N. Gonzalez Szwacki and Jacek A. Majewski Faculty of Physics, University of Warsaw, ul. Hoża 69, Warszawa, Poland

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1 Ab initio studies of Co 2 FeAl 1-x Si x Heusler alloys N. Gonzalez Szwacki and Jacek A. Majewski Faculty of Physics, University of Warsaw, ul. Hoża 69, Warszawa, Poland Abstract We present results of extensive theoretical studies of Co 2 FeAl 1-x Si x Heusler alloys, which have been performed in the framework of density functional theory employing the all-electron full-potential linearized augmented plane-wave scheme. It is shown that the Si-rich alloys are more resistive to structural disorder and as a consequence Si stabilizes the L2 1 structure. Si alloying changes position of the Fermi level, pushing it into the gap of the minority spin-band. It is also shown that the hyperfine field on Co nuclei increases with the Si concentration, and this increase originates mostly from the changes in the electronic density of the valence electrons. PACS number(s): Lp, i, Dm, y 1. Introduction Heusler compounds are usually ternary X 2 YZ compounds that consist of two transition metals X (e.g., Co, Ni, Cu, Pd) and Y (e.g., Ti, Mn, Fe, Zr, Hf), and one main group element Z (e.g., Al, Si, Ga, In, Sn, Sb) and crystallize in the L2 1 structure with the space group. 1 They have attracted considerable research attention in recent years due to their promising application in magneto-electronic and spintronic devices. 1,2 In particular, Heusler compounds based on cobalt behave like half-metallic ferromagnets, i.e., the electronic band calculations for these compounds show a metallic density of state (DOS) only for the spin direction of the majority band and a band gap around the Fermi level for the other spin direction of the minority band. 2 Co 2 YZ alloys have a compatible lattice structure with the industrially used zincblende semiconductors and possess a high Curie temperature ranging between 690 and 1100 K (or even larger) that allows the applications in the devices operating at room temperature. 2 Those materials exhibit also large values of the magnetic moment, e.g. 5 and 6 B for Co 2 FeAl and Co 2 FeSi, respectively, 2 and the magnetic properties are governed by the localized d electrons interacting via spin-polarized itinerant electrons. 3 Defects and antisite disordering play a crucial role among the factors destroying the half-metallic properties, therefore, reducing spin polarization, in such materials. 4 These alloys can transform from the L2 1 structure into B2 upon disorder between Y and Z atoms or A2 upon disorder between X, Y and Z atoms. 2 Such a mixture of atoms in Y and Z positions is harmful for the half-metallic properties. In this paper, we report results from first principle calculations devoted to Co 2 FeAl 1-x Si x (x= 0, 0.25, 0.5, 0.75, 1) Heusler alloys. These alloys have attracted considerable experimental 2,5,6 and theoretical 6,7 attention. We calculate the electronic structure, position of the Fermi level, magnetic moment, and spin polarization of the s-states on the Co nuclei. We also present calculations for structures, where positions of Fe atoms and atoms at the Z sites (i.e., Al or Si) have been swapped. This allows for the calculation of the energy difference, ΔE, between the structure containing the antisite defect and the highly ordered L2 1 structure, and further for the estimation of the defect occurrence for a given concentration x in the studied Co 2 FeAl 1-x Si x Heusler alloys. 2. Computational approach Computations were done using the ELK code, which is based on the all-electron fullpotential linearized augmented plane-wave (FLAPW) method. Various exchange-

