Effect of As and Nb doping on the magnetic properties for quaternary Heusler alloy FeCoZrGe

Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Effect of As and Nb doping on the magnetic properties for quaternary Heusler alloy FeCoZrGe Ge-Yong Mao, Xiao-Xiong Liu, Qiang Gao, Lei Li, Huan-Huan Xie, Gang Lei, Jian-Bo Deng n School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, People's Republic of China

art ic l e i nf o

a b s t r a c t

Article history: Received 1 June 2015 Received in revised form 13 August 2015 Accepted 30 August 2015 Available online 1 September 2015

We investigate the effect of doping on FeCoZrGe. Electronic structure calculations reveal that doping of As or Nb into FeCoZrGe will transform it into half-metallic materials. They have half-metallic properties in a large range of proportion of As or Nb's doping. So by doping with different proportion of As or Nb, the controllable half-metallic gaps can be realized. In addition, this doped system can have higher Curie temperature. & 2015 Elsevier B.V. All rights reserved.

Keywords: Half metal Quaternary Heusler alloy Doping

1. Introduction Heusler alloys consist of a large family of intermetallic compounds which attract considerable attention due to the variety of magnetic phenomenon which they present [1]. Half-metallic (HM) magnets are seen as the most promising candidates of high-spinpolarization materials, because their band structure is metallic in one of the two spin channels and semiconducting or insulating in the other one, which results in complete (100%) spin polarization of electrons at the Fermi level. A number of new half-metallic materials, such as CrAs, NiMnSb, Co2MnAl, etc. [2,3], have been initially predicted theoretically by first-principles calculations and later verified by experiments. Among these materials, the ones with Heusler structure have been widely concerned, because they can be synthesized easily and have high Curie temperature [4,5]. Usually, Heusler alloys have the structural formulas of X2YZ with L21 structure and XYZ with C1b structure, where X and Y are transition metals and Z is a main-group element. Many X2YZ and XYZ Heusler alloys have been found to be HM ferromagnets or ferrimagnets [6]. As for quaternary Heusler alloy XX′YZ , generally they crystallize in the LiMgPdSn-type crystal structure [7,8]. Half-metallic ferromagnetism (HMF) has been found in Co2ZrSn, Ni2ZrSn [9], Ni2ZrAl [10], Zr2CoZ (Z ¼Al, Ga, In, and Sn) [11], Ti2VZ (Z ¼Al, Ga, and In) [12], ZrNiSn [13], ZrCoSb [14], Co2CrX (X ¼As and Sb) [15] and CoFeScZ (Z¼P, As, and Sb) [16]. HMF meets most of the requirements for spintronics, as a result of the exceptional electronic structure. Zr-based quaternary Heusler n

Corresponding author. E-mail address: [email protected] (J.-B. Deng).

http://dx.doi.org/10.1016/j.jmmm.2015.08.123 0304-8853/& 2015 Elsevier B.V. All rights reserved.

ferromagnets, ZrFeTiAl, ZrFeTiSi, ZrFeTiGe and ZrNiTiAl, with large HM gaps have been reported lately [17]. Furthermore, our previous work has shown that FeCoZrGe is a nearly half-metallic material [18]. In recent years, some doped Heusler alloys are studied by Özdoǧ an et al., such as Co2Mn1  xCrxZ (Z ¼Si, Ge, and Sn), Co2Mn1  xFexZ (Z ¼Si, Ge, and Sn), and Co2[Cr1  xMnx][Al1  ySiy] [19–21]. Also there are some Zr-based quaternary Heusler doped systems that have been studied, for example Ti1  xZrxNiSn [22]. In present paper, we study new half-metallic materials with dopants. And in order to accurately control their properties, it is imperative to investigate the effect of doping on these properties. We study the effect of doping on the magnetic properties of the FeCoZrGe Heusler alloy. Doping is simulated by substituting As for Ge or substituting Nb for Zr in the alloys, and the calculation is simulated by virtual crystal approximation (VCA) and supercell approximation (SCA).

