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Half-metallic ferromagnetism and optical behavior in alkaline-earth metals based Beryllium perovskites: DFT calculations
Chemical Physics Letters 729 (2019) 11–16
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Half-metallic ferromagnetism and optical behavior in alkaline-earth metals based Beryllium perovskites: DFT calculations
T
⁎
Q. Mahmooda, , M. Hassanb, M. Yaseenc, A. Larefd a
Department of Physics, Faculty of Science, Imam Abdulrahman bin Faisal University, P.O. 383, Dammam 31113, Saudi Arabia Material Growth and Simulation Laboratory, Department of Physics, Quaid-e-Azam Campus, University of the Punjab, Lahore 54000, Pakistan c Department of Physics, University of Agriculture, Faisalabad 38040, Pakistan d Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia b
H I GH L IG H T S
structural, mechanical and thermodynamic stability ofperovskites. • The temperature ferromagnetism. • Room metallic ferromagnets with hundred percent spin polarization. • Half mechanism exceed the exchange energy than crystal field energy. • Exchange • The cause of ferromagnetism is spin of electron rather than clustering effect.
A R T I C LE I N FO
A B S T R A C T
Keywords: Spintronic Half metallic ferromagnetism (HMF) Spin polarization Curie temperature Double exchange mechanism
We investigate the Half-metallic ferromagnetism and optical behaviors of XBeO3 (X = Mg, Ca, Sr and Ba) using full-potential linearized augmented plane-wave method. The structural and thermodynamic stabilities are elucidated in terms of the calculated tolerance factor and enthalpy of formation, respectively. The room temperature (RT) ferromagnetism is shown by computing the Curie temperature and spin polarization. The strong hybridization between p-states of alkaline earth metals and 2p-states of oxygen near the Fermi level results total magnetic moment of 2μB. The ferromagnetism occurs due to holes those result in the exchange interactions between the p-states of alkaline earth metals and oxygen. The potential optical applications are also suggested by computing the dielectric constant and refraction.
1. Introduction The recent technological advancements have introduced half-metallic (HM) ferromagnets that have revolutionized the spintronic devices such as magnetic sensors, giant (GMR) and tunnel (TMR) magnetoresistance [1–4]. The half-metallic ferromagnets have one semiconducting spin channel, while other channel is metallic and exhibit 100% spin polarization at Fermi level [5–7]. The HM ferromagnets were firstly described by de Groot et al. (1983) for NiMnSb and PtMnSb Heusler alloys [8], later on, a variety of materials like transition-metal doped oxides, spinels, zincblende transition-metal chalcogenides, perovskites and other spin orientated materials were investigated to observe HM ferromagnetism [9–15]. The major limitations for practical applications of spintronic devices appear due to the lack of room temperature ferromagnetism (RTFM) and real factors stabilizing the
⁎
ferromagnetism. In the last decades, RTFM has been reported in various kinds of compound e.g. BaTiO3 [16], double perovskites Sr2FeMoO6 (400 k) [17], doped perovskites Bi0.5Na0.5TiO3 [18], transition-metals doped II-VI alloys ZnS/Se/Te [19,20], Cr doped GaN and AlN [21], transition-metals doped ZnO [22], In2O4 [23–25], TiO2 [26] etc. The real origin of ferromagnetism, either intrinsic exchange mediated or due to the clustering of transition-metals, is still in doubts. Although transition-metals doped compounds should form ordered alloys [27,28], but RTFM has been reported due to either transition-metal clusters or secondary phases [29–32]. To avoid such clustering of the magnetic impurities, doping with nonmagnetic elements has been carried for different nonmagnetic compounds, however, still ferromagnetism appears. For example, Mg, Al, Li and N doped ZnO [33], Mg doped SnO2 [34], C doped TiO2, ZnO, CdS and ZnS [35–38], nanoribbons and nonsheets of BeO [39], alkali based half-Heusler alloys XSrB
Corresponding author. E-mail address: [email protected] (Q. Mahmood).
https://doi.org/10.1016/j.cplett.2019.05.011 Received 21 March 2019; Received in revised form 30 April 2019; Accepted 7 May 2019 Available online 08 May 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Chemical Physics Letters 729 (2019) 11–16
Q. Mahmood, et al.
(X = Alkali metals) [40], B, C and N doped BeO [41] and Ca, Ti, N and C doped oxides [42–44] induce ferromagnetism. Therefore, ferromagnetism resulting due to nonmagnetic doping of nonmagnetic compounds clarifies the role of clustering and reveals the presence of exchange interactions. As is evident in the above discussion, HM ferromagnetism in the cubic nonmagnetic perovskite oxides could be attractive to explore because these have simple crystalline structure and are of low-cost. In the present report, full-potential linearized augmented planewave (FP-LAPW) method is employed using Wien2k software to find the electronic structure, HM ferromagnetism and the optical behavior of alkaline-earth metal based beryllium perovskites XBeO3 (X = Mg, Ca, Sr and Ba). The HM ferromagnetism is holes-mediated (evident from the electronic band structures) due to the exchange interactions and sp-hybridization and paramagnetic nature of oxygen. The magnetic moment computed for 1 × 1 × 1 super cell is 2.00 μB and 100% spin polarization has been observed. The existing literature about alkalineearth metals based perovskites is limited. However, the presented computed results may provide deep insight for the experimentalists to understand such unusual ferromagnetism.
