J Supercond Nov Magn DOI 10.1007/s10948-016-3387-4 ORIGINAL PAPER Electronic and Magnetic Properties of Cr 2 GeC with GGA+U Approximation M. Benouis 1 · Y. Azzaz 1 · M. Ameri 1 · O. Arbouche 1 · A. Bennadji 1 · D. Bensaid 1 · Y. Al-Douri 2 Received: 20 December 2015 / Accepted: 6 January 2016 © Springer Science+Business Media New York 2016 Abstract We have investigated the magnetic stability and electronic properties of the compound Cr 2 GeC using the framework of an all-electron full-potential linearized augmented-plane wave (FP-LAPW) method within the gen- eralized gradient (GGA) and +U corrected (GGA+U) approximations. An antiferromagnetic spin ordering of Cr atoms is shown to be the grand state for this compound. Based on its electronic band structures and density of state (DOS), Cr 2 GeC has a metallic character, and from the anal- ysis of the site and momentum projected densities, it is deduced that the bonding is achieved through hybridization of Cr-3d with C-2p states and Cr-3d with Ge-3p states. It is also pointed out that the Cr–C bonding is more cova- lent than that of Cr–Ge. In the ferromagnetic (FM) phase, the spin-polarized calculation indicates that the total mag- netic moment of Cr 2 GeC increases from 0.016 to 3.7 μ B . Finally, we conclude that the treatment of the correlated electrons is important for the correct description of this material. Keywords DFT · Phase MAX · GGA+U · Cr 2 GeC alloy  Y. Azzaz azzazyahia@yahoo.fr 1 Laboratory of Physico-Chemistry of Advanced Materials, University of Sidi Bel Abbes, Sidi Bel Abbes, 22000, Algeria 2 Institute of Nano Electronic Engineering, University Malaysia Perlis, 01000 Kangar, Perlis, Malaysia 1 Introduction The MAX phase is a group of layered crystals with the gen- eral formula M n+1 AX n ,(n = 1, 2, 3, or 4), where M is an early transition metal, A is an A-group element, and X is either C or N. In recent years, MAX phases have attracted immense attention from fundamental physics to their poten- tial applications due to their high strength and modulus, good damage tolerance, and high thermal and electrical con- ductivity [1, 2]. As is well known, giant magnetoresistance in a magnetic multilayer has a revolutionary impact on the magnetic recording and data storage industry. Like other MAX phases, Cr 2 GeC also behaves like metals with good electrical and thermal conductance, machinability, and duc- tility, while the rigidity, resistance to high temperatures, light weight, and resistance against oxidation reveal the ceramic-like properties of this material [3–6]. Having all these properties, Cr 2 GeC has become an attractive mate- rial for many useful applications. Cr 2 GeC was first reported by Jeitshko et al. in 1963 [7], and since then, a series of experimental and theoretical studies have been done to explore the physical, structural, and mechanical properties of this material [3–6, 8–11]. However, some disagreement appeared for instance in the experimentally reported values of bulk modulus of Cr 2 GeC [5, 12]. Therefore, a com- prehensive theoretical study is necessary to explore the correct electronic and mechanical properties of this mate- rial. In this paper, we use various computational methods to investigate the crystal structure and electronic properties of Cr 2 GeC and we calculate the bulk modulus of this mate- rial. This manuscript is organized as follows: computational details are described in Section 2; in Section 3, the results of Cr 2 GeC are discussed, and finally, Section 4 gives the conclusion.