2. Method of calculations We have carried out density functional calculations using the scalar relativistic version of the full-potential local-orbital (FPLO) minimum-basis band-structure method [23,24]. For the present calculations, the site-centered potentials and densities are expanded in spherical harmonic contributions up to lmax ¼12. The Perdew–Burke–Ernzerhof 96 (PBE) of the generalized gradient approximation (GGA) is used for exchange-correlation (XC) potential [25]. For the irreducible Brillouin zone, we use the k meshes of 20  20  20 for all calculations. The convergence criteria of selfconsistent iterations is set to 10  6 to the density and 10  8 Hartree

2

G.-Y. Mao et al. / Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

Table 1 Magnetic data and optimized lattice constant (LC) for a series of FeCoZrGe1  xAsx ( x = 0.25, 0.5, 0.75) under the VCA. Doped proportion

LC (Å)

Fe (μB)

Co (μB)

Zr (μB)

Ge(As) (μB)

Total (μB)

x ¼0.25 x ¼0.5 x ¼0.75

6.059 6.063 6.068

0.870 1.007 1.131

0.634 0.745 0.863

 0.223  0.245  0.263

 0.031  0.007 0.018

1.250 1.500 1.750

FeCoZrGe0.75As0.25

VCA SCA

5

0

-5

3. Results and discussions In the first part, we will discuss the As-doped FeCoZrGe systems. To simulate the doped system, we employ the virtual crystal approximation (VCA) approach to model the doped systems. Within VCA, a virtual atom with the desired number of electrons and protons is substituted at the Ge positions. The VCA is employed in as the following way: the input of our full potential method is the nuclear positions and charges and the basis functions (local orbitals). A virtual atom is constructed such that the number of effective valence electrons equals the one in the disordered alloy approximated by VCA. This is achieved by choosing an appropriate number of noninteger nuclear charge and a corresponding equal number of electrons for the disordered sites. The full potential scheme then solves the density functional theory (DFT) equations for this unit cell with noninteger nuclear or electron charges, automatically adapting the basis functions and the potential to this nuclear configuration as it does for any other arrangement of “natural” atoms [26]. In addition, in order to examine the truth of VCA approach, we simultaneously performed the ordered supercell approximation (SCA) calculations. In the SCA approach, some of the Ge positions are occupied by the substituent As. To compare between the two different approaches, the total density of states (DOS) and the total spin magnetic moments, which are used to measure the reliability of VCA and SCA results, are presented. In Tables 1 and 2, we have gathered the total and atomic spin moments for all cases. Fig. 1 shows the DOS of FeCoZrGe0.75As0.25, FeCoZrGe0.5As0.5 and FeCoZrGe0.25As0.75 which are similar with SCA and VCA. This proves that such calculation results have high reliability. We also can see that there is a gap around the Fermi level in the spin down DOS, while the spin up DOS shows a conductive property. Therefore, the doped compounds are half-metallic. Tables 1 and 2 show the contribution of Fe and Co atoms to the total magnetic moments. By comparing the results of SCA and VCA calculations, we find that the magnetic moment of Fe calculated by VCA is similar to that by SCA, so are Co, Zr and Ge. And this further proves our calculated results have high reliability. For doped system, the number of valence electrons in Slater– Pauling rule can be expressed by

Ztot = zZr + zCo + zFe + (1 − x) × zGe + x × zAs ,

(1)

where zZr, zCo, zFe, zGe and zAs are the number of valence electron of Zr, Co, Fe, Ge and As. x and Ztot are the As-doped proportion and the number of total valence electrons.

Density of states (states/eV)

to the total energy per formula unit. FeCoZrGe0.5As0.5

VCA SCA

5

0

-5

FeCoZrGe0.25As0.75

VCA SCA

5

0

-5

-6

-4

-2

0 E-EF (eV)

2

4

6

Fig. 1. Spin-resolved total density of states (DOS) for the case of FeCoZrGe1  xAsx ( x = 0.25, 0.5, 0.75). DOS marked by blue line represents virtual crystal approximation, while DOS of supercell approximation are marked by red line. Note that positive values of DOS refer to the majority-spin electrons and negative values refer to the minority-spin electrons. The Fermi level has been set as the zero of the energy axis. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

