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Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study
Journal Pre-proof Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study M.I. Khan, Hafsa Arshad, M. Rizwan, S.S.A. Gillani, M. Zafar, Shabbir Ahmed, M. Shakil PII:
S0925-8388(19)34210-0
DOI:
https://doi.org/10.1016/j.jallcom.2019.152964
Reference:
JALCOM 152964
To appear in:
Journal of Alloys and Compounds
Received Date: 25 August 2019 Revised Date:
6 November 2019
Accepted Date: 9 November 2019
Please cite this article as: M.I. Khan, H. Arshad, M. Rizwan, S.S.A. Gillani, M. Zafar, S. Ahmed, M. Shakil, Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152964. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study M. I. Khan,a, Hafsa Arshada, M. Rizwana, S. S. A. Gillanib, M. Zafarc, Shabbir Ahmedd, M. Shakil*,a a) Department of Physics, Hafiz Hayat Campus, University of Gujrat, Gujrat 50700, Pakistan b) Department of Physics, Govt. College University Lahore, Pakistan c) Department of Physics, Govt. Rizwiva Islamia Post Graduate College Haroon Abad, Punjab, Pakistan d) Department of Physics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan ___________________________________________________________________________ *
Corresponding author: [email protected], [email protected], (M. Shakil)
Abstract The structural stability, band structure, density of states (DOS), magnetic and mechanical properties of Co-based equiatomic quaternary Heusler alloys (EQHAs) CoYCrZ (Z = Si, Ge, Ga, Al) are examined by employing 1st principle calculations in the framework of density functional theory (DFT) as embedded in Wien2k code. The generalized gradient approximation (GGA) of Perdew-Burke Ernzehrof (PBE) is used for all these calculations. The lattice constants obtained by the optimization of structures and Type-II is found the most stable configuration for all alloys. The band diagrams and DOS calculations show that all these materials possess half metallic (HM) character because they have band gap in minority spin channel. The origin of band gap has been explained which is due to the robust d-d hybridization among transition metals (TMs). The obtained magnetic moments (MMs) are in accordance to the Slater-Pauling rule. The considered materials have high MMs and all alloys showed 100% spin polarization (SP). Curie temperature
has also been calculated and reported for all these alloys. In order to check the mechanical stability, the calculations for elastic constants and other mechanical parameters are carried out which have revealed that all alloys are stable and have ductile nature. All the considered alloys in this study are reported for the first time and no data is available for comparison. It is envisaged these alloys are suitable for spintronic applications as in magnetic tunnel junctions (MTJs), spin valves, and spin injectors etc. Keywords: Spintronics; Exchange splitting; Hybridization; Irreducible Brillouin zone; Magnetic moment; Spin polarization; 1. Introduction Now a days, the Heusler alloys are of great importance due to their innovative functionalities and substantial potential applications in the spintronics [1-3]. The spintronic devices are of great importance as compared to conventionally electronic devices due to the addition of electronic spin along with the electronic charge [4]. Spintronics is the newly expanding field in which transportation of spin polarized electrons is focused [5]. The speed of electrons in those materials which are entirely spin polarized is much quicker than the normal semi-conducting materials and the non-polar compounds. Due to having highly spin polarized charge carriers, HM materials are becoming prospective candidates for spintronic devices [6]. The devices based on the spintronics have the higher capacity of data storage, faster data processing and high transfer rate [7-9]. In 1903, first Heusler alloy was predicted by Friedrich Heusler. The materials with 100% SP are named half metals and spin gapless semiconductors (SGS) [9]. In these materials the holes and electrons can be completely spin polarized. These materials behave differently for the electrons
of minority and majority spin. The materials in which one spin band acts as metallic while other as semiconducting are known as HM materials [10]. The cause of inclination to form the HM materials can be clarified by the electronic properties. The Heusler alloys which are expected to half metal must have high Curie temperature. The realization of the Heusler alloys made the spintronic devices more useful and efficient [11, 12]. Recently, various HM materials in different material systems have been predicted theoretically such as chalcogenides [13], zinc-blende transition-metal pnictides [14], ferromagnetic metallic oxides and Heusler alloys [4]. Among these HM materials, Heusler alloys have attained much attention because they could be used to fabricate spintronic devices from these materials due to their compatibility with conventional semiconductors [15-17]. Some quaternary Heusler alloys (QHAs) have been successfully synthesized experimentally as reported in literature [18-23]. The exceptional properties of Heusler alloys are half metallicity and completely SP which make these materials applicable for spintronic devices. The spintronic devices made of HM Heusler alloys having 100% SP and high Curie temperature are considered more reliable [24]. In spintronic devices, HM materials have promising applications as tunnel magneto-resistance [25], giant magneto-resistance [4], magnetic sensors, spin light emitting diodes, spin injectors [26], and spin field effect transistor, spin valves [27], magnetic-recording tapes, non-volatile random access memories [28], spin-resonant tunneling devices, decoders, encoders, and quantum computation [8]. The HM Heusler alloys are being employed in spintronic devices such as MTJs and it is expected the implantation of QHAs will enhance the performance of MTJs due to their unique physical properties [29]. Heusler alloys are generally classified into two families named as ternary
Heusler alloys (THAs) and QHAs [8]. The THAs are further categorized into half Heusler alloys (HHAs) and full Heusler alloys (FHAs) having structural formula XYZ and X2YZ respectively.
FHAs and HHAs crystalizes in L21 and C1b-type crystal structures. The QHAs have the structural formula XX′YZ and space group F-43m [30, 31]. In the structural formula, X X′ and Y are TMs while Z represents sp elements. The structure of the QHAs contains 4 interpenetrate FCC sub-lattices which is an ordered super-lattice [32, 33]. In these alloys, the atomic number of X´ atom should less than the valance of the atom X, and the atomic number of Y atom should less than both other TMs [34]. The QHAs are crystallizes in the Y-type structure [19]. The QHAs with the stoichiometry 1:1:1:1 or EQHAs are more satisfactory and applicable than THAs due to their low power dissipation and very short length of spin diffusion in spintronic devices [18]. The first HHA which was predicted to be half metal was NiMnSb by de Groot et al. in 1983 [35, 36]. The strength of half metallicity also depends upon the band gap size. If band gap is very small then the material can lose its HM character by applying a very small amount of stress [37, 38]. For practical applications, it is necessary that Heusler alloys must have strong HM character along with high Curie temperature which is far beyond room temperature [38]. Some QHAs have been explored with zero or small HM gap [37, 39-43]. The material with small HM gap might not be suitable for applications in spintronic devices because temperature or any defect can easily demolish their half-metallicity [15]. Hence for spintronic applications, it is necessary to search HM materials with large HM gap and 100% SP. In literature, the HM properties of the CoMnCrSb have been reported theoretically by Saadi Berri et al. [44]. Many other EQHAs as CoFeCrZ (Z = Al, Ga, Si, Ge) [37], CoFeScZ (Z = P, As, Sb) [1], CoFeTiZ (Z = Si, Ge, Sn) [43], CoFeMnZ (Z = Al, Ga, Si, Ge) [45], CoFeCrZ (Z = P, As, Sb) [46], CoRhMnZ (Z = Al, Ga, Ge, Si) [47], CoRuTiZ (Z = Si, Ge, Sn) [5], CoFeTiZ and CoFeVZ (Z= Al, Ga, Si, Ge, As, Sb) [15], CoMnTiZ (Z = P, As, Sb) [34], CoFeScZ (Z = P, As, Sb), CoFeMnZ (Z = Si, As, Sb) [48], CoRuFeZ (Z = Si, Ge, Sn) [49], CoFeCrZ (Z = P, As, Sb) [46], CoCuMnZ (Z = In, Sn, Sb) [50] and CoRhMnGe [51]
have been investigated theoretically and reported as HM alloys. Although various studies have
been reported in the literature as mentioned above but the growing demand of spintronic devices has invoked the desire to explore more alloys with superior characteristics. Therefore, in this study, we have investigated the newly designed QHAs CoYCrZ (Z = Si, Ge, Ga, Al) and their structural optimization, electronic structures, half metallicity and mechanical parameters are discussed in detail. To the best of authors knowledge, there is no published experimental or theoretical data is available for these alloys. It is expected that the newly designed Heusler alloys in this study will be utilized for the fabrication of spintronic devices. 2. Computational details Firstly, the optimization of all structures were accomplished for three different types to find equilibrium lattice constants. Among three types (Type-I, Type-II & Type-III), the most optimized structure was Type-II due to minimum energy. All calculation were performed by FPLAPW method as executed by Wien2k within the scheme of DFT [52]. The effects of exchange and correlation are treated via GGA exchange correlation potential anticipated by PBE [53]. The cutoff parameter RmtKmax was 8.5, where Rmt and Kmax represent the smallest muffin tin (MT) radius and the magnitude of the largest k-vector in the extension of the plane-wave respectively. The largest k-vector of basis set controlled the exactness of the simulations. The MT radii used in these calculations are as 2.37a.u, 2.37a.u, 2.37a.u, 2.20a.u, 2.23a.u, 2.23a.u, and 2.24a.u for Co, Y, Cr, Si, Ga, Ge, and Si for respectively. The valance charge density depends upon the angular momentum within the MT spheres. By expanding the plane waves among the MT spheres, the value of the self-consistent potential (SCP) was obtained from the interstitial charge densities. The cut-off energy which separates the core and valance states was set as -6 Ry. For self-consistent calculations, the charge and energy convergence were kept as 0.00001e and
0.00001Ry respectively. Further calculations to determine the physical properties of Heusler alloys i.e. CoYCrZ (Z = Si, Ge, Ga, Al) were carried out on the optimized lattice constants. 3. Results and discussion 3.1. Structural stability The QHAs have the structural formula XX´YZ which crystalizes in the Y-Type structure having the space group F-43m. Before calculating the DOS and band structure, first step is to optimize the crystal structure and the determination of equilibrium lattice constants. For QHAs, there are three possible types of crystal structures depending on different Wyckoff positions named as Type-I, Type-II and Type-III. The Wyckoff positions [8, 54] for these three types are presented in Table 1 where the parameters of occupation for the elements X, X´, Y and Z are replaced. The structure optimization graphs of all three types are presented in Fig. 1. Before calculating the most stable type, the first step is to optimize the most stable phase. Hence, the calculations for ferromagnetic (FM), anti-ferromagnetic (AFM) and non-magnetic (NM) were performed and the results are presented in graphs as shown in Fig. 2. From graphs it can be observed that the most stable phase is FM among three due to having lowest ground state energy. Based on the FM phase, further calculations for three types were executed. For all three possible configurations, the stability of structure can be determined from the obtained total optimized energy as a function of volume. The most optimized structure is Type-II among three types. From Table 2 and Fig. 3, it can be observed that Type-II have lowest value of energy for each alloy which proves the stability of crystal structure. The equilibrium lattice constants
are determined by using Murnaghan’s Equation of state (EOS). It can also be seen from the Table 2 that the lattice constant of Type-II structure is small as compared to other both
structures. The atomic radius of sp elements effect the equilibrium lattice constant of the QHAs. The increase in atomic radius also enhances the lattice constant. The lattice parameters, optimized volume, optimized energy and bulk modulus for each compound is presented in Table 2. The obtained results of optimized volume vs. optimized energy for all three types of alloys (CoYCrZ (Z = Si, Ge, Ga, Al)) are plotted in Fig. 3. These graphs also revealed that the most favorable is Type-II configuration due to its lowest energy. The equilibrium lattice constants of CoYCrSi, CoYCrGe, CoYCrGa and CoYCrAl are 6.29Å, 6.36Å, 6.37Å and 6.39Å respectively. Another energy presented in Table 2 is formation energy (Ef) which imply that these materials can be synthesized experimentally due to negative values of Ef. Ef can be defined as the change in energy when any material is obtained from its integral elements in their bulk states. For CoYCrZ (Z = Si, Ge, Ga, Al) Ef can be calculated by [42]: =
−
+ =
Where ,
+ ,
,
+
,
represents calculated equilibrium total energy per formula unit while , and
(i)
,
are the total energies per atom of pure constituents Co, Y, Cr, Si, Ge,
Ga, Al in their individual bulk state. In Table 2, the values of Ef for CoYCrZ are listed which confirmed that these compounds are stable and can be experimentally synthesized. CoYCrSi can be easily synthesized because it has lowest Ef among four studied Heusler alloys. Hence, the further calculations of electronic and magnetic properties were carried out on Type-II configuration. 3.2. Electronic properties
The band structures for spin up and spin down are calculated using the equilibrium lattice constants. The band structures of these materials are shown in Figs. 4-7. For spin up channel an overlapping can be observed at the Fermi level in all these alloys because the energy orbitals cross the states as can be observed in Fig. 4(a)-7(a). While in minority spin, the Fermi level falls within energy gap which gives the HM character with 100% SP as shown in Fig. 4(b)-7(b). The main symmetric points are along the direction in the irrevocable Brillouin zone. From the band structures, it can be seen that either the band gap is direct or indirect. It can be observed that valance band maximum (VBM) is located at the Γ and conduction band minimum (CBM) is at ∆ predicting the indirect band gap in CoYCrGe and CoYCrAl alloys. The band gap nature of CoYCrSi and CoYCrGa alloys are also indirect but the CBM is positioned at X and L. The energy band gap obtained from the band structures and DOS are in accordance as CoYCrGe > CoYCrGa > CoYCrGa > CoYCrAl. To verify the findings of band structures, the DOS for CoYCrZ (Z = Si, Ge, Ga, Al) are plotted as shown in the Figs. 8 & 9. The graphs of total density of states (TDOS) show that the majority spin band for these four alloys have metallic character while the spin down band have distinct gap. The energy gaps in this band predicted the character of half metallicity in all these compounds. The strong d-d hybridization among the TMs is responsible of band gap formation in these materials. The contribution from main group element in the band gap is negligible because the states of said element are far distant from the Fermi level. The main group elements specify the position of Fermi level but does not correspond to size or value of band gap. Moreover, these elements stabilize the crystal structures. [24, 55].
