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Corroborating the Spin Gapless Character of Ti2Mnal Inverse Heusler Alloy: A study of Strains Effect
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 15421–15425
www.materialstoday.com/proceedings
ISCAS 2017
Corroborating the Spin Gapless Character of Ti2Mnal Inverse Heusler Alloy: A study of Strains Effect Mukhtiyar Singh1*, Manish K. Kashyap2 and Hardev S. Saini3 1 Department of Applied Physics, Delhi Technological University, Delhi, India 2 Department of Physics, Kurukshetra University, Kurukshetra, Haryana, India 3 Department of Physics, Guru Jambheshwar University of. Science & Technology, Hisar, Haryana, India
Abstract Nowadays, In the present study, inverse Heusler alloy based spin-gapless semiconductor (SGS), Ti2MnAl is investigated using full potential linearized augmented plane wave (FPLAPW) method implemented in WIEN2k crystal programme. Our investigation reveals that this alloy behaves as SGS, with zero total magnetic moment, for equilibrium lattice constant (6.23 Å). Further, it keeps its spin gapless state within -15% to 10% uniform strain. On the other hand, for -5% of tetragonal strain, the system behaves as SGS whereas the positive 5% tetragonal strain completely destroys the spin-gapless character of Ti2MnAl Heusler alloy. The up-spin band gap for Ti2MnAl is 0.55 eV and 0 eV for spin down channel for equilibrium lattice constant. It varies up to a maximum value of 0.31 eV and 0.36 eV for positive and negative uniform strain, respectively. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. Our calculations provide an exhaustive data to be compared with future experiments and advocate the future applications of this alloy in spintronic applications.
© 2018 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of 10th NATIONAL CONFERENCE ON SOLID STATE CHEMISTRY AND ALLIED AREAS (ISCAS - 2017).
Keywords: Heusler Alloys, Spin-Gapless Semiconductors, FPLAPW Method
*Email address: [email protected], [email protected]
2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of 10th NATIONAL CONFERENCE ON SOLID STATE CHEMISTRY AND ALLIED AREAS (ISCAS - 2017).
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M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
Introduction
The development of high performance computing during last decades along with the amazing predictive power of material modeling methods with consistent accuracy enable material scientists to discover new novel materials and motivates experimentalists to fabricate these for technological advancement. Heusler alloys are one of such novel materials. Since the discovery of ternary Heusler alloy NiMnSb [1] as half-metal, a large amount of scientific endeavor has been devoted to this arena. Apart from the conventional ternary Heusler alloys with stoichiometric composition, L21- and C1b-type structures, the new structural variant of Heusler structure i.e. inverse Heusler alloys (X-structure) have also potential in spintronics applications [2-4]. These alloys are known for high TC and small magnetic moment [5] due to strong direct exchange interaction between like atoms. Recently, Wang [6] suggested a new material terminology, namely, spin-gapless semiconductors (SGS) which is a class of materials bridging the gap between half-metals and magnetic semiconductors; where there is an almost vanishing zero-width energy gap at the Fermi level (EF) in the one spin-direction and a usual energy gap in the other spin-direction. The SGS can be thought as a combination of gapless semiconductor and a half-metallic (HM) ferromagnet [7]. In the case of SGS, the picture of the either spin band is similar to the HM ferromagnet but in the other spin band the EF falls within a zero-width gap. It is observed that when any material is incorporated as a device, such as thin films, mechanical strains may arise either naturally or unintentionally. This induced strain may substantially alter the electronic and magnetic properties of the device [8]. Therefore, it is very important to study a system under the effect of strains. With this motivation, we have treated Ti2MnAl SGS under volume conserving uniform and tetragonal strains. 2
Theoretical approach
The density functional theory (DFT) based all-electron full potential linearized augmented plane wave (FPLAPW) method, as implemented in WIEN2k code [9], has been used to perform the electronic structure calculations of SGS Ti2MnAl. In this method, the core states are treated fully relativistically whereas the valence states as semirelativistically. The exchange and correlation (XC) effects were taken in to account by GGA (Generalized Gradient Approximation) formalism under parameterization of Perdew-Burke-Ernzerhof (PBE) [10]. The nonoverlapping muffin-tin radii (RMT) of Ti, Mn and Al were chosen as large as possible so as to obtain nearly touching spheres and to ensure minimum charge leakage. The energy convergence criterion was set to 10-4 Ry and the charge convergences were also monitored along with it. 3
