Computational Insights into the Structural, Electronic, Mechanical, Magnetic, and Thermodynamic Properties of New Half-Metallic Ferromagnetic Full-Heusler Alloys Cr₂HfZ (Z = Ge, Sb, and Pb) Using FP-LAPW Method

Abstract

This study reports theoretical calculations of the structural, electronic, magnetic, elastic and thermodynamic properties of Cr₂HfZ ternary alloys (Z = Ge, Sb, and Pb) through the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method based on The Wien2k program is reported in structure type L2₁ (type AlCu₂Mnl).The exchange-correlation potential is evaluated using the generalized gradient approximation (GGA) within the Perdew–Burke–Ernzerhof (PBE) parameterization. The calculated lattice constants for Cr₂HfGe, Cr₂HfSb, and Cr₂HfPb are 6.1953, 6.1949, and 6.5100 Å, respectively. The electronic structures show that both compounds have Half-metallic properties by showing 100% spin polarization near the Fermi level. The mechanical stability reveals that, all our compounds are stable mechanically. The Young’s modulus, Poisson’s ratio, zener anisotropy factor and density were calculated and discussed in detail. The total magnetic moment of 4.00μ_B is mainly contributed by the Cr atom. Furthermore, the thermodynamic properties, such as the heat capacity ${{{\text{C}}}_{{\text{V}}}}$, the thermal expansion coefficient ${{\alpha }}$, bulk modulus ${{\beta }}$ and the Debye temperature ${{{{\theta }}}_{{\text{D}}}}$, are computed by using the quasi-harmonic Debye model within the same pressure range at a series of temperature from 0 to 1400 K. Our obtained results for these quantities make these compounds attractive candidates for materials used in spintronic devices.