Table 1 The lattice constant ao(Å), Bulk modulus Bo(Gpa), Enthalpy of formation Hf (eV), Tolerance factor t (2G), Curie temperature (Tc), electron density at Fermi level for up spin channel N↑ (EF ) , electron density at Fermi level for down spin channel, Polarization (P), Band gap Egup-gdn (eV), Half metallic gap EHM (eV), total magnetic moment Mtot (µB), and partial magnetic moments of MgBeO3, CaBeO3, SrBeO3, and BaBeO3calculated by GGA approximation. Properties
MgBeO3
CaBeO3 a
3.58 (3.61 ) 151.13 −2.40 (2.41a) 0.97 290 0
SrBeO3
BaBeO3
3.67 141.01 −2.15 0.98 281 0
3.81 122.55 −1.85 1.03 277 0
ao(Å) Bo(Gpa) Hf (eV) t2G Tc(k) N↑ (EF )
3.46 157.86 −2.45 0.95 295 0
N↓ (EF ) P Egup-gdn (eV), EHM (eV), Mtot (µB) MX(µB) MO (µB) MBe (µB) MInt (µB)
1.28
1.04
0.91
0.84
1 1.19 0.003 2.00 −0.036 1.413 −0.127 0.750
1 1.17 0.10 2.00 (1.99a) −0.047 1.53 −0.267 0.784
1 1.15 0.28 2.00 −0.068 1.582 −0.390 0.866
1 1.07 0.31 2.00 −0.075 1.656 −0.456 0.875
2. Method of calculations a
Ref. [54].
The calculations have been performed using FP-LAPW method as incorporated in Wien2k code [45]. The relaxed cubic structures of XBeO3 (X = Mg, Ca, Sr and Ba) are optimized for observing the lattice constants using generalized gradient approximation (GGA) [46]. The exchange correlation potential is worked out using surface charge density and its derivative at muffin-tin sphere where plane-wave solution is taken as spherical harmonic type. All relativistic effects are considered during computations. The product KmaxxRmin is taken as 8. Where Kmax is length of the maximum wave-vector (in reciprocal lattice) and Rmin is minimum muffin-tin radius. The angular momentum vector and Gaussian parameter are set as ℓmax = 10 and Gmax = 16, respectively. The k-mesh 12 × 12 × 12 has been taken for first Brillionzone integration. The released energy by varying the k-mesh remains invariant, which shows accuracy of calculations. Moreover, the selfconsistency set between the successive iterations is lower than 1 × 10−4 Ry. 3. Results and discussions
Fig. 1. (a) The optimized plots of MgBeO3, CaBeO3, SrBeO3 and BaBeO3 in the FM state done using GGA approximation (b) Crystal Structure designed by Xcrysden.
3.1. Structure stability and electronic properties The relaxed structures of MgBeO3 (MBO), CaBeO3 (CBO), SrBeO3 (SBO) and BaBeO3 (BBO) are optimized in ferromagnetic (FM) and antiferromagnetic (AFM) states. The positive energy difference (ΔE = EAFM − EFM) evidences that all compounds exhibit relatively more stable FM state, as shown in Table 1 (similar to that in Ref. [47]). For the sake of simplicity, we have only plotted the optimized graphs in FM state as shown in Fig. 1a. The optimized plots reveal increasing unit cell volume from MBO to BBO, due to which, lattice constant also improves, as shown in Table 1. The optimized cubic structure (2 × 1 × 1 supercell) with space group: Pm3m (2 2 1) is also shown in Fig. 1b. The Be atom is surrounded by oxygen ions due the formation of octahedron (BeO6), while alkaline-earth elements (Mg, Ca, Sr, Ba) occupy the edges. The thermodynamic and structural stabilities for the FM state are depicted by computing the enthalpy of formations and tolerance factors (see Table 1). The enthalpy of formation (Hf) has been elucidated from the energy difference between the compounds and the constituent elements using the expression ΔHf = ETotal (Xl Bem On ) − l EX − mEBe − nEO . Where, ETotal (Xl Bem On ) is the energy released by compound, while, EX , EBe and EO are the energies released by the lattices of X (Mg, Ca, Sr, Ba), Be and O, respectively. The l, m, n subscripts express number of atoms for the respective elemental unit cells [48]. The negative enthalpy of formations suggests stable FM state. The
Goldsmith’s tolerance factor [49] has been calculated, to show structural stability of the cubic phase, using tG = rX + rO/ rBe + rO , where rX , rBe and rO are the atomic radii of X, Be and O atoms, respectively. Higher deviations of the tolerance factor (tG) from unity are directly linked with the structural instability of the cubic perovskites, however, tG in the range of 0.93–1.04 illustrates structural stability. Therefore, the calculated tG values, as presented in the Table 1, elucidate structural stability. 3.2. Curie temperature and magnetic behavior The structural stability decreases from MBO to BBO because incompatibility between the ionic radii rises. After verifications of the structural and thermodynamic stabilities in the FM state, the knowledge of Curie temperature (TC) becomes important because it illustrates the maximum thermal energy up to which the FM state can sustain. The Curie temperatures are estimated using Heisenberg model, Tc = 2ΔE /3xKB , where ΔE shows energy difference between AFM and FM states and KB is Boltzmann constant [50,51]. The calculated values, presented in Table 1, reveal that MBO has TC approaching to room temperature (RT), which decreases from MBO to BBO because of ionic 12
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Q. Mahmood, et al.
