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Spin-polarized electromagnetic and optical response of full-Heusler Co2VZ (Z = Al, Be) alloys for spintronic application

The European Physical Journal Plus volume 136, Article number: 1009 (2021) Cite this article

Abstract

Magnetic materials with high spin polarization emerge as a potential candidate in spintronic applications. The present work reports the theoretical investigation of spin-polarized electronic, structural, magnetic, and optical properties of full-Heusler Co2VZ (Z = Al, Be) alloys calculated with full-potential linearized augmented plane wave method implemented in WIEN2k code. The spin orbital coupling effect is employed, and the structures are optimized at their ground state and lattice constants and bulk moduli are calculated. A metallic behavior is observed in the majority spin carriers, and an n-type semiconducting behavior is observed in the minority spin carriers for both alloys with generalized gradient approximation. A band gap of 0.55 eV and 0.41 eV is observed in the minority spin carriers with modified Becke–Johnson (mBJ) exchange potential for Co2VAl and Co2VBe, respectively. It shows 100% spin polarization at Fermi level with mBJ potential and confirms the half metallic nature of these alloys. The structure stability is confirmed with phonon dispersion curves. The calculated magnetic moments show the major contribution of cobalt (Co) atoms in the overall magnetic behavior of both alloys. In addition, the optical parameters such as real and imaginary parts of dielectric function, refractive index, extension coefficients, optical conductivity, absorption coefficients and energy loss are also calculated. The existence of complete spin polarization endorses these alloys as a promising candidate for spintronic and opto-electronic devices.

Graphic abstract

Introduction

Ferromagnetic intermetallic alloys have gained much attention throughout the world due to the development in the fields of memory devices, magneto-electronics and spintronic including magneto-resistive random access memories, spin transistors, spin torque oscillators and spin valve generators [1,2,3,4]. A high spin-polarized current is required for the best performance of spintronic devices. For this purpose, half metallic magnetic materials have been of special interest as they can produce nearly full spin-polarized current [5,6,7]. Coexistence of semiconducting behavior in one spin channel and metallic character in the other spin channel results in 100% spin polarization which intensified the importance of half metallic materials specially the Heusler alloys [8, 9]. Heusler alloys have high Curie temperature and are easy to be synthesized. Although Heusler alloys with face centered cubic structure having a formula X2YZ (full-Heusler alloys) have been studied widely for element substitutions at atomic positions of X, Y and Z [10,11,12,13,14,15,16], there are still large possibilities to explore their properties by substituting different elements. There are also other types of Heusler alloys such as half-Heusler alloys (XYZ) and quaternary Heusler alloys (XXYZ). In all types of Heusler alloys, X, X2 and Y are 3d, 4d and 5d transition metals, while Z is sp non-magnet element from III, IV and V groups [17,18,19,20]. Magnetic and mechanical properties of Heusler alloys such as Ti2CoB, Ni2MnB, Co2NbB have been studied under pressure because of their high resistance to oxidation, hardness and high melting point [21,22,23]. Due to the high temperature stability, Heusler alloys are best possible candidates for temperature power generation and shape memory devices [24, 25].

In last few decades, transition metal-based Heusler alloys are broadly studied and, in particular, the Cobalt-based Heusler alloys are considerably attracted interest because of the large tunnel magnetoresistance such as Co2Cr0.6Fe0.4Si [26]. Rai et al. [27] reported a comprehensive study of magnetic, optical and electronic properties of cobalt-based Heusler alloys and their use in spintronic. A half metallic character along with ferromagnetism is observed in most Heusler materials. Many other such as Co2MnSi [28], CoMnTiAl [29], CoMnVAs [30], Co2MnZ (Z = Ge, Sn) [31], CoVTiAl [32], Co2FeZ (Z = Al, Ga, Ge, Si) [33], CoCuMnZ (Z = In, Sn, Sb) [34], CoZrIrSi [35], NbVMnAl and NbFeCrAl [36], CoFeCrZ (Z = P, As, Sb) [37], FeRhCrZ (Z = Si & Ge) [38] and YFeCrz (Al, Sb and Sn) [39] have been studied intensively and reported as half metallic alloys. Guezlane et al. [40] calculated the electronic structure of Co2CrxFe1−xX (X = Al, Si) which predicts the full-Heusler ternary compounds with half metallic character. Although, in the literature, various studies on Heusler alloys have been reported but the demand for spintronic devices is growing day by day that invokes the need to discover more alloys with superior characteristics. Therefore, in this work, we have explored the properties of full-Heusler Co2VAl alloy with improved results and also the newly designed full-Heusler Co2VBe alloy. Co2VZ (Z = Al, Be) are important members of Heusler alloys and belong to the space group \(Fm\overline{3 }m\). They have cubic structures. From the literature view, so far, no density functional theory (DFT)-based study has been conducted on Co2VBe alloy and the band gap of Co2VAl is underestimated. The present work includes a comprehensive study of ground-state electronic structure, magnetic and optical properties of full-Heusler Co2VZ (Z = Al, Be) alloys. Generalized gradient approximation (GGA) and modified Beck and Johnson (mBJ) potentials are implemented via WIEN2k code to explore the detailed properties of these alloys.

