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Competition of L21 and XA structural ordering in Heusler alloys X2CuAl (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni)
Journal of Alloys and Compounds 665 (2016) 180e185
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Competition of L21 and XA structural ordering in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) Hongzhi Luo a, b, *, Yuepeng Xin a, Bohua Liu a, Fanbin Meng a, Heyan Liu a, Enke Liu b, Guangheng Wu b a b
School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 17 November 2015 Accepted 26 November 2015 Available online 30 November 2015
A competition between the conventional L21 ordering and inverse XA ordering has been observed in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). In X2CuAl, the site preference of Cu is strongly X element has a close-packed FCC or HCP When influenced by the crystal structure of pure X elements. andforms the L21 structure, but structure (Sc, Ti, Co and Ni), Cu prefers entering the 14; 14; 14 position when X has a BCC structure (V, Cr, Mn, Fe), Cu prefers entering the 12; 12; 12 position and forms the XA structure. So the crystal structure of pure X element should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. Mn2CuAl is found to be a spin gapless semiconductor (SGS) with fully-compensated total moment. Based on this, a possible rule to design SGS has been discussed. Finally, X2CuAl alloys all have a negative formation energy except for V2CuAl and Cr2CuAl. © 2016 Published by Elsevier B.V.
Keywords: Heusler alloys First-principles calculations Site preference Spin gapless semiconductor
1. Introduction Heusler alloys are promising candidates in many technical fields. They crystallize in a highly-ordered cubic structure and have a stoichiometric composition of X2YZ, where X and Y are transition metal elements, and Z is a main group element. In Heusler alloys there are four Wyckoff-positions namely A (0, 0, 0), B ð14; 14; 14Þ, C ð12; 12; 12Þ and D ð34; 34; 34Þ, respectively. The transition metal elements X, Y enter A, B, C sites and main group element Z enters D sites. Now interesting physical properties like half-metallicity, ferromagnetic shape memory effect and topological insulator have been reported [1e5]. Many experimental and theoretical efforts have been made to design and prepare novel Heusler alloys and also to improve their properties [6e8]. The highly-ordered structure is essential for the physical properties of Heusler alloys. There are two possible atomic orderings in Heusler alloys if we consider the highly-ordered structures only: One is L21 (Cu2MnAl-type, space group No.225), in which two X atoms occupy A and C positions and Y, Z atoms enter B and D
* Corresponding author. School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China. E-mail address: [email protected] (H. Luo). http://dx.doi.org/10.1016/j.jallcom.2015.11.207 0925-8388/© 2016 Published by Elsevier B.V.
positions, respectively. The other is XA (Hg2CuTi-type, space group No.216), in which the two X atoms occupy A and B positions and Y, Z atoms locate at C and D positions, respectively. This structure is also called “inverse” Heusler alloy. In Heusler alloys, people usually believe that the site preferences of transition metal atoms X and Y are determined by the number of their valence electrons: atoms with more electrons tend to occupy the A and C positions while the atoms with fewer electrons prefer the B position [9,10]. This rule has been widely used in the design of new Heusler alloys and explanation of their properties. But now some exceptions like Ni2CuZ (Z ¼ Sn and Sb) [11] and Ti2VAl [12] have been reported, in which the atoms with more valence electrons enter the B site and form L21 structure rather than entering A, C sites. According to the studies in Fe2CuGa [13] and Fe2CoGa [14], the crystal structure of the pure X metal can have influence on the structural ordering in Heusler alloys. But now there are few reports about the effect of different X elements on the ordering in Heusler alloys. In this paper, we investigated the site preference of Cu in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). Influence of different X atoms on the relative stability of L21 and XA structures has been discussed. In Fig. 1, we presented the crystal structure model of Heusler alloys as an example, it can be seen that when Cu entering different positions, different ordered structures will be
H. Luo et al. / Journal of Alloys and Compounds 665 (2016) 180e185
Fig. 1. Crystal structure of Heusler alloys, the four Wyckoff-positions are A (0, 0, 0), B ð14; 14; 14Þ, C ð12; 12; 12Þ and D (343434), respectively.
