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Electronic and magnetic properties of Cr-Mn-Ni-Al compound with LiMgPdSb-type structure
Solid State Communications 244 (2016) 38–42
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Electronic and magnetic properties of Cr-Mn-Ni-Al compound with LiMgPdSb-type structure L.Y. Wang a, X.T. Wang b, R.K. Guo b, T.T. Lin b, G.D. Liu b,n a b
Department of Physics, Tianjin University, Tianjin 300350, PR China School of Material Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 May 2016 Received in revised form 25 June 2016 Accepted 27 June 2016 Available online 27 June 2016
We investigate the electronic and magnetic properties of Cr-Mn-Ni-Al compound with a LiMgPdSn-type structure in three different atomic arrangement configurations (AAC) by using the first-principles calculations. It was found that Cr-Mn-Ni-Al compound with type I AAC exhibits a spin-gapless semiconductive characteristic. The type II AAC is the most stable one and exhibits an especial band structure where the Fermi level slightly crosses the top of the valence bands in spin-up channel and the bottom of conductive bands in spin-down channel, which leads to the electronic transport with the spin-resolved carrier type. The Cr-Mn-Ni-Al compound shows an ordinary metallic behavior in type III AAC. The three nonequivalent atomic arrangement configurations of Cr-Mn-Ni-Al are all in ferromagnetic ground state under their equilibrium lattice parameters. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Cr-Mn-Ni-Al First principles calculations Electronic structure Magnetic property
1. Introduction Spin-gapless semiconductors (SGS), as a new concept in spintronics, were first reported theoretically and verified experimentally in doped Pb-based oxide materials by Wang in 2008 [1,2]. They uniquely merges the properties of zero-gap semiconductor and half-metallic (HM) ferromagnets, and can be regarded as the combination of them. There are four possible band structure configurations with spin-gapless features as shown in Fig. 1(a)–(d). For the first case (Fig. 1(a)), one spin channel is gapless, while the other spin channel is semiconducting. In the second case (b), one spin channel is gapless, and the other spin channel is semiconducting with the top of the valence band next to the Fermi level. In the third case (c), one spin channel is gapless while the bottom of the conduction band for the other spin channel touches the Fermi level, which is separated from its corresponding valence band by a gap. In the fourth case (d), there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band. From these spin-gapless semiconductor band structures, one can see that no energy is required to excite electrons from the valence band to the conduction band and not only the excited electrons but also the holes can be completely spin-polarized. The special band structure of SGS leads to some novel transport n
Corresponding author. E-mail address: [email protected] (G.D. Liu).
http://dx.doi.org/10.1016/j.ssc.2016.06.019 0038-1098/& 2016 Elsevier Ltd. All rights reserved.
properties and new functionalities of spintronic devices. In recent several years, several different classes of materials have been theoretically and experimentally reported to be new SGSs, such as N-doped zigzag grapheme nanoribbons [3], zigzag silicone nanoribbons with asymmetric sp2–sp3 edges [4], and several binary, ternary and quaternary Heusler compounds [5–11]. Among them, Heusler compound is one of the most important one. Heusler compound Mn2CoAl [4], which was previously calculated to be a halfmetallic ferromagnet by our previous work [12], has been realized to be a SGS experimentally. A series of inverse Heusler compounds [5] and DO3-type Heusler compounds [5] were found to be promising candidates for SGSs. Most recently, I. Galanakis [9] and Xu et al. [8] show theoretically that five quaternary Heusler compounds: CoFeMnSi, CoFeCrAl, CoMnCrSi, CoFeVSi and FeMnCrSb would be probable SGSs. They also reveal a semi-empirical general rule: the spin-gapless feature should occurs in the Heusler compounds with the total valence electrons number of 26 or 28. Heusler compounds are a huge family that has been applied in many areas due to their multi-function and numerous properties [13]. In the present work, we substitute one of the Mn atom with Cr atom in the Mn2NiAl Heusler compound, which has been predicted to be a ferromagnetic shape-memory alloy (FSMA) [14], forming a new quaternary Heusler compound: Cr-Mn-Ni-Al with the total valence electrons number of 26. It follows the semi-empirical general rule that has been mentioned in reference 12. Cr-Mn-Ni-Al compound have three different atomic arrangement configurations (AAC). In this paper, we investigate the electronic and magnetic properties of Cr-Mn-Ni-Al compound with three different atomic arrangement configurations.
