- Email: [email protected]
Comment on ‘Study of electronic, magnetic, optical and elastic properties of Cu2MnAl a gapless full heusler compound’
Accepted Manuscript Comment on ’Study of Electronic, Magnetic, Optical and Elastic properties of Cu2MnAl a gapless full Heusler compound’ Jaafar Jalilian PII: DOI: Reference:
S0925-8388(14)02898-9 http://dx.doi.org/10.1016/j.jallcom.2014.12.039 JALCOM 32771
To appear in:
Journal of Alloys and Compounds
Received Date: Revised Date: Accepted Date:
18 November 2014 7 December 2014 8 December 2014
Please cite this article as: J. Jalilian, Comment on ’Study of Electronic, Magnetic, Optical and Elastic properties of Cu2MnAl a gapless full Heusler compound’, Journal of Alloys and Compounds (2014), doi: http://dx.doi.org/ 10.1016/j.jallcom.2014.12.039
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Comment on ’Study of Electronic, Magnetic, Optical and Elastic properties of Cu2MnAl a gapless full Heusler compound’ Jaafar Jaliliana,∗ a
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. Tel./ Fax: +98 831 726 5127
Abstract In a recent article by Rai et al. 1 , the electronic, Magnetic, Optical and Elastic properties of Cu2 MnAl heusler have been studied by using FPLAPW method. I studied their article and I found that there are some mistakes in represented electronic, optical and elastic data. The intraband contribution has not been considered in investigating optical properties. Also the values of elastic constants are very different from the experimental and my computed values. I investigated all data again by using similar method, so each spectrum has been compared with Rai et al. calculations. Keywords: Heusler alloy, Cu2 MnAl, Intraband transition, FPLAPW method
∗
Corresponding author Email address: [email protected] (Jaafar Jalilian)
Technical Note submitted to Elsevier
1. Introduction Recently, Rai et al. [1] reported results for electronic magnetic and optical properties of Cu2 MnAl full heusler alloy by using first principles calculations in the framework of full potential linear augmented plane waves (FPLAPW). After reading this paper carefully, I observed that there are some computational and physical description errors in this paper. In the following, I calculated some optical and elastic data and explained the existent differences. All calculations performed by using the FPLAPW method as implemented WIEN2k code 2 . The convergence parameter RM T Kmax was set to 8.5 and the maximum l quantum number for the wave function expansion inside the atomic sphere is confined to lmax = 10. The Gmax parameter was taken to be 14 Ry1/2 . The Brillouin zone k-point integrations are made by using the tetrahedron method 3 on a grid of 4735 k-points in the irreducible part of Brillouin zone (IBZ), which corresponds to 200000 k-points throughout the Brillouin zone.
2. Electronic properties The figure 1 in their manuscript shows the Mn2 CuAl crystal structure, not Cu2 MnAl. Here, the correct crystal structure of this compound is illustrated 2
in the figure 1. The total Density of states (DOS) of the authors show that both spin channels have metallic behavior, and the Cu-d orbitals in both spin channels lie in ∼ -4 eV. While, the Mn-d orbitals in spin up and down channels are situated in -2 and +1 eV, respectively. Therefore there are an exchange splitting about 3 eV between Mn-dt2g and Mn-deg states. But the authors said that this splitting is about 5 eV (top of the page 3). Also the partial DOS for Mn-d orbitals in figure 3 (right panel) is wrong and does not conformance with their total DOS (left panel). Therefore, the correct DOS figures have been plotted in figure 2.