Fig. 2. The electronic band structures of (a) MgBeO3, (b) CaBeO3, (c) SrBeO3 and (d) BaBeO3 in FM state calculated using GGA approximation.
holes in the majority spin channel. A wider HM gap (0.31 eV) suggests BBO as suitable HM ferromagnet for potential spintronic applications. The origin of ferromagnetism is exposed by computing the total density of states (TDOS) for XBeO3, as plotted in Fig. 3a, while the local density of states are shown in Fig. 3b. As evident from the computed band structures, TDOS also reveal HM ferromagnetic nature. To deeply understand the nature of interaction between the local/partial density of states, 2p-Mg, 3p-Ca, 4p-Sr, 5p-Ba and 2p-O states have been computed, which illustrate a strong exchange interaction near Fermi energy level in majority channel (↑), while states cross Fermi level in minority channel (↓) (similar to that in the Ref. [34]). The states around 1 eV above Fermi level belong to alkaline-earth metals and oxygen those form a tetrahedron. Therefore, accepter levels above Fermi level demonstrate holes mediated ferromagnetism. The hybridization of 2p-Mg, 3p-Ca, 4p-Sr, 5p-Ba and 2p-O states around Fermi level splits the energy states resulting a downward shift of the majority spin states to induce half metallic gap, while such a splitting shifts the minority spin states upward. Hence, overall energy reduces, while p-p exchange interaction is the major cause for the observed ferromagnetism. Furthermore, the energy states 2s-Be also hybridize slightly with 2p-O states and p-states of X elements within −3 eV to −6 eV, however, 2s-Be state appear away from Fermi level, as evident from Fig. 3b. In addition, the spin-up and down bands are fully and partially filled, respectively. The number of holes is equivalent to the total magnetic moment per unit cell i.e. 2μB [35]. The total and partial magnetic moments are also computed, as evident in Table 1. The manufacturing of the total magnetic moment primarily due to oxygen ions, while nearest neighbor alkaline-earth metals and Be atoms also have limited contributions. The magnetic moment of X ions and oxygen align parallel (exhibiting a FM interaction), while the magnetic moment is Be is aligned opposite to that of the oxygen ion (revealing AFM interaction). The Fig. 3b shows that FM coupling dominates the AFM coupling, and hence, FM nature of the studied compounds is evident. Various mechanisms exist to justify the ferromagnetism in diluted magnetic semiconductors (DMS) and half-metallic ferromagnets (HMF) [43,55–59]. In XBeO3 perovskites, carrier mediated mechanism mainly causes ferromagnetism. The electronic properties reveal that holes are induced due to the hybridization between the p-states of X and oxygen, and hence, position of p-states of alkaline earth metals (X) stabilizes a specific strength of ferromagnetism. Hence, the presence of free holes and interaction between the p-states may stabilize ferromagnetism due
radii mismatch between cations and anions increases that modifies the structural arrangement of constituent atoms. The compounds exhibit 100% spin-polarization at Fermi level (EF) because the majority spin channels have Fermi levels inside the band gap and minority spin channels have Fermi level at valence band edges. The polarization at Fermi level is calculated using the relation:
P=
N↑ (EF ) − N↓ (EF ) N↑ (EF ) + N↓ (EF )
Here, N↑ (EF ) and N↓ (EF ) express density of states of majority and minority spin channels at Fermi level, respectively [52]. The calculated density of states at Fermi level, for majority and minority spin channels, as well as the spin polarization are presented in Table 1. The description of ferromagnetism is presented in terms of the calculated band structures (BS), which are plotted in Fig. 2(a–d). The majority spin channels (↑) show that conduction band minima (CBM) and valence band maxima (VBM) appear at Г-point and R-point, respectively, for MBO, CBO and SBO (i.e. indirect band gap nature). While both lie at Г-point for BBO (i.e. direct band gap nature). On the other hand, the minority spin channel (↓) shows Fermi level crossing the valence states that reveal the metallic type behavior induced by the holes as free carriers. Hence, both spin channels of all four compounds collectively exhibit half metallic ferromagnetic (HMF) response [34,53]. Furthermore, the asymmetry between both channels is a direct evidence of the presence of exchange interactions. The exchange interaction energy has been deduced by separately calculating the energy differences between VBM and CBM for majority (↑) (Egup) and minority spin channels (↓)(Egdn). The