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Half-metallic properties of the new Zr2RhB inverse Heusler alloy with CuHg2Ti–type structure
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 18 (2019) 2590–2594
www.materialstoday.com/proceedings
ICMPC-2019
Half-metallic properties of the new Zr2RhB inverse Heusler alloy with CuHg2Ti–type structure Moaid K Hussain 1, Falah H. Abdulsadah 2 and Mawlood Maajal Ali 3* 1
2
AL-Hussain University College. Kerbala, Iraq. Department of Mechanical Engineering, Z. H. College of Engineering & Technology, Aligarh Muslim University, Aligarh-202002.India 3 Department of Applied Physics, Z. H. College of Engineering & Technology, Aligarh Muslim University, Aligarh-202002.India
Abstract
We examined the electronic and magnetic properties of the new inverse Heusler alloy Zr2RhB with CuHg2Ti–type structure, based on first principles calculation. We found that the Zr2RhB Heusler alloy appears to possess the halfmetallic property, and that the spin-minority states are formed with an energy gap equal to 0.45 eV and a magnetic moment of 2.00 μᵦ/f.u. Finally, the Zr2RhB alloy appears to preserve a full-spin polarisation at the Fermi state, with a wide range of lattice constants, from 6.80 Å to 7.70 Å, thus forming an alloy appropriate for applications of the spintronic. © 2019 Published by Elsevier Ltd. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Zr RhB; Electronic and Magnetic properties.
1. INTRODUCTION Variation Half-metallic (HM) properties, which appear as a metallic conductance in the first spin state and a semiconducting conductance in the second, which lead to full-spin polarisation (100%) in the Fermi state, are a source of considerable interest within spintronic research. Full-Heusler X YZ compounds are represented by two types: the CuHg2Ti structures, where the number of valence electrons in the transition of (X) Zr atoms is less than that in the Y (Rh) atoms; and the Cu2MnAl (L22) type, which forms under the inverse condition [1]. Zr2-inverse Heusler compounds obey the S–P rule Mt=Zt–18 [2] and our research focuses mainly on new Zr2RhB Heusler
* Corresponding author. Tel.: +917895533477. E-mail address: [email protected]
2214-7853 © 2019 Published by Elsevier Ltd. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019
M.K. Hussain et al. / Materials Today: Proceedings 18 (2019) 2590–2594
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compound based on the CuHg2Ti structure, with Zr(A) located at (1/4 ,1/4 ,1/4), Zr(B) at (0,0,0), Rh atom at (1/2,1/2,1/2) and B atom at (3/4,3/4,3/4). This work is structured to predict the calculation of the lattice parameters, electronic and magnetic properties of the new inverse Heusler Zr2RhB. 2. COMPUTATIONAL METHOD To examine the half metallic properties of inverse Heusler Zr2RhB, we used the (FP-LAPW) based on the Wien2k package [3]. For the exchange and correlation interactions we applied the local density approximation (LDA) with the Ceperley–Alder as parametrized by Perdew–Zunger (CA-PZ) [4]. For the Zr2RhB alloy, we selected lmax = 4 as the maximum value of the angular momentum potential within the MT spheres. The plane wave cut-off value was RmtKmax = 9. For the Brillouin zone, we used a 15 × 15 ×15 k mesh with the muffin-tin (MT) radius for Zr1, Zr2 and Rh being 2.41 a.u. with B equal to 2.27 a.u. The self-consistency and the total energy are taken as smaller than 0.00001e/(a.u.)³ 10⁻ ⁵ Ry/f.u. respectively. 3. RESULTS AND DISCUSSION Using the empirical Murnaghan equation of state [5] we determine the lattice constant parameters of the Zr2RhB alloy for two phases, magnetic (M) and non-magnetic (NM), and we note that the magnetic phase has lower energy and is more stable with respect to non-magnetic phase, as shown in Fig. 1. The values of the lattice constant, bulk modulus, derivative of bulk modulus and formation enthalpy of the Zr2RhB compound are a=6.91 Å, B=161.232 GPa, B =5.546 and ΔH= –0.54 eV/atom, respectively, where the negative value of the formation enthalpy means that it is possible to synthesise this compound experimentally. In the Zr2RhB alloy, the spin polarisation (P) equals 100% according to equation (1) [6]. P
N
N
/ N
N
Х 100%
Fig. 1. Total energy as a function of unit cell volume for the Zr2RhB compound in the CuHg2Ti-type
(1)
structures in M and NM states.