Computational details

Electronic structure, magnetic and optical properties of Co2VZ (Z = Al, Be) alloys are computed with full-potential linearized augmented plane wave (FP-LAPW) within the framework of DFT [41]. The spin-polarized calculations [42] within the DFT framework is a powerful tool to explain the itinerant electron’s magnetism in the materials. These calculations are useful to explain the occurrence of magnetism which is determined by a composition between exchange and kinetic energy effect. To accomplish the spin-polarized DFT calculations, WIEN2k simulation code is implemented [43]. For the calculation of self-consistent field electronic structure for the ground-state properties of solids, Kohn–Sham DFT [44] is widely used. The exchange correlation energy (\(E_{{{\text{XC}}}} = E_{{\text{X}}} + E_{{\text{C}}}\)) in Kohn–Sham DFT as a functional of electron spin densities must be approximated. For slow varying densities, the famous functional has appropriate form: the generalized gradient approximation (GGA).

$$ E_{{{\text{XC}}}}^{{{\text{LSD}}}} \left[ {n_{ \uparrow } , n_{ \downarrow } } \right] = \int d^{3} rf(n_{ \uparrow } , n_{ \downarrow } , \nabla n_{ \uparrow } , \nabla n_{ \downarrow } ) $$
(1)

where \(n_{ \uparrow } , n_{ \downarrow }\) are the electron spin densities.

The suitable exchange–correlation potential is solved with GGA of Perdew–Burke–Ernzerhof 96 [45, 46]. However, the application of GGA depends upon the studied solid and its property. The results obtained with GGA for the band gap of semiconductors and insulators are not in good agreement with experimental results, e.g., it severely underestimated band gap or sometimes even absent [47]. To solve this problem, a modified version of exchange potential called mBJ potential was proposed by Becke and Johnson [48]. The mBJ approximation uses both GGA exchange and correlation potentials and accurately calculates the total Hamiltonian of the system, which significantly improve the band gap accuracy comparable with experimental result [49]. The proposed mBJ potential is

$$ \upsilon_{\chi ,\sigma }^{{{\text{mBJ}}}} \left( r \right) = c\upsilon_{\chi ,\sigma }^{{{\text{BR}}}} \left( r \right) + \left( {3c - 2} \right)\frac{1}{\pi }\sqrt{\frac{5}{12}} \sqrt {\frac{{2t_{\sigma } \left( r \right)}}{{n_{\sigma } \left( r \right)}}} $$
(2)

where \(t_{\sigma }\) represents kinetic energy density and \(n_{\sigma }\) is the electron density and both spin-dependent, while \(\upsilon_{\chi ,\sigma }^{{{\text{BR}}}}\) is Becke–Roussel potential [50]. The parameter ‘c’ can be determined as:

$$ c = \alpha + \beta \left( {\frac{1}{{V_{{{\text{cell}}}} }}\mathop \int \limits_{{{\text{cell}}}} \frac{{\left| {\nabla_{n} \left( {r^{\prime}} \right)} \right|}}{{n\left( {r^{\prime}} \right)}}{\text{d}}^{3} r^{\prime}} \right)^{1/2} $$
(3)

where cell volume is Vcell. The parameters α and β are selected in the widespread scope of solids to fit band gap. Spin–orbit coupling (SOC) effect is very important while calculating the magnetic properties of the materials. Therefore, we have included the SOC effect in calculations by means of second variational method [51]. The Hamiltonian is expressed as

