J Supercond Nov Magn DOI 10.1007/s10948-015-3277-1 REVIEW PAPER Half-Metallic Magnetism of Quaternary Heusler Compounds Co 2 Fe x Mn 1-x Si(x =0,0.5, and 1.0): First-Principles Calculations Bennadji Abderrahim 1 · Mohammed Ameri 2 · Djillali Bensaid 2 · Yahia Azaz 2 · Bendouma Doumi 3 · Yaroub Al-Douri 4 · Fethi Benzoudji 1 Received: 29 July 2015 / Accepted: 28 October 2015 © Springer Science+Business Media New York 2015 Abstract Using first-principles calculations, the struc- tural, electronic, and magnetic properties of ferromag- netic half-metallic full-Heusler Co 2 FeSi, Co 2 MnSi and Co 2 Fe 0.5 Mn 0.5 Si alloy via the full-potential linearized aug- mented plane-wave (FP-LAPW) method in the generalized gradient (GGA) and GGA + U approximations are com- pared with other experimental and theoretical results. The electronic band structures and density of states (DOS) of the compounds indicate they are half metallic because of the existence of the energy gap in the minority spin (DOS and band structure), which yields perfect spin polarization. The half metallicity of the obtained material may prove useful for applications in spin-polarizers and spin-injectors  Djillali Bensaid djizer@yahoo.fr; djillali.bensaid@cuniv-aintemouchent.dz http://univ-sba.dz/lpcma/ 1 Faculty of Exact Sciences, Department of Physics, Djillali Liabes University, PO Box 089, Sidi Bel Abbes, 22000, Algeria 2 Laboratory Physico-chemistry of Advanced Materials, University of Djillali Liabes, BP 89, Sidi-Bel-Abbes, 22000, Algeria 3 Faculty of Sciences, Department of Physics, Dr. Tahar Moulay University of Sa¨ ıda, 20000 Sa¨ ıda, Algeria 4 Institute of Nano Electronic Engineering, University Malaysia Perlis, 01000 Kangar, Perlis, Malaysia of magnetic nanodevices. The calculated total spin mag- netic moments are almost exactly that expected from the Slater-Pauling rule. Keywords Structural properties · Electronic and magnetic properties · Co-based full-Heusler alloys · FP-LAPW method · Half metallicity · Quaternary Heusler 1 Introduction Heusler alloys (HA) attract significant attention due to their interesting physical properties promising various practical applications in the fields of smart and magneto-electronic materials Furthermore another important application is in spintronics, such as tunneling magnetoresistance (TMR) and spin injection into semiconductors. They can also be used as perfect spin filters and spin-injection devices as an alternative to ferromagnetic 3d metals These materials are considered half-metallic ferromagnets because in these sys- tems at the Fermi energy E F one spin direction is metallic and the other has an energy gap, resulting in 100 % spin polarization. Among these materials is Co 2 MnSi which is half metallic and Co 2 MnSi was studied experimentally by Kammer et al. Half-metallic Heusler alloys generally display high Curie temperatures, but more importantly, they are in certain cases closely lattice-matched to semiconductors. For example, Co2FeSi is ferromagnetic up to temperatures beyond 100 K and is lattice-matched to GaAs within 0.08 % [1–5]. Most Co-based full Heusler compounds in the cubic L2 1 struc- ture are ferromagnetic with a high Curie temperature and a significant magnetic moment [6]. In particular, Co 2 MnSi