# Electronic, Structural, Mechanical, and Thermodynamic Properties of CoYSb (Y = Cr, Mo, W) Half-Heusler Compounds as Potential Spintronic Materials

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Details

## 3. Results

#### 3.1. Structural Properties

#### 3.2. Magnetic Properties

#### 3.3. Electronic Band Structure

#### 3.4. Mechanical Properties

#### 3.5. Thermodynamic Properties

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kieven, D.; Klenk, R.; Naghavi, S.; Felser, C.; Gruhn, T. I-II-V half-Heusler compounds for optoelectronics: Ab initio calculations. Phys. Rev.
**2010**, B81, 075208. [Google Scholar] [CrossRef] - Wurmehl, S.; Fecher, G.H.; Kandpal, H.C.; Kseno-fontov, V.; Felser, C.; Lin, H.J.; Morais, J. Geometric, electronic, and magnetic structure of Co
_{2}FeSi: Curie temperature and magnetic moment measurements and calculations. Phys. Rev. B**2005**, 72, 184434. [Google Scholar] [CrossRef] [Green Version] - Wolf, S.A.; Awschalom, D.D.; Buhrman, R.A.; Daughton, J.M.; von Molnar, S.; Roukes, M.L.; Chtchelkanova, A.Y.; Treger, D.M. Spintronics: A spin-based electronics vision for the future. Science
**2001**, 294, 1488–1495. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Roy, A.; Bennett, J.W.; Rabe, K.M.; Vanderbilt, D. Half-Heusler semiconductors as piezoelectrics. Phys. Rev. Lett.
**2012**, 109, 037602. [Google Scholar] [CrossRef] [Green Version] - Xiao, D.; Yao, Y.; Feng, W.; Wen, J.; Zhu, W.; Chen, X.Q.; Stocks, G.M.; Zhang, Z. Half-Heusler compounds as a new class of three-dimensional topological insulators. Phys. Rev. Lett.
**2010**, 105, 096404. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lin, H.; Wray, L.A.; Xia, Y.; Xu, S.; Jia, S.; Cava, R.J.; Bansil, A.; Hasan, M.Z. Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena. Nat. Mater.
**2010**, 9, 546–549. [Google Scholar] [CrossRef] [Green Version] - Zeeshan, M.; Singh, H.K.; den Brink, J.V.; Kandpal, H.C. Ab initio design of new cobalt based half-Heusler materials for thermoelectric application. Phys. Rev. Mater.
**2017**, 1, 075407. [Google Scholar] [CrossRef] [Green Version] - Minami, S.; Fumiyuki, I.; Yo, M.P.; Mineo, S. First-Principle study on thermoelectric properties of half-Heusler compound CoMSb (M= Sc, Ti, V, Cr and Mn). Appl. Phys. Lett.
**2018**, 113, 032403. [Google Scholar] [CrossRef] [Green Version] - Li, S.D.; Yuan, Z.R.; Lu, L.Y.; Liu, M.M.; Huang, Z.G.; Zhang, F.M.; Du, Y.W. Effect of annealing on the magnetic entropy change of CoMnSb alloy. Mater. Sci. Eng. A
**2006**, 428, 332. [Google Scholar] [CrossRef] - Larson, P.; Mahanti, S.D.; Kanatzidis, M.G. Structural stability of Ni-containing half-Heusler compounds. Phys. Rev. B
**2000**, 62, 12754. [Google Scholar] [CrossRef] [Green Version] - Mancoff, F.B.; Bobo, J.F.; Richter, O.E.; Bessho, K.; Johnson, P.R.; Sinclair, R.; Nix, W.D.; White, R.; Clemens, B.M. Growth and characterization of epitaxial NiMnSb/PtMnSb C1b Heusler alloy superlattices. J. Mater. Res.
**1999**, 14, 1560. [Google Scholar] [CrossRef] - De Groot, R.A.; Mueller, F.M.; van Engen, P.G.; Buschow, K.H.J. New class of materials: Half-metallic ferromagnets. Phys. Rev. Lett.
**1983**, 50, 2024. [Google Scholar] [CrossRef] [Green Version] - Galanakis, I.; Mavropoulos, P.; Dederichs, P.H. Electronic structure and Slater Pauling behaviour in half-metallic Heusler alloys calculated from first principles. J. Phys. D
**2006**, 39, 765. [Google Scholar] [CrossRef] - Nanda, B.R.K.; Dasgupta, J.I. Electronic structure and magnetism in half-Heusler compounds. Phys. Condens. Matter
**2003**, 15, 73077323. [Google Scholar] [CrossRef] - Kanpal, H.C.; Felse, C.; Seshadri, R. Covalent bonding and the nature of band gaps in some half-Heusler compounds. J. Phys. D Appl. Phys.
**2006**, 39, 776. [Google Scholar] [CrossRef] - Zhong-Yu, Y.; Li, S.; Meng-Mei, P.; Shu-Juan, S. First-principle studies of half-metallicities and magnetisms of the semi-Heusler alloys CoCrTe and CoCrSb. Acta Phys. Sin.
**2016**, 65, 127501. [Google Scholar] [CrossRef] - Tobola, J.; Pierre, J. Electronic phase diagram of the XTZ (X= Fe, Co, Ni; T= Ti, V, Zr, Nb, Mn; Z= Sn, Sb) semi-Heusler compounds. J. Alloys Compd.