formed. In fact, Heusler alloy containing Cu itself is also interesting. In half-metallic Cu-based Heusler alloys like Mn2CuSb, the total spin moment M and number of valence electrons Z follow a SlaterPauling curve of M ¼ Z 28 rather than Z - 24 in many Heusler alloys [15]. Recently, a new ferromagnetic Heusler alloy V2CuAl has been reported, which is completely composed of non-magnetic elements V, Cu and Al, but the site occupation of Cu in which was only determined by the valence electrons rule and only XA structure was considered [16]. Our work can help to understand the ordering in Heusler alloys and to discover new functional materials in these alloys. 2. Computational methods The electronic structure was calculated by means of CASTEP code based on pseudopotential method with a plane-wave basis set [17,18]. The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudopotential [19]. The electronic exchangeecorrelation energy was treated under the local-density-approximation (LDA) [20,21]. For all cases, a planewave basis set cut-off of 500 eV was used. A mesh of 16 16 16 k-points was employed for Brillouin zone integrations for both L21 and XA structures. These parameters ensured good convergences for total energy. The convergence tolerance for the calculations was selected as a difference on total energy within 1 106 eV/atom. Structural optimization has been carried out to determine the stable structure of X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). In the calculations, we considered ferromagnetic (FM), non-magnetic (NM) and antiferromagnetic (AFM) states for X2CuAl alloys to determine the stable ground state. In the AFM state, antiparallel coupled spin moments between the two X atoms have been considered. 3. Results and discussions 3.1. Structural optimization In Fig. 2 we presented the calculated total energies of L21 and XA type X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) as functions of the lattice constants (E-a curve). For each structure, we gave the ground state E-a curve (relative to the lowest total energy) for visibility. The
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stable magnetic structure of these alloys can be found in Table 1. It is clear that the relative stability of the L21 and XA structures is different in these alloys and strongly related to the X atoms. At two ends of the 3d elements in the Periodic table, X ¼ Sc, Ti and Co, Ni, the L21 E-a curve locates below the XA curve and has lower total energy. But in the middle of 3d elements, X ¼ V, Cr, Mn and Fe, the XA curve has lower energy and is stabler. The detailed energy differences DE between XA and L21 structures for each alloy have been listed in Table 1 and presented as a function of X elements in Fig. 3. DE has the highest positive value (1.14 eV/cell) in Sc2CuAl, then decreases with increasing atomic number of the X atom, indicating that the site preference of Cu to the B site has been weakened. DE becomes negative in V2CuAl and decreases further till a minimum (0.61 eV/cell) in Mn2CuAl, then it begins to increase and becomes positive again in Co2CuAl. Finally, the DE in Ni2CuAl is þ0.32 eV/cell. Thus we can conclude that the L21 structure can also be stable in some X2CuAl Heusler alloys, especially in Sc2CuAl and Ti2CuAl, though Cu has more valence electrons than Sc or Ti. It should be noticed that, for the alloys with DE close to zero (V2CuAl and Co2CuAl), the stability of the XA and L21 structures are similar and may lead to an “inherent ” preference for disordered arrangements [13,22]. So in Ref. [16], it is not enough to consider only the ordered XA structure in the electronic structure calculation of V2CuAl. The equilibrium lattice constants of X2CuAl alloys were derived by minimizing the total energy and listed in Table 1. The variation of lattice constants with X atoms has been summarized in Fig. 3. It can be seen that for both L21 and XA structures, the equilibrium lattice constants of X2CuAl decrease with increasing atomic number of X atoms. Especially when X ¼ Sc, Ti and V, the lattice constants decrease rapidly. This coincides with the variation of atomic radii of 3d elements [23]. There is a little “jump” between the lattice constants of L21-type V2CuAl and Cr2CuAl, we think this is related to the change of magnetic ground state: V2CuAl is paramagnetic while Cr2CuAl is antiferromagnetic. 3.2. Electronic structure In order to discuss why the site preference rule depending on number of valence electrons does not work well in X2CuAl alloys, we compared the DOS structure of X2CuAl with L21 and XA structures in Fig. 4 first. The total DOSs of Sc2CuAl show rather localized character in both L21 and XA structures, due to the large lattice constant. The high-energy Sc d-states are basically above the Fermi level EF, while the d-states of Cu are far below EF and form a sharp DOS peak at 3.1 eV (L21) and 3.7 eV (XA). According to Ref. [13,14,24], the strong hybridization of the d states from the nearest neighbor (nn) atoms at B and C sites can be important for the stabilization of the XA structure. In the XA DOS of Sc2CuAl, the hybridization between Sc (B) and Cu (C) is weak and this can be a possible reason for the instability of this structure. In the L21 DOS, the Cu d-states are higher in energy and closer to the Sc d-states, this may help to enhance the hybridization between them. As X atom varies from Sc to V, the Cu states in the L21 DOS move to low energy and finally in the same energy region compared with the XA DOS. At the same time, the d-states of X atom also move from high energy above EF to low energy and finally locate below EF in Ni2CuAl. All this can have influence on the hybridization between the d-states of X atoms and Cu. In these alloys, the DOS of XA-type Mn2CuAl is particularly interesting: the DOS of which exhibits a bandgap in one spin direction and an energy valley approaching zero at the Fermi level in the other spin direction. This fulfills the requirements of spin gapless semiconductors (SGSs) and is worth further investigation. We will discuss the detailed electronic structure of Mn2CuAl in the next section.
