volume V and c/a ratio for AMnSe2 (A¼ Rb, Cs) tetragonal crystals compared to experimental data.

RbMnSe2

CsMnSe2

RbMnSe2

CsMnSe2

a

c

3.1. Crystal structure The X-ray powder data of the studied materials, reported by Kim and Hughbanks [26], reveal that under normal conditions, the AMnSe2 (A ¼Rb, Cs) compounds are isostructural with AgTiTe2 phase prototype, space group I-4m2 (No. 119) of the tetragonal system, with 2 formula units per one unit cell. Fig. 1 presents a 2×2×1 super cell of the studied compounds. Accordingly, RbMnSe2 and CsMnSe2 are layered compounds in which [MnSe4/2]  1 layers are built up by four-corner-shared MnSe4 tetrahedra and each layer is separated by alkali atoms [26]. The obtained equilibrium lattice parameters a and c, unit cell equilibrium volume V and c/a ration are summarized in Table 1 along with the available experimental data for the sake of comparison. Our calculated lattice parameters are in good agreement

Fig. 1. (a) 2 × 2 × 1 Unit cell of AMnSe2 (A ¼ Rb, Cs) tetragonal layered structure, the Mn atom is centered inside the tetrahedron and each Se atom occupies a corner of the tetrahedron and (b) the high-symmetry points in the Brillouin zone.

°) c (A

° ) V (A

3.99 4.04 4.27(4) 4.17 4.10 4.32(7)

14.20 14.49 14.03(2) 14.22 15.22 14.47(2)

226.16 236.53 255.38 247.27 255.85 270.04

c/a 3.56 3.59 3.29 3.41 3.71 3.35

Table 2 Calculated atomic coordinates of the AMnSe2 (A ¼Rb, Cs).

b

3. Results and discussions

Present GGA Present GGA þ U Expt. [26] Present GGA Present GGA þ U Expt. [26]

3

°) a (A

Atom

Position

x

y

z

Rb Mn Se Cs Mn Se

2a 2d 4e 2a 2d 4e

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.50 0.00 0.00 0.50 0.00

0.00 0.75 0.349a; 0.354b; 0.3521c 0.00 0.75 0.338a; 0.347b; 0.369c

Present GGA. Present GGA þ U. Expt. [26].

with the previously reported data. Better agreement between the calculated and experimental unit cell volume is obtained using GGA þU formalism. Calculated atomic coordinates of both considered systems are listed in Table 2. One can see that for RbMnSe2, the relative deviation of the calculated z-atomic position of the Se atom from the measured one is less than 0.88% (0.54%) using GGA (GA þ U) and less than 8.4% (5.96%) using GGA (GGA þU) in the case of CsMnSe2. If we take into account the uncertainty over the results calculated using GGA–PBE functional [33], one can appreciate that the computational methodology employed in the present work is appropriate and the obtained results are trustworthy. 3.2. Electronic properties Calculated spin-polarized band structures of the title materials along some high symmetry directions in the first Brillouin zone using the GGA and GGA þU functionals are shown in Fig. 2. It can be seen that for each studied compound the two electronic band structures obtained by using GGA and GGA þU have similar profiles. From Fig. 2, one can clearly observe that the majority-spin band structure exhibits metallic character and the minority-spin one shows an energy band gap around the Fermi level, revealing a half-metal character of RbMnSe2 and CsMnSe2 compounds. For the minority-spin band, the valence band maximum (VBM) is located at the N point in BZ and the conduction band minimum (CBM) is located at X point for both materials, indicating an indirect band gap semiconductor. The calculated band gap Eg and half-metallic gap EHM, which is determined as the minimum energy difference between the lowest energy of majority (minority) spin conduction bands with respect to the Fermi level and the absolute value of the highest energy of the majority (minority) spin valence band [34], are summarized in Table 4. Even the general features of the electronic band dispersions of each compound of the examined series obtained using GGA and GGA þU are qualitatively almost similar, there is a quantitative difference between the band gaps yielded by these two functionals; this difference is important (see Table 4). In order to elucidate the contribution of orbitals to the band structure, we have calculated the spin-polarized total and partial densities of states (TDOS and PDOS, respectively) for both

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181

Fig. 2. Spin-polarized band structure (a) for RbMnSe2 majority spin (↑) and minority spin (↓) using GGA, (b) for RbMnSe2 majority spin (↑) and minority spin (↓) using GGA þU, (c) for CsMnSe2 majority spin (↑) and minority spin (↓) using GGA and (d) for CsMnSe2 majority spin (↑) and minority spin (↓) using GGA þU.