The participation from individual atoms to TDOS has also been shown in Figs. 8 & 9. The core states which are below the energy range -6eV to 6eV for TDOS and partial density of states
(PDOS) have shown in graphs. From PDOS graphs, it can be concluded that the involvement of the Co and Cr atoms is larger while lower for Y and slightest from main group elements in all alloys. Although, the contribution from p states of sp elements is negligible but the hybridization among p-states of the Z element and d-states of the TM for the degree of occupation of p-d orbitals is strong. Hence, p-d hybridization influences the creation, and size of the energy band gap. In the majority spin state, the effect of exchange splitting causes non-bonding t1u to cross the Fermi level by shifting towards the lower energy. The mechanisms for origin of band gap in HM can be distributed into three forms: (i) d-d hybridization band gap, (ii) charge transfer band gap, and (iii) covalent band gap [10, 56]. Furthermore, a strong d-d hybridization among TMs that originates the band gap has been pointed out. The schematic representation to examine the creation of band gap in spin down band is presented in Fig. 10, where d-d hybridization among the TMs can be seen. The bands of sp elements are less contributing to the gap because they are lying at the deep energy range. According to the molecular orbital theory (MOT), first of all consider the hybridization among the Co and Y atoms as displayed in Fig. 10(a). The Co-Y bonding creates five bonding having the tetrahedral symmetry and five anti-bonding orbitals alongwith the octahedral symmetry. The d-orbitals of the Co and Y break into double degenerated (dz2, dx2-y2) and triple degenerated (dxy, dyz, dzx) orbitals. The double degenerate orbitals dz2, dx2-y2 of Co and Y atom couple and originates the bonding eg and anti-bonding eu orbitals. The triple degenerated orbitals dxy, dyz, and dzx also combine and form the bonding and anti-bonding, t2g and t1u respectively. Then the resultant states of Co-Y hybridize with d-states of Cr as presented in Fig. 10(b). The doubly (eg) and triply (t2g) degenerate bonding orbitals of Co-Y hybridize with dz2, dx2-y2 and dxy, dyz, dzx orbitals of the Cr atoms respectively. As a result of this hybridization, the formation of the low
energy bonding orbitals eg(t2g) and high energy anti-bonding orbitals occurs. The anti-bonding orbitals of Co-Y hybridization cannot couple with any d-orbital of the Cr atom. Hence, the energy relation for these orbitals does not change as E(eg) > E(t1u). The Co and Y atoms exist in the middle of the octahedron. According to crystal field theory (CFT), the energy of the splitting bonding and anti-bonding orbitals is Eeg > Et2g and Eeu > Et1u correspondingly. The energy of bonding and anti-bonding orbitals are Eeg < Et2g because the Co-Y atoms are present in the midpoint of Cr tetrahedron. The complete orbital hybridization of CoYCrZ is shown in Fig. 10(c). In CoYCrSi, and CoYCrGe alloys, the graphs of TDOS showed that in the bonding region of the majority spin band, the most contributed atom is Co, the less contributor is Y and least contributors are Cr and main group elements. In the anti-bonding region the main participation is from Y atom as compared to other atoms and similarity in this region can be observed in all alloys appeared at the energy above 1eV as compared to others appearing at less than 1eV. In this region, the contribution of Co, Cr, Si, and Ge atoms is very less. While in anti-bonding state of minority spin, the main contribution is of Co atom. In CoYCrGa and CoYCrAl, the more contribution is from Co and Cr in the bonding section of spin up band and minimum contribution from Ga, Al, and Y. In the minority spin band, the most contribution is from Co atom that appears at the energy above 5eV in anti-bonding region. Cr atom is mainly contributing in the bonding region of the minority spin band at an energy above -4eV, while all other atoms are contributing at the energy < 1eV. From all these contributions, it can be observed that the participation from Z elements to the TDOS is less as compared to the TMs. Among these four sp elements, the main contribution was found from Ge atom in both spin states. The graphs of DOS show that CoYCrGa, and CoYCrAl are very close to SGS which means that by the addition of
some suitable impurity atoms these materials can be suitable candidates for SGS. From the obtained results of band structures and DOS of all these considered alloys i.e. CoYCrZ (Z = Si, Ge, Ga, Al), it can be concluded that all studied compounds have HM nature with 100% SP. 3.3. Magnetic properties In Table 3, the calculated total MMs, interstitial MMs and the contribution from each atom in the respective alloy is presented. From these results, it can be observed that the highest contribution is of the Cr atom. This is because the d-orbital of the Cr-atom shows the exchange splitting in majority and minority spin state. Due to having the higher exchange splitting, the magnetic moment of Cr atom is comparatively higher as compared to other atoms in the respective compound. The interaction among the Cr and Co atom is FM in CoYCrSi and CoYCrGe, while in other both alloys these atoms are linked anti-ferromagnetically. Y atom has almost symmetrical DOS due to having less MMs in both spin states. The contribution from the main group elements is almost -0.05 which is negligible to the total MMs. In CoYCrSi, and CoYCrGe, the Co is anti-ferromagnetically linked with Si and Ge while ferromagnetically linked with Cr atom. In CoYCrGa, and CoYCrAl, the interaction of Co with Al and Ga is FM. The interstitial MMs of all these alloys can be presented as CoYCrGa > CoYCrSi > CoYCrAl > CoYCrGe. The total spin MMs is an integral value of 3µ B in case of CoYCrAl and CoYCrGa while 4 µ B for CoYCrSi and CoYCrGe. 3.4. Slater-Pauling rule This rule can be explained into three different ways as =
=
− 18,
=
− 24 and
− 28. This explanation is based on the difference of the origin of various band gaps in
EQHAs. The detailed description on these alloys can be obtained in a study reported by Ozdogan
et al. [57]. As, there is different generalized electron filling rule exists for different band gap origins. Here, we have calculated the MMs according to the rule as provided below; = Where
− 18
represents the no. of valance electrons and
(ii) shows the total MMs according to
Slater-Pauling rule. All these calculated results are given in Table 4. From these results, it can be understood that the calculated MMs and the MMs obtained from the Slater-Pauling rule are in good agreement. The total no. of valance electrons in CoYCrAl, and CoYCrGa are 21, and in CoYCrSi, and CoYCrGe are 22, which leads to MMs of 3µ B and 4 µ B respectively. Furthermore, it is necessary for HM materials that they should obey Slater-Pauling rule. 3.5. Spin polarization For any FM material, the SP can be defined as a method that can differentiate among the states of majority and minority channel near the Fermi level. The SP of Heusler alloys can be obtained from the formula as [58-60]; &'((* (↑)).&'((* (↓))
SP = &'((*+ (↑))0&'((* +(↓)) +
+
The symbol for majority state and minority state are ↑ and ↓ respectively, while 12 (
(iii) 3 )
represents the densities of states lie at the Fermi level. The SP of the normal metal is zero (P = 0) because metals have no band gap. As, these considered alloys are completely HM and hence have 100% SP as presented in Table 5. This 100% SP confirmed that electrons can participate in conduction in just one spin channel. Due to the existence of complete SP in these i.e. CoYCrZ (Z = Si, Ge, Ga, Al) alloys, it is predicted that these materials may be used in the fabrication of spintronic devices.
In addition to SP calculations, Curie temperature is also calculated from the linear relationship as presented in the former investigations [46, 48, 61, 62]. The crystal structure mainly influences the Curie temperature. Higher the MMs of the materials corresponds to high Curie temperature. 4. Elastic properties Elastic properties link the mechanical and dynamical behavior of materials. The elastic constants explain the properties of those materials which endure stress and then return to their original position after removal of stress. Hence, elastic constants are the parameters which determine the mechanical stability of materials. These parameters are the key factors to relate various phenomena as EOS, phonon spectra, and interatomic bonding [46, 63, 64]. As CoYCrZ (Z = Si, Ge, Ga, Al) have cubic symmetry, so only three independent elastic parameters C11, C12, C44 are calculated. These constants give the information about stiffness and stability of materials. C55 determines the longitudinal deformation while C56 measures the transverse expansion in compounds. The calculated values of elastic parameters are presented in Table 6. For cubic symmetry, the mechanical stability criteria given by Born and Haung must be satisfied as [65]: 755 > 0; 7;; > 0; 755 − 756 > 0; & 755 + 2756 > 0
(iv)
The value of bulk modulus (B) calculated from elastic constants is very close to the value obtained from the Murnaghan’s EOS. The hardness of compounds can be determined more precisely by calculating shear modulus (G). B and G indicate the resistance to fracture and resistance to plastic deformation respectively. The results of B and G explain stiffness and compressibility of materials as given below [66]: = =
>> 0 6 >?