In Fig. 2, we give the relationship curve between spin magnetic moment and valence electrons concentration. It can be seen that the magnetic moment obeys the so-called Slater–Pauling rule:

Mtot = (Ztot − 18)μB,

(2)

where Mtot and Ztot are the total magnetic moment and the number of total valence electrons. In order to study the stability of the doped system, one should calculate their cohesive energies. So we calculate the cohesive energy of the system by both SCA and VCA. Calculation results are shown in Table 3. As can be seen from Table 3, the values of total energy through the SCA overall approximate right below the values through the VCA, and with different doped proportion, the values of the cohesive energy are also very stable. So obviously the energy values

Table 2 Magnetic data and optimized lattice constant (LC) for a series of FeCoZrGe1  xAsx ( x = 0.25, 0.5, 0.75) under the SCA. Doped proportion

LC (Å)

Fe (μB)

Co (μB)

Zr1 (μB)

Zr2 (μB)

Ge (μB)

As (μB)

Total (μB)

x ¼0.25 x ¼0.50 x ¼0.75

6.061 6.066 6.072

0.876 1.018 1.140

0.633 0.744 0.863

 0.232  0.263  0.281

 0.207  0.237  0.263

 0.049  0.047  0.034

0.014 0.024 0.031

1.250 1.500 1.750

G.-Y. Mao et al. / Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

2

Table 5 Magnetic data and optimized lattice constant (LC) for a series of FeCoZr1  xNbxGe ( x = 0.25, 0.5, 0.75) under the VCA.

SCA VCA

Magnetic moment (µB)

1.8

1.6

1.4

1.2

1 19

19.2

19.4 19.6 Valence-electron concentration

19.8

20

Fig. 2. The calculated total spin moments on valence-electron concentration for the FeCoZrGe1  xAsx alloys. Table 3 The cohesive energy and total energy in SCA or VCA system of FeCoZrGe1  xAsx x = 0.25, 0.5, 0.75. Doped proportion

Etot(VCA) (Hartree)

Etot(SCA) (Hartree)

Ecoh(VCA) (eV)

Ecoh(SCA) (eV)

x ¼ 0.25 x ¼ 0.50 x ¼ 0.75

 8404.485  8444.760  8485.477

 8405.146  8445.643  8486.139

3.777  2.534 3.162

21.773 21.505 21.197

Table 4 Curie temperature of FeCoZrGe1  xAsx ( x = 0.25, 0.5, 0.75). FeCoZrGe1-xAsx

FeCoZrGe0.75As0.25 FeCoZrGe0.5As0.5 FeCoZrGe0.25As0.75

Curie temperature (K)

401.83

543.78

3

686.92

Fig. 3. FeCoZrGe1  xAsx.

of SCA get higher reliability. In principle, due to a lower energy than the Ge, As may cause the VCA to not accurately calculate the value of energy of virtual atoms, making the overall final energy high and volatile. For SCA, because of replacing the target atoms with real atoms, the absolute energy calculation will not be influenced. Therefore, we believe that when it comes to the absolute energy, it is necessary to replace the VCA by SCA. From the results

Doped proportion

LC (Å)

Fe (μB)

Co (μB)

Zr(Nb) (μB)

Ge (μB)

Total (μB)

x ¼0.25 x ¼0.5 x ¼0.75

6.031 6.008 5.986

0.863 0.971 1.037

0.647 0.783 0.935

 0.220  0.223  0.198

 0.040  0.031  0.025

1.250 1.500 1.750

of SCA as shown in Table 3, the dissociation energy is still quite large. This means that the doped system may be stable. Curie temperature is another important aspect of application for spintronic material. Only with high Curie temperature can the magnetic materials be used in practice. Therefore, we also study the Curie temperature of the doped system. We estimate the Curie temperature by [27]

