Electronic structure, elastic and optical properties of MnIn2S4

The elastic constants and various optical properties of MnIn2S4 including the dielectric constant, absorption coefficient, electron energy loss function and reflectivity were calculated as a function of incident photon energy. Those results are discussed in this study and compared with available experimental results.

This paper is available online at http://stdb.hnue.edu.vn

ELECTRONIC STRUCTURE, ELASTIC AND OPTICAL PROPERTIES OF MnIn2S4

Nguyen Minh Thuy and Pham Van Hai

Faculty of Physics, Hanoi National University of Education

Abstract. The electronic, elastic, and optical properties of MnIn2S4 were

investigated using first-principle calculations based on density functional theory

(DFT) with the plane wave basis set as implemented in the CASTEP code Our

study revealed that MnIn2S4has indirect allowed transitions for both DFT and DFT

+ U (U = 6 eV) with energy band gaps of 1.57 eV and 2.095 eV, respectively The

elastic constants and various optical properties of MnIn2S4including the dielectric

constant, absorption coefficient, electron energy loss function and reflectivity were

calculated as a function of incident photon energy Those results are discussed in

this study and compared with available experimental results

Keywords: Inorganic compounds, Ab initio calculations, electronic structure.

Recently, MnIn2S4 which are ternary compounds of the AB2X2 type have received much attention as materials which have potential for optoelectronic application and as magnetic semiconductors [1] In the literature, physical properties of MnIn2S4have been reported [1, 2] Recently, the optical absorption spectra of MnIn2S2 single crystals have been measured and it was found that the fundamental absorption edge is formed by direct

allowed transitions [3, 4] However, Bodnar et al showed that MnIn2S4has both direct and indirect transitions [5] Therefore further calculations of MnIn2S4are needed to clarify the origin of its band gap structure

Density functional theory (DFT) has been the dominant method used when making electronic structure calculations in solid state physics In this work we report on the band structure, optical and elastic properties of MnIn2S4 using density functional theory The calculated results can provide a good model for understanding and predicting other behaviors of this material

Received August 26, 2014 Accepted October 23, 2014.

Contact Nguyen Minh Thuy, e-mail address: thuynm@hnue.edu.vn

2 Content

2.1 Calculation models and methods

MnIn2S4is a spinel-type compound and crystallizes in the space group Fd3m with lattice parameters a = b = c = 10.722 ˚A [4] In this structure, the Mn atoms share the tetrahedral sites, while the In atoms share the octahedral sites, as shown in Figure 1

Figure 1 Crystal structure of cubic MnIn2S4

First principle calculations were performed using the CASTEP module in Materials Studio 6.0 developed by Accelrys Software, Inc Electron-ion interactions were modeled using ultrasoft pseudopotentials The wave functions of the valence electrons were expanded through a plane wave basis set and the cutoff energy was selected as 380 eV The Monkhorst-Pack scheme k-points grid sampling was set at 8× 8 × 8 The convergence

threshold for self-consistent iterations was set at 2× 10 −6 eV/atom In the optimization

process, the energy change, maximum force, maximum stress and maximum displacement tolerances were set at 10−5eV, 0.03 eV/ ˚A, 0.05 GPa and 0.001 ˚A, respectively

2.2 Results and discussion

2.2.1 Electronic structure

We used density functional theory (DFT) to calculate the band structure and the density of states (DOS) of MnIn2S4 The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional were used to describe the exchange-correlation effects The core electrons were replaced by the ultrasoft core potentials Electron configurations were 3p64s23d5 for Mn, 4d10525p1 for In and 3s23p4 for S atoms Both the lattice parameter and the atomic position are optimized

The optimized lattice constants calculated by GGA + PBE (10.854 ˚A) show good

agreement with experimental details 10.722 ˚A [4] in which the difference value is about 3

- 5 percent As is well known, the GGA structural results are somewhat overestimated in comparison with experimental values Calculated band structures of MnIn2S4 are shown

in Figure 2a Coordinates of the special points of the Brillouin zone area are as follow (in terms of unit vectors of the reciprocal lattice): W (0.5, 0.25, 0.75), L (0.5, 0.5, 0.5), G (0,

0, 0), X (0.5, 0, 0.5) and K (0.375, 0.375, 0.750) The calculated band gap Eg 1.57 eV by GGA is smaller than that derived by experiment data, 1.97 eV [4], due to the well-known underestimation of conduction band state energies in DFT calculations One can seen that in MnIn2S4 the top of the valence band and the bottom of the conduction band are simply realized at different points of the Brillouin zone Determination of an appropriate effective Hubbard U parameter is necessary in DFT + U calculation to correctly interpret the intra-atomic electron correlation Here, the effective on-site Coulomb interaction is

U = 6.0 eV and the calculated band gap of spinel MnIn2S4 is 2.095 eV (see Figure 2b) The compound has indirect band gap, which is in agreement with previous data [5] Since the energy gap is indirect, the phonon contribution to the absorption processes should be important