$$ H = - \frac{\hbar }{2m}\Delta^{2} + V_{{{\text{eff}}}} + H_{{{\text{SO}}}} $$
(4)

where \(H_{SO}\) is the spin–orbit Hamiltonian and is given as:

$$ H_{{{\text{SO}}}} = \frac{1}{{2{\text{Mc}}^{2} }}\frac{1}{{r^{2} }}\frac{{{\text{d}}V_{{{\text{MT}}}} }}{{{\text{d}}r}}\left( {\begin{array}{*{20}c} {\vec{\sigma }.\quad \vec{l} 0} \\ {0 \quad 0} \\ \end{array} } \right) $$
(5)

where \(\vec{\sigma }\) is the Pauli spin matrix.

The Wien2k is a very useful tool to calculate the physical properties of the materials. It has advantages on other available commercial codes in calculating the accurate properties [52, 53]. In our calculations, mBJ exchange potential is implemented with GGA correlation. The minimum selected values of RMT radii are Al = 2.06, V = 2.17 and Co = 2.28 for Co2VAl and Be = 1.81, V = 2.07 and Co = 2.18 for Co2VBe. In terms of crystal harmonics, the potential and charge density are expanded in the interstitial region as a Fourier series with wave vector up to Gmax = 12 a.u. The electron density and potential are expressed inside the muffin tin spheres with spherical harmonics [54] up to lmax = 10. The spherical plane wave cutoff Kmax ⨯ RMT = 7 is used. A number of 1000 K-points are used in the irreducible Brillion zone for more accurate results. The achieved self-consistency for energy is up to 10–5 Ry.

Structural properties

Full-Heusler alloys have the general composition of X2YZ with X atoms present at (0, 0, 0) and (1/2, 1/2, 1/2) positions, Y occupies (1/4, 1/4., 1/4) position, while Z is present at (3/4, 3/4, 3/4) position in Wyckoff coordinates. The crystal structure of both alloys is presented in Fig. 1.

Fig. 1
figure1

Crystal structure and energy–volume curves of Co2VAl and Co2VBe full-Heusler alloys in most stable atomic structures

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The unit cell of both structures has been optimized in non-magnetic (NM), anti-ferromagnetic (AFM) and ferromagnetic (FM) states to achieve the most stable atomic arrangement, stable magnetic state and optimized lattice constants. The optimization curves of both alloys are presented in Fig. 1. Minimum energy value on the parabolic curve shows the ground-state energy, and the volume corresponding to this energy is the ground-state volume. It can be seen that the non-magnetic and anti-ferromagnetic states are less stable than the ferromagnetic state in both alloys. Optimized lattice parameters are used for the calculation of properties. The formation energy is calculated to check the stability of the alloys. The formation energy of a compound is the difference between the energies of that compound and the stable phases of the elements.

$$ E_{{{\text{FE}}}} = E_{{{\text{Co}}_{2} {\text{VZ}}}} - 2E_{{{\text{Co}}_{2} }} - E_{{\text{V}}} - E_{{\text{z}}} $$
(6)

where \(E_{{{\text{Co}}_{2} {\text{VZ}}}}\) is the calculated equilibrium total energy of Co2VZ (Z = Al, Be) and \(E_{{{\text{Co}}_{2} }} ,E_{{\text{V}}} ,E_{{\text{z}}}\) are the energies per atom of the pure Co, V and Z (Z = Al, Be) in the bulk structures, respectively.

Table 1 shows the calculated values of lattice parameters \(a \left( {{\text{A}}^{0} } \right)\), bulk modulus B(GPa), pressure derivative of bulk modulus B’, equilibrium volume, ground-state energies \(E_{0} \left( {Ry} \right)\) and formation energies.

Table 1 Calculated lattice parameters, bulk modulus, pressure derivative of bulk modulus and ground-state energies
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To check the stability of Co2VAl and Co2VBe structures, we have also carried out the phonon dispersion calculations as shown in Fig. 2.

