Correlation effects on the electronic structure of Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si quaternary alloys

Intermetallics 37 (2013) 27e31

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Correlation effects on the electronic structure of Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si quaternary alloys S. Amari*, R. Mebsout, S. Méçabih, B. Abbar, B. Bouhafs Laboratoire de Modélisation et de Simulation en Sciences des Matériaux, Département de Physique, Université Djillali Liabès, Sidi Bel-Abbes, Algeria

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 July 2012 Received in revised form 3 January 2013 Accepted 4 January 2013 Available online 19 February 2013

In this work, density functional FP-LAPW þ lo calculations have been performed to study the structural, electronic and magnetic properties of the quaternary full Heusler compounds Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si. For the exchangeecorrelation potential we have adopted the generalized gradient approximation (GGA). In order to take into account the correlation effects, we have also performed the GGA þ U calculations. The calculated atomic resolved density of states of the systems indicates nearly half-metallic behavior with small spin-down electronic density of states at Fermi level. This behavior is corrected by including Hubbard parameters. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: A. Magnetic intermetallics E. Ab-initio calculations G. Magnetic applications

1. Introduction The Heusler alloys represent a class of ternary intermetallic compounds of general formula X2YZ in which X is a transition metal element such as Ni, Co, Fe or Pt, Y is a second transition metal element, e.g. Mn, Cr or Ti and Z is an atom from 3rd, 4th or 5th group of the periodic table such as Al, Ge, Sn or Sb. Heusler compounds containing Co and Mn have attracted during the last century a great interest due to their possible applications in spintronics [1]. Many experimental groups during the last years have worked on these compounds and have tried to synthesize them mainly in the form of thin films. Despite these efforts, there is a marked discrepancy in the properties observed in these materials, not only across but even within synthesis methods as well as in the theoretical predictions. The first clear indication of half metallic ferromagnetism in Co2MnZ, compounds was reported by Ishida and collaborators [2e5]. Kammerer et al. [6] managed to build magnetic tunnel junctions based on Co2MnSi and found a tunneling magnetoresistance effect much larger when the Ni0.8Fe0.2 or Co0.3Fe0.7 are used as magnetic electrodes. Similar experiments have been undertaken by Inomata and collaborators [7] using Co2Cr0.6Fe0.4Al as the magnetic electrode. Kallmayer et al. [8] studied the effect of substituting Fe for Mn in Co2MnSi films and have shown that the experimental extracted

* Corresponding author. Faculté des sciences, Université Djillali Liabes, BP 89 Sidi Bel Abbes 22000, Algeria. Tel./fax: þ213 48 54 43 44. E-mail address: [email protected] (S. Amari). 0966-9795/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.intermet.2013.01.002

magnetic spin moments are compatible with the half-metallicity for small degrees of doping. Besides ternary X2YZ compounds, there exist also large assortments of substitutional quaternary alloys of the type X2Y1  xY0 xZ, X2YZ1  xZ0 x and (X1  xX0 x)2YZ [9]. One of the early substitutional series that attracted interest as potential material for magneto-electronics was Co2Cr1  xFexAl [10]. A half-metallic ferromagnetic ground state was found for the complete series Co2Cr1  xFexAl, when the full symmetry potentials were used along with the GGA in the calculations. Fecher et al. [11] have investigated the electronic structure of Co2FeSi1  xAlx. The series Co2FeSi1  xAlx is found to exhibit half-metallic ferromagnetism and it is shown that the electron-doping stabilizes the gap in the minority states for x ¼ 0.5. Co2Fe0.5Mn0.5Si is another candidate with Fermi energy in the middle of the minority states gap and has been used for fabrication of magnetic tunnel junctions [12,13]. Karthik et al. [14] have studied the microstructure, magnetic properties and spin polarization of quaternary Co2Cr1  xFexAl, Co2Cr1  xVxAl and Co2Fe1  xVxAl Heusler alloys. Recently, Korth et al. [15] reported the substitution of Fe for Ti in semiconducting half-Heusler alloy CoTiSb. Their result suggest that the doped Co(Ti1  xFex)Sb are also promising half metallic ferromagnets. Ahmadian and Boochani [16] have investigated the electronic and magnetic properties of the bulk Co2Ti1  xFexGa Heusler alloys and Co2Ti0.5Fe0.5Ga (001) surfaces. Therefore, Balke et al. [17] synthesized and investigated experimentally mixed compounds Co2Mn1  xFexSi to search for a stable half-metallic character. Recently, Grasin et al. [18] has found that the half-metallicity is preserved when Gd substitute Mn sites. The main task of the present work is the study of the electronic structure and

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S. Amari et al. / Intermetallics 37 (2013) 27e31

Table 1 The calculated values of the lattice parameter (in Å), bulk modulus (in GPa) and its pressure derivative of the quaternary full Heusler compounds Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si.