L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
39
Fig. 1. Density-of-states (DOS) scheme of the four possible band structure configurations with spin gapless features: (a)–(d). Filled areas represent occupied states, and the arrows indicate majority (↑) spin and minority (↓) spin.
2. Computational details
MnNiCrAl MnCrNiAl CrMnNiAl
1.5
Energy(eV)
Our calculation used the CASTEP code based on the pseudopotential method with a plane-wave basis set [15,16]. We adopt the generalized gradient approximation (GGA) in the Perdew– Bueke–Ernzerhof scheme for the electronic exchange-correlation functional [17,18]. The interactions between the valence electrons and the atomic core were described by the ultrasoft pseudopotential [19]. A plane-wave basis set cut-off energy of 400 eV and a mesh of 12 12 12 k-points were employed to ensure good convergence. The calculations continue until the energy deviation is less than 1 10 6 eV/atom. By performing the geometry optimization calculation, we obtained the equilibrium lattice constants.
1.0 0.5 0.0 -0.5 -1.0
5.5
3. Results and discussion
5.7
5.8
5.9
lattice constant(Å) Fig. 2. (Color online) The optimization curves of lattice parameter for MnCrNiAl (five-pointed star line), MnNiCrAl (hollow triangle line), CrNiMnAl (hollow round line) compounds. The total energy is a relative value.
Majority
4
Minority
2
Energy(eV)
Quaternary Heusler compound has the chemical formula X-YM-Z, where the X, Y and M are transition metal atoms. The structural prototype of the quaternary Heusler compounds is the ¯ LiMgPdSb [20], with the space group of F 43m . There are three possible different types of atom arrangement in the quaternary Heusler compound X-Y-M-Z: typeⅠ(XMYZ) X (0,0,0), Y (1/4,1/4,1/4), M (1/2,1/2,1/2) and Z (3/4,3/4,3/4); typeⅡ(YMXZ) X (1/4,1/4,1/4), Y (0,0,0), M (1/2,1/2,1/2) and Z (3/4,3/4,3/4); type Ⅲ (YXMZ) X (1/2,1/ 2,1/2), Y (0,0,0), M (1/4,1/4,1/4) and Z (3/4,3/4,3/4). In order to determine the equilibrium structure of the quaternary Heusler compounds Cr-Mn-Ni-Al studied, we firstly perform geometry optimization for Cr-Mn-Ni-Al in their respective three different configurations by calculating the total energy as a function of volumes, the optimized results are shown in Fig. 2. For all the Cr-MnNi-Al, the structure of type Ⅱ AAC (MnNiCrAl) is the most stable one among the three configurations due to the lowest energy and type Ⅲ AAC (MnNiCrAl) is the highest one. This indicates that this quaternary Heusler compound with a 1:1:1:1 stoichiometry prefers crystallizing in the type Ⅱ AAC (MnNiCrAl) structure. The type Ⅰ (CrNiMnAl) structure is the metastable state, and it is possible to transform from type Ⅱ (MnNiCrAl) to type Ⅰ (CrNiMnAl) structure under an external driving force. The obtained equilibrium lattice parameters of CrNiMnAl, MnNiCrAl and MnCrNiAl are 5.665 Å, 5.638 Å and 5.660 Å, respectively. The band structures of the three nonequivalent structures were calculated with the optimized lattice parameter. The calculated results are shown in Figs. 3–5. From Fig. 3, it can be seen that the
5.6
eu
t1u
0 -2 -4 -6
W
L
G
X WK W
L
G
X WK
Fig. 3. (Color online) Part of the band structure and density of states (DOS) of CrNiMnAl (a) majority spin (the bold lines are used to emphasize the top of the valence band in majority spin and the bottom of the conduction band in minority spin), (b) minority spin.
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L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
Table 1 Calculated total and atomic magnetic moment of Cr-Mn-Ni-Al alloy for its respective three different configurations.