TCMF = 2

EAFM − EFM , 3kB

(3)

where EAFM and EFM are the energy in antiferromagnetic state and the energy in ferromagnetic state. kB is the Boltzmann constant. The results in Table 4 show that the Curie temperature of halfmetallic ferromagnetic doped system is higher than room temperature, so it can accommodate a wide range of scenarios. In addition, the Curie temperature increases with the proportion of As-doped linearly. In order to find the materials which may have controllable halfmetallic gap, we study the variation of half-metallic gap of FeCoZrGe1  xAsx with the As-doped proportion. Fig. 3 shows that FeCoZrGe1  xAsx will maintain half-metallic gap when 0.10 ≤ x ≤ 0.84 . At the point x ¼0.81, the half-metallic gap of FeCoZrGe1  xAsx reaches the maximum value of 0.091 eV. When 0.10 ≤ x ≤ 0.81, the half-metallic gap linearly increases with x. So we can control the half-metallic gap of FeCoZrGe1  xAsx with different proportion of As. If x > 0.81, the half-metallic gap will drop sharply. At the point x = 0.84 the half-metallic gap disappears. In the second part, we study the effect of doping Nb to the Zr sites. The same as previous, in order to examine the reliability of VCA approach, we simultaneously perform the SCA calculations. In the SCA approach, some of the Zr positions are occupied by the substituent Nb. To compare between the two different approaches, the total DOS and the total spin magnetic moments, which are used to measure the reliability of VCA and SCA results, are presented. In Tables 5 and 6 we have gathered the total and atomic spin moments for all cases. Fig. 4 shows the DOS of FeCoZr0.75Nb0.25Ge, FeCoZr0.5Nb0.5Ge and FeCoZr0.25Nb0.75Ge which are similar with SCA and VCA. This proves that such calculation results have high reliability. We also can see that there is a gap around the Fermi level in the spin down DOS, while the spin up DOS shows a conductive property. Therefore, they are half-metallic. Tables 5 and 6 show the contribution of Fe and Co atoms to the total magnetic moment. By comparing the results of the SCA and VCA calculation, we can find that the magnetic moment of Fe calculated by VCA is similar to that by SCA, so are Co, Zr and Ge. And this further proves that the results have high reliability. For doped system, the Slater–Pauling rule can be expressed by Eq. (1). As can be seen in Tables 5 and 6, FeCoZr1  xNbxGe ( x = 0.25, 0.5, 0.75) compounds are inconsistent with Slater– Pauling rule expressed by Eq. (2). The figure between magnetic moment and valence electrons concentration is similar with Fig. 2. We also calculated the cohesive energy of FeCoZr1  xNbxGe by SCA and VCA. As can be see from Table 7, the values of energy through the

4

G.-Y. Mao et al. / Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

Table 6 Magnetic data and optimized lattice constant (LC) for a series of FeCoZr1  xNbxGe ( x = 0.25, 0.5, 0.75) under the SCA. Doped proportion

LC (Å)

Fe (μB)

Co (μB)

Zr (μB)

Nb (μB)

Ge1 (μB)

Ge2 (μB)

Total (μB)

x ¼0.25 x ¼0.50 x ¼0.75

6.034 6.012 5.991

0.858 0.964 1.034

0.648 0.786 0.936

 0.216  0.226  0.215

 0.204  0.200  0.184

 0.049  0.049  0.044

 0.024  0.024  0.024

1.250 1.500 1.750

FeCoZr0.75Nb0.25Ge

VCA SCA

5

0

Density of states (states/eV)

-5

FeCoZr0.5Nb0.5Ge

VCA SCA

5

0 Fig. 5. FeCoZr1  xNbxGe.

-5

FeCoZr0.25Nb0.75Ge

VCA SCA

5

0

-5

-6

-4

-2

0 E-EF (eV)

2

4

6

Fig. 4. Spin-resolved total density of states (DOS) for the case of FeCoZr1  xNbxGe (x¼ 0.25, 0.5, 0.75). DOS marked by blue line represents VCA, while DOS of SCA are marked by red line. Note that positive values of DOS refer to the majority-spin electrons and negative values refer to the minority-spin electrons. The Fermi level has been set as the zero of the energy axis. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.) Table 7 The cohesive energy and total energy in SCA or VCA system of FeCoZr1  xNbxGe ( x = 0.25, 0.5, 0.75). Doped proportion

Etot(VCA) (Hartree)