**2000**, 296, 243. [Google Scholar] [CrossRef] - Kulkova, S.E.; Eremeev, S.V.; Kakeshita, T.; Kulkov, S.S.; Rudenski, G.E. The electronic structure and magnetic properties of full-and half-Heusler alloys. Mater. Trans.
**2006**, 47, 604. [Google Scholar] [CrossRef] [Green Version] - Scandolo, S.; Giannozzi, P.; Cavaoni, C.; de Gironcoli, S.; Pasquarello, A.; Baroni, S. First-principles codes for computational crystallography in the Quantum-ESPRESSO package. Z. Krist.
**2005**, 220, 574579. [Google Scholar] [CrossRef] - Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G.L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum. J. Phys. Condens. Matter
**2009**, 21, 395502. [Google Scholar] [CrossRef] - Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Nardelli, M.B.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter
**2017**, 29, 465901. [Google Scholar] [CrossRef] [Green Version] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865. [Google Scholar] [CrossRef] [Green Version] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188. [Google Scholar] [CrossRef] - Available online: https://dalcorso.github.io/thermopw (accessed on 29 November 2021).
- Corso, A.D. Elastic constants of beryllium: A first-principles investigation. J. Phys. Condens. Matter
**2016**, 28, 075401. [Google Scholar] [CrossRef] [PubMed] - Wyckoff, R.W.G. Crystal Structures, Crystal Structures, 2nd ed.; John Wiley and Sons: Hoboken, NJ, USA, 1963; Volume 1. [Google Scholar]
- Murnaghan, F.D. The Compressibility of Media under Extreme Pressures. Proc. Natl. Acad. Sci. USA
**1944**, 30, 244. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kubler, J. First principle theory of metallic magnetism. Phys. B+C
**1984**, 127, 257. [Google Scholar] [CrossRef] - Galanakis, I.; Dederichs, P.H.; Mavropoulous, P.H. Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys. Phys. Rev. B
**2002**, 66, 174429. [Google Scholar] [CrossRef] [Green Version] - Page, Y.L.; Saxe, P. Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress. Phys. Rev. B
**2002**, 65, 104104. [Google Scholar] [CrossRef] - Born, M.; Huang, K. Dynamical Theory of Crystal Lattices. Dynamical Theory of Crystal Lattices; Oxford Clarendon Press: Oxford, UK, 1956; pp. 120–156. [Google Scholar]
- Voigt, W. Lehrbuck der Kristallphysik; B. B. Teubner: Leipzig, Germany, 1928; p. 739. [Google Scholar]
- Reuss, A.; Angew, Z. Calculation of the centrifugal limit of mixed crystals due to the plasticity condition for single crystals. Math. Mech.
**1929**, 9, 49. [Google Scholar] - Hill, R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. Lond.
**1952**, 65, 349. [Google Scholar] [CrossRef] - Huntington, H.B. Solid State Physics, F. Seitz and D. Properties of Engineering Ceramics; Kriegel, W., Palmour, H., Eds.; Academic Press Inc.: New York, NY, USA, 1958; Volume 7. [Google Scholar]
- Pugh, S.F. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag.
**1954**, 45, 823. [Google Scholar] [CrossRef] - Rakesh, J.; Jain, V.k.; Chandra, A.R.; Jain, V.; Lakshmi, N. Joural of Superconductivity and Magnetism; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Zener, C. Elasticity and Anelasticity of Metals; University of Chicago Press: Chicago, UK, 1948. [Google Scholar]
- Degheidy, A.R.; Elkenany, E.B. Electronic, optical, and mechanical properties of BN, AlN, and InN with zinc-blende structure under pressure. Chin. Phys.
**2017**, 26, 086103. [Google Scholar] [CrossRef] - Gupta, D.C.; Ghosh, S.J. First-principal study of full Heusler alloys Co
_{2}VZ (Z = As, In). Magn. Magn. Mater.**2017**, 435, 107–116. [Google Scholar] [CrossRef] - Fu, H.; Li, D.; Peng, F.; Gao, T.; Cheng, X. Ab initio calculations of elastic constants and thermodynamic properties of NiAl under high pressures. Comput. Mater. Sci.
**2008**, 44, 774–778. [Google Scholar] [CrossRef] - Anderson, O.L. A simplified method for calculating the Debye temperature from elastic constants. J. Phys. Chem. Solids
**1963**, 24, 909. [Google Scholar] [CrossRef] - Fine, M.E.; Brown, L.D.; Marcus, H.L. Elastic constants versus melting temperature in metals. Scr. Metall.
**1984**, 18, 951–956. [Google Scholar] [CrossRef]