Co2Mn0.5Fe0.5Si GGA GGA þ Ud-Co GGA þ Ud-Co þ d-Mn GGA þ Ud-Co þ d-Mn-d-Fe Co2Mn0.5Gd0.5Si GGA GGA þ Ud-Co GGA þ Ud-Co þ d-Mn GGA þ Ud-Co þ d-Mn-f-Gd

A) a0(

B0(Gpa)

B0

5.6647 5.6683 5.6742 5.6832 5.64 [27]

217.5192 210.5286 207.7424 206.6785

4.8869 4.8499 3.1376 4.4529

5.9231 5.9295 5.9450 5.9496 5.654 [18]

167.2942 160.6659 152.5312 152.4221

3.8966 4.0658 4.1861 4.1573

magnetic properties of the Heusler alloys Co2MnSi and the effect of Gd and Fe substitution at Mn sites. The outline of this paper is as follows: In Section 2, we briefly describe the calculation method used in this work. The results and discussions are presented in Section 3, and a brief summary is given in Section 4. 2. Computational details In our calculations we have used the full-potential linearized augmented plane-wave plus local orbitals (FP-LAPW þ lo) method

Fig. 1. Spin-dependent total and partial density of states for Co2Mn0.5Fe0.5Si using GGA.

as implemented in the WIEN2K code [19] within the density functional theory [20]. For the exchange correlation functional, the generalized gradient approximation (GGA) [21] and GGA þ U are adopted. We have investigated the effects of the effective on site Coulomb exchange correlations Ueff ¼ U  J (where U and J are the Coulomb and exchange parameters). In this study, the 4f orbitals of Gd and 3d of Co, Mn and Fe were treated using the GGA þ U approach [22e24]. The values of Ueff were set to 1.69, 1.80, 1.92 and 2.3 eV for Mn, Fe, Co and Gd [18,25], respectively. We have chosen the muffin-tin (MT) radii of 2.15 bohr for Co, Mn, Fe, Gd and 2 bohr for Si atoms. The valence wave functions inside the MT spheres are expanded in terms of spherical harmonics up to lmax ¼ 10, and in terms of plane waves with a wave vector cutoff Kmax in the interstitial region. We set the parameter RMT.Kmax ¼ 8 (where RMT is the average radius of the MT spheres). The magnitude of the largest vector in charge density Fourier expansion (Gmax) was 14. The self-consistent calculations are considered to be converged only when the total energy of the crystal is converged to less than 1 mRy. 3. Results and discussion 3.1. Structural properties The full-Heusler alloys are ternary intermetallic compounds based on the X2Y Z stoichiometry for the L21 phase (Fm3m space group). X atoms are transition metals which stand on (0, 0, 0) and   1 1 1 ; ; Wyckoff crystallographic positions, while Y and Z are 2 2 2

Fig. 2. Spin-dependent total and partial density of states for Co2Mn0.5Gd0.5Si using GGA.

S. Amari et al. / Intermetallics 37 (2013) 27e31

magnetic transition metal and IIIeV group element occupying the     1 1 1 3 3 3 ; ; and ; ; , respectively. In order to simulate positions 4 4 4 4 4 4 Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si quaternary alloys we have used a (1  1  1) supercell with 8 atoms and we substituted one atom of Mn by Fe in Co2Mn0.5Fe0.5Si and by Gd in Co2Mn0.5Gd0.5Si. In order to calculate the ground states properties for both quaternary alloys Co2Mn0.5Gd0.5Si and Co2Mn0.5Fe0.5Si, we optimize the total energy as a function of unit cell volume. We have computed the lattice constants, bulk moduli and the first pressure derivatives of the bulk moduli by fitting the total energy versus volume according to Murnaghan’s equation of state [26]. We have used the GGA and GGA þ U schemes for better visualization of the efficiency and improvement of this approximation on the various properties, in other words, to verify the influence of these corrections on the structural and electronic properties. So we have studied the effect of the orbital (d-Co), (dCo þ d-Mn) and (d-Co þ d-Mn þ d-Fe) for Co2Mn0.5Fe0.5Si and the orbital (d-Co), (d-Co þ d-Mn) and (d-Co þ d-Mn þ f-Gd) for Co2Mn0.5Gd0.5Si. We summarized our results and the experimental values [18,27] in Table 1. One can notice that the lattice parameter (a0) increases when we use the GGA þ U approach and the bulk modulus (B) decreases since it is inversely proportional to the lattice constant.