Etot(SCA) (Hartree)

Ecoh (VCA) (eV)

Ecoh(SCA) (eV)

x ¼0.25 x ¼0.50 x ¼0.75

 8419.232  8474.299  8529.851

 8419.959  8475.270  8530.580

2.259  4.381 2.199

22.043 22.055 22.043

Table 8 Curie temperature of FeCoZr1  xNbxGe ( x = 0.25, 0.5, 0.75). FeCoZr1-xNbxGe

FeCoZr0.75Nb0.25Ge FeCoZr0.5Nb0.5Ge FeCoZr0.25Nb0.75Ge

Curie temperature 381.32 (K)

495.90

612.62

SCA are overall lower than the VCA's. As previously done, we still take the energy value of SCA as absolute energy values of FeCoZr1  xNbxGe. From the results of SCA, the cohesive energy shown in Table 7 is still quite large. This means that the doped system may be stable. We also have adopted SCA to estimate the Curie temperature. The results are shown in Table 8. As can be seen in Table 8, the Curie temperature of doped system is also higher than room temperature. So it can be adapted to a wide range of scenarios. In addition, we also see that the Curie temperature rises linearly with the increasing proportion of Nb doping. Finally, we study the variation of half-metallic gap of FeCoZr1  xNbxGe with the Nb-doped proportion. Fig. 5 shows that FeCoZr1  xNbxGe will maintain the half-metallic gap when 0.07 ≤ x ≤ 0.92. At the point x ¼0.84, the halfmetallic gap of FeCoZr1  xNbxGe reaches the maximum value of 0.11 eV. The rang of dopant for maintaining half-metallic of FeCoZr1  xNbxGe is wider than that of FeCoZrGe1  xAsx. In addition, FeCoZr1  xNbxGe has higher maximum half-metallic gap. So FeCoZr1  xNbxGe is more suitable as a half-metallic gap controllable material than FeCoZrGe1  xAsx. When 0.07 ≤ x ≤ 0.84 , the half-metallic gap of FeCoZr1  xNbxGe nearly linearly increases with x. So we can control the half-metallic gap of FeCoZr1  xNbxGe at this range with maximum half-metallic gap of 0.11 eV. If x > 0.85, the half-metallic gap will drop sharply. At the point x = 0.93 the half-metallic gap disappears. Finally, we will address the fixed spin moment (FSM) calculation results within GGA. We will only make a brief discussion with doped proportions (x) of x ¼0.25, x ¼0.50 and x¼ 0.75 as a representative, and the calculation reveals that the conclusions of different doped proportions are very similar. The energy vs. total magnetic moment plots are shown in Fig. 6 in which (a), (b) and (c) stand for x ¼0.25, x ¼0.50 and x ¼0.75, respectively. As can be seen in Fig. 6, by both VCA and SCA calculations, the energy local minimum points have the same magnetic moment values for each doped proportion in both As and Nb doped systems. In addition, we can directly get the conclusion that the previous calculation spin moment is indeed the energy local minimum points for each

G.-Y. Mao et al. / Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

As-doped

Nb-doped

5

As-doped

-8405.1

Nb-doped

-8445.6

-8475.3

-8420 -8405.1

-8475.3

-8445.6

-8420

-8405.1 0.8

1

1.2

1.4

1.6

1.8

2

-8420

1

1.2

1.4

1.6

1.8

2

-8419.2 -8404.5 -8419.2

-8475.3 -8475.3

-8445.6

1

1.5

2

2.5

3

-8419.2 0

0.5

1

1.5

2

2.5

3

0.5

1

1.5

2

2.5

-8474.3

-8444.8

-8474.3

3

SCA

1.8

2

-8474.3 0

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

Magnetic moment (µB) As-doped

Energy (Hartree)

1.6

-8474.3

-8444.8

Magnetic moment (µB) Nb-doped

-8486.1

-8530.6

-8486.1

-8530.6

-8486.1

-8530.6

-8486.1

-8530.6

-8486.1

-8530.6

-8486.1

1.5

-8530.6

2

1.5

2

-8529.8 -8485.5 -8529.8 -8485.5

VCA

1.4

-8474.3

-8444.8

-8444.8

0

1.2

-8474.3

-8419.2

-8404.5

1

-8444.8 -8444.8

-8419.2

-8475.3 -8474.3

-8404.5

-8404.5

-8475.3 -8445.6

-8445.6

-8420

Energy (Hartree)