4
Energy(eV)
2 CrNiMnAl MnNiCrAl MnCrNiAl
0
MCr(μB)
MMn(μB)
MNi(μB)
MAl(μB)
2.00 1.83 1.76
1.48(A) 2.52(B) 1.08(C)
2.94(B) 1.08(A) 1.0 (A)
0.54(C) 0.42(C) 0.20(B)
0.00(D) 0.02(D) 0.12(D)
-2 -4 -6
W L
G
X WK W L
G
X WK
Fig. 4. Part of the band structure and density of states (DOS) of MnNiCrAl (a) majority spin, (b) minority spin.
4 2
Energy(eV)
MTotal (μB)
0 -2 -4 -6 W
L
G
X
W K W
L
G
X W K
Fig. 5. Part of the band structure and density of states (DOS) of MnCrNiAl (a) majority spin, (b) minority spin.
electronic structure of Cr-Mn-Ni-Al Heusler compound with type ⅠAAC (CrNiMnAl) is special. No matter in majority-spin or minority-spin channels, the Fermi level locates at an energy gap, which indicates that the CrNiMnAl compound is a semiconductive material. While, it should be noted that the CrNiMnAl compound has an asymmetric band structure in majority-spin and minority-spin channels due to the spin-spilling, which is different from the conventional semiconductor where the band structures are symmetric in majority-spin and minority-spin channels. In the minority-spin states, there is a direct band gap of 0.3 eV between eu and t1u states at G point and the bottom of the conduction bands touch the Fermi level. While, we emphasize the band structure is different in the majority-spin channel. The gap is indirect, and the valence bands at G and L points touch the Fermi level. The band structure characteristics discussed above indicate that there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band, which has been presented in Fig. 1(d). And the total magnetic moment of this unit cell is 2.00μB as tabulated in Table 1. The closed band gap characteristic and the integrate magnetic moment suggest that CrNiMnAl is a SGS rather than a normal half-metallic (HM) ferromagnet, and this deserves further experimental studies to be confirmed. Fig. 4 shows the band structure of Cr-Mn-Ni-Al with the type Ⅱ AAC (MnNiCrAl). It can be observed that there is a metallic cross with the Fermi level in the two spin channels. While, this is an
special band structure where the Fermi level slightly crosses the top of the valence bands in majority-spin channel and the bottom of conductive bands in minority-spin channel. It means that in the majority-spin channel, the conductive carrier is hole, while, in the minority-spin channel, is the electron carrier. This special band structure would lead to the electronic transport with the spinresolved carrier type. In addition, despite the overlapping with the Fermi level in the two spin channels, one can see that the cross is very slight. Thus, it can be consider as a special SGS. Besides, it can be found that it exhibits a narrow gap in both the majority and minority spin channel around the Fermi level. And the physical nature can be usually changed when the lattice constant is expanded or compressed appropriately. Therefore, it is likely to achieve a half-metal or spin-gapless semiconductor through lattice distortion. For the Cr-Mn-Ni-Al compound with type III AAC, it shows an ordinary metallic behavior as shown in Fig. 5. In Fig. 6, we have drawn the total and atom-projected density of states (DOS) for the three different type of Cr-Mn-Ni-Al compound at their equilibrium lattice parameters. It is clearly that for the type ⅠAAC (CrNiMnAl) structure, the Fermi level indeed lies in the top of the valence band in the majority-spin channel and touches the bottom of the conduction band in the minority-spin channel. Furthermore, for the type Ⅱ AAC (MnNiCrAl) structure, it can be seen that the electronic structure is similar to that of type Ⅰ AAC (CrNiMnAl). However, the majority-spin DOS shifts to a higher energy region and the minority-spin DOS moves to a lower energy region, leading to the Fermi level has a small metallic cross in the two spin directions. While, there is still a band gap in the two spin channels around the Fermi level. In the type Ⅲ AAC (MnCrNiAl) structure, there is no gap in the majority-and minority-spin channels, so it is a ordinary ferromagnet. These results indicate that the Cr-Mn-Ni-Al compound with type ⅠAAC (CrNiMnAl) structure is a SGS, and type Ⅱ AAC (MnNiCrAl) structure is likely to be a half-metal or SGS through lattice distortion. While, the type Ⅲ AAC (MnCrNiAl) destroy this property to be a common ferromagnet. In order to understand the electronic structure of CrNiMnAl better, we will give a particular description on the DOS. From the total DOS (as shown in Fig. 6), one an see that there appear to be three peaks in the majority-spin channel. The two peaks at the lower energies can be traced to be the eg-t2g splitting of 3d bands for Mn at B sites [Mn(B)] atom in the cubic crystal field, and the peak at the higher energy is composed of the antibonding of d bands of Cr(A) atom. For the minority-spin channel, two peaks can be observed. The peak at about 1.8 eV above Fermi level is of the antibonding nature mainly arising from the Mn(B) atom. The large spin splitting in DOS between majority- and minority-spin states suggests a strong exchange, which leads to large localized spin magnetic moments at the Mn(B) sites [21]. For Cr(A) atom, the minority-spin states are mostly situated below the Fermi level, while the majority-spin bands shows a maxim above the Fermi level. It is also clear that the exchange splitting of Cr(A) d states is weaker than that of Mn(B) atoms in this compound. The majorityand minority-spin bands of Ni atoms are equally populated with negligible contributions to the total moment.