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The total and partial density of states of the Zr2RhB Heusler compound were obtained by using the above equilibrium lattice parameters, and the results are given in Fig. 2 and Fig. 3. We observed that the majority-spin state has a metallic character, while the minority-spin state is semiconducting and appeared with an energy gap at the Fermi level. The calculated magnetic moments of the Zr2RhB alloy are integers of 2 μᵦ/f.u. with atomic magnetic moments of 0.75 μᵦ for Zr (A), 0.47 μᵦ for Zr (B), –0.13 μᵦ for Rh and −0.08 μᵦ for B. The results obey the Slater– Pauling rule of Mt = Zt–18, where Mt is the total spin magnetic moment and Zt the total number of valence electrons in the unit cell. We observed that atoms of Zr (A) are larger than those of Zr (B). We also note that the magnetic moment of the Rh atom is a negative value and less than that of the Zr atom. This means that the Zr atoms have a spin magnetic moment. This is due to the number of valence electrons of the Zr atoms. The energy gap formed in the minority-spin channel by the valance state maximum (Ev) and the conduction state minimum (Ec) equalled –0.39 eV and 0. 6 eV, respectively, thus the width of the energy gap at the Fermi level is 0.45 eV. This is caused by the hybridization between the Rh–d, Zr (A)-d and Zr (B) –d states. The band structures of Zr2RhB for spin-majority and spin-minority states are shown in Fig. 3. We observed clearly that the spin-majority state is metallic, while the spin-minority appears to have a clearer energy gap at the Fermi level. Furthermore, to discuss the relation between the half-metallic property and the wide range of the lattice constants, between 6.80 Å and 7.70 Å, due to this property is important in the application of the spintronic. We calculate the total and partial magnetic moments for lattice constants between 6.80 Å and 7.75 Å and observed that the magnetic moments for the Zr (A), Zr (B), Rh and B atoms of the Zr2RhB Heusler compound increase with an increase in the lattice constants, while the width of the energy gaps decrease with an increase in the lattice constant within the range of 6.80 Å and 7.70 Å. We also observed that when the lattice constant was above 7.70 Å, the energy gap disappeared, due to the breaking of the hybridization and that this leads to the loss of the compound’s HM properties (see table 1).
Fig. 2. Density of states (DOS) of Zr RhB compound for both Total density and Atom resolved density. The blue (red) collars are denoted to spin-up and spin-down, respectively.
M.K. Hussain et al. / Materials Today: Proceedings 18 (2019) 2590–2594
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Fig. 3. Band structure of the Zr RhB compound. (Spin-up and spin-down)
Table 1. Total and atom-resolved spin magnetic moments in (μB) and Energy gap in (eV) as a function of lattice constant of Zr2RhB compound a (Å) 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.75
Zr(A) 0.73 0.74 0.75 0.77 0.78 0.81 0.84 0.78 0.90 0.94 0.92
Zr(B) 0.44 0.47 0.51 0.54 0.58 0.63 0.69 0.75 0.80 0.86 0.85
Rh -0.10 -0.13 -0.17 -0.21 -0.26 -0.33 -0.40 -0.48 -0.56 -0.64 -0.62
B -0.07 -0.08 -0.08 -0.09 -0.10 -0.11 –0.12 –0.13 –0.14 -0.14 -0.14
Total 1.99 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 1.98
Energy gap (eV) 0.45 0.45 0.45 0.35 0.44 0.44 0.44 0.44 0.43 0.32 --
4. CONCLUSIONS We have predicted the electronic and magnetic properties of the new Zr2RhB Heusler alloy. The calculations showed the stable HM ferromagnetic characteristic of the Zr2RhB alloy with a magnetic moment of 2.00μᵦ/f.u, also appeared and the energy gap in the minority-spin state equaled 0.45 eV based on a lattice constant equal to 6.91 Å. The Zr2RhB compound appears to have the half-metallic property for a wide range of lattice constants between 6.80 Å and 7.70 Å.
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M.K. Hussain et al. / Materials Today: Proceedings 18 (2019) 2590–2594
ACKNOWLEDGMENTS This work was supported by the AL-Hussain University College, Iraq. References [1] J. K¨ubler, A. R. Williams, and C. B. Sommers, Phys. Rev B, 28, (1983) 1745. [2] A. Birsan, V. Kuncser, arXiv:1411.7154v1 [cond-mat.mtrl-sci] 26, Nov (2014). [3] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Hvasnicka, J. Luitz, Karlheinz Schwarz, WIEN2k,( Techn. Universit Wien, AustriaISBN (2001) 12. [4] D. D. Koelling and B. N. Harmon, J. Phys. C 10, (1977) 3107. [5] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, (1947) 244. [6] R.J. Soulen Jr., et al., Science 282,(1998) 85.