Table 3 Calculated Mullikan charges (in electrons), bond lengths (in Å) and selected bond populations for the RbMnSe2 and CsMnSe2 compounds. Species Charge

Mn

 0.15a;  0.21b  0.06a; 0.04b

Rb

0.35a; 0.39b

Se Mn

 0.25a;  0.23b 0.06a;  0.02b

Cs

0.45a; 0.47b

RbMnSe2 Se

CsMnSe2

Bond length

Bond population



–

Mn–Se ( × 4) 2.441a; 2.517b; 2.569c Rb–Se ( × 8) 3.544a; 3.559b; 3.662c –

0.99a; 0.90b

–

Mn–Se ( × 4) 2.431a; 2.527b; 2.617c Cs–Se ( × 8) 3.746a; 3.715b 3.732c

0.89a; 0.80b

–

–

Table 4 Calculated and measured total magnetic moments per unit cell ( μtot , in μB ), magnetic moment per atom: μMn,μSe and μX (X ¼ Rb, Cs), virtual semiconducting gap Eg (ineV), half-metallic gap EHM (in eV) and density of states of the majority spin N (up,EF ) (in states eV  1spin  1atom  1). RbMnSe2

CsMnSe2

Eg

4.00a,b; 4.79c 2.17a; 2.44b  0.12a;  0.24b 0.07a; 0.05b 1.46a; 2.12b

4.00a,b; 5.06c 2.36a; 2.45b  0.19a;  0.25b 0.02a; 0.05b 2.14a; 2.27b

EHM N (up,EF )

0.82a; 0.40b 2.10a; 1.68b

0.84a; 0.47b 2.74a; 1.68b

μtot μMn μSe μX

a b c

Present GGA. Present GGA þ U. Expt. [26].

a

Present GGA. b Present GGA þ U. c Expt. [26].

examined materials. The calculated densities of states for RbMnSe2 and CsMnSe2 are depicted in Fig. 3. One can clearly see that the same DOS features characterize the two compounds. The influence of Coulomb repulsion U on the DOS is restricted to the empty d band and, thus, does not qualitatively change the electronic distribution. By introducing the Coulomb repulsion U, the d states around the Fermi level are shifted either up or down. The lowest structure in the TDOS diagrams of RbMnSe2 and CsMnSe2, centered at around  12.28 eV, derives from the chalcogen Se-s states

with a small contribution from the Mn-p and Rb-p (Cs-p) states in both spin channels. The valence bands localized at around  10 eV and  8 eV in RbMnSe2 and CsMnSe2, respectively, are originated from the Rb-p (Cs-p) states. In the energy range from  5 eV up to the Fermi level (0 eV), the DOS is mainly dominated by the cooperative contributions of the chalcogen p states and manganese d states. Moreover, it is worth mentioning here that the peak at Fermi level is dominated by the Se-p states. The Mn-d states experience strong exchange splitting, and the resultant Mn-d bands tend to be polarized away from the Fermi level, giving rise to majority bands in the valence band in the energy range between

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Fig. 3. Spin-dependent total and partial density of states (a) for RbMnSe2 using GGA, (b) for RbMnSe2 using GGA þU, (c) for CsMnSe2 using GGA and (d) for CsMnSe2 using GGA þU.↑and↓denote the spin-up and spin- down directions. The Fermi energy is aligned to zero.