@
(v)
=
D
G
Where
D and
G
AB 0 AC
=
=
(vi)
6 >> . >? 0 @ EE
F
F EE ( >> . >? ) ; EE 0@( >> . >? )
(vii)
(viii)
represents Voigt and Reuss shear modulus respectively. To predict the nature
of material, the most favorable criteria are Pugh’s ratio (B/G). According to this empirical criterion, the material is ductile when the value of Pugh’s ratio is greater than 1.75. From the calculated results, it can be observed that CoYCrZ (Z = Si, Ge, Ga, Al) shows the ductile behavior. Cauchy pressure (CP) also determines the nature of material. The positive value of CP corresponds the ductility of the materials. CP = C56 − C;;
(ix)
Another mechanical parameter which demonstrates the stiffness of materials is Young’s Modulus (E). It determines the response of material to linear strain along edges. IJK
E = @J0K
(x)
If the value of E is higher, then the compound is stiffer. For CoYCrZ (Z = Si, Ge, Ga, Al) alloys, the highest value of E is observed for CoYCrSi and the least for CoYCrGe. The measure of compressibility is known as Poisson’s ratio (ν) which indicates the ratio of lateral to longitudinal strain with the range of 0.2 to 0.49. The materials having the value approximately 0.3 are less compressible and more stable against the exterior deformation. From Table 6, the value of ν is ~0.3 for CoYCrZ (Z = Si, Ge, Ga, Al) indicating that all these alloys are less compressible materials.
(@K.6J)
ν = 6(@K0J)
(xi)
From the results of mechanical properties, it can be concluded that all these considered CoYCrZ (Z = Si, Ge, Ga, Al) alloys are stable and have ductile nature. For practical point of view, the investigation of mechanical properties is very important. The information obtained from the elastic constants is relatively more important to explain the stability of materials. These alloys are reported for the first time and there is no theoretical or experimental data for elastic parameters for these CoYCrZ (Z = Si, Ge, Ga, Al) alloys is available. However, this work can provide the reference for future studies. 5. Conclusions In summary, 1st principles calculations are carried out to explore the structural, electronic, magnetic and mechanical properties of CoYCrZ (Z = Si, Ge, Ga, Al) Heusler alloys. It is observed from the structural optimization results that the most stable configuration is Type-II among all three types. Further calculation are carried out using optimized lattice parameters. The results of band structures are in accordance with the DOS plots which show complete SP. The majority spin band contains no gap, while in minority spin Fermi level lays in energy gap. The band structure plots showed that the nature of energy band gap is indirect in all these alloys. The origin of the band gap is located in the spin down channel which is due to the presence of strong d-d hybridization between TMs. The results of electronic properties revealed the existence of HM character in all these alloys. The energy band gaps of CoYCrSi, CoYCrGe, CoYCrGa, and CoYCrAl are 0.82, 0.86, 0.64, and 0.61 eV, while HM gaps are 0.215eV, 0.351eV, 0.415eV, and 0.40eV respectively. These materials have 100% SP and the calculated total MMs are in complete agreement with the Slater-Pauling rule
=
− 18. The total integer MMs are 3µ B
and 4 µ B for CoYCrAl, CoYCrGa and CoYCrSi, CoYCrGe respectively. In addition, DOS of CoYCrAl, CoYCrGa predicted that these materials may be the promising candidates for SGS by the addition of a suitable impurity. The calculations of mechanical parameters show that these materials are stable and have positive CP which showed its ductile nature. It can be concluded from calculations that these materials have high Curie temperature, HM gap, mechanically stable and are completely spin polarized. So, these are suitable candidates for spintronics application (MTJs and Spin valves) which will enhance the efficiency of these devices. Acknowledgement The authors are very grateful to Prof. Dr. Muhammad Arshad Choudhary for providing the fruitful discussion.
References 1.
Gao, Y. and X. Gao, The half-metallicity of LiMgPdSn-type quaternary Heusler alloys FeMnScZ (Z= Al, Ga, In): A first-principle study. AIP Advances, 2015. 5(5): p. 057157.
2.
Wolf, S., SA Wolf, DD Awschalom, RA Buhrman, JM Daughton, S. von Molnár, ML Roukes, AY Chtchelkanova, and DM Treger, Science 294, 1488 (2001). Science, 2001. 294: p. 1488.
3.
Julliere, M., Tunneling between ferromagnetic films. Physics letters A, 1975. 54(3): p. 225-226.
4.
Li, Y., et al., First-principles study on electronic structure, magnetism and halfmetallicity of the NbCoCrAl and NbRhCrAl compounds. Results in physics, 2017. 7: p. 2248-2254.
5.
Bahramian, S. and F. Ahmadian, Half-metallicity and magnetism of quaternary Heusler compounds CoRuTiZ (Z= Si, Ge, and Sn). Journal of Magnetism and Magnetic Materials, 2017. 424: p. 122-129.
6.
Koshi, N.A. and R. John, Half-Metallic Ferrimagnetism in CoFeNbZ (Z= Al, Si, Ge, Sn) Quaternary Heusler Alloys: a DFT Study. Journal of Superconductivity and Novel Magnetism, 2019. 32(4): p. 977-986.
7.
Wang, X., Proposal for a new class of materials: spin gapless semiconductors. Physical review letters, 2008. 100(15): p. 156404.
8.
Rasool, M.N., et al., Investigation of structural, electronic and magnetic properties of 1: 1: 1: 1 stoichiometric quaternary Heusler alloys YCoCrZ (Z= Si, Ge, Ga, Al): An abinitio study. Journal of Magnetism and Magnetic Materials, 2015. 395: p. 97-108.
9.
Pandey, B., R.B. Ray, and G.C. Kaphle, First-principles study of structural, electronic and magnetic properties of Co-based quaternary Heusler compounds: CoFeCrAl, CoFeTiAs, CoFeCrGa and CoMnVAs. BIBECHANA, 2018. 15: p. 50-59.
10.
Wang, X., et al., Origin of the half-metallic band-gap in newly designed quaternary Heusler compounds ZrVTiZ (Z= Al, Ga). RSC Advances, 2016. 6(62): p. 57041-57047.
11.
Bainsla, L. and K. Suresh, Equiatomic quaternary Heusler alloys: A material perspective for spintronic applications. Applied Physics Reviews, 2016. 3(3): p. 031101.
12.
Wang, X., et al., Structural, electronic, magnetic, half-metallic, mechanical, and thermodynamic properties of the quaternary Heusler compound FeCrRuSi: A firstprinciples study. Scientific reports, 2017. 7(1): p. 16183.
13.
Galanakis, I. and P. Mavropoulos, Zinc-blende compounds of transition elements with N, P, As, Sb, S, Se, and Te as half-metallic systems. Physical Review B, 2003. 67(10): p. 104417.
14.
Song, W., J. Wang, and Z. Wu, Half metallic properties of Sr2CuOsO6. Chemical Physics Letters, 2009. 482(4-6): p. 246-248.
15.
Xiong, L., L. Yi, and G. Gao, Search for half-metallic magnets with large half-metallic gaps in the quaternary Heusler alloys CoFeTiZ and CoFeVZ (Z= Al, Ga, Si, Ge, As, Sb). Journal of Magnetism and Magnetic Materials, 2014. 360: p. 98-103.
16.
Kervan, N., Half-metallicity in the full-Heusler Co2ScP compound: A density functional study. Journal of Magnetism and Magnetic Materials, 2012. 324(23): p. 4114-4117.
17.
Graf, T., C. Felser, and S.S. Parkin, Simple rules for the understanding of Heusler compounds. Progress in solid state chemistry, 2011. 39(1): p. 1-50.
18.
Bainsla, L., et al., High spin polarization in CoFeMnGe equiatomic quaternary Heusler alloy. Journal of Applied Physics, 2014. 116(20): p. 203902.
19.
Alijani, V., et al., Electronic, structural, and magnetic properties of the half-metallic ferromagnetic quaternary Heusler compounds CoFeMn Z (Z= Al, Ga, Si, Ge). Physical Review B, 2011. 84(22): p. 224416.
20.
Rani, D., et al., Experimental and theoretical investigation on the possible half-metallic behaviour of equiatomic quaternary Heusler alloys: CoRuMnGe and CoRuVZ (Z= Al, Ga). Journal of Magnetism and Magnetic Materials, 2019. 492: p. 165662.
21.
Şarlı, N., et al., Key role of central antimony in magnetization of Ni0. 5Co1. 5MnSb quaternary Heusler alloy revealed by comparison between theory and experiment. Physica B: Condensed Matter, 2019. 560: p. 46-50.
22.
Stephen, G.M., et al., Structural and electronic properties of the spin-filter material CrVTiAl with disorder. Journal of Applied Physics, 2019. 125(12): p. 123903.
23.
Venkateswara, Y., et al., Competing magnetic and spin-gapless semiconducting behavior in fully compensated ferrimagnetic CrVTiAl: Theory and experiment. Physical Review B, 2018. 97(5): p. 054407.
24.
Felser, C. and A. Hirohata, Heusler alloys. 2015: Springer.
25.
Kubota, T., et al., Half-metallicity and Gilbert damping constant in Co 2 Fe x Mn 1− x Si Heusler alloys depending on the film composition. Applied Physics Letters, 2009. 94(12): p. 122504.
26.
Saito, T., et al., Spin injection, transport, and detection at room temperature in a lateral spin transport device with Co2FeAl0. 5Si0. 5/n-GaAs schottky tunnel junctions. Applied Physics Express, 2013. 6(10): p. 103006.
27.
Ikhtiar, et al., Magneto-transport and microstructure of Co2Fe (Ga0. 5Ge0. 5)/Cu lateral spin valves prepared by top-down microfabrication process. Journal of Applied Physics, 2014. 115(17): p. 173912.
28.
Winterlik, J., et al., Design Scheme of New Tetragonal Heusler Compounds for Spin Transfer Torque Applications and its Experimental Realization. Advanced Materials, 2012. 24(47): p. 6283-6287.
29.
Bainsla, L., et al., Magnetic tunnel junctions with an equiatomic quaternary CoFeMnSi Heusler alloy electrode. Applied Physics Letters, 2018. 112(5): p. 052403.
30.
Luo, H., et al., Prediction of half-metallic properties for the Heusler alloys Mn2CrZ (Z= Al, Ga, Si, Ge, Sb): A first-principles study. Journal of Magnetism and Magnetic Materials, 2008. 320(3-4): p. 421-428.
31.
Ahmadian, F., Half-metallic ferromagnetism in the Ti 2 FeGe Heusler compound: A firstprinciples study. Journal of superconductivity and novel magnetism, 2013. 26(2): p. 381388.
32.
Kervan, S. and N. Kervan, Half-metallic properties of the CuHg2Ti-type Mn2ZnSi fullHeusler compound. Current Applied Physics, 2013. 13(1): p. 80-83.
33.
Gilleßen, M. and R. Dronskowski, A combinatorial study of inverse Heusler alloys by first principles computational methods. Journal of computational chemistry, 2010. 31(3): p. 612-619.
34.
Khodami, M. and F. Ahmadian, First-principles study of magnetism and half-metallic properties for the quaternary Heusler alloys CoMnTiZ (Z= P, As, and Sb). Journal of Superconductivity and Novel Magnetism, 2015. 28(10): p. 3027-3035.
35.
