PHYSICAL REVIEW B 90, 064408 (2014) Voids-driven breakdown of the local-symmetry and Slater-Pauling rule in half-metallic Heusler compounds I. Galanakis, 1 , * E. S ¸as ¸ıo˘ glu, 2 , † S. Bl¨ ugel, 2 and K. ¨ Ozdo˘ gan 3 , ‡ 1 Department of Materials Science, School of Natural Sciences, University of Patras, GR-26504 Patra, Greece 2 Peter Gr¨ unberg Institut and Institute for Advanced Simulation, Forschungszentrum J¨ ulich and JARA, 52425 J¨ ulich, Germany 3 Department of Physics, Yildiz Technical University, 34210 ˙ Istanbul, Turkey (Received 20 June 2014; revised manuscript received 23 July 2014; published 8 August 2014) Slater-Pauling (SP) rules connect the magnetic and electronic properties of the half-metallic (HM) Heusler compounds. Employing first-principles electronic structure calculations we explore the validity of the SP rules in the case of transition from HM semi-Heusler compounds to various cases of HM full-Heusler compounds. We show that the coherent-potential approximation yields half-metallicity and thus a generalized version of the SP rules can be derived. On the contrary, supercell calculations, which are expected to describe the experimental situation more accurately, show that the energy gap considerably shrinks for the intermediate compounds and in several cases the half-metallicity is completely destroyed. The origin of this behavior is attributed to the voids, which influence the symmetry of the lattice. DOI: 10.1103/PhysRevB.90.064408 PACS number(s): 75.50.Cc, 75.30.Et, 71.15.Mb I. INTRODUCTION The research on magnetic nanomaterials and their incor- poration in functional devices is a central issue in modern electronics and consequently the field of spintronics, where both magnetic and semiconducting elements are combined, and of magnetoelectronics (incorporating exclusively mag- netic elements) are rapidly developing [1]. Half-metallic (HM) magnetic compounds play a crucial role in this development [2]. These materials present usual metallic behavior for the one spin direction while an energy gap in the band structure is present in the other spin direction similarly to semiconductors [3]. The possibility of creating 100% spin- polarized current and their potential advantages in electronic devices has triggered the interest on such compounds [4,5]. De Groot and collaborators in 1983 have initially suggested based on electronic structure calculations that NiMnSb, a semi-Heusler compound, is a half-metal [6] and since then several HM compounds have been discovered [7,8]. Several aspects concerning the implementation of HM compounds in realistic devices, like tunneling magnetic junctions or giant magnetoresistive junctions and spin injectors, have been discussed in literature (see Ref. [4] for a review). Heusler compounds are a promising family to achieve half-metallicity since they encompass a large number of members. Most of them crystallize in cubic structures similar to the zincblende structure of semiconductors and several have very high Curie temperatures [9,10]. Computational materials science has played a crucial role in the design of HM Heusler compounds and several have been initially predicted and half-metallicity was later experimentally confirmed [3]. The lattice for all Heusler compounds is an fcc with four equidistant sites as basis along the diagonal of the unit cell. In Fig. 1, we give a schematic representation of the various structures of the Heusler compounds. The first family are the so-called * galanakis@upatras.gr † e.sasioglu@fz-juelich.de ‡ kozdogan@yildiz.edu.tr semi-Heuslers, which have the chemical formula XYZ where the sequence of the sites along the diagonal is X-Y -void-Z. The X and Y are transition-metal elements and Z is an sp element and the structure is known as the C1 b lattice [9]. The second family consists (i) of the usual full-Heusler compounds with the chemical formula X 2 YZ, where the valence of the X is larger than Y [known as the L2 1 structure illustrated in Fig. (1)], (ii) the inverse Heuslers when the valence of the Y elements is the largest and the compounds crystallize in the so-called XA structure where the sequence of the atoms changes, and finally, (iii) the ordered quaternary LiMgPdSn-type compounds with chemical type (XX  )YZ where the valence of X and X  is larger than that of Y [9,10]. In two pioneering papers, Slater and Pauling have shown that in the case of binary magnetic compounds when one valence electron is added to the compound, this occupies spin-down states only and the total spin magnetic moment decreases by about 1μ B [11,12]. Interestingly, a similar behavior can be also found in HM magnets as confirmed by first-principles (ab initio) electronic structure calculations. In HM Heusler compounds, the spin-down band structure is fixed; the number of spin-down occupied bands and their character does not change within the HM members of the same family of compounds. The extra valence electrons now occupy exclusively spin-up states. These Slater-Pauling (SP) rules connect the electronic properties (appearance of the HM behavior) directly to the magnetic properties (total spin magnetic moments) and thus offer a powerful tool to the study of HM compounds since (i) magnetic measurements can be used to confirm the HM character of a compound and (ii) simple valence electrons counting can predefine the magnetic properties of a half-metal. However, in realistic situations, the vacant site of the semi-Heusler compounds (see Fig. 1) can be partially occupied as in Mn 2 Ru x Ga films recently studied [13]. Thus the question rises if half-metallicity is present and SP rules exist for such compounds being in-between the semi- and full-Heuslers. In this paper, we have studied six such families where the end compound (x = 1) belongs to another subfamily of full-Heuslers: (i) Co 1+x CrSi and Co 1+x MnSi (end compounds usual full-Heuslers), (ii) (Co x Fe)MnSi 1098-0121/2014/90(6)/064408(5) 064408-1 ©2014 American Physical Society