difference between both terms Egup − Egdn shows the exchange interaction energy for each compound [54], which is shown in Table 1 and it decreases from MBO to BBO that is resulted due to the addition of more shells that modify the states distribution to cause the decaying exchange energy. The half metallic (HM) gap or the spin flip gap is determined from the energy difference between VBM and Fermi level (zero energy) that expresses the minimum energy required to flip a majority (minority) spin from top of the occupied valence to the Fermi level [53]. The HM gap, as given in Table 1, increases from MBO to BBO because oxygen 2p-states interact with p-states of alkaline-earth metals resulting the valence band states shifting down to more negative energy around Rpoint (down from Fermi level). The HM gap is significant parameter to observe the minimum energy required for spin excitation to induce 13
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Fig. 3. (a) Total (TDOS) and (b) partial (PDOS) density of states computed for MgBeO3, CaBeO3, SrBeO3 and BaBeO3 using GGA approximation.
shown in Fig. 4a. The static value ε1 (0) is very large for metals, which shows that metals are highly transparent to the light. The ε1 (0) is related to the refractive index n (ω) as n 02 ≅ ε1 (0) . The ε1 (ω) computed for all perovskites becomes negative at varying energies revealing the reflective behavior to the incident photons because negative ε1 (ω) demonstrate the metallic nature. The imaginary dielectric constant ε2 (ω) for the perovskites demonstrate the light absorption, as shown in Fig. 4b. The absorption peaks lying at 0.1 eV, 0.3 eV, 0.5 eV, 0.52 eV for MBO, CBO, SBO, BBO, respectively, appear due to absorption of incident energy. The small shift in the absorption peaks from MBO to BBO might be exhibited due to the exchange splitting induced slight energy difference between up and down spin channels, as evident from Table 1. The Penn’s model [65] ε1(0) ≈ 1 + (ħωp/Eg)2 is found stratified because decaying band gap is linked to the increasing ε1 (0) (see Fig. 4(a and c)). The trend of ε1 (ω) and ε2 (ω) reveal similar information as by n (ω) and k(ω), respectively, and all four parameters are related as n2 − k 2 = ε1 (ω) and 2nk = ε2 (ω) [60]. Hence, the studied compounds also illustrate their high potential for practical applications in magneto-
to holes mediated double exchange type mechanism. Therefore, the presence of ferromagnetism in such perovskites offers novel spintronic applications. 3.3. Optical properties The optical properties of typical metals mainly depend upon the intra-band transitions, while according to Drude model free carrier caused transport properties are important to know for practical applications. As the half-metallic (HM) ferromagnets XBeO3 with metallic character exhibit complete spin polarization, therefore, various optical properties such as dispersion, polarization, absorption and transparency are important for device applications, which are elucidated by computing the complex dielectric constant and refraction [60–64]. The calculated real ε1 (ω) and imaginary dielectric constants ε2 (ω), refractive index n (ω) and extinction coefficient k(ω), are plotted in Fig. 4(a–d), respectively. The ε1 (ω) reveals dispersion due to polarization of the incoming photons by exhibiting plasmonic resonances, as 14
Chemical Physics Letters 729 (2019) 11–16
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Fig. 4. The (a) real and (b) imaginary dielectric constants, (c) refractive index and (d) extinction coefficient computed for MgBeO3, CaBeO3, SrBeO3 and BaBeO3 using GGA approximation.
optical devices.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Half-metallic ferromagnetism and optical behavior in alkaline-earth metals based Beryllium perovskites: DFT calculations
T
⁎
Q. Mahmooda, , M. Hassanb, M. Yaseenc, A. Larefd a
Department of Physics, Faculty of Science, Imam Abdulrahman bin Faisal University, P.O. 383, Dammam 31113, Saudi Arabia Material Growth and Simulation Laboratory, Department of Physics, Quaid-e-Azam Campus, University of the Punjab, Lahore 54000, Pakistan c Department of Physics, University of Agriculture, Faisalabad 38040, Pakistan d Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia b
H I GH L IG H T S
structural, mechanical and thermodynamic stability ofperovskites. • The temperature ferromagnetism. • Room metallic ferromagnets with hundred percent spin polarization. • Half mechanism exceed the exchange energy than crystal field energy. • Exchange • The cause of ferromagnetism is spin of electron rather than clustering effect.