De Groot, R., et al., New class of materials: half-metallic ferromagnets. Physical Review Letters, 1983. 50(25): p. 2024.
36.
Ghimire, M., T. Sinha, and R. Thapa, First principles study of the electronic and magnetic properties of semi-Heusler alloys NiXSb (X= Ti, V, Cr and Mn). Journal of Alloys and Compounds, 2011. 509(41): p. 9742-9752.
37.
Gao, G., et al., Large half-metallic gaps in the quaternary Heusler alloys CoFeCrZ (Z= Al, Si, Ga, Ge): A first-principles study. Journal of Alloys and Compounds, 2013. 551: p. 539-543.
38.
Jin, Y., et al., Magnetism and electronic structure of CoFeCrX (X= Si, Ge) Heusler alloys. Journal of Applied Physics, 2016. 120(5): p. 053903.
39.
Arshad, H., et al., Theoretical study of structural, electronic and magnetic properties of equiatomic quaternary CoPdCrZ (Z= Si, Ge, P) Heusler alloys. Modern Physics Letters B, 2019: p. 1950389.
40.
Kundu, A., et al., New quaternary half-metallic ferromagnets with large Curie temperatures. Scientific reports, 2017. 7(1): p. 1803.
41.
Xie, H.-H., et al., First-principles study of four quaternary Heusler alloys ZrMnVZ and ZrCoFeZ (Z= Si, Ge). Computational Materials Science, 2015. 103: p. 52-55.
42.
Karimian, N. and F. Ahmadian, Electronic structure and half-metallicity of new quaternary Heusler alloys NiFeTiZ (Z= Si, P, Ge, and As). Solid State Communications, 2015. 223: p. 60-66.
43.
Zhang, Y., et al., Magnetism, band gap and stability of half-metallic property for the quaternary Heusler alloys CoFeTiZ (Z= Si, Ge, Sn). Journal of Alloys and Compounds, 2014. 616: p. 449-453.
44.
Berri, S., First-principles study on half-metallic properties of the CoMnCrSb quaternary Heusler compound. Journal of Superconductivity and Novel Magnetism, 2016. 29(5): p. 1309-1315.
45.
Klaer, P., et al., Element-specific magnetic moments and spin-resolved density of states in CoFeMn Z (Z= Al, Ga; Si, Ge). Physical Review B, 2011. 84(14): p. 144413.
46.
Bahnes, A., et al., Half-metallic ferromagnets behavior of a new quaternary Heusler alloys CoFeCrZ (Z= P, As and Sb): Ab-initio study. Journal of Alloys and Compounds, 2018. 731: p. 1208-1213.
47.
Benkabou, M., et al., Electronic structure and magnetic properties of quaternary Heusler alloys CoRhMnZ (Z= Al, Ga, Ge and Si) via first-principle calculations. Journal of Alloys and Compounds, 2015. 647: p. 276-286.
48.
Elahmar, M., et al., Structural, mechanical, electronic and magnetic properties of a new series of quaternary Heusler alloys CoFeMnZ (Z= Si, As, Sb): a first-principle study. Journal of Magnetism and Magnetic Materials, 2015. 393: p. 165-174.
49.
Benkaddour, K., et al., First-principles study of structural, elastic, thermodynamic, electronic and magnetic properties for the quaternary Heusler alloys CoRuFeZ (Z= Si, Ge, Sn). Journal of Alloys and Compounds, 2016. 687: p. 211-220.
50.
Chandra, A.R., et al., Electronic structure properties of new equiatomic CoCuMnZ (Z= In, Sn, Sb) quaternary Heusler alloys: An ab-initio study. Journal of Alloys and Compounds, 2018. 748: p. 298-304.
51.
Rani, D., et al., Structural, electronic, magnetic, and transport properties of the equiatomic quaternary Heusler alloy CoRhMnGe: Theory and experiment. Physical Review B, 2017. 96(18): p. 184404.
52.
Blaha, P., et al., wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties, 2001.
53.
Perdew, J., K. Burke, and M. Ernzerhof, Perdew, burke, and ernzerhof reply. Physical Review Letters, 1998. 80(4): p. 891.
54.
Singh, M., et al., Electronic structure, magnetism and robust half-metallicity of new quaternary Heusler alloy FeCrMnSb. Journal of Alloys and Compounds, 2013. 580: p. 201-204.
55.
Liu, H., et al., Influence of main-group element on half-metallic properties in halfHeusler compound. Modern Physics Letters B, 2016. 30(11): p. 1650206.
56.
Fang, C.M., G. De Wijs, and R. De Groot, Spin-polarization in half-metals. Journal of Applied Physics, 2002. 91(10): p. 8340-8344.
57.
Özdoğan, K., E. Şaşıoğlu, and I. Galanakis, Slater-Pauling behavior in LiMgPdSn-type multifunctional quaternary Heusler materials: Half-metallicity, spin-gapless and magnetic semiconductors. Journal of Applied Physics, 2013. 113(19): p. 193903.
58.
Xing, N., et al., First-principle prediction of half-metallic properties for the Heusler alloys V2YSb (Y= Cr, Mn, Fe, Co). Computational Materials Science, 2009. 45(2): p. 489-493.
59.
Rai, D., et al., A comparative study of a Heusler alloy Co2FeGe using LSDA and LSDA+ U. Physica B: Condensed Matter, 2012. 407(18): p. 3689-3693.
60.
Seema, K., M. Kaur, and R. Kumar, First Principles Study of Fe based Full Heusler Alloy. Journal of Integrated Science and Technology, 2013. 1(1): p. 41-43.
61.
Kandpal, H.C., G.H. Fecher, and C. Felser, Calculated electronic and magnetic properties of the half-metallic, transition metal based Heusler compounds. Journal of Physics D: Applied Physics, 2007. 40(6): p. 1507.
62.
Wurmehl, S., et al., Geometric, electronic, and magnetic structure of Co 2 FeSi: Curie temperature and magnetic moment measurements and calculations. Physical Review B, 2005. 72(18): p. 184434.
63.
Bhat, T.M. and D.C. Gupta, Magneto-electronic, thermal, and thermoelectric properties of some Co-based quaternary alloys. Journal of Physics and Chemistry of Solids, 2018. 112: p. 190-199.
64.
İyigör, A. and Ş. Uğur, Elastic and phonon properties of quaternary Heusler alloys CoFeCrZ (Z= Al, Si, Ga and Ge) from density functional theory. Philosophical Magazine Letters, 2014. 94(11): p. 708-715.
65.
Rahman, M.A., M.Z. Rahaman, and M.A. Rahman, The structural, elastic, electronic and optical properties of MgCu under pressure: A first-principles study. International Journal of Modern Physics B, 2016. 30(27): p. 1650199.
66.
Shakil, M., et al., Theoretical investigation of structural, magnetic and elastic properties of half Heusler LiCrZ (Z= P, As, Bi, Sb) alloys. Physica B: Condensed Matter, 2019. 575: p. 411677.
Table 1 Type
Co
Y
Cr
Z
Type-I
(0.75, 0.75, 0.75)
(0, 0, 0)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
Type-II
(0.75, 0.75, 0.75)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
(0, 0, 0)
Type-III
(0, 0, 0)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
(0.75, 0.75, 0.75)
Table 2 (revised) Alloy
CoYCrSi
CoYCrGe
CoYCrGa
CoYCrAl
Type
Lattice parameter a( )
Optimized Volume (Vo) (a.u.^3)
Optimized energy
Bulk modulus
Eo (Ry)
(GPa)
Type-I
6.4234
447.1382
-12240. 223657
98.2262
Type-II
6.2904
419.9187
-12240. 235051
122.5199
Type-III
6.3676
435.5700
-12240. 168361
106.3269
Type-I
6.5206
467.7417
-15858. 330133
91.0994
Type-II
6.3669
435.4258
-15858. 334675
115.9462
Type-III
6.4594
454.6806
-15858. 282663
94.0628
Type-I
6.5146
466.4528
-15548. 369849
92.0549
Type-II
6.3735
436.7828
-15548. 394893
96.2258
Type-III
6.4799
459.0297
-15548.331313
74.0191
Type-I
6.5298
469.7084
-12145. 752410
86.2312
Type-II
6.3989
442.0324
-12145. 810531
95.4493
Type-III
6.4715
457.2540
-12145. 725586
83.9860
Optimized Type
Formation Energy Ef (Ry)
Type-II
-1.71505
Type-II
-1.62307
Type-II
-1.55189
Type-II
-1.638732
Table 3 Alloy
Mint(µB)
MCo(µB)
MY(µB)
MCr(µB)
MZ(µB)
Mtot(µB)
CoYCrAl
0.25309
-0.33773
0.03301
3.10459
-0.04740
3.00057
CoYCrGe
0.17759
0.63984
-0.01294
3.23609
-0.05067
3.99991
CoYCrGa
0.26349
-0.41224
0.04404
3.15511
-0.05004
3.00035
CoYCrSi
0.19384
0.73153
-0.00902
3.13917
-0.05569
3.99983
Table 4 Alloy
Fermi energy
Band gap (eV)
Half-Metallic gap (eV)
Nature
Location
CoYCrSi
0.66293
0.825
0.215
Indirect
Γ→X
CoYCrGe
0.64459
0.863
0.351
Indirect
Γ→∆
CoYCrGa
0.60090
0.645
0.645
Indirect
Γ→L
CoYCrAl
0.57674
0.610
0.40
Indirect
Γ→∆
Table 5 Alloy
Mtot(µB)
Number Slaterof Pauling valance rule electron magnetic s moment
(
(↑))
(
(↓))
Spin polarization
Curie Temperature (K)
CoYCrSi
3.00057
21
3
1.99
0
100%
566
CoYCrGe
3.99991
22
4
2.42
0
100%
747
CoYCrGa
3.00035
21
3
0.15
0
100%
566
CoYCrAl
3.99983
22
4
0.09
0
100%
747
Table 6
Parameters
CoYCrSi
CoYCrGe
CoYCrGa
CoYCrAl
149.7
133.9
128.5
136.7
85.9
88.3
88.2
79.5
43.4
41.8
51.8
52.7
107.17
103.5
101.6
98.6
42.5
46.5
36.4
26.8
0.34
0.35
0.34
0.32
166.46
151.28
155.92
164.61
38.8
34.2
39.14
43.06
37.9
31.35
31.8
39.41
38.35
32.78
35.47
41.24
2.79
3.15
2.86
2.39
Fig. 1
Fig. 2(revised)
Fig. 3 (revised)
CoYCrSi
Eg = 0.82eV
Fig. 4 (revised)
CoYCrGe
Eg= 0.86eV
Fig. 5 (revised)
CoYCrGa
Eg = 0.64eV
Fig. 6 (revised)
CoYCrAl
Eg = 0.61eV
Fig. 7 (revised)
(a)
(b)
(a)
(b)
Fig. 10
Highlights •
First principle study of EQHAs CoYCrZ (Z = Si, Ge, Ga, Al)
•
Calculations of structural stability, electronic, magnetic and elastic properties
•
Calculations for FM, AFM and Non-magnetic phases
•
Half metallic nature and high spin polarization
•
Analysis of the origin of band gap
Declaration of Interest It is stated that the work submitted have been performed by us and all authors have contributed. Furthermore, this work has not been submitted elsewhere partially or complete. Also, there is no ethical issue in any regard. Regards! Dr. M. Shakil et al.