Result and Discussion
The equilibrium lattice constants of unstrained Ti2MnAl inverse Heusler alloy were estimated for both X- and L21structures by fitting the semi-empirical Murnaghan equation of state [11]. It is observed that this alloy is stable in Xstructure and the corresponding optimized lattice constant is found to be 6.23 Å which is in a close agreement with 6.24 Å, as calculated by Skaftouros et al. [12]. Our investigation reveals that this alloy behaves as SGS, with zero total magnetic moment, for equilibrium lattice constant. Since the spin-gapless property is very delicative and often attributed to unstrained structure, it is very important to analyse, for realistic application, whether the spin-gapless character of Ti2MnAl inverse Heusler alloy retains or not with the strains. We have treated this system with uniform and tetragonal strains. The total density of states (DOS) for various values of uniform and tetragonal strains are represented in Fig.1(a) and 1(b), respectively. Ti2MnAl Heusler alloy retains its spin-gapless state from -15% to 10% of uniform strain. On the other hand, for negative 5% of tetragonal strain the system behaves as SGS whereas the positive 5% tetragonal strain completely destroys the spin-gapless character of Ti2MnAl Heusler alloy. We have also studied the effect of both types of strains on magnetic moment of Ti2MnAl. The total magnetic moment for unstrained Ti2MnAl and for all studied strain values remains zero. This makes Ti2MnAl of special interest for spintronics application since it creates no external stray fields and thus exhibiting minimum energy loses. The magnetic moment at Mn site positive and of the order of 2.2 µB but magnetic moment at two Ti sites alling antiferromagnetically to the Mn atom, which fully compensate the total magnetic moment to zero.
M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
Fig. 1(a): Calculated total DOS of Ti2MnAl under uniform strain.
Fig. 1(b): Calculated total DOS of Ti2MnAl under tetragonal strain.
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M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
The origin of band gap in upper spin channel in this SGS is same as in other inverse Heusler alloys. It mainly d-dhybridizations between transtiom metal atoms which lead to the band formation in the particular spin channel. The sp-element (Al) does not affect the band-gap, its interaction with transition metal atoms i.e. p-d hybriizations only covers up the effect of lattice constant. This is due to the fact that expansion or contraction of lattice parameter only affect the delocalized p electrons not the well localized transition metal d electrons [13]. The value of band gap in up spin channel for equilibrium lattice constant is 0.55 eV and 0 eV for down spin channel. It varies up to 0.31 eV and 0.36 eV for 10% of positive and 15% of negative uniform strain, respectively as shown in Fig. 2. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. Thus, an appreciable magnetic moment and SGS character makes Ti2MnAl makes the an important material for magnetic storage devices also.
Fig. 2: Variation of energy band gap in up spin channel vs uniform strain.
4
Conclusions
we have focused on the investigating the effect of volume conserving uniform and tetragonal strains on the spin gapless character of Ti2MnAl inverse Heusler alloy. We carried out this work using DFT based FPLAPW method. Ti2MnAl is a perfect spin-gapless semiconductor at equilibrium lattice constant. The spin-gapless character of this alloy analyzed under uniform and tetragonal strains keeping the volume of unit cell constant and it is found that the spin-gapless character is robust against the uniform strain from -15% to 10% whereas it retains for -5% of tetragonal strain. However, the value of tetragonal strain equal to or more than 5% completely destroy the spin-gapless character of Ti2MnAl. Its total spin magnetic moment is found to be 0.0 µB and not affected by any type of strains. The energy band gap in up spin channel varies up to 0.31 eV and 0.36 eV for maximum values of positive and negative uniform strain, respectively.. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. The present theoretical data could play a key role for the possible future experiment on this type of spin-gapless semiconductor. References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8].
