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Mar 9, 2016 - The Hashemite University, Zarqa 13115, Jordan. ‡ahmadd [email protected]. Received 27 September 2015. Revised 2 December 2015.
International Journal of Modern Physics B Vol. 30, No. 7 (2016) 1650031 (15 pages) c World Scientific Publishing Company  DOI: 10.1142/S0217979216500314

Ab initio investigation of the structural, electronic, magnetic and optical properties of the perovskite TlMnX3 (X = F, Cl) compounds

Farida Hamioud∗ , Ghadah S. AlGhamdi∗ , Saleh Al-Omari† and A. A. Mubarak∗,‡ ∗ Department of Physics, Rabigh College of Science and Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia † Department of Physics, Faculty of Science, The Hashemite University, Zarqa 13115, Jordan ‡ ahmadd [email protected]

Received 27 September 2015 Revised 2 December 2015 Accepted 6 December 2015 Published 9 March 2016 We have performed ab initio investigation of some physical properties of the perovskite TlMnX3 (X = F, Cl) compounds using the full-potential linearized augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) is employed as exchange-correlation potential. The calculated lattice constant and bulk modulus agree with previous studies. Both compounds are found to be elastically stable. TlMnF3 and TlMnCl3 are classified as anisotropic and ductile compounds. The calculations of the band structure of the studied compounds showed the semiconductor behavior with the indirect (M–X) energy gap. Both compounds are classified as a ferromagnetic due to the integer value of the total magnetic moment of the compounds. The different optical spectra are calculated from the real and the imaginary parts of the dielectric function and connected to the electronic structure of the compounds. The static refractive index n(0) is inversely proportional to the energy bandgap of the two compounds. Beneficial optics technology applications are predicted based on the optical spectra. Keywords: Perovskite; ab initio; anisotropy; bandgap; optical properties. PACS numbers: 71.15.±m, 71.15.Mb, 71.20.±b, 78.20.±e, 78.20.Ci

1. Introduction The wide range usage of the cubic perovskite compounds in technology is the reason behind their studies. Applications include, but not limited to, lenses, semiconductor industry and material science.1 Thus, structural, electronic and optical properties have been the subject of study of several researchers.2– 7 The perovskite compounds such as RbCaX3 and CsXF3 (X = Cl, F) were studied using calculations based ‡ Corresponding

author. 1650031-1

F. Hamioud et al.

on the density functional theory (DFT).3,4 They were found to be stable, ductile and elastic anisotropic. In addition to the previous compounds, CsXF3 (X = Ca, Sr and Hg) were benefited from a wide indirect bandgap.7 The magnetic study of KMnF3 unveiled its ferromagnetic behavior.5 From optical responses, RbCaX3 , CsSrX3 (X = Cl, F) and RbMF3 (M = Fe, Ni) compounds can be used in optoelectronics and optics technology.3,5 – 8 For the compounds of our interest, TlMnF3 and TlMnCl3 , the antiferromagnetic resonance (AFMR) study was available in the literature for the cubic TlMnF3 .9 The AFMR at 25 GHz was used and we determined that TIMnF3 is an undistorted cubic antiferromagnet at 4.2 K with 111 easy axes. Thus, it can be an interesting material for magnetic studies. Navalgund et al.10 reported that the observation of a single exchange narrowed the resonance line for TlMnX3 (X = Cl, F). They found that the lattice constant of TlMnCl3 , which is determined by X-ray diffraction using the single crystal, is in agreement with those presented in the literature. The preparation and characterization of TlMnCl3 have been conducted by Kestigian.11 The author reported that the X-ray powder diffraction data obtained above 30◦ C indicate that TlMnCl3 possesses cubic perovskite structure; however, below 30◦ C TIMnC13 becomes anisotropic. Kotlyarskii12 had studied the manifestation of phonons in TlMnCl3 absorption spectrum. The author reported that the TlMnC13 absorption spectrum compared to KMnF3 is displaced to the low-frequency region. This displacement proves that the crystal field in chlorides is smaller than that in fluorides.13 The theoretical studies provide good approach to investigate the distinct properties and potential applications for specific compounds. DFT14 within the fullpotential linearized augmented plane wave (FP-LAPW) method15 becomes a powerful theoretical tool utilized to predict the ground state properties of compounds. This method uses only the lattice constants as input parameters. We present a systematic study for extracting different properties of the TlMnX3 (X = F, Cl) compounds using the FP-LAPW method. The scarcity of research in studying the two cubic perovskites compounds TlMnF3 and TlMnCl3 is behind our interest in putting some light on their different properties. To the best of our knowledge, there are no empirical nor theoretical data on elastic and magnetic properties for the two studied compounds. The calculated values of the different properties of TlMnF3 and TlMnCl3 are compared with some previously published structurally similar fluoroperovskite and chloroperovskite compounds. Also, other properties such as structural, optical and electronic characteristics were elaborated for the maximum scientific benefit. The appropriate applications were suggested based on the determined properties. 2. Method of Calculations We have performed the spin-polarized study of the structural, electronic, magnetic and optical properties of the perovskite TlMnX3 (X = F, Cl) compounds 1650031-2

Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds

using DFT14 and the FP-LAPW method,15 as implemented in WIEN2k code.16 The exchange-correlation potential was calculated using the generalized gradient approximation (GGA) as proposed by Perdew et al.17 In this study, valence electrons are treated semirelativistically, while the core electrons are treated fully relativistically. The muffin-tin radii (RMT) are taken to be 2.50, 2.22, 1.84 and 2.10 a.u for Tl, Mn, F and Cl, respectively. The unit cell of the compound is divided into two regions. These are the muffin-tin sphere region and the interstitial region. The wavefunctions within muffin-tin spheres were expanded in spherical harmonics up to max = 10, while the charge density was Fourier expanded up to Gmax = 12 (Ry)1/2 . In the interstitial region, the wavefunctions are expanded in plane waves with a cut-off Kmax = 8/RMT. We have used 56 k-points in the irreducible part of the Brillouin zone (IBZ). The self-consistent calculations are considered to converge when the convergence tolerance of energy and charge are less than 0.1 mRy and 0.1 m electron charges, respectively. We have calculated the elastic constants (C11 , C12 and C44 ) using the cubic– elastic package.18 This package was used to perform the calculations numerically at zero pressure by second-order derivative of polynomial fit of energy versus strain at the zero strain. The mechanical properties of the studied compounds were calculated using the elastic constants Cij . 2.1. The structural properties In this subsection, we have determined the structural properties of TlMnX3 (X = F and Cl) compounds. The ideal cubic unit cell of these compounds has one molecule with a space group of Pm-3m. The atoms of this unit cell are located at (0, 0, 0) 1a for Tl, (0.5, 0.5, 0.5) 2b for Mn and (0.5, 0.5, 0) 3c for X with respect to atomic Wyckoff positions. The structural parameters of the two perovskites compounds TlMnF3 and TlMnCl3 are calculated using Birch–Murnaghan’s equation where energy was fitted as a function of the cell volume.19 The calculated parameters, namely the lattice constant (a), the bulk modulus (B0 ), its pressure derivative (B0 ), the bond lengths between constituent atoms and the tolerance factor (t), are ˚), bulk modulus (B in GPa), pressure Table 1. Lattice constant (a in A A) and tolerance derivative of the bulk modulus (B0 ), bond length (in ˚ factor (t) for TlMnF3 and TlMnCl3 . a

B

B0

Tl–Mn

Mn–X

Tl–X

TlMnF3

4.123 4.26a 4.243b

86.71

8.57

3.57

2.06

2.92

1.00 0.926b

TlMnCl3

4.83 5.02a 5.087b

49.33

4.91

4.18

2.41

3.41

1.00 0.887b

a Ref.

b Ref.