Composition of the calculated energy bands can be resolved with the help of projected density of states (PDOS) and a total density of states (DOS) diagram Figure

3 describes the total and projected density of states of MnIn2S4

Figure 2a Calculated band structure of MnIn2S4with GGA

In Figure 2a Fermi level is set as zero of energy and is shown by the dashed line Coordinates of the special points in the Brillouin zone are in units of the reciprocal lattice unit vectors

Figure 2b Calculated band structure of MnIn2S4 with GGA + U, U = 6 eV

From these diagrams one can seen that the conduction band is about 5 eV wide and

is formed by the Mn 4s and 3d states, which are hybridized with the S 3p states and the In 4s and 3p states The valence band is wider by about 7 eV and consists of two sub-bands that are clearly seen in the band structure as well; the upper one (between -5 and 0 eV)

is a mixture of the S 3p states and Mn 3d states and the lower one is narrow (between -7 and -5 eV) due to the In 5s states Another band between -10 and -15 eV consists of two sub-bands created by the In 4d states (between -15 and -13 eV) and the S 4s states (between -12 and -10 eV)

Figure 3 Calculated total DOS (bottom) and partial density

of states PDOS for In, Mn (middle) and S (top)

2.2.2 Elastic properties and bulk modulus

Elastic properties of single cubic crystal can be described using the independent elastic moduli C11, C12 and C44 For the cubic crystal, its mechanical stability requires Born’s stability criteria: [6, 7]

(C11− C12 ) > 0, C11> 0, C44 > 0, (C11 + 2C12) > 0 (2.1) These conditions also lead to a restriction on the magnitude of the bulk modulus

B [7]:

These conditions are satisfied by the calculated elastic constants at zero external pressure in Table 1 This ensures the elastic stability of the compound and the accuracy

of the calculated elastic modulus The anisotropy factor A = (2C44+ C12)

C11 = 1.45 shows

that MnIn2S4 can be regarded as elastically anisotropic [8] The value of the B/G ratio of MnIn2S4is 2.96 (where G is the isotropic shear modulus), which is larger than the critical value 2.75 in Ref [9], separating the ductile and brittle materials, indicating that MnIn2S4 behaves in a ductile manner

Young’s modulus and Poisson’s ratio are major elasticity related characteristic properties for a material and are calculated using the following relations [10]:

γ = 1

2

[

B − (2/3) G

B + (1/3) G

]

(2.4)

Table 1 Elastic constants C ij , bulk modulus B, shear modulus G, Young’s modulus Y

(all in GPa), Poisson’s ratio γ at zero pressure and anisotropy factor A

The numbers in parantheses are the estimated errors of the mean in the last decimal place,

e.g., 77(1) = 77 ± 1, or 3.2(1) = 3.2 ± 0.1

It is known that the values of the Poisson ratio are minimal for covalent materials and increase for ionic systems In our case, the calculated Poisson ratio is 0.35, which means a sizable ionic contribution in intra-bonding

Comparing the bulk modulus and its pressure derivate with the above calculations,

we calculated the optimized geometry for different values of pressure in the range from 0 to 8 GPa, which corresponds to typical range of pressure experiments [10, 11] Experimental studies have shown that MnIn2S4 maintains a spinel-type crystal structure

until a pressure of up to around 7 GPa Figure 3 presents the dependence of the relative volume change V/V0 on pressure P for MnIn2S4 The calculated results shown by squares

in Figure 3 were fitted to the Birch-Murnaghan equation of state (EOS):

P (V ) = 3B0

2

[(

V0 V

)7 3

−

(

V0 V

)5 3

] {

1 + 3

4(B

′

0− 4)

[(

V0 V

)2 3

− 1

]}

(2.5)

where B0 and B’0 are the bulk modulus and its pressure derivative, respectively

Figure 4 Dependence of V/V0volume ratio on pressure

The least-squares fits to Eq (5) are shown in Figure 4 by solid lines From these approximations, the values of B0 and B’0 are 66± 1 GPa and 4.4 ± 0.1 GPa, respectively.

Table 2 shows the bulk moduli B0values obtained using different methods The plot value extracted from the bulk moduli B0(fitted EOS) is smaller than those obtained as the results

of the elastic constants calculations (Table 1) and experiments in Ref [10], indicating that elastic constant calculations provide better results

Table 2 Summary of elastic parameters for MnIn2S4

Calculations

[3]

Exp

[3]

Theor

[10]

Fitted from Birch-Murnaghan EOS

Calculated from elastic constants

Bulk modulus pressure

2.2.3 Optical properties

The optical properties of MnIn2S4 are determined by the frequency dependent

dielectric function ε (ω) = ε1(ω)+iε2(ω) that describes the response of the system in the

presence of electromagnetic radiation and governs the propagation behavior of radiation in

a medium The imaginary part of the dielectric constant ε1 (ω) can be calculated from the

momentum matrix elements between the occupied and unoccupied electronic states within the selection rule, and its real part can be derived from the Kramer–Kronig relationship

All of the other optical constants, such as the refractive index n(ω), absorption coefficient

α (ω), reflectivity R(ω) and electron energy-loss function L(ω), can be deduced from ε1

(ω) and ε2 (ω).