S0925-8388(19)34210-0
DOI:
https://doi.org/10.1016/j.jallcom.2019.152964
Reference:
JALCOM 152964
To appear in:
Journal of Alloys and Compounds
Received Date: 25 August 2019 Revised Date:
6 November 2019
Accepted Date: 9 November 2019
Please cite this article as: M.I. Khan, H. Arshad, M. Rizwan, S.S.A. Gillani, M. Zafar, S. Ahmed, M. Shakil, Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152964. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Investigation of structural, electronic, magnetic and mechanical properties of a new series of equiatomic quaternary Heusler alloys CoYCrZ (Z = Si, Ge, Ga, Al): A DFT study M. I. Khan,a, Hafsa Arshada, M. Rizwana, S. S. A. Gillanib, M. Zafarc, Shabbir Ahmedd, M. Shakil*,a a) Department of Physics, Hafiz Hayat Campus, University of Gujrat, Gujrat 50700, Pakistan b) Department of Physics, Govt. College University Lahore, Pakistan c) Department of Physics, Govt. Rizwiva Islamia Post Graduate College Haroon Abad, Punjab, Pakistan d) Department of Physics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan ___________________________________________________________________________ *
Corresponding author: [email protected], [email protected], (M. Shakil)
Abstract The structural stability, band structure, density of states (DOS), magnetic and mechanical properties of Co-based equiatomic quaternary Heusler alloys (EQHAs) CoYCrZ (Z = Si, Ge, Ga, Al) are examined by employing 1st principle calculations in the framework of density functional theory (DFT) as embedded in Wien2k code. The generalized gradient approximation (GGA) of Perdew-Burke Ernzehrof (PBE) is used for all these calculations. The lattice constants obtained by the optimization of structures and Type-II is found the most stable configuration for all alloys. The band diagrams and DOS calculations show that all these materials possess half metallic (HM) character because they have band gap in minority spin channel. The origin of band gap has been explained which is due to the robust d-d hybridization among transition metals (TMs). The obtained magnetic moments (MMs) are in accordance to the Slater-Pauling rule. The considered materials have high MMs and all alloys showed 100% spin polarization (SP). Curie temperature
has also been calculated and reported for all these alloys. In order to check the mechanical stability, the calculations for elastic constants and other mechanical parameters are carried out which have revealed that all alloys are stable and have ductile nature. All the considered alloys in this study are reported for the first time and no data is available for comparison. It is envisaged these alloys are suitable for spintronic applications as in magnetic tunnel junctions (MTJs), spin valves, and spin injectors etc. Keywords: Spintronics; Exchange splitting; Hybridization; Irreducible Brillouin zone; Magnetic moment; Spin polarization; 1. Introduction Now a days, the Heusler alloys are of great importance due to their innovative functionalities and substantial potential applications in the spintronics [1-3]. The spintronic devices are of great importance as compared to conventionally electronic devices due to the addition of electronic spin along with the electronic charge [4]. Spintronics is the newly expanding field in which transportation of spin polarized electrons is focused [5]. The speed of electrons in those materials which are entirely spin polarized is much quicker than the normal semi-conducting materials and the non-polar compounds. Due to having highly spin polarized charge carriers, HM materials are becoming prospective candidates for spintronic devices [6]. The devices based on the spintronics have the higher capacity of data storage, faster data processing and high transfer rate [7-9]. In 1903, first Heusler alloy was predicted by Friedrich Heusler. The materials with 100% SP are named half metals and spin gapless semiconductors (SGS) [9]. In these materials the holes and electrons can be completely spin polarized. These materials behave differently for the electrons
of minority and majority spin. The materials in which one spin band acts as metallic while other as semiconducting are known as HM materials [10]. The cause of inclination to form the HM materials can be clarified by the electronic properties. The Heusler alloys which are expected to half metal must have high Curie temperature. The realization of the Heusler alloys made the spintronic devices more useful and efficient [11, 12]. Recently, various HM materials in different material systems have been predicted theoretically such as chalcogenides [13], zinc-blende transition-metal pnictides [14], ferromagnetic metallic oxides and Heusler alloys [4]. Among these HM materials, Heusler alloys have attained much attention because they could be used to fabricate spintronic devices from these materials due to their compatibility with conventional semiconductors [15-17]. Some quaternary Heusler alloys (QHAs) have been successfully synthesized experimentally as reported in literature [18-23]. The exceptional properties of Heusler alloys are half metallicity and completely SP which make these materials applicable for spintronic devices. The spintronic devices made of HM Heusler alloys having 100% SP and high Curie temperature are considered more reliable [24]. In spintronic devices, HM materials have promising applications as tunnel magneto-resistance [25], giant magneto-resistance [4], magnetic sensors, spin light emitting diodes, spin injectors [26], and spin field effect transistor, spin valves [27], magnetic-recording tapes, non-volatile random access memories [28], spin-resonant tunneling devices, decoders, encoders, and quantum computation [8]. The HM Heusler alloys are being employed in spintronic devices such as MTJs and it is expected the implantation of QHAs will enhance the performance of MTJs due to their unique physical properties [29]. Heusler alloys are generally classified into two families named as ternary
Heusler alloys (THAs) and QHAs [8]. The THAs are further categorized into half Heusler alloys (HHAs) and full Heusler alloys (FHAs) having structural formula XYZ and X2YZ respectively.
FHAs and HHAs crystalizes in L21 and C1b-type crystal structures. The QHAs have the structural formula XX′YZ and space group F-43m [30, 31]. In the structural formula, X X′ and Y are TMs while Z represents sp elements. The structure of the QHAs contains 4 interpenetrate FCC sub-lattices which is an ordered super-lattice [32, 33]. In these alloys, the atomic number of X´ atom should less than the valance of the atom X, and the atomic number of Y atom should less than both other TMs [34]. The QHAs are crystallizes in the Y-type structure [19]. The QHAs with the stoichiometry 1:1:1:1 or EQHAs are more satisfactory and applicable than THAs due to their low power dissipation and very short length of spin diffusion in spintronic devices [18]. The first HHA which was predicted to be half metal was NiMnSb by de Groot et al. in 1983 [35, 36]. The strength of half metallicity also depends upon the band gap size. If band gap is very small then the material can lose its HM character by applying a very small amount of stress [37, 38]. For practical applications, it is necessary that Heusler alloys must have strong HM character along with high Curie temperature which is far beyond room temperature [38]. Some QHAs have been explored with zero or small HM gap [37, 39-43]. The material with small HM gap might not be suitable for applications in spintronic devices because temperature or any defect can easily demolish their half-metallicity [15]. Hence for spintronic applications, it is necessary to search HM materials with large HM gap and 100% SP. In literature, the HM properties of the CoMnCrSb have been reported theoretically by Saadi Berri et al. [44]. Many other EQHAs as CoFeCrZ (Z = Al, Ga, Si, Ge) [37], CoFeScZ (Z = P, As, Sb) [1], CoFeTiZ (Z = Si, Ge, Sn) [43], CoFeMnZ (Z = Al, Ga, Si, Ge) [45], CoFeCrZ (Z = P, As, Sb) [46], CoRhMnZ (Z = Al, Ga, Ge, Si) [47], CoRuTiZ (Z = Si, Ge, Sn) [5], CoFeTiZ and CoFeVZ (Z= Al, Ga, Si, Ge, As, Sb) [15], CoMnTiZ (Z = P, As, Sb) [34], CoFeScZ (Z = P, As, Sb), CoFeMnZ (Z = Si, As, Sb) [48], CoRuFeZ (Z = Si, Ge, Sn) [49], CoFeCrZ (Z = P, As, Sb) [46], CoCuMnZ (Z = In, Sn, Sb) [50] and CoRhMnGe [51]
have been investigated theoretically and reported as HM alloys. Although various studies have
been reported in the literature as mentioned above but the growing demand of spintronic devices has invoked the desire to explore more alloys with superior characteristics. Therefore, in this study, we have investigated the newly designed QHAs CoYCrZ (Z = Si, Ge, Ga, Al) and their structural optimization, electronic structures, half metallicity and mechanical parameters are discussed in detail. To the best of authors knowledge, there is no published experimental or theoretical data is available for these alloys. It is expected that the newly designed Heusler alloys in this study will be utilized for the fabrication of spintronic devices. 2. Computational details Firstly, the optimization of all structures were accomplished for three different types to find equilibrium lattice constants. Among three types (Type-I, Type-II & Type-III), the most optimized structure was Type-II due to minimum energy. All calculation were performed by FPLAPW method as executed by Wien2k within the scheme of DFT [52]. The effects of exchange and correlation are treated via GGA exchange correlation potential anticipated by PBE [53]. The cutoff parameter RmtKmax was 8.5, where Rmt and Kmax represent the smallest muffin tin (MT) radius and the magnitude of the largest k-vector in the extension of the plane-wave respectively. The largest k-vector of basis set controlled the exactness of the simulations. The MT radii used in these calculations are as 2.37a.u, 2.37a.u, 2.37a.u, 2.20a.u, 2.23a.u, 2.23a.u, and 2.24a.u for Co, Y, Cr, Si, Ga, Ge, and Si for respectively. The valance charge density depends upon the angular momentum within the MT spheres. By expanding the plane waves among the MT spheres, the value of the self-consistent potential (SCP) was obtained from the interstitial charge densities. The cut-off energy which separates the core and valance states was set as -6 Ry. For self-consistent calculations, the charge and energy convergence were kept as 0.00001e and
0.00001Ry respectively. Further calculations to determine the physical properties of Heusler alloys i.e. CoYCrZ (Z = Si, Ge, Ga, Al) were carried out on the optimized lattice constants. 3. Results and discussion 3.1. Structural stability The QHAs have the structural formula XX´YZ which crystalizes in the Y-Type structure having the space group F-43m. Before calculating the DOS and band structure, first step is to optimize the crystal structure and the determination of equilibrium lattice constants. For QHAs, there are three possible types of crystal structures depending on different Wyckoff positions named as Type-I, Type-II and Type-III. The Wyckoff positions [8, 54] for these three types are presented in Table 1 where the parameters of occupation for the elements X, X´, Y and Z are replaced. The structure optimization graphs of all three types are presented in Fig. 1. Before calculating the most stable type, the first step is to optimize the most stable phase. Hence, the calculations for ferromagnetic (FM), anti-ferromagnetic (AFM) and non-magnetic (NM) were performed and the results are presented in graphs as shown in Fig. 2. From graphs it can be observed that the most stable phase is FM among three due to having lowest ground state energy. Based on the FM phase, further calculations for three types were executed. For all three possible configurations, the stability of structure can be determined from the obtained total optimized energy as a function of volume. The most optimized structure is Type-II among three types. From Table 2 and Fig. 3, it can be observed that Type-II have lowest value of energy for each alloy which proves the stability of crystal structure. The equilibrium lattice constants
are determined by using Murnaghan’s Equation of state (EOS). It can also be seen from the Table 2 that the lattice constant of Type-II structure is small as compared to other both
structures. The atomic radius of sp elements effect the equilibrium lattice constant of the QHAs. The increase in atomic radius also enhances the lattice constant. The lattice parameters, optimized volume, optimized energy and bulk modulus for each compound is presented in Table 2. The obtained results of optimized volume vs. optimized energy for all three types of alloys (CoYCrZ (Z = Si, Ge, Ga, Al)) are plotted in Fig. 3. These graphs also revealed that the most favorable is Type-II configuration due to its lowest energy. The equilibrium lattice constants of CoYCrSi, CoYCrGe, CoYCrGa and CoYCrAl are 6.29Å, 6.36Å, 6.37Å and 6.39Å respectively. Another energy presented in Table 2 is formation energy (Ef) which imply that these materials can be synthesized experimentally due to negative values of Ef. Ef can be defined as the change in energy when any material is obtained from its integral elements in their bulk states. For CoYCrZ (Z = Si, Ge, Ga, Al) Ef can be calculated by [42]: =
−
+ =
Where ,
+ ,
,
+
,
represents calculated equilibrium total energy per formula unit while , and
(i)
,
are the total energies per atom of pure constituents Co, Y, Cr, Si, Ge,
Ga, Al in their individual bulk state. In Table 2, the values of Ef for CoYCrZ are listed which confirmed that these compounds are stable and can be experimentally synthesized. CoYCrSi can be easily synthesized because it has lowest Ef among four studied Heusler alloys. Hence, the further calculations of electronic and magnetic properties were carried out on Type-II configuration. 3.2. Electronic properties
The band structures for spin up and spin down are calculated using the equilibrium lattice constants. The band structures of these materials are shown in Figs. 4-7. For spin up channel an overlapping can be observed at the Fermi level in all these alloys because the energy orbitals cross the states as can be observed in Fig. 4(a)-7(a). While in minority spin, the Fermi level falls within energy gap which gives the HM character with 100% SP as shown in Fig. 4(b)-7(b). The main symmetric points are along the direction in the irrevocable Brillouin zone. From the band structures, it can be seen that either the band gap is direct or indirect. It can be observed that valance band maximum (VBM) is located at the Γ and conduction band minimum (CBM) is at ∆ predicting the indirect band gap in CoYCrGe and CoYCrAl alloys. The band gap nature of CoYCrSi and CoYCrGa alloys are also indirect but the CBM is positioned at X and L. The energy band gap obtained from the band structures and DOS are in accordance as CoYCrGe > CoYCrGa > CoYCrGa > CoYCrAl. To verify the findings of band structures, the DOS for CoYCrZ (Z = Si, Ge, Ga, Al) are plotted as shown in the Figs. 8 & 9. The graphs of total density of states (TDOS) show that the majority spin band for these four alloys have metallic character while the spin down band have distinct gap. The energy gaps in this band predicted the character of half metallicity in all these compounds. The strong d-d hybridization among the TMs is responsible of band gap formation in these materials. The contribution from main group element in the band gap is negligible because the states of said element are far distant from the Fermi level. The main group elements specify the position of Fermi level but does not correspond to size or value of band gap. Moreover, these elements stabilize the crystal structures. [24, 55].