Fig. 2
figure2

Phonon dispersion curves of Co2VAl (a) and Co2VBe (b) structures

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For this purpose, we use the finite difference method to calculate the phonon spectra and analyzed it using the Phonopy code [59] with VASP [60] as a calculator. From the phonon dispersion calculation, it is confirmed that the both Co2VAl and Co2VBe structures are dynamically favorable due to no-imaginary modes, as shown in the figure. The calculated phonon band spectrum along the high symmetry directions (W-L- Г -X-W-K) of the Brillouin zone confirms the absence of imaginary frequency at Г-point, indicating the dynamical stability of the corresponding compounds, in analogy to AlGaX2 (X = As, Sb) [61], hBN [62] and many more [63,64,65]. Both Co2VAl and Co2VBe are composed of four atoms in a primitive unit cell, which corresponds to three acoustic branches and nine optical modes, as displayed in Fig. 2. There are no phonon gaps between optical phonon branches because of the slight mass difference between Co, V and Al/Be atoms, and the phonon frequency of Co2VAl is smaller than that of Co2VBe due to heavier Al atoms in the primitive cell.

Electronic and magnetic properties

The electronic structure of a material provides important information about the possible outcomes regarding the application point of view. The material’s efficiency for memory/smart/spintronic device applications is based upon the energy gap which provides a way to handle the required properties in a significant manner to meet the needs of modern day technologies. The band structure, total and partial density of states (DOS) are used to characterize the electronic behavior of the present Heusler alloys. The spin-polarized electronic band structure of Co2VZ (Z = Al, Be) for both majority spin (spin-up) and minority spin (spin-down) with greater symmetry points in the 1st Brillion zone is calculated with GGA and mBJ potentials and represented in Fig. 3.

Fig. 3
figure3

Calculated band structure for Co2VAl and Co2VBe alloys with GGA and mBJ potentials

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No band gap is observed with GGA potential (Fig. 3a, c) for the majority (spin-up) channels, while an n-type semiconductor behavior is observed (Fig. 3a, c) in the minority (spin-down) spin channels with a band gap of 0.37 eV and 0.16 eV for Co2VAl and Co2VBe, respectively. The calculation of energy-band can be misinterpreted with GGA potential. The band gap width can be improved by the use of an exchange potential called modified Backe–Johnson (mBJ) potential [49]. The half metallic character of compounds can be precisely described with mBJ rather than with GGA potential. In the case of mBJ potential (Fig. 3b, d), a conducting behavior is observed in majority spin, while an indirect (Г − X) band gap is observed in the minority spin which confirms a semiconductor behavior at the Fermi level for the minority spin of both alloys. The calculated band gap values with mBJ potential are 0.55 eV and 0.41 eV for Co2VAl and Co2VBe, respectively. This reveals that both alloys are half metallic in nature. The reason for the low band gap in the case of Be as compared to Al is that the atomic number of Be (4) is less than the atomic number of Al (13). When we replace atom from high atomic numbers to lower ones, the band gap decreases because of the lower atomic number. The half metallic nature is usually described with half metallic gap which is also known as the spin flip gap, and it measures the required energy to move the minority spin electrons to the Fermi level of majority spin electrons. From the practical perspective, compounds with half spin gap are highly desired. A comparison of calculated values of band gap is given in Table 2.

Table 2 Calculated band gap of Co2VAl and Co2VBe with mBJ potential
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In the case of Co2VAl, a maximum value of band gap is obtained as compared to the available literature, while there is no literature available in the case of for Co2VBe.

Along with the band structure, spin-polarized total densities of states (DOS) and partial densities of states (pDOS) are calculated for the complete description of full-Heusler alloys. The magnetic properties at the Fermi level are revealed with the distribution of total and partial DOS. Figure 4 represents the total DOS as a function of energy for Co2VZ (Z = Al, Be) alloys with GGA and mBJ potentials. The results of total DOS are comparable with the band structure.

Fig. 4
figure4

Total spin-polarized density of states in Co2VZ (Z = Al, Be) alloys with GGA and mBJ potentials

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The contribution of different states in the electronic structure is illustrated through partial density of states (pDOS) and represented in Fig. 5. It can be seen that the p-states of Al/Be show their contribution in conduction band in both spin-up and spin-down channel. The d−eg \({{(d}_{\mathrm{z}}^{2}, d}_{{x}^{2}-{y}^{2}})\) states of transition elements have their contribution in conduction and valance band in both spin channels but their contribution is small as compared to the d−t2g \({(d}_{\mathrm{xy}},{d}_{\mathrm{yz}},{d}_{\mathrm{xz}})\) states of transition elements. The d−t2g has major contribution in valance band in both spin channels and conduction band of spin-down channel. The Fermi level split in spin-down channel with mBJ potential which shows its consistence with the band structure results. The density of states around the Fermi level are generated by the d-d states of transition elements (Co/V), and it plays a major role in forming an energy gap in minority spin channel.