15. 16. 1650031-3

t

F. Hamioud et al.

presented in Table 1 along with empirical values collected from the works suggested in Refs. 20 and 21. The results have shown that the lattice parameters and the tolerance factor are in agreement with the previous works.20,21 We notice that the lattice constant of TlMnCl3 is higher than that for TIMnF3 . This might be related to the fact that the Mn–X bond length is more affected by the lattice constant than the Tl–Mn bond length and the as-known the atomic volume of Cl is larger than that of F.22 Our results showed that the bulk modulus decreases as the lattice constant increases which is in agreement with the previous studies.23,24 Also, the compound rigidity decreases consequently on the increase of the lattice constant.2 Thus, TlMnF3 is less compressible and more rigid than TlMnCl3 due to its higher bulk modulus. However, the t values for the studied compounds are within the range of 0.75–1.00 which applies to almost all known perovskites compounds.20 These results confirm the reliability of our calculations. 2.2. Elastic properties The elastic constants Cij provided useful information that lies behind their importance. The independent elastic constants C11 , C12 and C44 are enough to characterize the mechanical properties of the cubic compound symmetry. The cubic-elastic method integrated in WIEN2k code was used to calculate the elastic constants for TlMnF3 and TlMnCl3 compounds.18 The calculated constants C11 , C12 and C44 represent uniaxial deformation along [001] direction, the pure shear stress at (110) crystal plane along [1¯ 10] direction and the pure shear deformation at (100) crystal plane, respectively.25 Elastic constants and mechanical properties values are displayed in Table 2. As far as we know, there are no empirical nor theoretical data on elastic properties for the two studied compounds. The results which are displayed in Table 2 show that the values of C11 are about 86.5% and 71.8% higher than the values of C44 for TlMnF3 and TlMnCl3 , respectively. Thus, the two compounds are more likely to undergo pure shear deformation than the unidirectional compression. Mechanical stability in a cubic structure is reached when the restriction formulae26 are satisfied: 1/3(C11 + 2C12 ) > 0, (C44 ) > 0, 1/2(C11 − C12 ) > 0 and C12 < B < C11 . The two compounds are elastically stable as the calculated elastic constants satisfy the restriction formulae. The C44 value of TlMnF3 is higher than that of TlMnCl3 , which indicates that the first compound is expected to be stiffer than the second compound. Table 2. Calculated elastic constants (C11 , C12 and C44 in GPa), bulk modulus (B0 in GPa), shear modulus (G in GPa), anisotropic factor A, Young’s modulus (E in GPa), Kleinman parameter ζ, Poisson’s ration (υ) and Pugh’s index ratio (B/G) for TlMnF3 and TlMnCl3 . C11

C12

C44

B0

G

A

E

ξ

υ

B/G

TlMnF3

144.08

56.37

19.4

85.61

27.07

0.44

73.47

0.53

0.356

3.2

TlMnCl3

36.2

19.51

10.2

25.07

9.41

1.22

25.09

0.66

0.333

2.7

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Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds

The anisotropy factor (A) is given by A = 2(C44 /(C11 − C12 )). For A = 1, the material is said to be isotropic. However, the material is said to be anisotropic for values higher or lower than one. This difference measures the crystal elastic anisotropy degree. From our results we conclude that the two compounds benefit from a large elastic anisotropy. The TlMnF3 compound is highly anisotropic compared to TlMnCl3 . These results agree with previous studies conducted on the compounds RbCaX3 (see Ref. 3) and CsSrX3 (see Ref. 4) where (X = F, Cl). The Voigt–Reus–Hill approximation27–29 has been used to calculate the shear modulus (G), Young’s modulus (E), Poisson’s ratio (v) and Kleinman parameter (ζ). The Young’s modulus can be seen as a good measure of the compound stiffness. Another stiffness indicator is G which determines the resistance to plastic deformation. Thus, according to Table 2, TlMnF3 tends to be stiffer than TlMnCl3 which is in line with the previous studies.3,4 In order to predict the ductile (brittle) behavior of a material, three parameters have to be analyzed; Pugh’s ratio (B/G), Poisson’s ratio (v) and Cauchy’s pressure (C12 − C44 ). Pugh’s criterion30 suggests that a material is classified as ductile (brittle) if B/G is bigger (smaller for brittle) than 1.75. Based on Poisson’s ratio, according to Frantsevich rule,31 the material is said to be ductile (brittle) if v is bigger (smaller) than 0.26. However, for a positive (negative) value of the Cauchy’s pressure, the material will be classified as ductile (brittle).8 According to Table 2 and since B/G is greater than 1.75, v is greater than 0.26 and (C12 − C44 ) is positive, therefore the two compounds are of ductile nature. The characteristics of bonding force between atoms are given by Poisson’s ratio where the central force solid is limited between 0.25 and 0.5. The value of v for TlMnF3 and TlMnCl3 compounds are 0.36 and 0.33, respectively. Thus, the two studied compounds have central inter-atomic forces. The relative positions of cation and anion sublattices under volume-conserving strain distortions are described by the Kleinman parameter ζ which is calculated as follows: C11 + 8C12 . (1) ζ= 7C11 + 2C12 Minimizing bond bending (bond stretching) results in ζ = 0 (ζ = 1). The calculated values of ζ for TlMnF3 and TlMnCl3 compounds, listed in Table 2, indicate that they are both resistant to bond bending. The TlMnCl3 is more resistant to bond bending than TlMnF3 . However, they are both less resistant to bond bending when comparing to KMnF3 .5 2.3. Debye temperature The Debye temperature or Debye cut-off frequency is the temperature at which the phonon frequency wavelength equals the unit cell length. The importance of the Debye temperature comes from its relation to some physical properties such as melting point and specific heat. 1650031-5