ScienceDirect Materials Today: Proceedings 18 (2019) 2590–2594
www.materialstoday.com/proceedings
ICMPC-2019
Half-metallic properties of the new Zr2RhB inverse Heusler alloy with CuHg2Ti–type structure Moaid K Hussain 1, Falah H. Abdulsadah 2 and Mawlood Maajal Ali 3* 1
2
AL-Hussain University College. Kerbala, Iraq. Department of Mechanical Engineering, Z. H. College of Engineering & Technology, Aligarh Muslim University, Aligarh-202002.India 3 Department of Applied Physics, Z. H. College of Engineering & Technology, Aligarh Muslim University, Aligarh-202002.India
Abstract
We examined the electronic and magnetic properties of the new inverse Heusler alloy Zr2RhB with CuHg2Ti–type structure, based on first principles calculation. We found that the Zr2RhB Heusler alloy appears to possess the halfmetallic property, and that the spin-minority states are formed with an energy gap equal to 0.45 eV and a magnetic moment of 2.00 μᵦ/f.u. Finally, the Zr2RhB alloy appears to preserve a full-spin polarisation at the Fermi state, with a wide range of lattice constants, from 6.80 Å to 7.70 Å, thus forming an alloy appropriate for applications of the spintronic. © 2019 Published by Elsevier Ltd. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Zr RhB; Electronic and Magnetic properties.
1. INTRODUCTION Variation Half-metallic (HM) properties, which appear as a metallic conductance in the first spin state and a semiconducting conductance in the second, which lead to full-spin polarisation (100%) in the Fermi state, are a source of considerable interest within spintronic research. Full-Heusler X YZ compounds are represented by two types: the CuHg2Ti structures, where the number of valence electrons in the transition of (X) Zr atoms is less than that in the Y (Rh) atoms; and the Cu2MnAl (L22) type, which forms under the inverse condition [1]. Zr2-inverse Heusler compounds obey the S–P rule Mt=Zt–18 [2] and our research focuses mainly on new Zr2RhB Heusler
* Corresponding author. Tel.: +917895533477. E-mail address: [email protected]
2214-7853 © 2019 Published by Elsevier Ltd. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019
M.K. Hussain et al. / Materials Today: Proceedings 18 (2019) 2590–2594
2591
compound based on the CuHg2Ti structure, with Zr(A) located at (1/4 ,1/4 ,1/4), Zr(B) at (0,0,0), Rh atom at (1/2,1/2,1/2) and B atom at (3/4,3/4,3/4). This work is structured to predict the calculation of the lattice parameters, electronic and magnetic properties of the new inverse Heusler Zr2RhB. 2. COMPUTATIONAL METHOD To examine the half metallic properties of inverse Heusler Zr2RhB, we used the (FP-LAPW) based on the Wien2k package [3]. For the exchange and correlation interactions we applied the local density approximation (LDA) with the Ceperley–Alder as parametrized by Perdew–Zunger (CA-PZ) [4]. For the Zr2RhB alloy, we selected lmax = 4 as the maximum value of the angular momentum potential within the MT spheres. The plane wave cut-off value was RmtKmax = 9. For the Brillouin zone, we used a 15 × 15 ×15 k mesh with the muffin-tin (MT) radius for Zr1, Zr2 and Rh being 2.41 a.u. with B equal to 2.27 a.u. The self-consistency and the total energy are taken as smaller than 0.00001e/(a.u.)³ 10⁻ ⁵ Ry/f.u. respectively. 3. RESULTS AND DISCUSSION Using the empirical Murnaghan equation of state [5] we determine the lattice constant parameters of the Zr2RhB alloy for two phases, magnetic (M) and non-magnetic (NM), and we note that the magnetic phase has lower energy and is more stable with respect to non-magnetic phase, as shown in Fig. 1. The values of the lattice constant, bulk modulus, derivative of bulk modulus and formation enthalpy of the Zr2RhB compound are a=6.91 Å, B=161.232 GPa, B =5.546 and ΔH= –0.54 eV/atom, respectively, where the negative value of the formation enthalpy means that it is possible to synthesise this compound experimentally. In the Zr2RhB alloy, the spin polarisation (P) equals 100% according to equation (1) [6]. P
N
N
/ N
N
Х 100%
Fig. 1. Total energy as a function of unit cell volume for the Zr2RhB compound in the CuHg2Ti-type
(1)
structures in M and NM states.