L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
CrNiMnAl
The calculated magnetic moments per formula unit and the atomic magnetic moment are listed in Table 1. The type Ⅰ(MnNiCrAl) structure shows an integral total moment of 2.00μB, which is consistent to the characteristic of SGS. The total magnetic moment of type Ⅱ(MnNiCrAl) structure is 1.83μB. From this table, we also see that the atoms at B site always have large magnetic moment for type Ⅰ(MnNiCrAl) and type Ⅱ(MnNiCrAl) structures. For example, the Mn(B) atom in type Ⅰ(MnNiCrAl) structure has a magnetic moment of 2.94μB while the magnetic moment decreases to 1.08μB in type Ⅱ(MnNiCrAl) structure. The same occurs for Cr atom. For the three nonequivalent Cr-Mn-Ni-Al structures, the Ni moment is small and contributes little to the total spin moment. In CrNiMnAl and MnNiCrAl compounds, there is a ferrimagnetic coupling between the atom at A sites and the atom at B or C sites. For MnCrNiAl compound, a ferrimagnetic coupling occurs between the Ni(B) and the Mn(A) or Cr(C) moment.
Total
5 0 -5 4
Cr d(A)
2 0
DOS(states/eV)
-2 -4
Mn-d(B)
2 0 -2
Ni-d(C)
2 0 -2 -4
Al-p(D)
0.4
41
0.0 -0.4 -6
-4
-2
0
2
4
Energy(eV)
In conclusion, we investigated the electronic and magnetic properties of a new quaternary Heusler compound Cr-Mn-Ni-Al with three different AAC. The Cr-Mn-Ni-Al compound with type I AAC (CrNiMnAl) was predicted to possess a special electronic structure: there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band, showing a SGS behavior. The type II AAC (MnNiCrAl) exhibits a very similar electronic structure with type I AAC, while, showing a slight cross with the Fermi level in the top of the valence bands (majority-spin channel) and the bottom of conductive bands (minority-spin channel) and it can be regarded as a special SGS. This special band structure will lead to the electronic transport with the spin-resolved carrier type.
MnCrNiAl
10
Total
5 0
DOS(states/eV)
-5 -102 1 0 -1 -2 2
Cr-d (C)
Mn-d (A)
0 -2
Ni-d (B)
3
4. Conclusions
0 -3 -6
Al-p(D)
0.4
Acknowledgments
0.0 -0.4 -6
-4
-2
0
2
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51271071), Key Basic Research Program of Applied Basic Research Program of Hebei Province (12965136D), Hebei Province Natural Science Foundation (No. E2013202181), Hebei Province Higher Education Science and Technology Research Foundation for Youth Scholars (No. Q2012008).
4
Energy(eV)
MnCrNiAl
10
Total
5 0
DOS(states/eV)
-5 -102 1 0 -1 -2 2
Cr-d (C)
References Mn-d (A)
0 -2
Ni-d (B)
3 0 -3 -6
Al-p(D)
0.4 0.0 -0.4 -6
-4
-2
0
2
4
Energy(eV) Fig. 6. The calculated total and atom-projected DOS for CrNiMnAl, MnNiCrAl and MnCrNiAl at their equilibrium lattice parameters. The vertical solid line in zero energy represents the Fermi level.