The participation from individual atoms to TDOS has also been shown in Figs. 8 & 9. The core states which are below the energy range -6eV to 6eV for TDOS and partial density of states
(PDOS) have shown in graphs. From PDOS graphs, it can be concluded that the involvement of the Co and Cr atoms is larger while lower for Y and slightest from main group elements in all alloys. Although, the contribution from p states of sp elements is negligible but the hybridization among p-states of the Z element and d-states of the TM for the degree of occupation of p-d orbitals is strong. Hence, p-d hybridization influences the creation, and size of the energy band gap. In the majority spin state, the effect of exchange splitting causes non-bonding t1u to cross the Fermi level by shifting towards the lower energy. The mechanisms for origin of band gap in HM can be distributed into three forms: (i) d-d hybridization band gap, (ii) charge transfer band gap, and (iii) covalent band gap [10, 56]. Furthermore, a strong d-d hybridization among TMs that originates the band gap has been pointed out. The schematic representation to examine the creation of band gap in spin down band is presented in Fig. 10, where d-d hybridization among the TMs can be seen. The bands of sp elements are less contributing to the gap because they are lying at the deep energy range. According to the molecular orbital theory (MOT), first of all consider the hybridization among the Co and Y atoms as displayed in Fig. 10(a). The Co-Y bonding creates five bonding having the tetrahedral symmetry and five anti-bonding orbitals alongwith the octahedral symmetry. The d-orbitals of the Co and Y break into double degenerated (dz2, dx2-y2) and triple degenerated (dxy, dyz, dzx) orbitals. The double degenerate orbitals dz2, dx2-y2 of Co and Y atom couple and originates the bonding eg and anti-bonding eu orbitals. The triple degenerated orbitals dxy, dyz, and dzx also combine and form the bonding and anti-bonding, t2g and t1u respectively. Then the resultant states of Co-Y hybridize with d-states of Cr as presented in Fig. 10(b). The doubly (eg) and triply (t2g) degenerate bonding orbitals of Co-Y hybridize with dz2, dx2-y2 and dxy, dyz, dzx orbitals of the Cr atoms respectively. As a result of this hybridization, the formation of the low
energy bonding orbitals eg(t2g) and high energy anti-bonding orbitals occurs. The anti-bonding orbitals of Co-Y hybridization cannot couple with any d-orbital of the Cr atom. Hence, the energy relation for these orbitals does not change as E(eg) > E(t1u). The Co and Y atoms exist in the middle of the octahedron. According to crystal field theory (CFT), the energy of the splitting bonding and anti-bonding orbitals is Eeg > Et2g and Eeu > Et1u correspondingly. The energy of bonding and anti-bonding orbitals are Eeg < Et2g because the Co-Y atoms are present in the midpoint of Cr tetrahedron. The complete orbital hybridization of CoYCrZ is shown in Fig. 10(c). In CoYCrSi, and CoYCrGe alloys, the graphs of TDOS showed that in the bonding region of the majority spin band, the most contributed atom is Co, the less contributor is Y and least contributors are Cr and main group elements. In the anti-bonding region the main participation is from Y atom as compared to other atoms and similarity in this region can be observed in all alloys appeared at the energy above 1eV as compared to others appearing at less than 1eV. In this region, the contribution of Co, Cr, Si, and Ge atoms is very less. While in anti-bonding state of minority spin, the main contribution is of Co atom. In CoYCrGa and CoYCrAl, the more contribution is from Co and Cr in the bonding section of spin up band and minimum contribution from Ga, Al, and Y. In the minority spin band, the most contribution is from Co atom that appears at the energy above 5eV in anti-bonding region. Cr atom is mainly contributing in the bonding region of the minority spin band at an energy above -4eV, while all other atoms are contributing at the energy < 1eV. From all these contributions, it can be observed that the participation from Z elements to the TDOS is less as compared to the TMs. Among these four sp elements, the main contribution was found from Ge atom in both spin states. The graphs of DOS show that CoYCrGa, and CoYCrAl are very close to SGS which means that by the addition of
some suitable impurity atoms these materials can be suitable candidates for SGS. From the obtained results of band structures and DOS of all these considered alloys i.e. CoYCrZ (Z = Si, Ge, Ga, Al), it can be concluded that all studied compounds have HM nature with 100% SP. 3.3. Magnetic properties In Table 3, the calculated total MMs, interstitial MMs and the contribution from each atom in the respective alloy is presented. From these results, it can be observed that the highest contribution is of the Cr atom. This is because the d-orbital of the Cr-atom shows the exchange splitting in majority and minority spin state. Due to having the higher exchange splitting, the magnetic moment of Cr atom is comparatively higher as compared to other atoms in the respective compound. The interaction among the Cr and Co atom is FM in CoYCrSi and CoYCrGe, while in other both alloys these atoms are linked anti-ferromagnetically. Y atom has almost symmetrical DOS due to having less MMs in both spin states. The contribution from the main group elements is almost -0.05 which is negligible to the total MMs. In CoYCrSi, and CoYCrGe, the Co is anti-ferromagnetically linked with Si and Ge while ferromagnetically linked with Cr atom. In CoYCrGa, and CoYCrAl, the interaction of Co with Al and Ga is FM. The interstitial MMs of all these alloys can be presented as CoYCrGa > CoYCrSi > CoYCrAl > CoYCrGe. The total spin MMs is an integral value of 3µ B in case of CoYCrAl and CoYCrGa while 4 µ B for CoYCrSi and CoYCrGe. 3.4. Slater-Pauling rule This rule can be explained into three different ways as =
=
− 18,
=
− 24 and
− 28. This explanation is based on the difference of the origin of various band gaps in
EQHAs. The detailed description on these alloys can be obtained in a study reported by Ozdogan
et al. [57]. As, there is different generalized electron filling rule exists for different band gap origins. Here, we have calculated the MMs according to the rule as provided below; = Where
− 18
represents the no. of valance electrons and
(ii) shows the total MMs according to
Slater-Pauling rule. All these calculated results are given in Table 4. From these results, it can be understood that the calculated MMs and the MMs obtained from the Slater-Pauling rule are in good agreement. The total no. of valance electrons in CoYCrAl, and CoYCrGa are 21, and in CoYCrSi, and CoYCrGe are 22, which leads to MMs of 3µ B and 4 µ B respectively. Furthermore, it is necessary for HM materials that they should obey Slater-Pauling rule. 3.5. Spin polarization For any FM material, the SP can be defined as a method that can differentiate among the states of majority and minority channel near the Fermi level. The SP of Heusler alloys can be obtained from the formula as [58-60]; &'((* (↑)).&'((* (↓))
SP = &'((*+ (↑))0&'((* +(↓)) +
+
The symbol for majority state and minority state are ↑ and ↓ respectively, while 12 (
(iii) 3 )
represents the densities of states lie at the Fermi level. The SP of the normal metal is zero (P = 0) because metals have no band gap. As, these considered alloys are completely HM and hence have 100% SP as presented in Table 5. This 100% SP confirmed that electrons can participate in conduction in just one spin channel. Due to the existence of complete SP in these i.e. CoYCrZ (Z = Si, Ge, Ga, Al) alloys, it is predicted that these materials may be used in the fabrication of spintronic devices.
In addition to SP calculations, Curie temperature is also calculated from the linear relationship as presented in the former investigations [46, 48, 61, 62]. The crystal structure mainly influences the Curie temperature. Higher the MMs of the materials corresponds to high Curie temperature. 4. Elastic properties Elastic properties link the mechanical and dynamical behavior of materials. The elastic constants explain the properties of those materials which endure stress and then return to their original position after removal of stress. Hence, elastic constants are the parameters which determine the mechanical stability of materials. These parameters are the key factors to relate various phenomena as EOS, phonon spectra, and interatomic bonding [46, 63, 64]. As CoYCrZ (Z = Si, Ge, Ga, Al) have cubic symmetry, so only three independent elastic parameters C11, C12, C44 are calculated. These constants give the information about stiffness and stability of materials. C55 determines the longitudinal deformation while C56 measures the transverse expansion in compounds. The calculated values of elastic parameters are presented in Table 6. For cubic symmetry, the mechanical stability criteria given by Born and Haung must be satisfied as [65]: 755 > 0; 7;; > 0; 755 − 756 > 0; & 755 + 2756 > 0
(iv)
The value of bulk modulus (B) calculated from elastic constants is very close to the value obtained from the Murnaghan’s EOS. The hardness of compounds can be determined more precisely by calculating shear modulus (G). B and G indicate the resistance to fracture and resistance to plastic deformation respectively. The results of B and G explain stiffness and compressibility of materials as given below [66]: = =
>> 0 6 >?