**Figure 1.**The optimized crystal structure of CoYSb (Y = Cr, Mo, and W) for (

**a**) Type-I, (

**b**) Type-II, and (

**c**) Type-III.

**Figure 2.**Calculated total energy as a function of volume in ferromagnetic state for the three possible structural phases (

**a**) CoCrSb, (

**b**) CoMoSb, and (

**c**) CoWSb, respectively.

**Figure 3.**Band structures for CoCrSb (

**a**) majority-spin and (

**b**) minority-spin. The Fermi level is indicated by the dashed horizontal line.

**Figure 4.**Band structures for CoMoSb (

**a**) majority-spin and (

**b**) minority-spin. The Fermi level is indicated by the dashed horizontal line.

**Table 1.**The Wyckoff positions of the three atoms, X, Y, and Z: 4a = (0, 0, 0) a, 4b = (0.5, 0.5, 0.5) a and 4c = (0.25, 0.25, 0.25) a, with the 4d site vacant.

Structural Phase | X | Y | Z |
---|---|---|---|

Type I | 4c | 4b | 4a |

Type II | 4b | 4a | 4c |

Type III | 4a | 4c | 4b |

**Table 2.**The optimized lattice constants, ${a}_{o}$ (Å), equilibrium energies, ${E}_{min}$ (Ry), bulk modulus, B (GPa), and pressure derivative for the bulk modulus, B${}^{\prime}$ for CoYSb (Y = Cr, Mo, W) for the three possible structural phases.

Alloys | Calculations | Structural Phase | ${\mathit{a}}_{\mathit{o}}$ (Å) | B (GPa) | B${}^{\prime}$ | ${\mathit{E}}_{\mathbf{min}}$ (Ry) |
---|---|---|---|---|---|---|

CoCrSb | This work | Type I | 5.848 | 121.4 | 4.66 | −757.944 |

other calculations | ${5.79}^{\mathrm{a}}$ | |||||

${5.820}^{\mathrm{b}}$ | ${135.4}^{\mathrm{b}}$ | |||||

${5.800}^{\mathrm{c}}$ | ||||||

Type II | 6.031 | 97.6 | 4.33 | −757.856 | ||

Type III | 5.935 | 98.6 | 4.71 | −757.869 | ||

${5.935}^{\mathrm{d}}$ | ||||||

CoMoSb | Type I | 5.937 | 152.2 | 4.62 | −873.598 | |

other calculations | ${5.935}^{\mathrm{d}}$ | |||||

Type II | 6.134 | 124.1 | 4.13 | −873.484 | ||

Type III | 6.140 | 131.6 | 3.94 | −873.520 | ||

CoWSb | Type I | 5.939 | 164.9 | 4.32 | −1269.888 | |

Type II | 6.133 | 138.7 | 4.01 | −1269.758 | ||

Type III | 6.145 | 148.2 | 3.81 | −1269.819 |

**Table 3.**The calculated spin magnetic moments in ${\mu}_{B}$ for CoYSb (Y = Cr, Mo, W) compounds for the three possible structural phases comparing with available data.

${\mathit{m}}^{\mathit{spin}}$ (${\mathit{\mu}}_{\mathit{B}}$) | Calculations | Structural Phase | Co | Y | Sb | Void | Total |
---|---|---|---|---|---|---|---|

CoCrSb | This work | Type I | −0.4473 | 2.3766 | −0.0573 | 0.138 | 2.01 |

other calculations | $-{0.36}^{\mathrm{a}}$ | ${2.37}^{\mathrm{a}}$ | $-{0.06}^{\mathrm{a}}$ | ${2.00}^{\mathrm{a}}$ | |||

Type II | −0.4917 | 3.0659 | −0.0625 | 0.328 | 2.84 | ||

Type III | 1.1219 | 1.8089 | −0.0177 | 0.01169 | 3.03 | ||

CoMoSb | Type I | 0.6685 | 0.9017 | −0.0148 | 0.2346 | 1.79 | |

Type II | 1.0329 | 0.4100 | 0.0136 | 0.0435 | 1.20 | ||

Type III | 0.9274 | 0.0711 | 0.0297 | 0.0082 | 1.02 | ||

other calculations | ${0.650}^{\mathrm{b}}$ | ${1.111}^{\mathrm{b}}$ | $-{0.037}^{\mathrm{b}}$ | ${1.82}^{\mathrm{b}}$ | |||