3. Optical properties The half-metal is an ideal ferromagnet metal. For this class of materials, one spin channel has metallic behavior, while in the other spin channel there is an energy gap in the Fermi level 4,5,6,7 . But generally, these materials behaves as a metal. For Cu2 MnAl, both spin channels have metallic behavior and does not half-metallic energy gap in one spin channel. Therefore, when the optical properties of these materials are investigated, the intraband and interband transitions contributions must be considered 8 . In metallic materials in low frequency range, the refractive index (n(ω)) is fewer than the
3
extinction coefficient (k(ω)), so the real part of dielectric function has negative value, ε1 = n2 − k 2 < 0 (see Ref. 7- page 54). In Rai et al. calculations, the intraband transition contribution is not considered in calculating optical properties. Therefore all presented optical spectra for Cu2 MnAl compound are incorrect. Figure 3 illustrate the real and imaginary parts of dielectric function without (top panel) and with (lower panel) considering intraband transitions. For real part, it is obvious that the spectra are very different in 0-2 eV energy ranges. Also in imaginary part, the intraband transitions cause an asymptotic behavior in low energy ranges. Rai et al. in optical properties section represented some reasons for behavior of optical spectra that they do not have scientific background (pages 4 and 5 of the manuscript). They used Penn formula about relation between static dielectric constant and energy gap 9 that this model is correct only for semiconductor materials while the authors used this model for a metal. In following, the other optical spectra such as refractive index, extinction coefficient, optical conductivity and reflectivity are represented. It is obvious that the intraband transition has remarkable effects on optical behavior of Cu2 MnAl compound.
4
4. Elastic properties In this section, Rai et al. calculated the elastic parameters of Cu2 MnAl heusler alloy such as, elastic constants Cij , bulk modulus, shear modulus and etc. The WIEN2k code calculated three independent elastic constants C11 , C12 , C44 for cubic systems by calculating energy of crystal versus volume changes and applying different tetragonal and rhombohedral stress and strain 2 . Then, the others elastic parameters such as bulk, elastic and shear modulus, elastic anisotropy, Poison’s ratio and etc can be determined by these independent constants. Table 1 indicates the Rai et al. and my calculations and available experimental values for elastic parameters. The results show that the Rai et al. calculation for elastic constants is very different from the experimental value. They obtained C44 =460 GPa that is much higher than the experimental value, C44 (exp)=94 GPa 10 . Therefore the other presented elastic parameters by Rai et al. are wrong, so their physical descriptions about elastic properties of Cu2 MnAl are incorrect. All obtained elastic parameters are summarized in table 1. In conclusion, the new results showed that the intraband transition has remarkable effects on behavior of optical spectra of the heusler compounds, and the Rai et al. did not considered this contribution of transition in their 5
calculations. Also the new results for elastic parameters of Cu2 MnAl was presented in this manuscript. The obtained results help scientists to design new applications of heusler materials.
5. Acknowledgements I gratefully acknowledge financial support from the scientific Research Fund of the Young Researchers and Elite club of Islamic Azad University of Kermanshah.
6
Table 1: Elastic constants presented by Rai et al., my calculations and the experimental values at room temperature. All units are in GPa.
B
C
Y
γ
GH
GV
ξ
C11
C12
C44
Rai et al.
115 16.54
237
0.02
116
282
0.83
137
104
460
This work
122
11
84
0.29
48
72
0.89
137
115
112
Exp (Ref 10 )
-
-
-
-
-
-
-
135.3
97.3
94
References [1] D.P. Raia, R.K. Thapab, Study of electronic, magnetic, optical and elastic properties of Cu2 MnAl a gapless full Heusler compound, J. Alloys. Comp. 612 (2014) 355-360. [2] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, J. Luitz and K. Schwarz,. An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties revised edition WIEN2k 13.1 (Release 06/26/2013) Wien2K Users Guide, ISBN 3-9501031-1-2. [3] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 51885192. [4] T. Jungwirth, J. Sinova, J. Masek, J. Kucera, A.H. MacDonald, Theory
7
of ferromagnetic (III,Mn)V semiconductors, Rev. Mod. Phys. 78 (2006) 809-864. [5] Z.H. Liu,H.N. Hu,G.D. Liu,Y.T. Cui,M. Zhang,J.L. Chen,G.H. Wu, Electronic structure and ferromagnetism in the martensitictransformation material Ni2 FeGa , Phys.Rev.B 69 (2004) 134415. [6] L. Hongzhi, Z. Zhiyong, M. Li, X. Shifeng, L. Heyan, Q. Jingping, L. Yangxian, W. Guangheng, Electronic structure and magnetic properties of Fe2 YSi (Y = Cr, Mn, Fe, Co, Ni) Heusler alloys: a theoretical and experimental study, J. Phys. D: Appl. Phys. 40 (2007) 71217127. [7] I. Galanakis, Ph. Mavropoulos, P. H. Dederichs, Electronic structure and SlaterPauling behaviour in half-metallic Heusler alloys calculated from first principles, J. Phys. D: Appl. Phys. 39 (2006) 765775. [8] F. Wooten, Optical Properties of Solids, Academic press, New York, 1972. [9] D. Penn, Wavenuumber-Dependent Dielectric Function of Semiconductors, Phys. Rev. B 128 (1962) 2093.