@
(v)
=
D
G
Where
D and
G
AB 0 AC
=
=
(vi)
6 >> . >? 0 @ EE
F
F EE ( >> . >? ) ; EE 0@( >> . >? )
(vii)
(viii)
represents Voigt and Reuss shear modulus respectively. To predict the nature
of material, the most favorable criteria are Pugh’s ratio (B/G). According to this empirical criterion, the material is ductile when the value of Pugh’s ratio is greater than 1.75. From the calculated results, it can be observed that CoYCrZ (Z = Si, Ge, Ga, Al) shows the ductile behavior. Cauchy pressure (CP) also determines the nature of material. The positive value of CP corresponds the ductility of the materials. CP = C56 − C;;
(ix)
Another mechanical parameter which demonstrates the stiffness of materials is Young’s Modulus (E). It determines the response of material to linear strain along edges. IJK
E = @J0K
(x)
If the value of E is higher, then the compound is stiffer. For CoYCrZ (Z = Si, Ge, Ga, Al) alloys, the highest value of E is observed for CoYCrSi and the least for CoYCrGe. The measure of compressibility is known as Poisson’s ratio (ν) which indicates the ratio of lateral to longitudinal strain with the range of 0.2 to 0.49. The materials having the value approximately 0.3 are less compressible and more stable against the exterior deformation. From Table 6, the value of ν is ~0.3 for CoYCrZ (Z = Si, Ge, Ga, Al) indicating that all these alloys are less compressible materials.
(@K.6J)
ν = 6(@K0J)
(xi)
From the results of mechanical properties, it can be concluded that all these considered CoYCrZ (Z = Si, Ge, Ga, Al) alloys are stable and have ductile nature. For practical point of view, the investigation of mechanical properties is very important. The information obtained from the elastic constants is relatively more important to explain the stability of materials. These alloys are reported for the first time and there is no theoretical or experimental data for elastic parameters for these CoYCrZ (Z = Si, Ge, Ga, Al) alloys is available. However, this work can provide the reference for future studies. 5. Conclusions In summary, 1st principles calculations are carried out to explore the structural, electronic, magnetic and mechanical properties of CoYCrZ (Z = Si, Ge, Ga, Al) Heusler alloys. It is observed from the structural optimization results that the most stable configuration is Type-II among all three types. Further calculation are carried out using optimized lattice parameters. The results of band structures are in accordance with the DOS plots which show complete SP. The majority spin band contains no gap, while in minority spin Fermi level lays in energy gap. The band structure plots showed that the nature of energy band gap is indirect in all these alloys. The origin of the band gap is located in the spin down channel which is due to the presence of strong d-d hybridization between TMs. The results of electronic properties revealed the existence of HM character in all these alloys. The energy band gaps of CoYCrSi, CoYCrGe, CoYCrGa, and CoYCrAl are 0.82, 0.86, 0.64, and 0.61 eV, while HM gaps are 0.215eV, 0.351eV, 0.415eV, and 0.40eV respectively. These materials have 100% SP and the calculated total MMs are in complete agreement with the Slater-Pauling rule
=
− 18. The total integer MMs are 3µ B
and 4 µ B for CoYCrAl, CoYCrGa and CoYCrSi, CoYCrGe respectively. In addition, DOS of CoYCrAl, CoYCrGa predicted that these materials may be the promising candidates for SGS by the addition of a suitable impurity. The calculations of mechanical parameters show that these materials are stable and have positive CP which showed its ductile nature. It can be concluded from calculations that these materials have high Curie temperature, HM gap, mechanically stable and are completely spin polarized. So, these are suitable candidates for spintronics application (MTJs and Spin valves) which will enhance the efficiency of these devices. Acknowledgement The authors are very grateful to Prof. Dr. Muhammad Arshad Choudhary for providing the fruitful discussion.
References 1.
Gao, Y. and X. Gao, The half-metallicity of LiMgPdSn-type quaternary Heusler alloys FeMnScZ (Z= Al, Ga, In): A first-principle study. AIP Advances, 2015. 5(5): p. 057157.
2.
Wolf, S., SA Wolf, DD Awschalom, RA Buhrman, JM Daughton, S. von Molnár, ML Roukes, AY Chtchelkanova, and DM Treger, Science 294, 1488 (2001). Science, 2001. 294: p. 1488.
3.
Julliere, M., Tunneling between ferromagnetic films. Physics letters A, 1975. 54(3): p. 225-226.
4.
Li, Y., et al., First-principles study on electronic structure, magnetism and halfmetallicity of the NbCoCrAl and NbRhCrAl compounds. Results in physics, 2017. 7: p. 2248-2254.
5.
Bahramian, S. and F. Ahmadian, Half-metallicity and magnetism of quaternary Heusler compounds CoRuTiZ (Z= Si, Ge, and Sn). Journal of Magnetism and Magnetic Materials, 2017. 424: p. 122-129.
6.
Koshi, N.A. and R. John, Half-Metallic Ferrimagnetism in CoFeNbZ (Z= Al, Si, Ge, Sn) Quaternary Heusler Alloys: a DFT Study. Journal of Superconductivity and Novel Magnetism, 2019. 32(4): p. 977-986.
7.
Wang, X., Proposal for a new class of materials: spin gapless semiconductors. Physical review letters, 2008. 100(15): p. 156404.
8.
Rasool, M.N., et al., Investigation of structural, electronic and magnetic properties of 1: 1: 1: 1 stoichiometric quaternary Heusler alloys YCoCrZ (Z= Si, Ge, Ga, Al): An abinitio study. Journal of Magnetism and Magnetic Materials, 2015. 395: p. 97-108.
9.
Pandey, B., R.B. Ray, and G.C. Kaphle, First-principles study of structural, electronic and magnetic properties of Co-based quaternary Heusler compounds: CoFeCrAl, CoFeTiAs, CoFeCrGa and CoMnVAs. BIBECHANA, 2018. 15: p. 50-59.
10.
Wang, X., et al., Origin of the half-metallic band-gap in newly designed quaternary Heusler compounds ZrVTiZ (Z= Al, Ga). RSC Advances, 2016. 6(62): p. 57041-57047.
11.
Bainsla, L. and K. Suresh, Equiatomic quaternary Heusler alloys: A material perspective for spintronic applications. Applied Physics Reviews, 2016. 3(3): p. 031101.
12.
Wang, X., et al., Structural, electronic, magnetic, half-metallic, mechanical, and thermodynamic properties of the quaternary Heusler compound FeCrRuSi: A firstprinciples study. Scientific reports, 2017. 7(1): p. 16183.
13.
Galanakis, I. and P. Mavropoulos, Zinc-blende compounds of transition elements with N, P, As, Sb, S, Se, and Te as half-metallic systems. Physical Review B, 2003. 67(10): p. 104417.
14.
Song, W., J. Wang, and Z. Wu, Half metallic properties of Sr2CuOsO6. Chemical Physics Letters, 2009. 482(4-6): p. 246-248.
15.
Xiong, L., L. Yi, and G. Gao, Search for half-metallic magnets with large half-metallic gaps in the quaternary Heusler alloys CoFeTiZ and CoFeVZ (Z= Al, Ga, Si, Ge, As, Sb). Journal of Magnetism and Magnetic Materials, 2014. 360: p. 98-103.
16.
Kervan, N., Half-metallicity in the full-Heusler Co2ScP compound: A density functional study. Journal of Magnetism and Magnetic Materials, 2012. 324(23): p. 4114-4117.
17.
Graf, T., C. Felser, and S.S. Parkin, Simple rules for the understanding of Heusler compounds. Progress in solid state chemistry, 2011. 39(1): p. 1-50.
18.
Bainsla, L., et al., High spin polarization in CoFeMnGe equiatomic quaternary Heusler alloy. Journal of Applied Physics, 2014. 116(20): p. 203902.
19.
Alijani, V., et al., Electronic, structural, and magnetic properties of the half-metallic ferromagnetic quaternary Heusler compounds CoFeMn Z (Z= Al, Ga, Si, Ge). Physical Review B, 2011. 84(22): p. 224416.
20.
Rani, D., et al., Experimental and theoretical investigation on the possible half-metallic behaviour of equiatomic quaternary Heusler alloys: CoRuMnGe and CoRuVZ (Z= Al, Ga). Journal of Magnetism and Magnetic Materials, 2019. 492: p. 165662.
21.
Şarlı, N., et al., Key role of central antimony in magnetization of Ni0. 5Co1. 5MnSb quaternary Heusler alloy revealed by comparison between theory and experiment. Physica B: Condensed Matter, 2019. 560: p. 46-50.
22.
Stephen, G.M., et al., Structural and electronic properties of the spin-filter material CrVTiAl with disorder. Journal of Applied Physics, 2019. 125(12): p. 123903.
23.
Venkateswara, Y., et al., Competing magnetic and spin-gapless semiconducting behavior in fully compensated ferrimagnetic CrVTiAl: Theory and experiment. Physical Review B, 2018. 97(5): p. 054407.
24.
Felser, C. and A. Hirohata, Heusler alloys. 2015: Springer.
25.
Kubota, T., et al., Half-metallicity and Gilbert damping constant in Co 2 Fe x Mn 1− x Si Heusler alloys depending on the film composition. Applied Physics Letters, 2009. 94(12): p. 122504.
26.
Saito, T., et al., Spin injection, transport, and detection at room temperature in a lateral spin transport device with Co2FeAl0. 5Si0. 5/n-GaAs schottky tunnel junctions. Applied Physics Express, 2013. 6(10): p. 103006.
27.
Ikhtiar, et al., Magneto-transport and microstructure of Co2Fe (Ga0. 5Ge0. 5)/Cu lateral spin valves prepared by top-down microfabrication process. Journal of Applied Physics, 2014. 115(17): p. 173912.
28.
Winterlik, J., et al., Design Scheme of New Tetragonal Heusler Compounds for Spin Transfer Torque Applications and its Experimental Realization. Advanced Materials, 2012. 24(47): p. 6283-6287.
29.
Bainsla, L., et al., Magnetic tunnel junctions with an equiatomic quaternary CoFeMnSi Heusler alloy electrode. Applied Physics Letters, 2018. 112(5): p. 052403.
30.
Luo, H., et al., Prediction of half-metallic properties for the Heusler alloys Mn2CrZ (Z= Al, Ga, Si, Ge, Sb): A first-principles study. Journal of Magnetism and Magnetic Materials, 2008. 320(3-4): p. 421-428.
31.
Ahmadian, F., Half-metallic ferromagnetism in the Ti 2 FeGe Heusler compound: A firstprinciples study. Journal of superconductivity and novel magnetism, 2013. 26(2): p. 381388.
32.
Kervan, S. and N. Kervan, Half-metallic properties of the CuHg2Ti-type Mn2ZnSi fullHeusler compound. Current Applied Physics, 2013. 13(1): p. 80-83.
33.
Gilleßen, M. and R. Dronskowski, A combinatorial study of inverse Heusler alloys by first principles computational methods. Journal of computational chemistry, 2010. 31(3): p. 612-619.
34.
Khodami, M. and F. Ahmadian, First-principles study of magnetism and half-metallic properties for the quaternary Heusler alloys CoMnTiZ (Z= P, As, and Sb). Journal of Superconductivity and Novel Magnetism, 2015. 28(10): p. 3027-3035.
35.
De Groot, R., et al., New class of materials: half-metallic ferromagnets. Physical Review Letters, 1983. 50(25): p. 2024.