Figure 5 shows the imaginary part ε2 (ω) and the real part ε1 (ω) of the dielectric

function for MnIn2S4 Here we have calculated the dielectric constant within GGA and

a scissors operator 0.9 eV is used to correct the theoretical and experimental band gap Experimental dielectric functions measured for single crystals of MnIn2S4 using variable angle spectroscopic ellipsometry [12] are taken for comparison Very good agreement with experiment data is obtained for the dielectric functions in both components The

static dielectric constants at ω → 0 are ε1 = 6.21, which show consistent agreement with

an experimental value of 6.24 [4], suggesting that the choice of parameters is reasonable

The regions in which the imaginary part ε2 (ω) is different from zero can be related to the

absorption spectrum and originate predominantly from the transitions of O1 2p and O2 2p electrons into the Mn 5d and In 3d conduction band

Figure 5 Calculated dielectric function of MnIn2S4

The optical parameters of interest, namely, the complex refractive index, n, the normal incidence reflectivity and the absorption coefficient, have been computed using well known mathematical expressions (Figure 6) The values obtained are in good agreement with those estimated using optical absorption measurements performed on MnIn2S4single crystals [4, 11]

Electron energy-loss function (ELF) is an important optical parameter, indicating the energy-loss of a fast electron traversing the material The prominent peak in the spectrum is identified as the energy of plasmon oscillation, signaling the collective excitations of the electronic charge density in the material For MnIn2S4 (Figure 7), this energy is found to be approximately 13 eV

Figure 6 Calculated optical properties of MnIn2S4

Figure 7 Electron energy loss function for MnIn2S4

3 Conclusion

In summary, DFT and DFT + U approaches are used to study the electronic structure and the optical and elastic propeties of MnIn2S4 bulk crystal in the present paper The band structure reveals that MnIn2S4 has a K-G indirect band transition in the Brillouin zone The top valance band consists mainly of a mixture of the S 3p and Mn 3d states whereas the bottom of the conduction band is formed by Mn 4s and Mn 3d states An effective Hubbard parameter U = 6 eV was added to the Mn d-d interaction in order to correct the energy band gap using experimental values The obtained values of lattice constant, elastic constants and optical parameters are in very good agreement with other studies Therefore, this model can be useful to investigate different properties of AB2X4 compounds

REFERENCES

[1] N N Niftiev, 1994 Solid State Communications 92 (9), pp 781-783.

[2] V Sagredo, M C Moron, L Betancourt and G E Delgado, 2007 Journal of Magnetism and Magnetic Materials 312 (2), pp 294-297

[3] F J Manjon, A Segura, M Amboage, J Pellicer-Porres, J F Sanchez-Royo, J P Itie, A M Flank, P Lagarde, A Polian, V V Ursaki and I M Tiginyanu, 2007 Physica Status Solidi B-Basic, Solid State Physics 244 (1), pp 229-233

[4] M Leon, S Levcenko, I Bodnar, R Serna, J M Merino, M Guc, E J Friedrich and E Arushanov, 2012 Journal of Physics and Chemistry of Solids 73 (6), pp 720-723

[5] I V Bodnar, V Y Rud and Y V Rud, 2009 Semiconductors 43 (11), pp 1506-1509 [6] M D Segall, P J D Lindan, M J Probert, C J Pickard, P J Hasnip, S J Clark and M C Payne, 2002 Journal of Physics-Condensed Matter 14 (11), 2717-2744 [7] J J Wang, F Y Meng, X Q Ma, M X Xu and L Q Chen, 2010 Journal of Applied Physics 108 (3), 034107-034106

[8] A M Hao, X C Yang, X M Wang, Y Zhu, X Liu and R P Liu, 2010 Journal of Applied Physics 108 (6)

[9] G Vaitheeswaran, V Kanchana, R S Kumar, A L Cornelius, M F Nicol, A Svane, A Delin and B Johansson, 2007 Physical Review B 76 (1), 014107

[10] D Santamaría-Pérez, M Amboage, F J Manjón, D Errandonea, A Mu˜noz, P Rodríguez-Hernández, A Mújica, S Radescu, V V Ursaki and I M Tiginyanu,

2012 The Journal of Physical Chemistry C 116 (26), pp 14078-14087

[11] J Ruiz-Fuertes, D Errandonea, F J Manjon, D Martinez-Garcia, A Segura,

V V Ursaki and I M Tiginyanu, 2008 Journal of Applied Physics 103 (6), 063710-063715