29

Figs. 1 and 2 show the calculated total and partial DOS of Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si using GGA. The Fermi level

falls within a region of very small spin-down DOS for both compounds. Our results agree with the calculations of Kübler et al. [28] who studied the Co2MnAl and Co2MnSn compounds and those of Galanakis et al. [29] who found also a very small spin-down DOS at the Fermi level and not a real gap. The origin of this pseudo-gap according to Galanakis et al. [29], arise from the hybridization between the nearest neighbors of the CoeCo d states and also between the next nearest neighbors MneCo d states. These quaternary alloys are nearly half-metallic. It can be seen also that the substitution of Fe for Mn in Co2Mn0.5Fe0.5Si does not change the general shape of the DOS obviously. The low-energy region around 12 and 9 eV is mainly the s states of the Si atoms, the states above 7 eV are mainly the p electrons of Si atom in the occupied valence states, which hybridize with p electrons of the 3d atoms. The main part of the total DOS (from the energy of 6 to þ4 eV) is chiefly governed by 3d states of Co, Mn and Fe atoms for Co2Mn0.5Fe0.5Si and by 3d states of Co, Mn and 4f of Gd for Co2Mn0.5Gd0.5Si. The substitution of Fe for Mn in Co2Mn0.5Fe0.5Si affects the de d hybridization and leads to the reconstruction of the bands. It is important to mention that in the case of Co2Mn0.5Gd0.5Si Gd (4f) orbitals do not hybridize with the 3d orbitals near the Fermi level. Figs. 3 and 4 compare the total densities of states for Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si using GGA and GGA þ U. The important point which should be mentioned that the overall shape

Fig. 3. Spin-dependent total density of states for Co2Mn0.5Fe0.5Si using GGA and GGA þ U.

Fig. 4. Spin-dependent total density of states for Co2Mn0.5Gd0.5Si using GGA and GGA þ U.

3.2. Electronic properties

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S. Amari et al. / Intermetallics 37 (2013) 27e31

of majority states do not change with the inclusion of Ueff. The principal effect of Hubbard correction is on the minority states and in particular on their unoccupied part. For all values of Ueff a half-metallic solution is obtained with a minority gap. The advantage of the GGA þ U method is the ability to treat simultaneously delocalized conduction band electrons and localized 3d and 4f electrons in the same computational scheme. The effect of adding Ueff is simply to push up the empty 3d and 4f states higher in the conduction band. The calculated partial densities of states (PDOSs) of Co, Mn and Fe atoms in Co2Mn0.5Fe0.5Si using GGA and GGA þ U are shown in Fig. 5. We found that the energy gaps of the minority DOS near the Fermi level are mostly dominated by the Co 3d states while the Fe 3d states have a smaller contribution. Fig. 6 exhibits the partial densities of states for Co, Mn 3d and 4f Gd of Co2Mn0.5Gd0.5Si using GGA and GGA þ U, which clearly show the effect of the U corrections. It is found that the Fermi level is mostly dominated by the Co 3d states. As discussed in Ref. [3] the gap is created between states located exclusively at the Co sites. The calculated band gaps in minority states for Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si are listed in Table 2. We observe that when the GGA þ U approach is taken into account the size of the gap increases. In general, the width of the band gap increases with the inclusion of U in both quaternary alloys.

Fig. 6. The calculated partial densities of states of Co, Mn and Gd in Co2Mn0.5Gd0.5Si using GGA and GGA þ U.

3.3. Magnetic properties

Fig. 5. The calculated partial densities of states of Co, Mn and Fe atoms in Co2Mn0.5Fe0.5Si using GGA and GGA þ U.