A R T I C LE I N FO
A B S T R A C T
Keywords: Spintronic Half metallic ferromagnetism (HMF) Spin polarization Curie temperature Double exchange mechanism
We investigate the Half-metallic ferromagnetism and optical behaviors of XBeO3 (X = Mg, Ca, Sr and Ba) using full-potential linearized augmented plane-wave method. The structural and thermodynamic stabilities are elucidated in terms of the calculated tolerance factor and enthalpy of formation, respectively. The room temperature (RT) ferromagnetism is shown by computing the Curie temperature and spin polarization. The strong hybridization between p-states of alkaline earth metals and 2p-states of oxygen near the Fermi level results total magnetic moment of 2μB. The ferromagnetism occurs due to holes those result in the exchange interactions between the p-states of alkaline earth metals and oxygen. The potential optical applications are also suggested by computing the dielectric constant and refraction.
1. Introduction The recent technological advancements have introduced half-metallic (HM) ferromagnets that have revolutionized the spintronic devices such as magnetic sensors, giant (GMR) and tunnel (TMR) magnetoresistance [1–4]. The half-metallic ferromagnets have one semiconducting spin channel, while other channel is metallic and exhibit 100% spin polarization at Fermi level [5–7]. The HM ferromagnets were firstly described by de Groot et al. (1983) for NiMnSb and PtMnSb Heusler alloys [8], later on, a variety of materials like transition-metal doped oxides, spinels, zincblende transition-metal chalcogenides, perovskites and other spin orientated materials were investigated to observe HM ferromagnetism [9–15]. The major limitations for practical applications of spintronic devices appear due to the lack of room temperature ferromagnetism (RTFM) and real factors stabilizing the
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ferromagnetism. In the last decades, RTFM has been reported in various kinds of compound e.g. BaTiO3 [16], double perovskites Sr2FeMoO6 (400 k) [17], doped perovskites Bi0.5Na0.5TiO3 [18], transition-metals doped II-VI alloys ZnS/Se/Te [19,20], Cr doped GaN and AlN [21], transition-metals doped ZnO [22], In2O4 [23–25], TiO2 [26] etc. The real origin of ferromagnetism, either intrinsic exchange mediated or due to the clustering of transition-metals, is still in doubts. Although transition-metals doped compounds should form ordered alloys [27,28], but RTFM has been reported due to either transition-metal clusters or secondary phases [29–32]. To avoid such clustering of the magnetic impurities, doping with nonmagnetic elements has been carried for different nonmagnetic compounds, however, still ferromagnetism appears. For example, Mg, Al, Li and N doped ZnO [33], Mg doped SnO2 [34], C doped TiO2, ZnO, CdS and ZnS [35–38], nanoribbons and nonsheets of BeO [39], alkali based half-Heusler alloys XSrB
Corresponding author. E-mail address: [email protected] (Q. Mahmood).
https://doi.org/10.1016/j.cplett.2019.05.011 Received 21 March 2019; Received in revised form 30 April 2019; Accepted 7 May 2019 Available online 08 May 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
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(X = Alkali metals) [40], B, C and N doped BeO [41] and Ca, Ti, N and C doped oxides [42–44] induce ferromagnetism. Therefore, ferromagnetism resulting due to nonmagnetic doping of nonmagnetic compounds clarifies the role of clustering and reveals the presence of exchange interactions. As is evident in the above discussion, HM ferromagnetism in the cubic nonmagnetic perovskite oxides could be attractive to explore because these have simple crystalline structure and are of low-cost. In the present report, full-potential linearized augmented planewave (FP-LAPW) method is employed using Wien2k software to find the electronic structure, HM ferromagnetism and the optical behavior of alkaline-earth metal based beryllium perovskites XBeO3 (X = Mg, Ca, Sr and Ba). The HM ferromagnetism is holes-mediated (evident from the electronic band structures) due to the exchange interactions and sp-hybridization and paramagnetic nature of oxygen. The magnetic moment computed for 1 × 1 × 1 super cell is 2.00 μB and 100% spin polarization has been observed. The existing literature about alkalineearth metals based perovskites is limited. However, the presented computed results may provide deep insight for the experimentalists to understand such unusual ferromagnetism.