36.
Ghimire, M., T. Sinha, and R. Thapa, First principles study of the electronic and magnetic properties of semi-Heusler alloys NiXSb (X= Ti, V, Cr and Mn). Journal of Alloys and Compounds, 2011. 509(41): p. 9742-9752.
37.
Gao, G., et al., Large half-metallic gaps in the quaternary Heusler alloys CoFeCrZ (Z= Al, Si, Ga, Ge): A first-principles study. Journal of Alloys and Compounds, 2013. 551: p. 539-543.
38.
Jin, Y., et al., Magnetism and electronic structure of CoFeCrX (X= Si, Ge) Heusler alloys. Journal of Applied Physics, 2016. 120(5): p. 053903.
39.
Arshad, H., et al., Theoretical study of structural, electronic and magnetic properties of equiatomic quaternary CoPdCrZ (Z= Si, Ge, P) Heusler alloys. Modern Physics Letters B, 2019: p. 1950389.
40.
Kundu, A., et al., New quaternary half-metallic ferromagnets with large Curie temperatures. Scientific reports, 2017. 7(1): p. 1803.
41.
Xie, H.-H., et al., First-principles study of four quaternary Heusler alloys ZrMnVZ and ZrCoFeZ (Z= Si, Ge). Computational Materials Science, 2015. 103: p. 52-55.
42.
Karimian, N. and F. Ahmadian, Electronic structure and half-metallicity of new quaternary Heusler alloys NiFeTiZ (Z= Si, P, Ge, and As). Solid State Communications, 2015. 223: p. 60-66.
43.
Zhang, Y., et al., Magnetism, band gap and stability of half-metallic property for the quaternary Heusler alloys CoFeTiZ (Z= Si, Ge, Sn). Journal of Alloys and Compounds, 2014. 616: p. 449-453.
44.
Berri, S., First-principles study on half-metallic properties of the CoMnCrSb quaternary Heusler compound. Journal of Superconductivity and Novel Magnetism, 2016. 29(5): p. 1309-1315.
45.
Klaer, P., et al., Element-specific magnetic moments and spin-resolved density of states in CoFeMn Z (Z= Al, Ga; Si, Ge). Physical Review B, 2011. 84(14): p. 144413.
46.
Bahnes, A., et al., Half-metallic ferromagnets behavior of a new quaternary Heusler alloys CoFeCrZ (Z= P, As and Sb): Ab-initio study. Journal of Alloys and Compounds, 2018. 731: p. 1208-1213.
47.
Benkabou, M., et al., Electronic structure and magnetic properties of quaternary Heusler alloys CoRhMnZ (Z= Al, Ga, Ge and Si) via first-principle calculations. Journal of Alloys and Compounds, 2015. 647: p. 276-286.
48.
Elahmar, M., et al., Structural, mechanical, electronic and magnetic properties of a new series of quaternary Heusler alloys CoFeMnZ (Z= Si, As, Sb): a first-principle study. Journal of Magnetism and Magnetic Materials, 2015. 393: p. 165-174.
49.
Benkaddour, K., et al., First-principles study of structural, elastic, thermodynamic, electronic and magnetic properties for the quaternary Heusler alloys CoRuFeZ (Z= Si, Ge, Sn). Journal of Alloys and Compounds, 2016. 687: p. 211-220.
50.
Chandra, A.R., et al., Electronic structure properties of new equiatomic CoCuMnZ (Z= In, Sn, Sb) quaternary Heusler alloys: An ab-initio study. Journal of Alloys and Compounds, 2018. 748: p. 298-304.
51.
Rani, D., et al., Structural, electronic, magnetic, and transport properties of the equiatomic quaternary Heusler alloy CoRhMnGe: Theory and experiment. Physical Review B, 2017. 96(18): p. 184404.
52.
Blaha, P., et al., wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties, 2001.
53.
Perdew, J., K. Burke, and M. Ernzerhof, Perdew, burke, and ernzerhof reply. Physical Review Letters, 1998. 80(4): p. 891.
54.
Singh, M., et al., Electronic structure, magnetism and robust half-metallicity of new quaternary Heusler alloy FeCrMnSb. Journal of Alloys and Compounds, 2013. 580: p. 201-204.
55.
Liu, H., et al., Influence of main-group element on half-metallic properties in halfHeusler compound. Modern Physics Letters B, 2016. 30(11): p. 1650206.
56.
Fang, C.M., G. De Wijs, and R. De Groot, Spin-polarization in half-metals. Journal of Applied Physics, 2002. 91(10): p. 8340-8344.
57.
Özdoğan, K., E. Şaşıoğlu, and I. Galanakis, Slater-Pauling behavior in LiMgPdSn-type multifunctional quaternary Heusler materials: Half-metallicity, spin-gapless and magnetic semiconductors. Journal of Applied Physics, 2013. 113(19): p. 193903.
58.
Xing, N., et al., First-principle prediction of half-metallic properties for the Heusler alloys V2YSb (Y= Cr, Mn, Fe, Co). Computational Materials Science, 2009. 45(2): p. 489-493.
59.
Rai, D., et al., A comparative study of a Heusler alloy Co2FeGe using LSDA and LSDA+ U. Physica B: Condensed Matter, 2012. 407(18): p. 3689-3693.
60.
Seema, K., M. Kaur, and R. Kumar, First Principles Study of Fe based Full Heusler Alloy. Journal of Integrated Science and Technology, 2013. 1(1): p. 41-43.
61.
Kandpal, H.C., G.H. Fecher, and C. Felser, Calculated electronic and magnetic properties of the half-metallic, transition metal based Heusler compounds. Journal of Physics D: Applied Physics, 2007. 40(6): p. 1507.
62.
Wurmehl, S., et al., Geometric, electronic, and magnetic structure of Co 2 FeSi: Curie temperature and magnetic moment measurements and calculations. Physical Review B, 2005. 72(18): p. 184434.
63.
Bhat, T.M. and D.C. Gupta, Magneto-electronic, thermal, and thermoelectric properties of some Co-based quaternary alloys. Journal of Physics and Chemistry of Solids, 2018. 112: p. 190-199.
64.
İyigör, A. and Ş. Uğur, Elastic and phonon properties of quaternary Heusler alloys CoFeCrZ (Z= Al, Si, Ga and Ge) from density functional theory. Philosophical Magazine Letters, 2014. 94(11): p. 708-715.
65.
Rahman, M.A., M.Z. Rahaman, and M.A. Rahman, The structural, elastic, electronic and optical properties of MgCu under pressure: A first-principles study. International Journal of Modern Physics B, 2016. 30(27): p. 1650199.
66.
Shakil, M., et al., Theoretical investigation of structural, magnetic and elastic properties of half Heusler LiCrZ (Z= P, As, Bi, Sb) alloys. Physica B: Condensed Matter, 2019. 575: p. 411677.
Table 1 Type
Co
Y
Cr
Z
Type-I
(0.75, 0.75, 0.75)
(0, 0, 0)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
Type-II
(0.75, 0.75, 0.75)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
(0, 0, 0)
Type-III
(0, 0, 0)
(0.5, 0.5, 0.5)
(0.25, 0.25, 0.25)
(0.75, 0.75, 0.75)
Table 2 (revised) Alloy
CoYCrSi
CoYCrGe
CoYCrGa
CoYCrAl
Type
Lattice parameter a( )
Optimized Volume (Vo) (a.u.^3)
Optimized energy
Bulk modulus
Eo (Ry)
(GPa)
Type-I
6.4234
447.1382
-12240. 223657
98.2262
Type-II
6.2904
419.9187
-12240. 235051
122.5199
Type-III
6.3676
435.5700
-12240. 168361
106.3269
Type-I
6.5206
467.7417
-15858. 330133
91.0994
Type-II
6.3669
435.4258
-15858. 334675
115.9462
Type-III
6.4594
454.6806
-15858. 282663
94.0628
Type-I
6.5146
466.4528
-15548. 369849
92.0549
Type-II
6.3735
436.7828
-15548. 394893
96.2258
Type-III
6.4799
459.0297
-15548.331313
74.0191
Type-I
6.5298
469.7084
-12145. 752410
86.2312
Type-II
6.3989
442.0324
-12145. 810531
95.4493
Type-III
6.4715
457.2540
-12145. 725586
83.9860
Optimized Type
Formation Energy Ef (Ry)
Type-II
-1.71505
Type-II
-1.62307
Type-II
-1.55189
Type-II
-1.638732
Table 3 Alloy
Mint(µB)
MCo(µB)
MY(µB)
MCr(µB)
MZ(µB)
Mtot(µB)
CoYCrAl
0.25309
-0.33773
0.03301
3.10459
-0.04740
3.00057
CoYCrGe
0.17759
0.63984
-0.01294
3.23609
-0.05067
3.99991
CoYCrGa
0.26349
-0.41224
0.04404
3.15511
-0.05004
3.00035
CoYCrSi
0.19384
0.73153
-0.00902
3.13917
-0.05569
3.99983
Table 4 Alloy
Fermi energy
Band gap (eV)
Half-Metallic gap (eV)
Nature
Location
CoYCrSi
0.66293
0.825
0.215
Indirect
Γ→X
CoYCrGe
0.64459
0.863
0.351
Indirect
Γ→∆
CoYCrGa
0.60090
0.645
0.645
Indirect
Γ→L
CoYCrAl
0.57674
0.610
0.40
Indirect
Γ→∆
Table 5 Alloy
Mtot(µB)
Number Slaterof Pauling valance rule electron magnetic s moment
(
(↑))
(
(↓))
Spin polarization
Curie Temperature (K)
CoYCrSi
3.00057
21
3
1.99
0
100%
566
CoYCrGe
3.99991
22
4
2.42
0
100%
747
CoYCrGa
3.00035
21
3
0.15
0
100%
566
CoYCrAl
3.99983
22
4
0.09
0
100%
747
Table 6
Parameters
CoYCrSi
CoYCrGe
CoYCrGa
CoYCrAl
149.7
133.9
128.5
136.7
85.9
88.3
88.2
79.5
43.4
41.8
51.8
52.7
107.17
103.5
101.6
98.6
42.5
46.5
36.4
26.8
0.34
0.35
0.34
0.32
166.46
151.28
155.92
164.61
38.8
34.2
39.14
43.06
37.9
31.35
31.8
39.41
38.35
32.78
35.47
41.24
2.79
3.15
2.86
2.39
Fig. 1
Fig. 2(revised)
Fig. 3 (revised)
CoYCrSi
Eg = 0.82eV
Fig. 4 (revised)
CoYCrGe
Eg= 0.86eV
Fig. 5 (revised)
CoYCrGa
Eg = 0.64eV
Fig. 6 (revised)
CoYCrAl
Eg = 0.61eV
Fig. 7 (revised)
(a)
(b)
(a)
(b)
Fig. 10
Highlights •
First principle study of EQHAs CoYCrZ (Z = Si, Ge, Ga, Al)
•
Calculations of structural stability, electronic, magnetic and elastic properties
•
Calculations for FM, AFM and Non-magnetic phases
•
Half metallic nature and high spin polarization
•
Analysis of the origin of band gap
Declaration of Interest It is stated that the work submitted have been performed by us and all authors have contributed. Furthermore, this work has not been submitted elsewhere partially or complete. Also, there is no ethical issue in any regard. Regards! Dr. M. Shakil et al.