Fig. 5
figure5

Spin-polarized partial density of states in Co2VZ (Z = Al, Be) alloys with GGA and mBJ potentials

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Total and local magnetic moments of full-Heusler Co2VZ (Z = Al, Be) alloys are calculated and summarized in Table 3. In the case of both alloys, Co shows main contribution for large exchange splitting of 3d states and the maximum spin polarization at Fermi level with both GGA and mBJ potentials. At the same time, V atoms in both alloys show small magnetic moments and have small contribution toward magnetism in the alloys. The participation of Al and Be is negligibly small in the magnetism and can be easily neglected. The total magnetic moment values of Co2VAl are 1.998 and 2.007 μB with GGA and mBJ potentials, respectively. The calculated results of Co2VAl are also compared with the other results from the literature. The total magnetic moment values of Co2VBe are 0.997 and 1.004 μB with GGA and mBJ potentials, respectively. The overall magnetic moment values and band structure profile show that the studied alloys have half metallic ferromagnetism.

Table 3 Calculated total and partial magnetic moments of Co2VAl and Co2VBe with GGA and mBJ potentials
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The bonding nature along their constituent atoms is defined with the spin-polarized electron density plots along (110) planes for both Co2VAl and Co2VBe alloys and represented in Fig. 6. Figure 6a shows the localized charge distribution between Al, Co and V atoms which is the prediction of ionic bonding between these atoms for both spin-up and spin-down states. As Al and Be both have electronegativity difference, they show a slight difference in topology and charge transfer among atoms. Figure 6b shows a weak covalent bond between valance electrons of cobalt and beryllium. Hence, the Co2VBe alloy is neither covalent nor ionic but exhibits a mixing behavior of both in both spin-up and spin-down states. The change in the shape of Co from spherical (spin-up) to dumbbell (spin-down) states for both alloys is possibly due to the transition of electrons from almost filled to incomplete filled d bands.

Fig. 6
figure6

Spin-polarized electron charge densities of Co2VZ (Z = Al, Be) alloys along 110 plane

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Optical properties

The interaction of materials with light predict their optical properties. To study the optical properties of full-Heusler Co2VZ (Z = Al, Be) alloys, optical parameters such as real and imaginary parts of dielectric function (\(\varepsilon_{1} \left( \omega \right), \varepsilon_{2} \left( \omega \right)\)), optical conductivity (σ(ω)), absorption coefficient (α(ω)), extinction coefficient (K(ω)), energy loss (L(ω)) and refractive index (n(ω)) as a function of photon energy are calculated. The dielectric function is described as

$$ \varepsilon \left( \omega \right) = \varepsilon_{1} \left( \omega \right) + i\varepsilon_{2} \left( \omega \right) $$
(7)

where \(\varepsilon_{1} \left( \omega \right)\) is the real and \(\varepsilon_{2} \left( \omega \right)\) is the imaginary part of dielectric function. The following Kramer–Kroning equations are used to determine the real and imaginary parts of complex dielectric functions.

$$ \varepsilon_{1} \left( \omega \right) = 1 + \frac{2}{\pi }P\mathop \int \limits_{0}^{\infty } \frac{{\omega^{\prime } \varepsilon_{2} \left( {\omega^{\prime } } \right)}}{{\omega^{\prime 2} - \omega^{2} }}{\text{d}}\omega^{\prime } $$
(8)
$$ \varepsilon_{2} \left( \omega \right) = \frac{8}{{2\pi \omega^{2} }}\mathop \sum \limits_{{nn^{\prime}}}^{{}} \left| {P_{{nn^{\prime}}} } \right|^{2} \frac{{dS_{k} }}{{\nabla \omega_{{nn^{\prime}}} \left( k \right)}} $$
(9)