2 correlation functionals (PBE, PBEsol, and WC06) were tested within the GGA+U approximation. The same U parameter was used for both Fe and Co atoms and the intraatomic exchange parameter, J, was set to zero. The muffin-tin radii RMT were set to 2.0 a.u. for all atoms. The plane-waves cutoff was set to RMT k max = 8.0 and a k-point mesh of was used. The angular momentum expansion in the muffin tins was taken to be l max = 7 for both the potential and density. The maximum G-vector length for the density and potential expansion in the interstitial was set to 12 a.u -1. The spin orbit coupling was neglected and the experimental lattice parameters (5.73 and 5.64 Å for Co 2 FeAl and Co 2 FeSi, respectively 2 ) were used in the calculations. To study the alloying effects, we use a supercell containing 16 atoms (4 times the primitive unit cell of Co 2 FeAl or Co 2 FeSi) with 4 Z sites, which are occupied by Al and Si atoms, with Si concentration, x, equal to 0.0, 0.25, 0.5, 0.75, and 1.0. The lattice constants for the intermediate compositions of Co 2 FeAl 1-x Si x where estimated from the Vegard s law. For each configuration, we perform optimization of the atomic positions. 3. Results The properties of Co 2 FeAl and Co 2 FeSi alloys have been already presented in details in previous theoretical works (see Refs. 6,7 and references therein). It is known, for instance, that it is necessary to include the on-site correlation, U, in the calculations for Co 2 FeSi in order to have the half-metallic ground state. Our first step, therefore, was to calibrate the U parameter in order to obtain experimental 2 results for the magnetic moment and electronic properties of Co 2 FeAl and Co 2 FeSi. As it is seen in Fig. 1a (left) the magnetic moment of Co 2 FeAl is close (or equal) to 5 B for all U values up to ~3 ev. For 0 ev<u<~4 ev (~3 ev for the PBEsol+U functional) a nonzero minority energy gap is present for this alloy as it is shown in Fig. 1b (left). The half metallic character of Co 2 FeSi is reproduced only for certain values of U. This is shown in Fig. 1b (right) where the minority energy gap opens up for values of U around or larger than 2 ev. For those values, the magnetic moment is close (or equal) to 6 B. It is worth mentioning that the above-described picture is almost independent on the exchangecorrelation functional that have been used (PBE, WC06 or PBEsol). Therefore, from now on, we will present results only for the PBE exchange-correlation functional. The U parameter is set to be 2.5 ev in order to reproduce the properties of the end members of Co 2 FeAl 1-x Si x, although as discussed above, there is some freedom in choosing the U parameter. Figure 2 shows the spin resolved density of states for Co 2 FeAl 0.5 Si 0.5. For that composition, calculations predict that the Fermi level is located in the middle of the gap of the minority band. This result is in accord with previous reports that also show a shift of the majority spin density that is compensated by a shift of the minority spin density with increasing Si content, and as a result a virtual movement of the Fermi energy in the minority gap is observed. 7,9 Our calculations also demonstrate, in accordance with experiment, 5 that the probability of creation of Fe-Al antisites decreases with the growing Si concentration. This is shown in Fig. 3, where we plotted the energy cost, ΔE, for the formation of Fe-Al and also Fe-Si antisites as a function of the Si composition. ΔE clearly increases with x both for Fe-Al and Fe-Si antisites. From Fig. 3 it is also clear that the formation of Fe-Si antisites is less probable than that of Fe-Al antisites, what helps to explain the luck of satellite structures in the 59 Co NMR spectra for Co 2 FeSi as oppose to the case of Co 2 FeAl. 5 It has been shown experimentally 5 that the hyperfine field on Co nuclei increases with the Si concentration, and this increase originates mostly from the changes in the electronic density of the valence electrons. To study this, we have calculated the onsite