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Fig. 2. The calculated total energies as functions of lattice constants for X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) with L21 and XA structures.
Table 1 The ground state structure, energy difference DE between XA and L21 structures, formation energy DEf, lattice constant a and magnetic structure for Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). The crystal structure of pure X element has also been presented. Here PM, FM and FIM are paramagnetic, ferromagnetic and ferrimagnetic, respectively. Alloys
Sc2CuAl
Ti2CuAl
V2CuAl
Cr2CuAl
Mn2CuAl
Fe2CuAl
Co2CuAl
Ni2CuAl
Stable structure Structure of X DE (eV/cell) DEf (eV/cell) a (Å) Magnetic structure
L21 HCP 1.14 1.47 6.52 PM
L21 HCP 0.80 0.93 6.13 PM
XA BCC 0.04 0.30 5.87 FM
XA BCC 0.54 0.32 5.74 FIM
XA BCC 0.61 0.44 5.65 FIM
XA BCC 0.24 0.91 5.58 FIM
L21 HCP 0.16 1.04 5.55 FM
L21 FCC 0.32 1.80 5.58 PM
Fig. 3. Energy differences DE between XA and L21 structures, lattice constants of X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) with L21 and XA structures, respectively. The crystal structure of pure X element has also been presented with DE.
It may be noticed that the DOS structure can not completely explain the site preference in X2CuAl. Usually, it is known that the DOS at EF (marked as N(EF)) is important for the phase stability of intermetallics. A lower N(EF) corresponds to a stabler structure [25,26]. But in the total DOS of X2CuAl, the inverse XA structure
does not specifically lower the DOS at EF compared with the conventional L21 one. This is quite obvious in the DOS of Cr2CuAl or Fe2CuAl. So further works are still necessary to find other possible factors which can influence the site preference in Heusler alloys. According to Refs. [13,14], the original crystal structure of the pure X metal will have influence on the structural ordering of the Heusler alloys X2YZ. When the X element prefers a close-packed FCC or HCP structure, it will stabilize the conventional L21 structure, while a X element with a BCC structure will stabilize the inverse XA structure. For example, in XA type Fe2CoGa, there are two different kinds of Fe, Fe (A) and Fe (B). Fe (B) occupies the ð14; 14; 14Þ position and is tetrahedrally coordinated by four nn Fe (A) and four nn Co, while Fe (A) occupies the (0, 0, 0) position and possesses Ga instead of Co as nearest neighbors. This introduces a strong FeeCo hybridization and stabilizes the XA structure [14]. Similar result has also been observed in Fe2CuGa by crystal orbital Hamilton population (COHP) calculation [13]. This inverse structure in Fe2CuGa has been confirmed by experimental observation though with some FeeCu disorder [27]. But now there is still lack of systematic works on the relation between different X elements and the site preference in Heusler alloys. Here, the investigation on X2CuAl can be a good example. In Fig. 3, we presented the crystal structure of pure X elements together with the energy difference DE. There is a clear correlation between the original structure of X element and the relative stability between L21 and XA ordering. When X element is Sc or Ti
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Fig. 4. Spin-projected total DOS for L21 and XA type X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni).