R. A. de Groot, F. M. Mueller, P. G. van Engen and K. H. J. Buschow, Phys. Rev. Lett. 50 (1983) 2024-2027. X. Dai, G. Liu, G. H. Fecher, C. Felser and Y. Li, J. Appl. Phys. 105 (2009) 07E901-3. I. Galanakis, K. Ozdogan, E. Sasioglu and B. Aktas, Phys. Rev. B 75 (2007) 172405-4. M. Meinert, J.-M. Schmalhorst, C. Klewe, G. Reiss, E. Arenholz, T. Böhne and K. Nielsch, Phys. Rev. B 84 (2011) 132405-4. M. Meinert, J.-M. Schmalhorst and G. Reiss, J. Phys.: Condens. Matter 23 (2011) 116005-7. X. L. Wang, Phys. Rev. Lett. 100 (2008) 156404-4. G. Z. Xu, E. K. Liu, Y. Du, G. J. Li, G. D. Liu, W. H. Wang and G. H. Wu, Euro. Phys. Lett. 102 (2013) 17007-6. M. J. Carey, T. Block and B. A. Gurney, Appl. Phys. Lett. 85 (2004) 4442-4444.
M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425 [9]. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka and J. Luitz, WIEN2k, An augmented plane wave + Local Orbitals Program for calculating Crystal Properties, Karlheinz Schwarz, Techn. Universitat Wien, Wien, Austria, 2001, ISBN 3-9501031-1-2.P. [10]. Perdew, S. Burke and M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865-3868. [11]. F. D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 244-247. [12]. S. Skaftouros, K. Özdoğan, E. Şaşıoğlu and I. Galanakis, Appl. Phys. Lett. 102 (2013) 022402-022404. [13]. G. D. Liu, X. F. Dai, H. Y. Liu, J. L. Chen, Y. X. Li, G. Xiao and G. H. Wu, Phys. Rev. B 77 (2008) 014424-12.
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ScienceDirect Materials Today: Proceedings 5 (2018) 15421–15425
www.materialstoday.com/proceedings
ISCAS 2017
Corroborating the Spin Gapless Character of Ti2Mnal Inverse Heusler Alloy: A study of Strains Effect Mukhtiyar Singh1*, Manish K. Kashyap2 and Hardev S. Saini3 1 Department of Applied Physics, Delhi Technological University, Delhi, India 2 Department of Physics, Kurukshetra University, Kurukshetra, Haryana, India 3 Department of Physics, Guru Jambheshwar University of. Science & Technology, Hisar, Haryana, India
Abstract Nowadays, In the present study, inverse Heusler alloy based spin-gapless semiconductor (SGS), Ti2MnAl is investigated using full potential linearized augmented plane wave (FPLAPW) method implemented in WIEN2k crystal programme. Our investigation reveals that this alloy behaves as SGS, with zero total magnetic moment, for equilibrium lattice constant (6.23 Å). Further, it keeps its spin gapless state within -15% to 10% uniform strain. On the other hand, for -5% of tetragonal strain, the system behaves as SGS whereas the positive 5% tetragonal strain completely destroys the spin-gapless character of Ti2MnAl Heusler alloy. The up-spin band gap for Ti2MnAl is 0.55 eV and 0 eV for spin down channel for equilibrium lattice constant. It varies up to a maximum value of 0.31 eV and 0.36 eV for positive and negative uniform strain, respectively. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. Our calculations provide an exhaustive data to be compared with future experiments and advocate the future applications of this alloy in spintronic applications.
© 2018 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of 10th NATIONAL CONFERENCE ON SOLID STATE CHEMISTRY AND ALLIED AREAS (ISCAS - 2017).
Keywords: Heusler Alloys, Spin-Gapless Semiconductors, FPLAPW Method
*Email address: [email protected], [email protected]
2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of 10th NATIONAL CONFERENCE ON SOLID STATE CHEMISTRY AND ALLIED AREAS (ISCAS - 2017).