The real part \(\varepsilon_{1} \left( \omega \right)\) is associated with anomalous dispersion and polarization while the imaginary part \(\varepsilon_{2} \left( \omega \right)\) is related to the energy loss in the medium. Real and imaginary parts of dielectric functions for both Co2VAl and Co2VBe are shown in Fig. 7. The set energy range is 0–14 eV for both alloys. The static function \(\varepsilon_{1} \left( 0 \right)\) values of the real part are 52.6 and 45.7 eV for Co2VAl alloy (Fig. 7a) and 71.7 and 64.6 eV for Co2VBe alloy (Fig. 7c) with GGA and mBJ potentials, respectively. The first maximum peak value for Co2VAl is observed between 0 and 0.3 eV potential, while the second peak is observed between 1.70 and 1.75 eV for the respective potentials. In the case of Co2VBe, the peaks are observed between 0–0.31 eV and 1.71–1.82 eV for both potentials. Interband transition of top most valance electrons to the bottom of conduction band is responsible for these peaks [72]. A further increase in the energy results in the decrease in the peaks, and negative values are reached at 2.2 and 2.4 eV for Co2VAl and Co2VBe, respectively. The internal structure of material and its absorptive behavior can be determined with the imaginary part \(\varepsilon_{2} \left( \omega \right)\) of dielectric function. In the case of Co2VAl, the imaginary plots (Fig. 7b) have two sharp peaks at 0.64 and 2.0 eV with GGA, 0.6 and 2.1 eV with mBJ potential. For Co2VBe (Fig. 7d), the \(\varepsilon_{2} \left( \omega \right)\) plots also have two sharp peaks at 0.74 and 2.1 eV with GGA, 0.5 and 2.07 eV with mBJ potential. The accurate knowledge of real \(\varepsilon_{1} \left( \omega \right)\) and imaginary \(\varepsilon_{2} \left( \omega \right)\) parts helps in computing the necessary optical properties such as absorption coefficient, optical conductivity, extension coefficient, refractive index and energy loss. The imaginary part \(\varepsilon_{2} \left( \omega \right)\) peaks (both alloys) distribute in a sequence similar to that of density of states (Fig. 4, 5). As the photon energy increases, the transition from valance (mostly d-orbitals) to conduction band occurs (p and d-orbitals) represented by first peak for both alloys. The second peak also corresponds to such transitions. The next peaks might be owing to the transition from s and d-orbitals of Be and Al. The contribution in the optical parameters is due to the majority spin states more than that of minority spin states.

Fig. 7
figure7

The real \(\varepsilon_{1} \left( \omega \right)\) (a, c) and imaginary \(\varepsilon_{2} \left( \omega \right)\) (b, d) parts of dielectric functions as a function of energy for Co2VAl and Co2VBe alloys with GGA and mBJ potentials

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The amount of light reflecting from the interface can be determined with the refractive index which is considered to be very important optical property. The critical angle in optical devices such as wave guides, photonic crystal and solar cells can also be determined with refractive index. The refractive index and extension coefficient for Co2VAl and Co2VBe alloys are presented in Fig. 8. Figure 8a, b shows the refractive index as a function of energy for both alloys. Interestingly, the refractive index has the same pattern as the real part of dielectric function. The static frequency \(n\left( 0 \right)\) is observed at 7.3 and 6.9 for Co2VAl with GGA and mBJ, respectively. For Co2VBe, the static values are observed at 8.5 and 8.1 with GGA and mBJ potentials.

Fig. 8
figure8

Calculated refractive index (a, b) and extension coefficient (c, d) for Co2VAl and Co2VBe alloys as a function of energy with GGA and mBJ potentials, respectively

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As a band gap is observed with mBJ potential (Fig. 3) for both alloys, \(n\left( 0 \right)\) is relatively small for mBJ potential which shows an inverse relation between band gap and \(n\left( 0 \right)\). The refractive index \(n\left( \omega \right)\) values show a nonlinear decrease with the increase in the energy. The extension coefficient \(K\left( \omega \right)\) is the imaginary part of refractive index \(n\left( \omega \right)\). It acts in analogous way as imaginary part of dielectric function \(\varepsilon_{2} \left( \omega \right)\) and represents absorbed radiation. The threshold energy of extension coefficient \(K\left( \omega \right)\) is 0 eV for both alloys with GGA potential, while with mBJ is 0.18 eV for Co2VAl and 0.15 eV for Co2VBe as shown in Fig. 8c, d. With a further increase in the energy, \(K\left( \omega \right)\) values start increasing and reach at maximum of 4.54 at 2.24 eV with GGA and 4.91 at 2.18 eV with mBJ potential for Co2VAl alloy. In the case of Co2VBe alloy, \(K\left( \omega \right)\) has maximum peak of 5.02 at 2.27 eV with GGA and 4.76 at 2.37 eV with mBJ potential. The high peak means the maximum absorption, and a significant decrease is observed with the further increase in energy.