8
[10] E. D. T. de Lacheisserie, D. Gignoux, M. Schlenker, Magnetism: Fundamentals, Springer Science, ISBN: 0-38723062-9, 2005.
9
Figures captions: Figure 1: (Color online) Crystal structure of Cu2 MnAl full heusler. Figure 2: (Color online)Calculated total DOS of Cu2 MnAl and partial DOS for Cu, Mn and Al atoms. Figure 3: (Color online)Calculated real and imaginary parts of dielectric function without (top panel) and with (lower panel) intraband transition. Figure 4: (Color online)Calculated refractive index and extiction coefficient without (top panel) and with (lower panel) intraband transition. Figure 5: (Color online)Calculated real and imaginary parts of optical conductivity without (top panel) and with (lower panel) intraband transition. Figure 6: (Color online)Calculated reflectivity spectrum.
10
Figure 1:
Figure 2:
11
50
Real Imaginary
40
Interband
Dielectric function
30 20 10 0 25
Intraband + Interband
20 15 10 5 0 -5
-10
0
2
4
6
8
10
Energy (eV) Figure 3:
12
12
14
Refractive index & Extiction coefficient
8
Refractive index Extinction coefficient
6
Interband
4 2 08
Intraband+Interband
6 4 2 0
0
2
4
6
8
10
Energy (eV)
Figure 4:
13
12
14
6
Interband
4
Optical Conductivity
2 0
Real Imaginary
-2
-4 12
Intraband+Interband
9 6 3 0 -3
0
2
4
6
8
Energy (eV)
10
Figure 5:
Reflectivity (%)
100
Interband Intraband+Interband
80 60 40 20
0
2
4
6
8
10
Energy (eV)
Figure 6:
14
12
14
Graphical abstract
Highlights
• • •
There is not half-metallicity gap in both spin channels. The intraband transition has remarkable effects on optical properties of heusler compounds. The correct elastic parameters have been presented.
S0925-8388(14)02898-9 http://dx.doi.org/10.1016/j.jallcom.2014.12.039 JALCOM 32771
To appear in:
Journal of Alloys and Compounds
Received Date: Revised Date: Accepted Date:
18 November 2014 7 December 2014 8 December 2014
Please cite this article as: J. Jalilian, Comment on ’Study of Electronic, Magnetic, Optical and Elastic properties of Cu2MnAl a gapless full Heusler compound’, Journal of Alloys and Compounds (2014), doi: http://dx.doi.org/ 10.1016/j.jallcom.2014.12.039
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Comment on ’Study of Electronic, Magnetic, Optical and Elastic properties of Cu2MnAl a gapless full Heusler compound’ Jaafar Jaliliana,∗ a
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. Tel./ Fax: +98 831 726 5127
Abstract In a recent article by Rai et al. 1 , the electronic, Magnetic, Optical and Elastic properties of Cu2 MnAl heusler have been studied by using FPLAPW method. I studied their article and I found that there are some mistakes in represented electronic, optical and elastic data. The intraband contribution has not been considered in investigating optical properties. Also the values of elastic constants are very different from the experimental and my computed values. I investigated all data again by using similar method, so each spectrum has been compared with Rai et al. calculations. Keywords: Heusler alloy, Cu2 MnAl, Intraband transition, FPLAPW method
∗
Corresponding author Email address: [email protected] (Jaafar Jalilian)
Technical Note submitted to Elsevier
1. Introduction Recently, Rai et al. [1] reported results for electronic magnetic and optical properties of Cu2 MnAl full heusler alloy by using first principles calculations in the framework of full potential linear augmented plane waves (FPLAPW). After reading this paper carefully, I observed that there are some computational and physical description errors in this paper. In the following, I calculated some optical and elastic data and explained the existent differences. All calculations performed by using the FPLAPW method as implemented WIEN2k code 2 . The convergence parameter RM T Kmax was set to 8.5 and the maximum l quantum number for the wave function expansion inside the atomic sphere is confined to lmax = 10. The Gmax parameter was taken to be 14 Ry1/2 . The Brillouin zone k-point integrations are made by using the tetrahedron method 3 on a grid of 4735 k-points in the irreducible part of Brillouin zone (IBZ), which corresponds to 200000 k-points throughout the Brillouin zone.