15422
1
M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
Introduction
The development of high performance computing during last decades along with the amazing predictive power of material modeling methods with consistent accuracy enable material scientists to discover new novel materials and motivates experimentalists to fabricate these for technological advancement. Heusler alloys are one of such novel materials. Since the discovery of ternary Heusler alloy NiMnSb [1] as half-metal, a large amount of scientific endeavor has been devoted to this arena. Apart from the conventional ternary Heusler alloys with stoichiometric composition, L21- and C1b-type structures, the new structural variant of Heusler structure i.e. inverse Heusler alloys (X-structure) have also potential in spintronics applications [2-4]. These alloys are known for high TC and small magnetic moment [5] due to strong direct exchange interaction between like atoms. Recently, Wang [6] suggested a new material terminology, namely, spin-gapless semiconductors (SGS) which is a class of materials bridging the gap between half-metals and magnetic semiconductors; where there is an almost vanishing zero-width energy gap at the Fermi level (EF) in the one spin-direction and a usual energy gap in the other spin-direction. The SGS can be thought as a combination of gapless semiconductor and a half-metallic (HM) ferromagnet [7]. In the case of SGS, the picture of the either spin band is similar to the HM ferromagnet but in the other spin band the EF falls within a zero-width gap. It is observed that when any material is incorporated as a device, such as thin films, mechanical strains may arise either naturally or unintentionally. This induced strain may substantially alter the electronic and magnetic properties of the device [8]. Therefore, it is very important to study a system under the effect of strains. With this motivation, we have treated Ti2MnAl SGS under volume conserving uniform and tetragonal strains. 2
Theoretical approach
The density functional theory (DFT) based all-electron full potential linearized augmented plane wave (FPLAPW) method, as implemented in WIEN2k code [9], has been used to perform the electronic structure calculations of SGS Ti2MnAl. In this method, the core states are treated fully relativistically whereas the valence states as semirelativistically. The exchange and correlation (XC) effects were taken in to account by GGA (Generalized Gradient Approximation) formalism under parameterization of Perdew-Burke-Ernzerhof (PBE) [10]. The nonoverlapping muffin-tin radii (RMT) of Ti, Mn and Al were chosen as large as possible so as to obtain nearly touching spheres and to ensure minimum charge leakage. The energy convergence criterion was set to 10-4 Ry and the charge convergences were also monitored along with it. 3
Result and Discussion
The equilibrium lattice constants of unstrained Ti2MnAl inverse Heusler alloy were estimated for both X- and L21structures by fitting the semi-empirical Murnaghan equation of state [11]. It is observed that this alloy is stable in Xstructure and the corresponding optimized lattice constant is found to be 6.23 Å which is in a close agreement with 6.24 Å, as calculated by Skaftouros et al. [12]. Our investigation reveals that this alloy behaves as SGS, with zero total magnetic moment, for equilibrium lattice constant. Since the spin-gapless property is very delicative and often attributed to unstrained structure, it is very important to analyse, for realistic application, whether the spin-gapless character of Ti2MnAl inverse Heusler alloy retains or not with the strains. We have treated this system with uniform and tetragonal strains. The total density of states (DOS) for various values of uniform and tetragonal strains are represented in Fig.1(a) and 1(b), respectively. Ti2MnAl Heusler alloy retains its spin-gapless state from -15% to 10% of uniform strain. On the other hand, for negative 5% of tetragonal strain the system behaves as SGS whereas the positive 5% tetragonal strain completely destroys the spin-gapless character of Ti2MnAl Heusler alloy. We have also studied the effect of both types of strains on magnetic moment of Ti2MnAl. The total magnetic moment for unstrained Ti2MnAl and for all studied strain values remains zero. This makes Ti2MnAl of special interest for spintronics application since it creates no external stray fields and thus exhibiting minimum energy loses. The magnetic moment at Mn site positive and of the order of 2.2 µB but magnetic moment at two Ti sites alling antiferromagnetically to the Mn atom, which fully compensate the total magnetic moment to zero.
M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
Fig. 1(a): Calculated total DOS of Ti2MnAl under uniform strain.