F. Hamioud et al. Table 3. Calculated longitudinal (υl in m/s), transverse (υt in m/s) and average sound (υm in m/s) velocities, mass density (ρ in g/cm3 ), the Debye temperature (θD in K) and the melting point (Tmelt in K) using elastic moduli for TlMnF3 and TlMnCl3 .

TlMnF3

ρ

υl

υt

υm

θD

Tmelt

7.4945

4029.8

1900.5

2138.8

264.4

1405 ± 300 1093a

4447.60

2589.52

2872.71

324.16

1339

2642.0

1321.4

1482.3

156.4

3622.66

1402.87

1590.64

148.82

RbCaF3 ],b TlMnCl3 RbCaCl3 b

5.3891

767 ± 300 770 ± 242c 1167

a Ref.

9. b Ref. 3. c Ref. 34.

Two methods are to determine and calculate Debye temperature, namely specific heat measurements and using elastic constants, respectively. For the two compounds considered in this paper, the Debye temperature is calculated using the elastic constants as in Ref. 32. The findings of our calculations are displayed in Table 3; mass density ρ, longitudinal (υl ), transverse (υt ) and average sound (υm ) velocities, Debye temperature θD and the melting point TMelt . The calculated Debye temperature for TlMnF3 (TlMnCl3 ) is lower (higher) than that calculated for RbCaF3 (RbCaCl3 ) considered in Ref. 3, as listed in Table 3. The melting point of the two compounds is calculated by the following equation33 : Tmelt = [553 K + (5.91 K/GPa)C11 ] ± 300 K .

(2)

The calculated melting point for TlMnF3 is found overestimated than that found experimentally in Ref. 33. This difference can be attributed to the large error (±300 K) that has been used in Eq. (2). This error is believed to be due to the exchange-correlation does potential. This potential not quite cancel the errors between total energies of atoms with more homogeneous solid. The melting point of TlMnCl3 is found to be in agreement with previous studies.34 The melting point value for TlMnF3 is higher than that for TlMnCl3 . Therefore, TlMnF3 is stiffer than TlMnCl3 . This is in line with the conclusion stated in Sec. 3.2. In addition to that, the Tmelt for TlMnF3 is higher than those for RbCaF3 ,3 RbFeF3 and RbNiF3 (see Ref. 6) and the Tmelt for TlMnCl3 is lower than that for RbCaCl3 .3 2.4. Electronic and magnetic properties The electronic and magnetic properties of TlMnF3 and TlMnCl3 are studied in this subsection. To determine the electronic properties, we calculated the energy band structure, the partial and total energy densities of states (PDOS and TDOS). The energy band structures of the two studied compounds at zero pressure along the 1650031-6

Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds

TlMnF3

TlMnCl3

TlMnF3

TlMnCl3

Fig. 1. Band structures of TlMnF3 and TlMnCl3 at equilibrium lattice parameters along the symmetry line of BZ. The up (down) arrow represents the majority (minority) spin.

principal symmetry directions in the Brillouin zone (BZ) are represented in Fig. 1. The energy bandgap is the zero energy reference. It is bounded by the valence band maximum and the conduction band minimum. From Fig. 1, semiconductor behavior can be seen in TlMnF3 and TlMnCl3 with majority and minority spins. In the majority spin, the valence band maximum and the conduction band minimum are located at M and at X symmetry points, respectively. Thus, there is an indirect (M–X) energy gap in the majority spin which turns out to be 0.85 and 1.33 eV for TlMnF3 and TlMnCl3 , respectively. In the minority spin, the valence band maximum is located at M for TlMnF3 and at X for TlMnCl3 , while the conduction 1650031-7

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PDOS (states/eV)