In Table 2, we summarized the calculated total and local magnetic moments per atom within the muffin-tin spheres for Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si. The results show that the total magnetic moments come from the Mn, Fe and Gd ions. The Co atoms are ferromagnetically coupled to the Mn spin moments and they possess a spin moment that varies from; 0.8 mBe1.43 mB, while the Si atom has a very small negative moment. The negative sign of the induced Si moment characterizes most of the full- and halfHeusler alloys. In half-metallic materials the total spin moment should be an integer number. However, our results in Table 2 do not give integer numbers for the total moments. This arises from the number of K points used in our calculations. We note that the total spin magnetic moments of both compounds are calculated by integration over the entire cell. Therefore, it is not just the combination of the moments at the X (2 times), Y and Z sites but respects also the moment of the interstitial between the sites. The calculated total magnetic moment of Co2Mn0.5Fe0.5Si using GGA is 5.46 mB. This is in good agreement with the theoretical value (5.5 mB) given in Ref [30]. Galanakis et al. [31] found a value of 5.14 mB in the case of Co2Mn0.8Fe0.2Si and Kota et al. [32] have studied the Co2Mn0.6Fe0.4Si compound and found a value of 5.2 mB. For Co2Mn0.5Gd0.5Si the calculated total magnetic moment using GGA is 6.55 mB. Grasin et al. [18] found a value of 5.35 mB for Co2Mn0,875Gd0,125Si compound. When we use the GGA þ U, we see that the magnetic moments increase. This increase is explained by

S. Amari et al. / Intermetallics 37 (2013) 27e31

31

Table 2 Calculated magnetic moments (in mB) and energy gaps for Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si. Element-specific (per atom) and total spin magnetic moments (per formula unit). Compounds Co2Mn0.5Fe0.5Si GGA GGA þ Ud-Co GGA þ Ud-Co þ d-Mn GGA þ Ud-Co þ d-Mn

Co2Mn0.5Gd0.5Si GGA GGA þ Ud-Co GGA þ Ud-Co þ d-Mn GGA þ Ud-Co þ d-Mn

þ d-Fe

þ f-Gd

Tot

Co

Mn

Fe

Gd

Si

Eg (eV)

5.460 5.489 5.489 5.482 5.5 [30] 5.14 [31] 5.2 [32]

1.275 1.431 1.351 1.294

3.074 2.984 3.390 3.344

2.918 2.852 2.823 3.084

e e e e

0.024 0.053 0.066 0.065

0.68 0.81 0.84 1.17

6.556 6.688 6.830 6.793 5.36 [18]

0.843 1.064 0.984 0.965 1.09 [18]

3.044 2.921 3.421 3.406 3.03 [18]

e e e e

6.697 6.640 6.639 6.724 6.83 [18]

0.027 0.060 0.049 0.054 0.064 [18]

0.54 0.81 0.87 0.95

an energy shift of the partial densities of Co, Mn and Fe by the electroneelectron correlation in the LDA þ U calculation. 4. Summary and conclusions In conclusion, we have performed a first principle calculations based on the FP-L/APW þ lo method within the GGA and GGA þ U to evaluate the electronic and magnetic properties of quaternary Heusler compounds Co2Mn0.5Fe0.5Si and Co2Mn0.5Gd0.5Si. The optimized lattice parameters agree well with the available experimental data. We have studied the correlation effects on the electronic properties. The results indicate that both quaternary alloys are half-metallic. The Coulomb exchange correlations U is not creating the half-metallic feromagnetism but confirms the half-metallic property in both compounds and helps to explain the magnetic properties correctly. When the on-site Coulomb interaction is induced by means of GGA þ U, the magnetic moments increase. This increase is explained by an energy shift of the partial densities of Co, Mn and Fe by the electroneelectron correlation in the LDA þ U calculation. We can deduce from these results that the U-Hubbard correction influences the positions of the electronic states and increases the width of the band gap in both quaternary alloys. References [1] Coey JMD, Venkatesan M, Bari MA. Lecture notes in physics, vol. 595. Heidelberg: Springer; 2002. [2] Ishida S, Fujii S, Kashiwagi S, Asano S. J Phys Soc Jpn 1995;64:2152. [3] Ishida S, Kashiwagi S, Fujii S, Asano S. Physica B 1995;210:140e8. [4] Ishida S, Akazawa S, Kubo Y, Ishida J. J Phys F Met Phys 1982;12:1111. [5] Fujii S, Sugimura S, Ishida S, Asano S. J Phys Condens Matter 1990;2:8583. [6] Kammerer S, Thomas A, Hütten A, Reiss G. Appl Phys Lett 2004;85:79. [7] Inomata K, Okamura S, Goto R, Tezuka N. Jpn J Appl Phys 2003;42:L419.

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