2. Electronic properties The figure 1 in their manuscript shows the Mn2 CuAl crystal structure, not Cu2 MnAl. Here, the correct crystal structure of this compound is illustrated 2
in the figure 1. The total Density of states (DOS) of the authors show that both spin channels have metallic behavior, and the Cu-d orbitals in both spin channels lie in ∼ -4 eV. While, the Mn-d orbitals in spin up and down channels are situated in -2 and +1 eV, respectively. Therefore there are an exchange splitting about 3 eV between Mn-dt2g and Mn-deg states. But the authors said that this splitting is about 5 eV (top of the page 3). Also the partial DOS for Mn-d orbitals in figure 3 (right panel) is wrong and does not conformance with their total DOS (left panel). Therefore, the correct DOS figures have been plotted in figure 2.
3. Optical properties The half-metal is an ideal ferromagnet metal. For this class of materials, one spin channel has metallic behavior, while in the other spin channel there is an energy gap in the Fermi level 4,5,6,7 . But generally, these materials behaves as a metal. For Cu2 MnAl, both spin channels have metallic behavior and does not half-metallic energy gap in one spin channel. Therefore, when the optical properties of these materials are investigated, the intraband and interband transitions contributions must be considered 8 . In metallic materials in low frequency range, the refractive index (n(ω)) is fewer than the
3
extinction coefficient (k(ω)), so the real part of dielectric function has negative value, ε1 = n2 − k 2 < 0 (see Ref. 7- page 54). In Rai et al. calculations, the intraband transition contribution is not considered in calculating optical properties. Therefore all presented optical spectra for Cu2 MnAl compound are incorrect. Figure 3 illustrate the real and imaginary parts of dielectric function without (top panel) and with (lower panel) considering intraband transitions. For real part, it is obvious that the spectra are very different in 0-2 eV energy ranges. Also in imaginary part, the intraband transitions cause an asymptotic behavior in low energy ranges. Rai et al. in optical properties section represented some reasons for behavior of optical spectra that they do not have scientific background (pages 4 and 5 of the manuscript). They used Penn formula about relation between static dielectric constant and energy gap 9 that this model is correct only for semiconductor materials while the authors used this model for a metal. In following, the other optical spectra such as refractive index, extinction coefficient, optical conductivity and reflectivity are represented. It is obvious that the intraband transition has remarkable effects on optical behavior of Cu2 MnAl compound.
4
4. Elastic properties In this section, Rai et al. calculated the elastic parameters of Cu2 MnAl heusler alloy such as, elastic constants Cij , bulk modulus, shear modulus and etc. The WIEN2k code calculated three independent elastic constants C11 , C12 , C44 for cubic systems by calculating energy of crystal versus volume changes and applying different tetragonal and rhombohedral stress and strain 2 . Then, the others elastic parameters such as bulk, elastic and shear modulus, elastic anisotropy, Poison’s ratio and etc can be determined by these independent constants. Table 1 indicates the Rai et al. and my calculations and available experimental values for elastic parameters. The results show that the Rai et al. calculation for elastic constants is very different from the experimental value. They obtained C44 =460 GPa that is much higher than the experimental value, C44 (exp)=94 GPa 10 . Therefore the other presented elastic parameters by Rai et al. are wrong, so their physical descriptions about elastic properties of Cu2 MnAl are incorrect. All obtained elastic parameters are summarized in table 1. In conclusion, the new results showed that the intraband transition has remarkable effects on behavior of optical spectra of the heusler compounds, and the Rai et al. did not considered this contribution of transition in their 5
calculations. Also the new results for elastic parameters of Cu2 MnAl was presented in this manuscript. The obtained results help scientists to design new applications of heusler materials.
5. Acknowledgements I gratefully acknowledge financial support from the scientific Research Fund of the Young Researchers and Elite club of Islamic Azad University of Kermanshah.