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[15] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoolous, Rev. Mod. Phys. 64 (1992) 1065. [16] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M. C. Payne, J. Phys. Condens. Matter 14 (2002) 2717. [17] J.P. Perdew, J.A. Chevary, S.H. Vosko, A. Jackson, M.R. Pederson, C. Fiolhais,
[18] [19] [20] [21]
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Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Fast-track communication
Electronic and magnetic properties of Cr-Mn-Ni-Al compound with LiMgPdSb-type structure L.Y. Wang a, X.T. Wang b, R.K. Guo b, T.T. Lin b, G.D. Liu b,n a b
Department of Physics, Tianjin University, Tianjin 300350, PR China School of Material Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 May 2016 Received in revised form 25 June 2016 Accepted 27 June 2016 Available online 27 June 2016
We investigate the electronic and magnetic properties of Cr-Mn-Ni-Al compound with a LiMgPdSn-type structure in three different atomic arrangement configurations (AAC) by using the first-principles calculations. It was found that Cr-Mn-Ni-Al compound with type I AAC exhibits a spin-gapless semiconductive characteristic. The type II AAC is the most stable one and exhibits an especial band structure where the Fermi level slightly crosses the top of the valence bands in spin-up channel and the bottom of conductive bands in spin-down channel, which leads to the electronic transport with the spin-resolved carrier type. The Cr-Mn-Ni-Al compound shows an ordinary metallic behavior in type III AAC. The three nonequivalent atomic arrangement configurations of Cr-Mn-Ni-Al are all in ferromagnetic ground state under their equilibrium lattice parameters. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Cr-Mn-Ni-Al First principles calculations Electronic structure Magnetic property
1. Introduction Spin-gapless semiconductors (SGS), as a new concept in spintronics, were first reported theoretically and verified experimentally in doped Pb-based oxide materials by Wang in 2008 [1,2]. They uniquely merges the properties of zero-gap semiconductor and half-metallic (HM) ferromagnets, and can be regarded as the combination of them. There are four possible band structure configurations with spin-gapless features as shown in Fig. 1(a)–(d). For the first case (Fig. 1(a)), one spin channel is gapless, while the other spin channel is semiconducting. In the second case (b), one spin channel is gapless, and the other spin channel is semiconducting with the top of the valence band next to the Fermi level. In the third case (c), one spin channel is gapless while the bottom of the conduction band for the other spin channel touches the Fermi level, which is separated from its corresponding valence band by a gap. In the fourth case (d), there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band. From these spin-gapless semiconductor band structures, one can see that no energy is required to excite electrons from the valence band to the conduction band and not only the excited electrons but also the holes can be completely spin-polarized. The special band structure of SGS leads to some novel transport n
Corresponding author. E-mail address: [email protected] (G.D. Liu).
http://dx.doi.org/10.1016/j.ssc.2016.06.019 0038-1098/& 2016 Elsevier Ltd. All rights reserved.
properties and new functionalities of spintronic devices. In recent several years, several different classes of materials have been theoretically and experimentally reported to be new SGSs, such as N-doped zigzag grapheme nanoribbons [3], zigzag silicone nanoribbons with asymmetric sp2–sp3 edges [4], and several binary, ternary and quaternary Heusler compounds [5–11]. Among them, Heusler compound is one of the most important one. Heusler compound Mn2CoAl [4], which was previously calculated to be a halfmetallic ferromagnet by our previous work [12], has been realized to be a SGS experimentally. A series of inverse Heusler compounds [5] and DO3-type Heusler compounds [5] were found to be promising candidates for SGSs. Most recently, I. Galanakis [9] and Xu et al. [8] show theoretically that five quaternary Heusler compounds: CoFeMnSi, CoFeCrAl, CoMnCrSi, CoFeVSi and FeMnCrSb would be probable SGSs. They also reveal a semi-empirical general rule: the spin-gapless feature should occurs in the Heusler compounds with the total valence electrons number of 26 or 28. Heusler compounds are a huge family that has been applied in many areas due to their multi-function and numerous properties [13]. In the present work, we substitute one of the Mn atom with Cr atom in the Mn2NiAl Heusler compound, which has been predicted to be a ferromagnetic shape-memory alloy (FSMA) [14], forming a new quaternary Heusler compound: Cr-Mn-Ni-Al with the total valence electrons number of 26. It follows the semi-empirical general rule that has been mentioned in reference 12. Cr-Mn-Ni-Al compound have three different atomic arrangement configurations (AAC). In this paper, we investigate the electronic and magnetic properties of Cr-Mn-Ni-Al compound with three different atomic arrangement configurations.