4.5 and  3.5 eV and minority bands in the conduction band between 2 and 3.5 eV for both compounds. 3.3. Bonding behaviors In order to understand the interatomic bonding behaviors of the RbMnsSe2 and CsMnSe2 compounds, we have further computed selected interatomic distances, bond populations and Mullikan charge population. The results of these mentioned parameters are shown in Table 3. No significant difference is observed between the results obtained through the GGA and GGA þU approaches. The results presented here are that obtained using the GGA approach. In both compounds, the charge transfer is from the alkaline metal species Rb and Cs to the chalcogenide atom Se. For the case of RbMnsSe2, the charge transfer is about 0.21e, while for CsMnSe2 is about 0.25e. These suggest the following valence states: Rb0.39Mn0.04 (Se  0.21)2 and Cs0.45Mn0.06 (Se  0.25)2 for the RbMnsSe2 and CsMnSe2 compounds, respectively. The bond populations provide the overlap degree of the electron cloud of two bonding atoms and consequently it can be used to check the nature of the chemical bonding between these two atoms. Generally, a high value of positive population indicates a high degree of covalency in the considered bond [35]. According to this criterion, the Se–Mn bond possesses principally a covalent bonding character in both compounds.

3.4. Magnetic properties and origin of the half-metallic gap The integer magnetic moments μtot of RbMnSe2 and CsMnSe2 and atomic magnetic moments of Rb, Cs, Mn and Se atoms have been calculated using both GGA and GGA þU approaches. The obtained results are listed in Table 4 together with the available experimental data. The integer total magnetic moment (Mtot) is a typical characteristic of HM ferromagnets [36]. The calculated total magnetic moment for both AMnTe2 compounds is equal to 4μB per formula unit. Therefore, the total spin moment Mtot obeys the simple rule: Mtot ¼Ztot  24 as the full-Heusler alloys Co2MnZ [36], where Ztot is the total number of valence electrons. The total magnetic moment, which includes the contribution from the interstitial region, comes mainly from the Mn ions with a small contribution from the Se sites. The Rb and Cs atoms possess a very small moment. Our calculated total magnetic moment for RbMnSe2 (CsMnSe2) shows a deviation of 16.5% (21%) from the measured value. This difference could be due to the presence of impurities in the samples studied experimentally and a possible incertitude in the measured values. From Table 4, we can see that the GGA predicts smaller magnitude of the magnetic moments of Mn and Se ions than that predicted by the GGA þ U. The apparition of an open band gap in the minority-band structure is a result of the separation of occupied and unoccupied Mn-d states because of the shifting of Mn-d states to higher energies in the minority band and lower energies in the majority

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183

Table 5 Calculated bulk (B) and shear (G) moduli (in GPa) and B/G ratio.

Fig. 4. Calculated elastic constants (Cij, in GPa) for RbMnSe2 (Rb) and CsMnSe2 (Cs) compounds.

band. Because the Mn-d states above the Fermi level are polarized in the minority-spin, the interaction of Se-p and Mn-d states presses the Se-p energy levels below the Fermi level, giving rise to an open gap and produces a semiconducting behavior. In the majority-band case, the interaction of these states leads to a mutual repulsion so the Se-p states are pushed to energies above the Fermi level. These states of primarily Se-p character connect with lower states and are responsible for the metallic character of the majority-band structure. 3.5. Elastic constants and related properties The elastic constants of solids provide important information on their mechanical properties. Mostly, it is difficult to measure the elastic constants Cij experimentally; therefore, theoretical calculations of the Cij become necessary. The elastic properties of the tetragonal RbMnSe2 and CsMnSe2 crystals are described in terms of six independent elastic constants. The complete sets of single-crystal Cij of the considered crystals were calculated using both GGA and GGA þU. The obtained results are presented by a histogram in Fig. 4. The Hubbard U term mainly shifts energy curves and then creates noise in statistical fitting [37]. Therefore, as can be compared in Fig. 4, the inclusion of the Hubbard U slightly reduces the values of some elastic moduli (C12, C33, C44, and C66) and shows larger discrepancies for C11 regarding CsMnSe2. In the following description, we discuss only the results obtained using the GGA. The studied materials are characterized by a small value of C11 and C33, which indicates a weak resistance to compression along the principal crystallographic directions, i.e., a-, b- and c-axes. The C11 is larger than C33, reveling that the [001] direction (the stacking direction) is easily compressible than the [100] direction. The layered compounds are characterized by the facility of shear deformations. Physically, C44 represents the resistance to deformation with respect to a shearing stress applied across the (100) plane in the [010] direction. The value of C44 is smaller than C11 by about 69% and 71% for RbMnSe2 and CsMnSe2, respectively, indicating the weak resistance to shear deformation compared to the resistance to the unidirectional compression. To be mechanically stable, a tetragonal crystal has to obey the following restrictions of its elastic constants [38]:

C11 > 0, C33 > 0, C44 > 0, C66 > 0, C11 − C12 > 0, C11 + C33 − 2C13 > 0, 2 (C11 + C12 ) + C33 + 4C13 > 0

(1)

The calculated elastic constants of both studied compounds satisfy these criteria, indicating that both title compounds are

B

G

B/G

BV

RbMn SeGGA 2

30.71

12.92

2.38

30.99

30.43

14.03

11.81

U RbMn SeGGA+ 2 GGA CsMn Se2 U CsMn SeGGA+ 2

28.69

13.74

2.09

28.72

28.65

14.54

12.94

31.90

14.40

2.21

32.14

31.67

15.39

13.41

26.71

9.51

2.81

26.98

26.43

11.27

7.74

BR

GV

GR

mechanically stable. Using Voigt-Reuss-Hill approximations [39], the macroscopic elastic parameters: bulk modulus B and shear modulus G are determined. The small values of B indicate that these compounds can be classified as soft materials. According to the empirical criterion of Pugh [40], a material is brittle (ductile) if the B/G ratio is less (greater) than 1.75. The obtained values for the B/G ratio (Table 5) are greater than 1.75 for both compounds. Hence, these materials behave in a ductile manner. The layered crystals are elastically anisotropic. Recent research shows that the elastic anisotropy affects the nanoscale precursor textures in alloys [41,42]. Therefore, it is important to study the elastic anisotropy of solids to understand this property and hope to find mechanisms that will improve its durability. To accurately quantify the extent of the elastic anisotropy, a universal index AU has been proposed by Ranganathan and Ostoja-Starzewski [43]. The universal index AU is defined as follows: AU ¼5GV/GR þBV/BR-6, where B and G are the bulk and shear moduli, respectively, and the subscripts V and R stand to the Voigt [44] and Reuss [45] bounds, respectively. AU is equal to zero for an isotropic crystal and any deviation of AU from zero defines the extent of elastic anisotropy. The calculated value of AU, using GGA, is about 0.96 and 0.75 for RbMnTe2 and CsMnTe2, respectively, indicating the presence of a certain degree of elastic anisotropy in the considered compounds; the anisotropy in CsMnTe2 is more pronounced than in RbMnTe2. To the best of our knowledge, no experimental or theoretical data for the elastic constants of the studied materials are available in the scientific literature. Therefore, we hope that our results could provide baseline data for future investigations.

4. Conclusions In the present work, we have performed first-principle calculations of the structural, electronic, magnetic and elastic properties of the layered compounds RbMnSe2 and CsMnSe2. The exchangecorrelation energy was treated using the GGA and GGA þU. The calculated lattice constants are in good agreement with the available experimental data. The analysis of the density of states identify the half-metallic behavior of RbMnSe2 and CsMnSe2. The calculated total magnetic moment, including contribution from the interstitial region, is equal to 4μB in both studied compounds and is mainly originated from the transition metal Mn atoms with small contribution from the Se atoms. The calculated elastic constants suggest that RbMnSe2 and CsMnSe2 are very soft materials and mechanically stable and the findings confirm that the c-axis (the stacking direction) is more compressible than the a- and baxes. Apart of the cell parameters and total magnetic moment of the two examined materials, there are no previous experimental or theoretical data to be compared with our present results. Therefore, our results still await experimental confirmation.

Acknowledgments The

authors

(Benmakhlouf

and

Bentabet)

extend

their

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appreciation to the Director of “Laboratoire de physique des Matériaux” at Laghouat University for the full support given to this work.

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