Table 1 The lattice constant ao(Å), Bulk modulus Bo(Gpa), Enthalpy of formation Hf (eV), Tolerance factor t (2G), Curie temperature (Tc), electron density at Fermi level for up spin channel N↑ (EF ) , electron density at Fermi level for down spin channel, Polarization (P), Band gap Egup-gdn (eV), Half metallic gap EHM (eV), total magnetic moment Mtot (µB), and partial magnetic moments of MgBeO3, CaBeO3, SrBeO3, and BaBeO3calculated by GGA approximation. Properties
MgBeO3
CaBeO3 a
3.58 (3.61 ) 151.13 −2.40 (2.41a) 0.97 290 0
SrBeO3
BaBeO3
3.67 141.01 −2.15 0.98 281 0
3.81 122.55 −1.85 1.03 277 0
ao(Å) Bo(Gpa) Hf (eV) t2G Tc(k) N↑ (EF )
3.46 157.86 −2.45 0.95 295 0
N↓ (EF ) P Egup-gdn (eV), EHM (eV), Mtot (µB) MX(µB) MO (µB) MBe (µB) MInt (µB)
1.28
1.04
0.91
0.84
1 1.19 0.003 2.00 −0.036 1.413 −0.127 0.750
1 1.17 0.10 2.00 (1.99a) −0.047 1.53 −0.267 0.784
1 1.15 0.28 2.00 −0.068 1.582 −0.390 0.866
1 1.07 0.31 2.00 −0.075 1.656 −0.456 0.875
2. Method of calculations a
Ref. [54].
The calculations have been performed using FP-LAPW method as incorporated in Wien2k code [45]. The relaxed cubic structures of XBeO3 (X = Mg, Ca, Sr and Ba) are optimized for observing the lattice constants using generalized gradient approximation (GGA) [46]. The exchange correlation potential is worked out using surface charge density and its derivative at muffin-tin sphere where plane-wave solution is taken as spherical harmonic type. All relativistic effects are considered during computations. The product KmaxxRmin is taken as 8. Where Kmax is length of the maximum wave-vector (in reciprocal lattice) and Rmin is minimum muffin-tin radius. The angular momentum vector and Gaussian parameter are set as ℓmax = 10 and Gmax = 16, respectively. The k-mesh 12 × 12 × 12 has been taken for first Brillionzone integration. The released energy by varying the k-mesh remains invariant, which shows accuracy of calculations. Moreover, the selfconsistency set between the successive iterations is lower than 1 × 10−4 Ry. 3. Results and discussions
Fig. 1. (a) The optimized plots of MgBeO3, CaBeO3, SrBeO3 and BaBeO3 in the FM state done using GGA approximation (b) Crystal Structure designed by Xcrysden.
3.1. Structure stability and electronic properties The relaxed structures of MgBeO3 (MBO), CaBeO3 (CBO), SrBeO3 (SBO) and BaBeO3 (BBO) are optimized in ferromagnetic (FM) and antiferromagnetic (AFM) states. The positive energy difference (ΔE = EAFM − EFM) evidences that all compounds exhibit relatively more stable FM state, as shown in Table 1 (similar to that in Ref. [47]). For the sake of simplicity, we have only plotted the optimized graphs in FM state as shown in Fig. 1a. The optimized plots reveal increasing unit cell volume from MBO to BBO, due to which, lattice constant also improves, as shown in Table 1. The optimized cubic structure (2 × 1 × 1 supercell) with space group: Pm3m (2 2 1) is also shown in Fig. 1b. The Be atom is surrounded by oxygen ions due the formation of octahedron (BeO6), while alkaline-earth elements (Mg, Ca, Sr, Ba) occupy the edges. The thermodynamic and structural stabilities for the FM state are depicted by computing the enthalpy of formations and tolerance factors (see Table 1). The enthalpy of formation (Hf) has been elucidated from the energy difference between the compounds and the constituent elements using the expression ΔHf = ETotal (Xl Bem On ) − l EX − mEBe − nEO . Where, ETotal (Xl Bem On ) is the energy released by compound, while, EX , EBe and EO are the energies released by the lattices of X (Mg, Ca, Sr, Ba), Be and O, respectively. The l, m, n subscripts express number of atoms for the respective elemental unit cells [48]. The negative enthalpy of formations suggests stable FM state. The
Goldsmith’s tolerance factor [49] has been calculated, to show structural stability of the cubic phase, using tG = rX + rO/ rBe + rO , where rX , rBe and rO are the atomic radii of X, Be and O atoms, respectively. Higher deviations of the tolerance factor (tG) from unity are directly linked with the structural instability of the cubic perovskites, however, tG in the range of 0.93–1.04 illustrates structural stability. Therefore, the calculated tG values, as presented in the Table 1, elucidate structural stability. 3.2. Curie temperature and magnetic behavior The structural stability decreases from MBO to BBO because incompatibility between the ionic radii rises. After verifications of the structural and thermodynamic stabilities in the FM state, the knowledge of Curie temperature (TC) becomes important because it illustrates the maximum thermal energy up to which the FM state can sustain. The Curie temperatures are estimated using Heisenberg model, Tc = 2ΔE /3xKB , where ΔE shows energy difference between AFM and FM states and KB is Boltzmann constant [50,51]. The calculated values, presented in Table 1, reveal that MBO has TC approaching to room temperature (RT), which decreases from MBO to BBO because of ionic 12
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Fig. 2. The electronic band structures of (a) MgBeO3, (b) CaBeO3, (c) SrBeO3 and (d) BaBeO3 in FM state calculated using GGA approximation.