TDOS (state/eV)

band minimum is located at X symmetry point in both compounds. Thus, there are indirect (M–X) and direct (X–X) band which turn out to be 4.05 and 2.92 eV for TlMnF3 and TlMnCl3 , respectively. Therefore, these perovskites compounds show an indirect (M–X) bandgap for the sum of bands with values of 0.58 and 0.20 eV for TlMnF3 and TlMnCl3 , respectively. This confirms the semiconducting behavior of the two compounds alike the one found in Ref. 5 for KMnF3 . The energy bandgap for TlMnF3 (fluoride) is higher than that of TlMnCl3 (chloride) which is in line with Ref. 3. The energy bandgap for TlMnF3 is narrower than that for CsHgF3 .7 30 15 0 -15 -30 30 15 0 -15 -30 8

(a) TlMnF3

Tl states

Mn states

4 0 -4 10 5 0 -5 -10

F states

-30

-25

-20

-15

-10

-5

0

5

10

PDOS (state/eV)

TDOS (state/eV)

Energy (eV) 30 15 0 -15 -30 30 15 0 -15 -30 6 3 0 -3 -6 4 2 0 -2 -4

(b) TlMnCl3

Tl states

Mn states

Cl states

-30

-25

-20

-15

-10

-5

0

5

10

Energy (eV)

Fig. 2. (Color online) TDOS and PDOS of (a) TlMnF3 and (b) TlMnCl3 . The upper (lower) half of the graph represents the majority (minority) spin. The s, p and d states for PDOS are represented by red, blue and green colors, respectively. 1650031-8

Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds Table 4. Calculated magnetic moments (total: Mt , local: MTl , MMn , MF and MCl and interstitial: Minst ) in the unit of μB for TlMnF3 and TlMnCl3 . Minst

MTl

MMn

MX (X = F, Cl)

Mt

TlMnF3

0.36

0

4.38

0.09

5

TlMnCl3

0.25

0

4.47

0.09

5

The calculated values for TDOS and PDOS of the two studied compounds are displayed in Figs. 2(a) and 2(b). A wide dispersion of the valence band with distinct peaks is observed. This band can be divided into three regions. The top valence band region from Fermi level to −9 eV is formed with the hybridization of Mn-d states and X-p states. The next region is characterized by a sharp peak at about −11.9 eV (−11.5 eV) for TlMnF3 (TlMnCl3 ) due to Tl-d states. In the last region, a peak can be seen at about −24.5 eV for TlMnF3 and also a narrow band region located between −16 eV and −17 eV for TlMnCl3 is noticed. They are both due to X-s state. We conclude that an ionic bonding nature can be expected. The conduction band is believed to be mainly formed by Tl-p, Mn-d and X-p states above the Fermi level. To illustrate the magnetic properties for the two studied compounds, we have calculated their total, local and interstitial magnetic moments. These data are listed in Table 4. The magnetic moments for the interstitial sites and for the X atom have a positive value which confirms that they are parallel to the magnetic moment of Mn atom. These positive values increase the overall magnetic nature of the two compounds. The integer value of the total magnetic moment indicates the half metallic ferromagnetic behavior of the compound. According to Slater–Pauling rule,36 we conclude that TlMnF3 and TlMnCl3 have a ferromagnetic behavior. The total magnetic moments calculated for the two studied compounds have similar value and behavior to previously studied compound, KMnF3 .5 2.5. Optical properties The optical properties of TlMnX3 are described by the dielectric complex function ε(ω) defined as: ε(ω) = ε1 (ω) + iε2 (ω).37 They are usually connected to the electronic structure of the compounds.37,38 ε1 (ω) and ε2 (ω) represent the real and the imaginary parts of the dielectric function, respectively, which are shown in Fig. 3. ε2 (ω) which is represented in Fig. 3(a), describes the absorption behavior of the material and depends on the bandgap. It arises from all transitions of electrons from the valence band to the conduction band. The known threshold energy as well as the fundamental absorption edge are estimated to be 2.32 and 2.14 eV for TlMnF3 and TlMnCl3 , respectively. It is a result of the indirect transition of electrons from the Mn-d state at the M symmetry point of the valence band to the Mn-d state at the X point in the conduction band for both TlMnF3 and TlMnCl3 . The first peaks in the ε2 (ω) spectrum appears around 4.15 and 3.63 eV for TlMnF3 and TlMnCl3 , 1650031-9