L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
39
Fig. 1. Density-of-states (DOS) scheme of the four possible band structure configurations with spin gapless features: (a)–(d). Filled areas represent occupied states, and the arrows indicate majority (↑) spin and minority (↓) spin.
2. Computational details
MnNiCrAl MnCrNiAl CrMnNiAl
1.5
Energy(eV)
Our calculation used the CASTEP code based on the pseudopotential method with a plane-wave basis set [15,16]. We adopt the generalized gradient approximation (GGA) in the Perdew– Bueke–Ernzerhof scheme for the electronic exchange-correlation functional [17,18]. The interactions between the valence electrons and the atomic core were described by the ultrasoft pseudopotential [19]. A plane-wave basis set cut-off energy of 400 eV and a mesh of 12 12 12 k-points were employed to ensure good convergence. The calculations continue until the energy deviation is less than 1 10 6 eV/atom. By performing the geometry optimization calculation, we obtained the equilibrium lattice constants.
1.0 0.5 0.0 -0.5 -1.0
5.5
3. Results and discussion
5.7
5.8
5.9
lattice constant(Å) Fig. 2. (Color online) The optimization curves of lattice parameter for MnCrNiAl (five-pointed star line), MnNiCrAl (hollow triangle line), CrNiMnAl (hollow round line) compounds. The total energy is a relative value.
Majority
4
Minority
2
Energy(eV)
Quaternary Heusler compound has the chemical formula X-YM-Z, where the X, Y and M are transition metal atoms. The structural prototype of the quaternary Heusler compounds is the ¯ LiMgPdSb [20], with the space group of F 43m . There are three possible different types of atom arrangement in the quaternary Heusler compound X-Y-M-Z: typeⅠ(XMYZ) X (0,0,0), Y (1/4,1/4,1/4), M (1/2,1/2,1/2) and Z (3/4,3/4,3/4); typeⅡ(YMXZ) X (1/4,1/4,1/4), Y (0,0,0), M (1/2,1/2,1/2) and Z (3/4,3/4,3/4); type Ⅲ (YXMZ) X (1/2,1/ 2,1/2), Y (0,0,0), M (1/4,1/4,1/4) and Z (3/4,3/4,3/4). In order to determine the equilibrium structure of the quaternary Heusler compounds Cr-Mn-Ni-Al studied, we firstly perform geometry optimization for Cr-Mn-Ni-Al in their respective three different configurations by calculating the total energy as a function of volumes, the optimized results are shown in Fig. 2. For all the Cr-MnNi-Al, the structure of type Ⅱ AAC (MnNiCrAl) is the most stable one among the three configurations due to the lowest energy and type Ⅲ AAC (MnNiCrAl) is the highest one. This indicates that this quaternary Heusler compound with a 1:1:1:1 stoichiometry prefers crystallizing in the type Ⅱ AAC (MnNiCrAl) structure. The type Ⅰ (CrNiMnAl) structure is the metastable state, and it is possible to transform from type Ⅱ (MnNiCrAl) to type Ⅰ (CrNiMnAl) structure under an external driving force. The obtained equilibrium lattice parameters of CrNiMnAl, MnNiCrAl and MnCrNiAl are 5.665 Å, 5.638 Å and 5.660 Å, respectively. The band structures of the three nonequivalent structures were calculated with the optimized lattice parameter. The calculated results are shown in Figs. 3–5. From Fig. 3, it can be seen that the
5.6
eu
t1u
0 -2 -4 -6
W
L
G
X WK W
L
G
X WK
Fig. 3. (Color online) Part of the band structure and density of states (DOS) of CrNiMnAl (a) majority spin (the bold lines are used to emphasize the top of the valence band in majority spin and the bottom of the conduction band in minority spin), (b) minority spin.
40
L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
Table 1 Calculated total and atomic magnetic moment of Cr-Mn-Ni-Al alloy for its respective three different configurations.