holes in the majority spin channel. A wider HM gap (0.31 eV) suggests BBO as suitable HM ferromagnet for potential spintronic applications. The origin of ferromagnetism is exposed by computing the total density of states (TDOS) for XBeO3, as plotted in Fig. 3a, while the local density of states are shown in Fig. 3b. As evident from the computed band structures, TDOS also reveal HM ferromagnetic nature. To deeply understand the nature of interaction between the local/partial density of states, 2p-Mg, 3p-Ca, 4p-Sr, 5p-Ba and 2p-O states have been computed, which illustrate a strong exchange interaction near Fermi energy level in majority channel (↑), while states cross Fermi level in minority channel (↓) (similar to that in the Ref. [34]). The states around 1 eV above Fermi level belong to alkaline-earth metals and oxygen those form a tetrahedron. Therefore, accepter levels above Fermi level demonstrate holes mediated ferromagnetism. The hybridization of 2p-Mg, 3p-Ca, 4p-Sr, 5p-Ba and 2p-O states around Fermi level splits the energy states resulting a downward shift of the majority spin states to induce half metallic gap, while such a splitting shifts the minority spin states upward. Hence, overall energy reduces, while p-p exchange interaction is the major cause for the observed ferromagnetism. Furthermore, the energy states 2s-Be also hybridize slightly with 2p-O states and p-states of X elements within −3 eV to −6 eV, however, 2s-Be state appear away from Fermi level, as evident from Fig. 3b. In addition, the spin-up and down bands are fully and partially filled, respectively. The number of holes is equivalent to the total magnetic moment per unit cell i.e. 2μB [35]. The total and partial magnetic moments are also computed, as evident in Table 1. The manufacturing of the total magnetic moment primarily due to oxygen ions, while nearest neighbor alkaline-earth metals and Be atoms also have limited contributions. The magnetic moment of X ions and oxygen align parallel (exhibiting a FM interaction), while the magnetic moment is Be is aligned opposite to that of the oxygen ion (revealing AFM interaction). The Fig. 3b shows that FM coupling dominates the AFM coupling, and hence, FM nature of the studied compounds is evident. Various mechanisms exist to justify the ferromagnetism in diluted magnetic semiconductors (DMS) and half-metallic ferromagnets (HMF) [43,55–59]. In XBeO3 perovskites, carrier mediated mechanism mainly causes ferromagnetism. The electronic properties reveal that holes are induced due to the hybridization between the p-states of X and oxygen, and hence, position of p-states of alkaline earth metals (X) stabilizes a specific strength of ferromagnetism. Hence, the presence of free holes and interaction between the p-states may stabilize ferromagnetism due
radii mismatch between cations and anions increases that modifies the structural arrangement of constituent atoms. The compounds exhibit 100% spin-polarization at Fermi level (EF) because the majority spin channels have Fermi levels inside the band gap and minority spin channels have Fermi level at valence band edges. The polarization at Fermi level is calculated using the relation:
P=
N↑ (EF ) − N↓ (EF ) N↑ (EF ) + N↓ (EF )
Here, N↑ (EF ) and N↓ (EF ) express density of states of majority and minority spin channels at Fermi level, respectively [52]. The calculated density of states at Fermi level, for majority and minority spin channels, as well as the spin polarization are presented in Table 1. The description of ferromagnetism is presented in terms of the calculated band structures (BS), which are plotted in Fig. 2(a–d). The majority spin channels (↑) show that conduction band minima (CBM) and valence band maxima (VBM) appear at Г-point and R-point, respectively, for MBO, CBO and SBO (i.e. indirect band gap nature). While both lie at Г-point for BBO (i.e. direct band gap nature). On the other hand, the minority spin channel (↓) shows Fermi level crossing the valence states that reveal the metallic type behavior induced by the holes as free carriers. Hence, both spin channels of all four compounds collectively exhibit half metallic ferromagnetic (HMF) response [34,53]. Furthermore, the asymmetry between both channels is a direct evidence of the presence of exchange interactions. The exchange interaction energy has been deduced by separately calculating the energy differences between VBM and CBM for majority (↑) (Egup) and minority spin channels (↓)(Egdn). The difference between both terms Egup − Egdn shows the exchange interaction energy for each compound [54], which is shown in Table 1 and it decreases from MBO to BBO that is resulted due to the addition of more shells that modify the states distribution to cause the decaying exchange energy. The half metallic (HM) gap or the spin flip gap is determined from the energy difference between VBM and Fermi level (zero energy) that expresses the minimum energy required to flip a majority (minority) spin from top of the occupied valence to the Fermi level [53]. The HM gap, as given in Table 1, increases from MBO to BBO because oxygen 2p-states interact with p-states of alkaline-earth metals resulting the valence band states shifting down to more negative energy around Rpoint (down from Fermi level). The HM gap is significant parameter to observe the minimum energy required for spin excitation to induce 13
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Fig. 3. (a) Total (TDOS) and (b) partial (PDOS) density of states computed for MgBeO3, CaBeO3, SrBeO3 and BaBeO3 using GGA approximation.