Energy (Hartree)

-8405.1

VCA

SCA

-8405.1

VCA

SCA

-8420

-8529.8

-8485.5

-8529.8

-8485.5

-8529.8

-8485.5

-8529.8

-8485.5

-8529.9 0

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

Magnetic moment (µB)

Fig. 6. GGA fixed spin moment calculation results in As and Nb doped FeCoZrGe system by both SCA and VCA. We show the curves of energy as a function of magnetic moment for different doped proportions (x). (a), (b) and (c) stand for x ¼0.25, x ¼0.50 and x¼ 0.75, respectively.

doped proportion in both As and Nb doped systems. So our previous magnetic calculations are reasonable.

4. Conclusions To summarize, our results show that by doping As into the Ge sites or doping Nb into the Zr sites, FeCoZrGe could be transformed into a half-metallic material. Besides, as the doped proportion increases the system will have a wider half-metallic gap. This supports us to control the half-metallic gap by adjusting the doped proportion. Relatively FeCoZr1  xNbxGe can maintain its half-metallicity over a wider range of doping proportion. Also FeCoZr1  xNbxGe has a higher maximum half-metallic gap. At the same time, it can enhance the Curie temperature of the material by doping with As atoms or Nb atoms. Its Curie temperature is higher than room temperature where it is still maintaining halfmetallicity. In general, the As and Nb doped FeCoZrGe system may be widely used in the future.

References [1] I. Galanakis, Appearance of half-metallicity in the quaternary Heusler alloys, J. Phys.: Condens. Matter 16 (18) (2004) 3089, http://dx.doi.org/10.1088/

0953-8984/16/18/010 (URL 〈http://iopscience.iop.org/0953-8984/16/18/010〉). [2] I. Galanakis, Slater–Pauling Behavior in Half-Metallic Magnets (arXiv:1302. 4699 [cond-mat], URL 〈http://arxiv.org/abs/1302.4699〉). [3] A. Hirohata, M. Kikuchi, N. Tezuka, K. Inomata, J.S. Claydon, Y.B. Xu, G. van der Laan, Heusler alloy/semiconductor hybrid structures, Curr. Opin. Solid State Mater. Sci. 10 (2) (2006) 93–107, http://dx.doi.org/10.1016/j. cossms.2006.11.006 (URL 〈http://www.sciencedirect.com/science/article/pii/ S1359028606001124〉). [4] I. Galanakis, P. Mavropoulos, P.H. Dederichs, Electronic structure and Slater– Pauling behaviour in half-metallic Heusler alloys calculated from first principles, J. Phys. D: Appl. Phys. 39 (5) (2006) 765, http://dx.doi.org/10.1088/ 0022-3727/39/5/S01 (URL 〈http://iopscience.iop.org/0022-3727/39/5/S01〉). [5] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Slater–Pauling behavior and origin of the half-metallicity of the full-Heusler alloys, Phys. Rev. B 66 (17) (2002) 174429, http://dx.doi.org/10.1103/PhysRevB.66.174429 (URL 〈http:// link.aps.org/doi/10.1103/PhysRevB.66.174429〉). [6] T. Graf, C. Felser, S.S.P. Parkin, Simple rules for the understanding of Heusler compounds, Progr. Solid State Chem. 39 (1) (2011) 1–50, http://dx.doi.org/ 10.1016/j.progsolidstchem.2011.02.001 (URL 〈http://www.sciencedirect.com/ science/article/pii/S0079678611000021〉). [7] X. Dai, G. Liu, G.H. Fecher, C. Felser, Y. Li, H. Liu, New quarternary half metallic material CoFeMnSi, J. Appl. Phys. 105 (7) (2009) 07E901, http://dx.doi.org/ 10.1063/1.3062812 (URL 〈http://scitation.aip.org/content/aip/journal/jap/105/ 7/10.1063/1.3062812〉). [8] G.Z. Xu, E.K. Liu, Y. Du, G.J. Li, G.D. Liu, W.H. Wang, G.H. Wu, A new spin gapless semiconductors family: quaternary Heusler compounds, EPL (Europhys. Lett.) 102 (1) (2013) 17007, http://dx.doi.org/10.1209/0295-5075/102/17007 (URL 〈http://iopscience.iop.org/0295-5075/102/1/17007〉). [9] S. Rauf, S. Arif, M. Haneef, B. Amin, The first principle study of magnetic properties of Mn2WSn, Fe2YSn (Y ¼Ti, V), Co2YSn (Y¼ Ti, Zr, Hf, V, Mn) and Ni2YSn (Y ¼Ti, Zr, Hf, V, Mn) Heusler alloys, J. Phys. Chem. Solids 76 (2015) 153–169, http://dx.doi.org/10.1016/j.jpcs.2014.07.021 (WOS:000345183700021).