The current density produced due to the incident photon with certain frequency is described with optical conductivity. The optical conductivity as a function of energy for both alloys is shown in Fig. 9a, b. The critical values started at 0.13 and 0.17 for Co2VAl with GGA and mBJ potentials, respectively. For Co2VBe, it started at 0.09 and 0.13 with GGA and mBJ potentials, respectively. A considerable increase in optical conductivity is observed with the further increase in energy. The maximum values of optical conductivity for Co2VAl are 13,587.06 at 2.03 eV and 15,437.81 at 2.12 eV with GGA and mBJ potentials, respectively. For Co2VBe, the maximum values are 15,819.43 at 2.15 eV and 17,131.69 at 2.35 eV with GGA and mBJ potentials, respectively.

Fig. 9
figure9

Calculated optical conductivity (a, b) and absorption coefficient (c, d) for Co2VAl and Co2VBe alloys as a function of energy with GGA and mBJ potentials, respectively

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When the incident photon travels the unit length of a material, then the percentage decay of photon intensity is described with absorption coefficient \(\alpha \left( \omega \right)\). The spectra of \(\alpha \left( \omega \right)\) for both alloys are shown in Fig. 9c, d. It can be seen that the absorption coefficient shows a nonlinear increase with the increase in energy for both alloys. This abrupt increase in \(\alpha \left( \omega \right)\) shows maximum absorption of incident radiation. It is the property of semiconductors to absorb photons. After the absorption, these photons excite and shift the electrons from valance to the conduction band. The absorption coefficient is assigned referring to the imaginary part \(\varepsilon_{2} \left( \omega \right)\) (Fig. 7). The major absorption peaks are mainly due to the transition of from different valence band orbitals to different conduction band orbitals or higher empty orbitals.

Figure 10a, b represents the energy loss as a function of energy for Co2VAl and Co2VBe alloys. When fast moving electrons travel through the material, they loss energy that is given by energy loss function. Several peaks are observed for both alloys. The maximum values are observed at 11.84 and 12.03 eV for Co2VAl with GGA and mBJ potentials, respectively. For Co2VBe, the maximum peaks are at 8.22 and 8.10 eV with GGA and mBJ potentials, respectively.

Fig. 10
figure10

The energy loss as a function of energy for Co2VAl (a) and Co2VBe (b) alloys with GGA and mBJ potentials, respectively

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Conclusion

We have reported the magnetic and physical properties of full-Heusler Co2VZ (Z = Al, Be) alloys under the DFT framework via wien2k code. With spin–orbit coupling effect, the electronic properties reveal an n-type semiconducting response with GGA potential, while a half metallic behavior is observed with mBJ exchange potential. An indirect band gap of 0.55 and 0.41 eV between the points Г and X is observed with mBJ potential for Co2VAl and Co2VBe, respectively. The density of states shows a good agreement with the band structures of both alloys. The stability of the structures is achieved with formation energy and phonon dispersion curves. The total calculated magnetic moments are 2.007 and 1.004 μB with mBJ potential for Co2VAl and Co2VBe, respectively. The calculated formation energies show that these alloys can be synthesized. The optical parameters are also calculated which shows their availability as a possible candidate in optoelectronic devices. Based on the above-calculated properties, we can recommend Co2VZ (Z = Al, Be) alloys for spintronic and optoelectronic applications.

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Affiliations

  1. Department of Physics, Riphah International University, Lahore, Pakistan

    Junaid Munir, Muhammad Jamil, Kaneez Fatima & Hamid Ullah

  2. Physics Department, Science College, Al-Muthanna University, Samawh, 66001, Iraq

    Ahmed S. Jbara

  3. Department of Physics, University of Management and Technology, Lahore, Pakistan

    Quratul Ain

  4. Department of Physics, University of Education, Lahore, Pakistan

    Masood Yousaf

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  1. Junaid Munir
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Munir, J., Jamil, M., Jbara, A.S. et al. Spin-polarized electromagnetic and optical response of full-Heusler Co2VZ (Z = Al, Be) alloys for spintronic application. Eur. Phys. J. Plus 136, 1009 (2021). https://doi.org/10.1140/epjp/s13360-021-01968-x

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