shown in Fig. 4a. The static value ε1 (0) is very large for metals, which shows that metals are highly transparent to the light. The ε1 (0) is related to the refractive index n (ω) as n 02 ≅ ε1 (0) . The ε1 (ω) computed for all perovskites becomes negative at varying energies revealing the reflective behavior to the incident photons because negative ε1 (ω) demonstrate the metallic nature. The imaginary dielectric constant ε2 (ω) for the perovskites demonstrate the light absorption, as shown in Fig. 4b. The absorption peaks lying at 0.1 eV, 0.3 eV, 0.5 eV, 0.52 eV for MBO, CBO, SBO, BBO, respectively, appear due to absorption of incident energy. The small shift in the absorption peaks from MBO to BBO might be exhibited due to the exchange splitting induced slight energy difference between up and down spin channels, as evident from Table 1. The Penn’s model [65] ε1(0) ≈ 1 + (ħωp/Eg)2 is found stratified because decaying band gap is linked to the increasing ε1 (0) (see Fig. 4(a and c)). The trend of ε1 (ω) and ε2 (ω) reveal similar information as by n (ω) and k(ω), respectively, and all four parameters are related as n2 − k 2 = ε1 (ω) and 2nk = ε2 (ω) [60]. Hence, the studied compounds also illustrate their high potential for practical applications in magneto-
to holes mediated double exchange type mechanism. Therefore, the presence of ferromagnetism in such perovskites offers novel spintronic applications. 3.3. Optical properties The optical properties of typical metals mainly depend upon the intra-band transitions, while according to Drude model free carrier caused transport properties are important to know for practical applications. As the half-metallic (HM) ferromagnets XBeO3 with metallic character exhibit complete spin polarization, therefore, various optical properties such as dispersion, polarization, absorption and transparency are important for device applications, which are elucidated by computing the complex dielectric constant and refraction [60–64]. The calculated real ε1 (ω) and imaginary dielectric constants ε2 (ω), refractive index n (ω) and extinction coefficient k(ω), are plotted in Fig. 4(a–d), respectively. The ε1 (ω) reveals dispersion due to polarization of the incoming photons by exhibiting plasmonic resonances, as 14
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Fig. 4. The (a) real and (b) imaginary dielectric constants, (c) refractive index and (d) extinction coefficient computed for MgBeO3, CaBeO3, SrBeO3 and BaBeO3 using GGA approximation.
optical devices.
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4. Conclusion XBeO3 (X = Mg, Ca, Sr, Ba) have shown thermodynamically stable structures exhibiting ferromagnetic nature, which is reserved up to room temperature. Half-metallic ferromagnetism with high spin-polarization at the Fermi level has been found due to strong p-p hybridization between the p-states of alkaline-earth metals and oxygen. A p-type nature shows the role of holes to stabilize half-metallic ferromagnetic state. The studied compounds generate a total magnetic moment 2μB per unit cell. Due to the presence of free holes and interactions between the p-states, holes mediated double exchange type mechanism might be responsible to cause ferromagnetism. The studied perovskites also respond to the impinging optical energy. Therefore, novel magneto-optical applications can be realized. Acknowledgement This research project was supported by a grant from the “Research Centre of Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University. The author (A. Laref) acknowledges the financial support by a grant from the “Research Center of the Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University. References [1] F. Estrada, E.J. Guzman, O. Navarro, M. Avignon, Phys. Rev. B 97 (2018) 195155. [2] S.M. Thompson, The Nobel prize 2007, J. Phys. D-Appl. Phys. 41 (2008) 1–20. [3] G. Binasch, P. Grunberg, F. Saurenbach, W. Zinn, Phys. Rev. B 39 (1989) 4828–4830. [4] A. Fert, P. Grunberg, A. Barthelemy, F. Petroff, W. Zinn, J. Magn. Mater. 140 (1995) 1–8. [5] D. Bombor, C.G.F. Blum, O. Volkonskiy, S. Rodan, S. Wurmehl, C. Hess, B. Buchner, Phys. Rev. Lett. 110 (2013) 066601. [6] W.E. Pickett, D.J. Singh, Phys. Rev. B 53 (1996) 1146. [7] D.J. Singh, W.E. Pickett, Phys. Rev. B 57 (1998) 88. [8] R.A. de Groot, et al., Phys. Rev. Lett. 50 (1983) 2024.
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