3 hyperfine field on the Co atoms of Co 2 FeAl 1-x Si x as a function of the composition. The onsite hyperfine field which for ferromagnetic 3d metals consist mainly of the Fermi contact term 10,11 is plotted in Fig. 4. We have calculated the total hyperfine field (H tot ) that includes contributions from the core and valence s shell (1s, 2s, 3s, 4s) electrons and separately, the contribution coming from the 4s valence electrons (H valence ). The qualitative and for H valence also quantitative agreement between experimental results 5 and those reported here is very good. The slope of H valence as a function of composition is well reproduced and the H valence values are close to those estimated from experimental data. The H tot is shifted down with respect to experimental values and this discrepancy between theory and experiment could arise from the non-sufficient description (in GGA+U calculations) of the effect of correlation on the 3d-like electron wave functions. 10 The positive slope of the valence electron contribution to the hyperfine field means that the population of 4s electrons with spin up increases faster with Si content than the population of electrons with spin down. This is consistent with the theoretical predictions 7 that upon an increase of the Si content the electrons dope the majority-spin band, leading to a virtual shift of the Fermi level inside the gap of the minority-spin band. 4. Conclusions The stronger p-d hybridization in Si-rich than Al-rich alloys, makes the Si-rich alloys more resistive to structural disorder and as a consequence Si stabilizes the desired L2 1 structure. It was also shown that the hyperfine field on Co nuclei increases with the Si concentration, and this increase originates mostly from the changes in the electronic density of the valence electrons. The Si doping is, therefore, responsible for the shift of the Fermi energy in the energy gap of the minority band. Our theoretical findings agree fairly well with available experimental data. Acknowledgments This paper has been supported by the project No. N N of Ministry of Science and Higher Education. We also acknowledge the Interdisciplinary Center of Modeling at the University of Warsaw for the access to computer facilities. References T. Graf, S. S. P. Parkin, and C. Felser, IEEE Trans. Magn. 47 (2), 367 (2011). Simon Trudel, Oksana Gaier, Jaroslav Hamrle, and Burkard Hillebrands, J. Phys. D: Appl. Phys. 43 (19), (2010). S. Mizusaki, T. Ohnishi, T. C. Ozawa, Y. Noro, M. Itou, Y. Sakurai, and Y. Nagata, J. Appl. Phys. 111 (6), (2012). Vadim Ksenofontov, Marek Wojcik, Sabine Wurmehl, Horst Schneider, Benjamin Balke, Gerhard Jakob, and Claudia Felser, J. Appl. Phys. 107 (9), 09B106 (2010). M. Wójcik, E. Jedryka, H. Sukegawa, T. Nakatani, and K. Inomata, Phys. Rev. B 85 (10), (2012). T. M. Nakatani, A. Rajanikanth, Z. Gercsi, Y. K. Takahashi, K. Inomata, and K. Hono, J. Appl. Phys. 102 (3), (2007). Gerhard H. Fecher and Claudia Felser, J. Phys. D: Appl. Phys. 40 (6), 1582 (2007). Elk code, version: , Z. Gercsi, A. Rajanikanth, Y. K. Takahashi, K. Hono, M. Kikuchi, N. Tezuka, and K. Inomata, Appl. Phys. Lett. 89 (8), (2006).

4 10 11 C. M. Singal, B. Krawchuk, and T. P. Das, Phys. Rev. B 16 (11), 5108 (1977). Hisazumi Akai, Masako Akai, S. Bluegel, B. Drittler, H. Ebert, Kiyoyuki Terakura, R. Zeller, and P. H. Dederiches, Progr. Theoret. Phys. Suppl. 101, 11.

5 Figure captions Fig. 1 (a) Magnetic moment dependence on the choice of the U parameter for Co 2 FeAl (left) and Co 2 FeSi (right). (b) Energy gap, E g, in the minority band vs. the value of the U parameter for Co 2 FeAl (left) and Co 2 FeSi (right). Fig. 2 Spin resolved density of states of Co 2 FeAl 1-x Si x for x= 0.5. Fig. 3 Energy cost for the formation of Fe-Al and Fe-Si antisites in Co 2 FeAl 1-x Si x as a function of the composition. E is defined as the total energy difference of Co 2 FeAl 1- xsi x with and without the defect. Fig. 4 Co hyperfine field (H tot ) for Co 2 FeAl 1-x Si x as a function of the composition. Also it is included the 4s valence electrons contribution (H valence ) and the core electrons contribution calculated as H core = H tot H valence.

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Self-compensating incorporation of Mn in Ga 1 x Mn x As

Self-compensating incorporation of Mn in Ga 1 x Mn x As arxiv:cond-mat/0201131v1 [cond-mat.mtrl-sci] 9 Jan 2002 J. Mašek and F. Máca Institute of Physics, Academy of Sciences of the CR CZ-182 21 Praha