CoWSb | Type I | 1.0274 | 1.2957 | −0.0285 | 0.1955 | 2.49 | |

Type II | 0.8804 | 0.1896 | −0.0178 | 0.0078 | 1.06 | ||

Type III | 1.6376 | 0.4698 | 0.0133 | 0.0293 | 2.15 |

**Table 4.**The calculated minority-spin band gap, half-metallic (HM) gap, and % spin polarization (SP) of Type I CoYSb (Y = Cr, Mo, W).

Compound | Calculations | Band Gap (eV) | HM Gap (ev) | SP % |
---|---|---|---|---|

CoCrSb | This work | 0.81 | 0.21 | 100 |

others | $0.77{}^{\mathrm{a}}$ | $0.22{}^{\mathrm{a}}$ | ||

CoMoSb | 0.32 | 72 | ||

others | $23{}^{\mathrm{b}}$ | |||

CoWSb | 33 |

**Table 5.**Various mechanical properties of CoYSb (Y = Cr, Mo, W) stable phase obtained from the calculated lattice.

Calculated Properties | CoCrSb | CoMoSb | CoWSb |
---|---|---|---|

${C}_{11}$ (GPa) | 202.83 | 250.02 | 264.14 |

${C}_{12}$ (GPa) | 79.61 | 117.98 | 131.46 |

${C}_{44}$ (GPa) | 55.11 | 42.30 | 30.16 |

${C}_{11}-{C}_{12}$ (GPa) | 123.22 | 132.04 | 123.68 |

${C}_{11}$ + 2${C}_{12}$ (GPa) | 362.04 | 485.97 | 527.05 |

B (GPa) | 120.66 | 161.99 | 175.68 |

G (GPa) | 57.63 | 50.59 | 41.61 |

E (GPa) | 149.19 | 137.45 | 115.64 |

A | 0.49 | 0.64 | 0.45 |

$\nu $ | 0.29 | 0.36 | 0.39 |

Pugh’s ratio | 2.09 | 3.20 | 4.22 |

**Table 6.**Average sound velocity (${v}_{m}$), compressional velocity (${v}_{l}$), shear sound velocity (${v}_{s}$), Debye temperature (${\theta}_{D}$), and predicted melting temperature (${T}_{m}$) for the stable phase CoYSb (Y = Cr, Mo, W).

Compound | ${\mathit{v}}_{\mathit{l}}$ (m/s) | ${\mathit{v}}_{\mathit{s}}$ (m/s) | ${\mathit{v}}_{\mathit{m}}$ (m/s) | ${\mathit{\theta}}_{\mathit{D}}$ (K) | ${\mathit{T}}_{\mathit{m}}$ (K) |
---|---|---|---|---|---|

CoCrSb | 5027.79 | 2723.03 | 3037.67 | 354.68 | 1751.73 ± 300 |

CoMoSb | 5105.36 | 2397.30 | 2688.55 | 308.93 | 2030.62 ± 300 |

CoWSb | 4459.49 | 1891.93 | 2113.76 | 243.05 | 2114.07 ± 300 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Uto, O.T.; Adebambo, P.O.; Akinlami, J.O.; Kenmoe, S.; Adebayo, G.A.
Electronic, Structural, Mechanical, and Thermodynamic Properties of CoYSb (Y = Cr, Mo, W) Half-Heusler Compounds as Potential Spintronic Materials. *Solids* **2022**, *3*, 22-33.
https://doi.org/10.3390/solids3010002

**AMA Style**

Uto OT, Adebambo PO, Akinlami JO, Kenmoe S, Adebayo GA.
Electronic, Structural, Mechanical, and Thermodynamic Properties of CoYSb (Y = Cr, Mo, W) Half-Heusler Compounds as Potential Spintronic Materials. *Solids*. 2022; 3(1):22-33.
https://doi.org/10.3390/solids3010002

**Chicago/Turabian Style**

Uto, Oghenekevwe Timothy, Paul Olufunso Adebambo, Johnson Oluwafemi Akinlami, Stephane Kenmoe, and Gboyega Augustine Adebayo.
2022. "Electronic, Structural, Mechanical, and Thermodynamic Properties of CoYSb (Y = Cr, Mo, W) Half-Heusler Compounds as Potential Spintronic Materials" *Solids* 3, no. 1: 22-33.
https://doi.org/10.3390/solids3010002