Half-metallic ferromagnetism and thermoelectric performance of PdFeCrZ (Z = Al, Si, Sb, Ge) Quaternary Heusler alloys for thermo-spintronic applications

Density Functional Theory (DFT) was utilized for a comprehensive analysis of the structural, electronic, magnetic, and thermoelectric properties of PdFeCrZ (Z: Al, Si, Sb, Ge) Quaternary-Heusler alloys (QHAs). The initial phase involved a meticulous examination of the chemical phase of QHA, considering three distinct structural arrangements (Type I, II, and III structures). All the compounds are more stable in ferromagnetic type I structure. The thermodynamic and dynamic stabilities of the studied compounds were confirmed through the calculation of their formation energy and phonon dispersion curve. The band structure analysis was performed using the Generalized Gradient Approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional and the modified Becke-Johnson (mBJ) approach. The later shows a half metallic ferromagnetic behavior for both PdFeCrAl and PdFeCrSi compounds, nearly half-metallic ferromagnetic behavior for PdFeCrSb, and no band gap for PdFeCrGe (spin gapless). Moreover, the magnetic moments exhibit a value of 4.97 µB for PdFeCrSb, and an integer values of 3, 4 and 4 µB for PdFeCrAl, PdFeCrSi and PdFeCrGe, respectively, consistent with the Slater-Pauling rule. The Curie temperatures of the investigated PdFeCrZ (Z = Al, Si, Sb, Ge) compounds were calculated using the mean-field approximation. To assess thermal performance, Boltzmann’s transport theory was employed, allowing the calculation of essential thermoelectric properties across a broad temperature range (300 to 600 K). These properties include the Seebeck coefficient (S), electrical conductivity ($\sigma$/τ), thermal electronic conductivity (κ_e/τ), power factor (PF), and the figure of merit (zT). The calculated zT values range between 0.56 and 0.84. The obtained results confirm the potential applicability of these compounds in advanced thermo-spintronic devices. This study is important as it could pave the way for more efficient energy conversion and storage technologies, ultimately enhancing the performance of next-generation electronic devices.