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The total and partial density of states of the Zr2RhB Heusler compound were obtained by using the above equilibrium lattice parameters, and the results are given in Fig. 2 and Fig. 3. We observed that the majority-spin state has a metallic character, while the minority-spin state is semiconducting and appeared with an energy gap at the Fermi level. The calculated magnetic moments of the Zr2RhB alloy are integers of 2 μᵦ/f.u. with atomic magnetic moments of 0.75 μᵦ for Zr (A), 0.47 μᵦ for Zr (B), –0.13 μᵦ for Rh and −0.08 μᵦ for B. The results obey the Slater– Pauling rule of Mt = Zt–18, where Mt is the total spin magnetic moment and Zt the total number of valence electrons in the unit cell. We observed that atoms of Zr (A) are larger than those of Zr (B). We also note that the magnetic moment of the Rh atom is a negative value and less than that of the Zr atom. This means that the Zr atoms have a spin magnetic moment. This is due to the number of valence electrons of the Zr atoms. The energy gap formed in the minority-spin channel by the valance state maximum (Ev) and the conduction state minimum (Ec) equalled –0.39 eV and 0. 6 eV, respectively, thus the width of the energy gap at the Fermi level is 0.45 eV. This is caused by the hybridization between the Rh–d, Zr (A)-d and Zr (B) –d states. The band structures of Zr2RhB for spin-majority and spin-minority states are shown in Fig. 3. We observed clearly that the spin-majority state is metallic, while the spin-minority appears to have a clearer energy gap at the Fermi level. Furthermore, to discuss the relation between the half-metallic property and the wide range of the lattice constants, between 6.80 Å and 7.70 Å, due to this property is important in the application of the spintronic. We calculate the total and partial magnetic moments for lattice constants between 6.80 Å and 7.75 Å and observed that the magnetic moments for the Zr (A), Zr (B), Rh and B atoms of the Zr2RhB Heusler compound increase with an increase in the lattice constants, while the width of the energy gaps decrease with an increase in the lattice constant within the range of 6.80 Å and 7.70 Å. We also observed that when the lattice constant was above 7.70 Å, the energy gap disappeared, due to the breaking of the hybridization and that this leads to the loss of the compound’s HM properties (see table 1).
Fig. 2. Density of states (DOS) of Zr RhB compound for both Total density and Atom resolved density. The blue (red) collars are denoted to spin-up and spin-down, respectively.
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Fig. 3. Band structure of the Zr RhB compound. (Spin-up and spin-down)
Table 1. Total and atom-resolved spin magnetic moments in (μB) and Energy gap in (eV) as a function of lattice constant of Zr2RhB compound a (Å) 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.75
Zr(A) 0.73 0.74 0.75 0.77 0.78 0.81 0.84 0.78 0.90 0.94 0.92
Zr(B) 0.44 0.47 0.51 0.54 0.58 0.63 0.69 0.75 0.80 0.86 0.85
Rh -0.10 -0.13 -0.17 -0.21 -0.26 -0.33 -0.40 -0.48 -0.56 -0.64 -0.62
B -0.07 -0.08 -0.08 -0.09 -0.10 -0.11 –0.12 –0.13 –0.14 -0.14 -0.14
Total 1.99 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 1.98
Energy gap (eV) 0.45 0.45 0.45 0.35 0.44 0.44 0.44 0.44 0.43 0.32 --
4. CONCLUSIONS We have predicted the electronic and magnetic properties of the new Zr2RhB Heusler alloy. The calculations showed the stable HM ferromagnetic characteristic of the Zr2RhB alloy with a magnetic moment of 2.00μᵦ/f.u, also appeared and the energy gap in the minority-spin state equaled 0.45 eV based on a lattice constant equal to 6.91 Å. The Zr2RhB compound appears to have the half-metallic property for a wide range of lattice constants between 6.80 Å and 7.70 Å.
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M.K. Hussain et al. / Materials Today: Proceedings 18 (2019) 2590–2594
ACKNOWLEDGMENTS This work was supported by the AL-Hussain University College, Iraq. References [1] J. K¨ubler, A. R. Williams, and C. B. Sommers, Phys. Rev B, 28, (1983) 1745. [2] A. Birsan, V. Kuncser, arXiv:1411.7154v1 [cond-mat.mtrl-sci] 26, Nov (2014). [3] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Hvasnicka, J. Luitz, Karlheinz Schwarz, WIEN2k,( Techn. Universit Wien, AustriaISBN (2001) 12. [4] D. D. Koelling and B. N. Harmon, J. Phys. C 10, (1977) 3107. [5] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, (1947) 244. [6] R.J. Soulen Jr., et al., Science 282,(1998) 85.