Fig. 1(b): Calculated total DOS of Ti2MnAl under tetragonal strain.
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M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425
The origin of band gap in upper spin channel in this SGS is same as in other inverse Heusler alloys. It mainly d-dhybridizations between transtiom metal atoms which lead to the band formation in the particular spin channel. The sp-element (Al) does not affect the band-gap, its interaction with transition metal atoms i.e. p-d hybriizations only covers up the effect of lattice constant. This is due to the fact that expansion or contraction of lattice parameter only affect the delocalized p electrons not the well localized transition metal d electrons [13]. The value of band gap in up spin channel for equilibrium lattice constant is 0.55 eV and 0 eV for down spin channel. It varies up to 0.31 eV and 0.36 eV for 10% of positive and 15% of negative uniform strain, respectively as shown in Fig. 2. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. Thus, an appreciable magnetic moment and SGS character makes Ti2MnAl makes the an important material for magnetic storage devices also.
Fig. 2: Variation of energy band gap in up spin channel vs uniform strain.
4
Conclusions
we have focused on the investigating the effect of volume conserving uniform and tetragonal strains on the spin gapless character of Ti2MnAl inverse Heusler alloy. We carried out this work using DFT based FPLAPW method. Ti2MnAl is a perfect spin-gapless semiconductor at equilibrium lattice constant. The spin-gapless character of this alloy analyzed under uniform and tetragonal strains keeping the volume of unit cell constant and it is found that the spin-gapless character is robust against the uniform strain from -15% to 10% whereas it retains for -5% of tetragonal strain. However, the value of tetragonal strain equal to or more than 5% completely destroy the spin-gapless character of Ti2MnAl. Its total spin magnetic moment is found to be 0.0 µB and not affected by any type of strains. The energy band gap in up spin channel varies up to 0.31 eV and 0.36 eV for maximum values of positive and negative uniform strain, respectively.. The value of this gap for -5% and 5% of tetragonal strain is 0.51 eV and 0.46 eV, respectively. The present theoretical data could play a key role for the possible future experiment on this type of spin-gapless semiconductor. References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8].
R. A. de Groot, F. M. Mueller, P. G. van Engen and K. H. J. Buschow, Phys. Rev. Lett. 50 (1983) 2024-2027. X. Dai, G. Liu, G. H. Fecher, C. Felser and Y. Li, J. Appl. Phys. 105 (2009) 07E901-3. I. Galanakis, K. Ozdogan, E. Sasioglu and B. Aktas, Phys. Rev. B 75 (2007) 172405-4. M. Meinert, J.-M. Schmalhorst, C. Klewe, G. Reiss, E. Arenholz, T. Böhne and K. Nielsch, Phys. Rev. B 84 (2011) 132405-4. M. Meinert, J.-M. Schmalhorst and G. Reiss, J. Phys.: Condens. Matter 23 (2011) 116005-7. X. L. Wang, Phys. Rev. Lett. 100 (2008) 156404-4. G. Z. Xu, E. K. Liu, Y. Du, G. J. Li, G. D. Liu, W. H. Wang and G. H. Wu, Euro. Phys. Lett. 102 (2013) 17007-6. M. J. Carey, T. Block and B. A. Gurney, Appl. Phys. Lett. 85 (2004) 4442-4444.
M. Singh et al. / Materials Today: Proceedings 5 (2018) 15421–15425 [9]. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka and J. Luitz, WIEN2k, An augmented plane wave + Local Orbitals Program for calculating Crystal Properties, Karlheinz Schwarz, Techn. Universitat Wien, Wien, Austria, 2001, ISBN 3-9501031-1-2.P. [10]. Perdew, S. Burke and M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865-3868. [11]. F. D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 244-247. [12]. S. Skaftouros, K. Özdoğan, E. Şaşıoğlu and I. Galanakis, Appl. Phys. Lett. 102 (2013) 022402-022404. [13]. G. D. Liu, X. F. Dai, H. Y. Liu, J. L. Chen, Y. X. Li, G. Xiao and G. H. Wu, Phys. Rev. B 77 (2008) 014424-12.
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