Cobalt based new ferromagnetic quaternary Heusler alloys for spintronic applications: an ab-initio study

In this paper, we have studied the structural, mechanical, electronic, magnetic and thermodynamical properties of the Heusler alloys CoNbTiX (X=Al,Ga,In\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = Al, Ga, In$$\end{document}). We used full potential linearized augmented plane wave method based on density functional theory. We analysed and compared the various properties using both GGA and TB-mBJ XC functionals. Our analysis shows that among all the Y1, Y2 and Y3-type structures, Y1-structure is more stable and having ferromagnetic property. Also, the mechanical property analysis reveals that all the alloys are ductile in nature. The density of states of Heusler alloys CoNbTiX (X=Al,Ga,In\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = Al, Ga, In$$\end{document}) shows that in all the alloys the spin up channel having metallic and spin down channel having semi-conducting property. All the Heusler alloys under investigation having the integer spin magnetic moment and the values are concurrence with the Slater - Pauling rule. The thermodynamic properties of the Heusler alloys CoNbTiX (X=Al,Ga,In\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = Al, Ga, In$$\end{document}) like specific heat capacity, thermal expansion, Debye temperature, vibrational free energy, internal energy and entropy are studied using quasi-harmonic approximation.