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respectively. These peaks are due to the transition of Mn-d states and X-p states of the valence band to Mn-d and X-p states of the conduction band. The Kramers–Kronig relation is used to obtain the real part of dielectric function, ε1 (ω), using ε2 (ω). From Fig. 3(b), the ε1 (ω) spectra are decreasing while fluctuating. The curves reach maximum values of 6.76 at 5.62 eV and 8.14 at 5.01 eV for TlMnF3 and TlMnCl3 , respectively. They reach negative values in different energy ranges of 8.2–9.5 and 11.4–12.0 eV for TlMnF3 and 14.5–20.0 eV for TlMnCl3 . In these energy ranges, the two compounds have a metallic behavior while otherwise they have dielectric nature. The fluctuations begin to disappear at about 20 eV and disappear completely at the minimum energy range, where the photons’ propagation is attenuated in the optical medium. The calculated static dielectric constant values at zero frequency limits ε1 (0) are found to be 12.1 and 15.2 for TlMnF3 and TlMnCl3 , respectively. According to Penn model,39 ε1 (0) is inversely proportional to the energy bandgap. This explains the increase in ε1 (0) while the bandgap decreases from TlMnF3 to TlMnCl3 . The optical parameters of TlMnX3 namely the refractive index, n(ω), extinction coefficient, k(ω), absorption coefficient, I(ω), reflectivity, R(ω), energy loss function L(ω), sum rules, Neff and optical conductivity, σ(ω), can be obtained from the complex dielectric function along xx-direction. The peaks in the optical spectra, which are shown in Figs. 3–5, are arising from the transitions between the valance and conduction bands. These spectra can be divided into three main regions including 15 (a)

ε2(ω)

10

5

0 15 (b)

ε1(ω)

10 5 0 -5 0

5

10

15

20

25

30

Energy (eV) Fig. 3. (Color online) (a) Calculated imaginary part ε2 (ω) and (b) real part ε1 (ω) of the dielectric function ε(ω) for TlMnF3 in black line and TlMnCl3 in red line. 1650031-10

Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds

6 5

(a)

n(ω)

4 3 2 1 0 3

(b)

k(ω)

2

1

0 0

5

10

15

20

25

30

Energy (eV) Fig. 4. (Color online) (a) Calculated refractive index n(ω) and (b) extinction coefficient k(ω) of the dielectric function ε(ω) for TlMnF3 in black line and TlMnCl3 in red line. 250

I(ω)

200

(a)

150 100 50 0 0.6

R(ω)

(b) 0.4 0.2 0.0 3

L(ω)

2

(c)

1 0 0

5

10

15

20

25

30

Energy (eV) Fig. 5. (Color online) (a) Calculated absorption spectrum I(ω), (b) reflectivity R(ω) and (c) energy loss function L(ω) of the dielectric function ε(ω), for TlMnF3 in black line and TlMnCl3 in red line. 1650031-11