4
Energy(eV)
2 CrNiMnAl MnNiCrAl MnCrNiAl
0
MCr(μB)
MMn(μB)
MNi(μB)
MAl(μB)
2.00 1.83 1.76
1.48(A) 2.52(B) 1.08(C)
2.94(B) 1.08(A) 1.0 (A)
0.54(C) 0.42(C) 0.20(B)
0.00(D) 0.02(D) 0.12(D)
-2 -4 -6
W L
G
X WK W L
G
X WK
Fig. 4. Part of the band structure and density of states (DOS) of MnNiCrAl (a) majority spin, (b) minority spin.
4 2
Energy(eV)
MTotal (μB)
0 -2 -4 -6 W
L
G
X
W K W
L
G
X W K
Fig. 5. Part of the band structure and density of states (DOS) of MnCrNiAl (a) majority spin, (b) minority spin.
electronic structure of Cr-Mn-Ni-Al Heusler compound with type ⅠAAC (CrNiMnAl) is special. No matter in majority-spin or minority-spin channels, the Fermi level locates at an energy gap, which indicates that the CrNiMnAl compound is a semiconductive material. While, it should be noted that the CrNiMnAl compound has an asymmetric band structure in majority-spin and minority-spin channels due to the spin-spilling, which is different from the conventional semiconductor where the band structures are symmetric in majority-spin and minority-spin channels. In the minority-spin states, there is a direct band gap of 0.3 eV between eu and t1u states at G point and the bottom of the conduction bands touch the Fermi level. While, we emphasize the band structure is different in the majority-spin channel. The gap is indirect, and the valence bands at G and L points touch the Fermi level. The band structure characteristics discussed above indicate that there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band, which has been presented in Fig. 1(d). And the total magnetic moment of this unit cell is 2.00μB as tabulated in Table 1. The closed band gap characteristic and the integrate magnetic moment suggest that CrNiMnAl is a SGS rather than a normal half-metallic (HM) ferromagnet, and this deserves further experimental studies to be confirmed. Fig. 4 shows the band structure of Cr-Mn-Ni-Al with the type Ⅱ AAC (MnNiCrAl). It can be observed that there is a metallic cross with the Fermi level in the two spin channels. While, this is an
special band structure where the Fermi level slightly crosses the top of the valence bands in majority-spin channel and the bottom of conductive bands in minority-spin channel. It means that in the majority-spin channel, the conductive carrier is hole, while, in the minority-spin channel, is the electron carrier. This special band structure would lead to the electronic transport with the spinresolved carrier type. In addition, despite the overlapping with the Fermi level in the two spin channels, one can see that the cross is very slight. Thus, it can be consider as a special SGS. Besides, it can be found that it exhibits a narrow gap in both the majority and minority spin channel around the Fermi level. And the physical nature can be usually changed when the lattice constant is expanded or compressed appropriately. Therefore, it is likely to achieve a half-metal or spin-gapless semiconductor through lattice distortion. For the Cr-Mn-Ni-Al compound with type III AAC, it shows an ordinary metallic behavior as shown in Fig. 5. In Fig. 6, we have drawn the total and atom-projected density of states (DOS) for the three different type of Cr-Mn-Ni-Al compound at their equilibrium lattice parameters. It is clearly that for the type ⅠAAC (CrNiMnAl) structure, the Fermi level indeed lies in the top of the valence band in the majority-spin channel and touches the bottom of the conduction band in the minority-spin channel. Furthermore, for the type Ⅱ AAC (MnNiCrAl) structure, it can be seen that the electronic structure is similar to that of type Ⅰ AAC (CrNiMnAl). However, the majority-spin DOS shifts to a higher energy region and the minority-spin DOS moves to a lower energy region, leading to the Fermi level has a small metallic cross in the two spin directions. While, there is still a band gap in the two spin channels around the Fermi level. In the type Ⅲ AAC (MnCrNiAl) structure, there is no gap in the majority-and minority-spin channels, so it is a ordinary ferromagnet. These results indicate that the Cr-Mn-Ni-Al compound with type ⅠAAC (CrNiMnAl) structure is a SGS, and type Ⅱ AAC (MnNiCrAl) structure is likely to be a half-metal or SGS through lattice distortion. While, the type Ⅲ AAC (MnCrNiAl) destroy this property to be a common ferromagnet. In order to understand the electronic structure of CrNiMnAl better, we will give a particular description on the DOS. From the total DOS (as shown in Fig. 6), one an see that there appear to be three peaks in the majority-spin channel. The two peaks at the lower energies can be traced to be the eg-t2g splitting of 3d bands for Mn at B sites [Mn(B)] atom in the cubic crystal field, and the peak at the higher energy is composed of the antibonding of d bands of Cr(A) atom. For the minority-spin channel, two peaks can be observed. The peak at about 1.8 eV above Fermi level is of the antibonding nature mainly arising from the Mn(B) atom. The large spin splitting in DOS between majority- and minority-spin states suggests a strong exchange, which leads to large localized spin magnetic moments at the Mn(B) sites [21]. For Cr(A) atom, the minority-spin states are mostly situated below the Fermi level, while the majority-spin bands shows a maxim above the Fermi level. It is also clear that the exchange splitting of Cr(A) d states is weaker than that of Mn(B) atoms in this compound. The majorityand minority-spin bands of Ni atoms are equally populated with negligible contributions to the total moment.