6
Table 1: Elastic constants presented by Rai et al., my calculations and the experimental values at room temperature. All units are in GPa.
B
C
Y
γ
GH
GV
ξ
C11
C12
C44
Rai et al.
115 16.54
237
0.02
116
282
0.83
137
104
460
This work
122
11
84
0.29
48
72
0.89
137
115
112
Exp (Ref 10 )
-
-
-
-
-
-
-
135.3
97.3
94
References [1] D.P. Raia, R.K. Thapab, Study of electronic, magnetic, optical and elastic properties of Cu2 MnAl a gapless full Heusler compound, J. Alloys. Comp. 612 (2014) 355-360. [2] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, J. Luitz and K. Schwarz,. An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties revised edition WIEN2k 13.1 (Release 06/26/2013) Wien2K Users Guide, ISBN 3-9501031-1-2. [3] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 51885192. [4] T. Jungwirth, J. Sinova, J. Masek, J. Kucera, A.H. MacDonald, Theory
7
of ferromagnetic (III,Mn)V semiconductors, Rev. Mod. Phys. 78 (2006) 809-864. [5] Z.H. Liu,H.N. Hu,G.D. Liu,Y.T. Cui,M. Zhang,J.L. Chen,G.H. Wu, Electronic structure and ferromagnetism in the martensitictransformation material Ni2 FeGa , Phys.Rev.B 69 (2004) 134415. [6] L. Hongzhi, Z. Zhiyong, M. Li, X. Shifeng, L. Heyan, Q. Jingping, L. Yangxian, W. Guangheng, Electronic structure and magnetic properties of Fe2 YSi (Y = Cr, Mn, Fe, Co, Ni) Heusler alloys: a theoretical and experimental study, J. Phys. D: Appl. Phys. 40 (2007) 71217127. [7] I. Galanakis, Ph. Mavropoulos, P. H. Dederichs, Electronic structure and SlaterPauling behaviour in half-metallic Heusler alloys calculated from first principles, J. Phys. D: Appl. Phys. 39 (2006) 765775. [8] F. Wooten, Optical Properties of Solids, Academic press, New York, 1972. [9] D. Penn, Wavenuumber-Dependent Dielectric Function of Semiconductors, Phys. Rev. B 128 (1962) 2093.
8
[10] E. D. T. de Lacheisserie, D. Gignoux, M. Schlenker, Magnetism: Fundamentals, Springer Science, ISBN: 0-38723062-9, 2005.
9
Figures captions: Figure 1: (Color online) Crystal structure of Cu2 MnAl full heusler. Figure 2: (Color online)Calculated total DOS of Cu2 MnAl and partial DOS for Cu, Mn and Al atoms. Figure 3: (Color online)Calculated real and imaginary parts of dielectric function without (top panel) and with (lower panel) intraband transition. Figure 4: (Color online)Calculated refractive index and extiction coefficient without (top panel) and with (lower panel) intraband transition. Figure 5: (Color online)Calculated real and imaginary parts of optical conductivity without (top panel) and with (lower panel) intraband transition. Figure 6: (Color online)Calculated reflectivity spectrum.
10
Figure 1:
Figure 2:
11
50
Real Imaginary
40
Interband
Dielectric function
30 20 10 0 25
Intraband + Interband
20 15 10 5 0 -5
-10
0
2
4
6
8
10
Energy (eV) Figure 3:
12
12
14
Refractive index & Extiction coefficient
8
Refractive index Extinction coefficient
6
Interband
4 2 08
Intraband+Interband
6 4 2 0
0
2
4
6
8
10
Energy (eV)
Figure 4:
13
12
14
6
Interband
4
Optical Conductivity
2 0
Real Imaginary
-2
-4 12
Intraband+Interband
9 6 3 0 -3
0
2
4
6
8
Energy (eV)
10
Figure 5:
Reflectivity (%)
100
Interband Intraband+Interband
80 60 40 20
0
2
4
6
8
10
Energy (eV)
Figure 6:
14
12
14
Graphical abstract
Highlights
• • •
There is not half-metallicity gap in both spin channels. The intraband transition has remarkable effects on optical properties of heusler compounds. The correct elastic parameters have been presented.