6

G.-Y. Mao et al. / Journal of Magnetism and Magnetic Materials 398 (2016) 1–6

[10] P.V.S. Reddy, V. Kanchana, Ab initio study of fermi surface and dynamical properties of Ni2XAl (X ¼ Ti, V, Zr, Nb, Hf and Ta), J. Alloys Compd. 616 (2014) 527–534, http://dx.doi.org/10.1016/j.jallcom.2014.07.020 (WOS:000342654000079). [11] P.-L. Yan, J.-M. Zhang, K.-W. Xu, Electronic structures magnetic properties and half-metallicity in Heusler alloys Zr2CoZ (Z ¼Al, Ga, In, Sn), J. Magn. Magn. Mater. 391 (0) (2015) 43–48, http://dx.doi.org/10.1016/j.jmmm.2015.04.101 (URL 〈http://www.sciencedirect.com/science/article/pii/ S0304885315301050〉). [12] S. Galehgirian, F. Ahmadian, First principles study on half-metallic properties of Heusler compounds Ti2VZ (Z¼ Al, Ga, and In), Solid State Commun. 202 (0) (2015) 52–57, http://dx.doi.org/10.1016/j.ssc.2014.10.017 (URL 〈http://www. sciencedirect.com/science/article/pii/S0038109814004281〉). [13] H. Xie, H. Wang, C. Fu, Y. Liu, G.J. Snyder, X. Zhao, T. Zhu, The intrinsic disorder related alloy scattering in ZrNiSn half-Heusler thermoelectric materials, Sci. Rep. 4 (2014) 6888, http://dx.doi.org/10.1038/srep06888 (WOS:000344228700001). [14] V.V. Romaka, L. Romaka, P. Rogl, Y. Stadnyk, N. Melnychenko, R. Korzh, Z. Duriagina, A. Horyn, Peculiarities of thermoelectric half-Heusler phase formation in Zr–Co–Sb ternary system, J. Alloys Compd. 585 (2014) 448–454, http://dx.doi.org/10.1016/j.jallcom.2013.09.097 (WOS:000327492600066). [15] U. Kanbur, G. GÖkoǧ lu, Half-metallic magnetism of Co2CrX (X ¼As, Sb) Heusler compounds: an ab initio study, J. Magn. Magn. Mater. 323 (9) (2011) 1156–1160, http://dx.doi.org/10.1016/j.jmmm.2010.12.034 (URL 〈http://www. sciencedirect.com/science/article/pii/S030488531000939X〉). [16] Q. Gao, L. Li, G. Lei, J.-B. Deng, X.-R. Hu, A first-principle study on the properties of a new series of quaternary Heusler alloys CoFeScZ (Z¼ P, As, Sb), J. Magn. Magn. Mater. 379 (0) (2015) 288–293, http://dx.doi.org/10.1016/j. jmmm.2014.12.025 (URL 〈http://www.sciencedirect.com/science/article/pii/ S0304885314012384). [17] S. Berri, M. Ibrir, D. Maouche, M. Attallah, First principles study of structural, electronic and magnetic properties of ZrFeTiAl, ZrFeTiSi, ZrFeTiGe and ZrNiTiAl, J. Magn. Magn. Mater. 371 (2014) 106–111, http://dx.doi.org/10.1016/j. jmmm.2014.07.033 (URL 〈http://www.sciencedirect.com/science/article/pii/ S0304885314006441〉). [18] H.-H. Xie, Q. Gao, L. Li, G. Lei, G.-Y. Mao, X.-R. Hu, J.-B. Deng, First-principles study of four quaternary Heusler alloys ZrMnVZ and ZrCoFeZ (Z ¼Si, Ge), Comput. Mater. Sci. 103 (0) (2015) 52–55, http://dx.doi.org/10.1016/j.