F. Hamioud et al.

the extreme peaks. The first region of the optical spectra is in the range of about 2–4.7 eV. The main peak in this region is created by the optical transition from Mn-d and X-p states of the valance band to Mn-d and X-p states of the conduction band. The main peak in the second region (4.7–10.2 eV) is caused by the transition from Tl-d states of the valance band to Mn-d states of the conduction band. The third region is bounded by 10.2–30.0 eV. The main peak in this region is resulted from the transition of X-s state in the valance band to Tl-p, Mn-s and X-p states in the conduction band. The calculated refractive index n(ω) and extinction coefficient k(ω) along xxdirection are shown in Figs. 4(a) and 4(b), respectively. n(ω) has a similar character as that of ε1 (ω). The static refractive index n(0) values are found to be 3.7 and 5.2 for TlMnF3 and TlMnCl3 , respectively. These values are inversely proportional to the energy bandgap of the two compounds. Compared to previous studies, these values are higher than those calculated for RbCaF3 , RbCaCl3 , CsSrF3 , CsSrCl3 , RbFeF3 and RbNiF3 .3,4,6 The maximum values of n(ω) are found to be about 2.69 around 5.62 eV for TlMnF3 and 2.91 around 5.01 eV for TlMnCl3 . While the minimum values of n(ω) are about 0.71 around 11.50 eV for TlMnF3 and 0.40 around 18.33 eV for TlMnCl3 . The local maxima of k(ω) corresponding to the zero values of ωε1 (ω) are found to be 1.95 around 8.26 eV for TlMnF3 and 1.61 around 7.14 eV for TlMnCl3 . The absorption coefficient spectrum I(ω) is shown in Fig. 5(a). The spectra indicate clearly that TlMnX3 possesses a significant absorption. The I(ω) spectra are oscillating and reach the maximum absorption strengths of 211.22 × 104 cm−1 around 15.17 eV and 163.23 × 104 cm−1 around 8.26 eV for TlMnF3 and TlMnCl3 , respectively. After these maxima, the spectra keep oscillating while decreasing and reach low values at high energy level especially for TlMnCl3 . The absorption spectrum for TlMnCl3 are concenter in the low energy zone compared to TlMnF3 . This confirms that a crystal field in chlorides is smaller than that in fluorides.13 This has been confirmed in previous studies.6,40 The reflectivity spectrum R(ω) is represented in Fig. 5(b). The zero frequency reflectivity R(0) values are 6.3% and 3.7% for TlMnF3 and TlMnCl3 , respectively. The R(ω) spectra are below 10% in the higher energy range starting from around 12.5 and 22 eV for TlMnF3 and TlMnCl3 , respectively. Therefore, materials are transparent for the incident photons. Hence, the materials can be used for making contact lenses in this region and antireflection coatings in the higher energy range. The energy loss function L(ω) shown in Fig. 5(c) describes the plasma oscillations. It is the energy loss of the fast electrons traversing the compound. Different peaks appearing in the spectra of L(ω) correspond to the trailing peaks of R(ω). The plasmon peak values are found to be 2.59 around 20.77 eV for TlMnF3 and 1.31 around 20.15 eV for TlMnCl3 . At these energies, ε1 (ω) approaches zero as seen in Fig. 3(b). The effective number N (ω) of valence electrons contributing to optical transitions is calculated using the sum rule.38,39 The calculated oscillator strength of 1650031-12

Ab initio investigation of properties TlMnX3 (X = F, Cl) compounds 30

25

Neff(ω)

20

15

10

5

0 0

5

10

15

20

25

30

35

Energy (eV) Fig. 6. (Color online) Calculated sum rule Neff (ω) of the dielectric function ε(ω) for TlMnF3 in black line and TlMnCl3 in red line. 8000 7000 6000

σ(ω)

5000 4000 3000 2000 1000 0 0

5

10

15

20

25

30

Energy (eV) Fig. 7. (Color online) Calculated optical conductivity σ(ω) of the dielectric function ε(ω) for TlMnF3 in black line and TlMnCl3 in red line.

the sum rule is represented in Fig. 6. The effective numbers of electrons are zero up to approximately 2 and 3 eV for TlMnCl3 and TlMnF3 , respectively. Beyond these energies, N (ω) spectra increase until they saturate with values 15.04 around 31.33 eV for TlMnF3 and 26.36 around 31.58 eV for TlMnCl3 . 1650031-13

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The optical conductivity spectrum σ(ω) is shown in Fig. 7. This spectrum represents the conduction of electrons when applying electromagnetic field. They oscillate, increasing and decreasing, similar to that seen for the I(ω) spectra, with approximately the same locations of peaks in I(ω). The conductivities at zero energy are found to be 16.34 Ω−1 · cm−1 and 78.42 Ω−1 · cm−1 for TlMnF3 and TlMnCl3 , respectively. The maximum values of σ(ω) are found to be 8000 Ω−1 · cm−1 around 8.15 eV and 6285 Ω−1 · cm−1 around 6.00 eV for TlMnF3 and TlMnCl3 , respectively. 3. Conclusion Using ab initio calculations as implemented in WIEN2k code, we investigated the structural, elastic, electronic, magnetic and optical properties of the perovskite TlMnX3 (X = F, Cl) compounds. The calculated structural constants are in agreement with previous theoretical and experiment results. The present compounds are elastically stable and classified as anisotropic and ductile compounds. The melting temperature of the TlMnX3 is evaluated from C11 . It is found in agreement with previous studies. The studied compounds being semiconductors and have indirect (M–X) energy bandgap in the sum of the spin channel. TlMnF3 and TlMnCl3 have integer values of the total magnetic moments and are classified as ferromagnetic compounds. The main peaks of the optical spectra are analyzed by PDOS curve. The static refractive index n(0) is inversely proportional to the energy bandgap of the two compounds. TlMnF3 and TlMnCl3 compounds show beneficial optical properties. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

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