L.Y. Wang et al. / Solid State Communications 244 (2016) 38–42
CrNiMnAl
The calculated magnetic moments per formula unit and the atomic magnetic moment are listed in Table 1. The type Ⅰ(MnNiCrAl) structure shows an integral total moment of 2.00μB, which is consistent to the characteristic of SGS. The total magnetic moment of type Ⅱ(MnNiCrAl) structure is 1.83μB. From this table, we also see that the atoms at B site always have large magnetic moment for type Ⅰ(MnNiCrAl) and type Ⅱ(MnNiCrAl) structures. For example, the Mn(B) atom in type Ⅰ(MnNiCrAl) structure has a magnetic moment of 2.94μB while the magnetic moment decreases to 1.08μB in type Ⅱ(MnNiCrAl) structure. The same occurs for Cr atom. For the three nonequivalent Cr-Mn-Ni-Al structures, the Ni moment is small and contributes little to the total spin moment. In CrNiMnAl and MnNiCrAl compounds, there is a ferrimagnetic coupling between the atom at A sites and the atom at B or C sites. For MnCrNiAl compound, a ferrimagnetic coupling occurs between the Ni(B) and the Mn(A) or Cr(C) moment.
Total
5 0 -5 4
Cr d(A)
2 0
DOS(states/eV)
-2 -4
Mn-d(B)
2 0 -2
Ni-d(C)
2 0 -2 -4
Al-p(D)
0.4
41
0.0 -0.4 -6
-4
-2
0
2
4
Energy(eV)
In conclusion, we investigated the electronic and magnetic properties of a new quaternary Heusler compound Cr-Mn-Ni-Al with three different AAC. The Cr-Mn-Ni-Al compound with type I AAC (CrNiMnAl) was predicted to possess a special electronic structure: there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap between the majority electrons in the valence band and the minority electrons in the conduction band, showing a SGS behavior. The type II AAC (MnNiCrAl) exhibits a very similar electronic structure with type I AAC, while, showing a slight cross with the Fermi level in the top of the valence bands (majority-spin channel) and the bottom of conductive bands (minority-spin channel) and it can be regarded as a special SGS. This special band structure will lead to the electronic transport with the spin-resolved carrier type.
MnCrNiAl
10
Total
5 0
DOS(states/eV)
-5 -102 1 0 -1 -2 2
Cr-d (C)
Mn-d (A)
0 -2
Ni-d (B)
3
4. Conclusions
0 -3 -6
Al-p(D)
0.4
Acknowledgments
0.0 -0.4 -6
-4
-2
0
2
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51271071), Key Basic Research Program of Applied Basic Research Program of Hebei Province (12965136D), Hebei Province Natural Science Foundation (No. E2013202181), Hebei Province Higher Education Science and Technology Research Foundation for Youth Scholars (No. Q2012008).
4
Energy(eV)
MnCrNiAl
10
Total
5 0
DOS(states/eV)
-5 -102 1 0 -1 -2 2
Cr-d (C)
References Mn-d (A)
0 -2
Ni-d (B)
3 0 -3 -6
Al-p(D)
0.4 0.0 -0.4 -6
-4
-2
0
2
4
Energy(eV) Fig. 6. The calculated total and atom-projected DOS for CrNiMnAl, MnNiCrAl and MnCrNiAl at their equilibrium lattice parameters. The vertical solid line in zero energy represents the Fermi level.
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