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

commatsci.2015.03.010 (URL 〈http://www.sciencedirect.com/science/article/ pii/S092702561500172X〉). I. Galanakis, K. Özdoǧ an, B. Akta, E. Şaşǧ lu, Effect of doping and disorder on the half metallicity of full Heusler alloys, Appl. Phys. Lett. 89 (4) (2006), http://dx. doi.org/10.1063/1.2235913 (URL 〈http://scitation.aip.org/content/aip/journal/ apl/89/4/10.1063/1.2235913〉). K. Özdoǧ an, B. Aktaş, I. Galanakis, E. Şaşoǧ lu, Influence of mixing the lowvalent transition metal atoms (y, y⁎ = Cr, Mn, Fe) on the properties of the quaternary CO2[y1 − xy⁎x]z (z = Al, Ga, Si, Ge, or Sn) Heusler compounds, J. Appl. Phys. 101 (7), 2007. http://dx.doi.org/10.1063/1.2714502, (URL 〈http://scitation. aip.org/content/aip/journal/jap/101/7/10.1063/1.2714502〉). K. Özdoǧ an, E. Şaşoǧ lu, I. Galanakis, Engineering the electronic, magnetic, and gap-related properties of the quinternary half-metallic Heusler alloys, J. Appl. Phys. 103 (2), 2008, http://dx.doi.org/10.1063/1.2831224, (URL 〈http://scita tion.aip.org/content/aip/journal/jap/103/2/10.1063/1.2831224〉). R.A. Downie, S.R. Popuri, H. Ning, M.J. Reece, J.-W.G. Bos, Effect of spark plasma sintering on the structure and properties of Ti1− x ZrxNiSn half-Heusler alloys, Materials 7 (10) (2014) 7093–7104, http://dx.doi.org/10.3390/ma7107093 (WOS:000344459200015). I. Opahle, K. Koepernik, H. Eschrig, Full-potential band-structure calculation of iron pyrite, Phys. Rev. B 60 (20) (1999) 14035–14041, http://dx.doi.org/ 10.1103/PhysRevB.60.14035 (URL 〈http://link.aps.org/doi/10.1103/PhysRevB.60. 14035〉). K. Koepernik, H. Eschrig, Full-potential nonorthogonal local-orbital minimumbasis band-structure scheme, Phys. Rev. B 59 (3) (1999) 1743–1757, http://dx. doi.org/10.1103/PhysRevB.59.1743 (URL 〈http://link.aps.org/doi/10.1103/Phys RevB.59.1743〉). J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (18) (1996) 3865–3868, http://dx.doi.org/10.1103/ PhysRevLett.77.3865 (URL http://link.aps.org/doi/10.1103/PhysRevLett.77. 3865〉). D. Kasinathan, M. Wagner, K. Koepernik, R. Cardoso-Gil, Y. Grin, H. Rosner, Electronic and thermoelectric properties of ruin, Phys. Rev. B 85 (2012) 035207, http://dx.doi.org/10.1103/PhysRevB.85.035207 (URL 〈http://link.aps. org/doi/10.1103/PhysRevB.85.035207〉). P. Kurz, G. Bihlmayer, S. Blügel, Magnetism and electronic structure of hcp Gd and the Gd(0001) surface, J. Phys.: Condens. Matter 14 (25) (2002) 6353 (URL 〈http://stacks.iop.org/0953-8984/14/i¼ 25/a ¼ 305〉).