with a close-packed HCP structure, X2CuAl is in the L21-stable region. Beginning from V, the X element has a BCC structure, then the XA type X2CuAl has a lower ground state energy and is stabler. But when it comes to cobalt, which has a close-packed structure, the L21 structure becomes stable again. This picture agrees quite well with the conclusion in Refs. [13,14]. In Fig. 3 we can found that the atomic radii of the X atoms also have influence on the relative stability of the L21 and XA structures. Here Sc and Ti have quite large atomic radii compared with Cu [23], then large DE has been observed in Sc2CuAl and Ti2CuAl. So the crystal structure and atomic radius of pure X elements should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. 3.3. SGS character in Mn2CuAl In Section 3.2, XA-type Mn2CuAl has been predicted to be a SGS from its total DOS. SGS is an intermediate state between the well known half-metallic ferromagnets and gapless semiconductors. In the case of SGSs, one spin channel has an open band gap at EF like a half-metal but the other spin channel has a zero-width gap like a gapless semiconductor [28,29]. The SGS material can also be ferromagnetic when its two spin bands containing different number of electrons, though it is a semiconductor. This special band structure of SGS suggests some interesting transport properties and can have possible applications in spintronic devices, considering that the conducting electrons or holes are not only 100% spin polarized but also easily excited [29]. In Fig. 5 (a) the spin-projected band structure for Mn2CuAl at equilibrium lattice constant has been presented. In majority spin band, there is a wide energy gap around the Fermi level position, just like a half-metal. But in minority spin band, the valence and conduction bands overlap with each other and the Fermi level locates in a zero-width gap. This is an indirect gap with the maximum of the valence band at the W point and the minimum of the
conduction band at the X point. In Mn2CoAl, this gap is also an indirect gap [29], but in Ti2MnAl the gap is direct [30], so the detailed band structure of SGS Heusler alloys can be different and quite complicated. However, we can try to explain or predict the origin of SGS character in Heusler alloys from a simple picture based on the Slater-Pauling curve. It is known that there are several half-metallic energy gaps at EF in Heusler alloys, below this gap, there are 9, 12 or 14 valence electrons, respectively. This character is related to the origin of the half-metallic gap and can be traced back to the ded hybridization between X and Y atoms, the detail can be found in Ref. [31]. Then an easy way to realize energy gaps around EF in both spin-up and -down channels is that there are 9-9, 9e12, 12-12, 12e14 and 14-14 valence electrons filling in the two spin bands, respectively. So Heusler alloys with 18, 21, 24, 26 and 28 electrons are the most possible candidates for SGS character. Some information can also be found in Ref. [32]. It has been noticed that the appearance of a zero gap in one spin channel at EF is a rare phenomenon which is composition dependent and no exact rules have been observed [30]. But our findings can still help to make some on-demand designs of these alloys. Now, some SGS Heusler alloys Mn2CoAl [29], Ti2CoSi [30], Cr3Al [33] and Ti2MnAl [30] have 26, 21, 21 and 18 valence electrons, respectively. This agrees with our conclusion. In present work, Mn2CuAl has 28 valence electrons (7*2 from Mn, 11 from Cu and 3 from Al), they enter the spin-up and -down bands equally, so Mn2CuAl has a zero total moment and is a fully-compensated ferrimagnetic SGS. Till now, there are few reports on SGS character in other Heusler alloys containing 28 valence electrons. However, it should be mentioned that, the electronic structure of Mn2CuAl was reported by Li et al., in 2009. In their work, a quite large lattice constant of 5.855 Å and a total moment of 0.22mB were reported [34]. The large lattice constant can lead to a stronger exchange splitting effect and more localized partial moments. The Mn (A) and Mn (B) spin moments in Ref. [34] are about two times larger than ours, which is the cause of the non-zero total moment. But with the lattice constant decreasing to below 5.65 Å, the DOS structure and
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which locate mainly between 3.5 and þ1.5 eV and obvious exchange-splitting has been identified. Below 4 eV, Mn (A) and Mn (B) provide small d-peaks to hybridize with the huge DOS peak of Cu. It can also be found in Fig. 5(b) that, the contributions from Mn (A) and Mn (B) to the total DOS are opposite to each other. This implies an antiparallel alignment between the spin moments of Mn (A) and Mn (B). This is the main cause of the fully compensated total moment in Mn2CuAl. 3.4. Magnetism
Fig. 5. Band structure (a) and spin-projected total and partial DOS (b) for Mn2CuAl, the minority spin band is presented by dash line.
magnetism will become quite similar to ours. Considering their calculations were also base on the LDA functional, this difference is quite interesting. In calculations, we used a much preciser k-point set compared with Ref. [34]. This may be a possible reason. However, additional works are still necessary to find the exact reasons. In Ref. [35], Mn2CuAl ribbons have been prepared and its magnetic properties were investigated. In the M-T curve of Mn2CuAl a compensated point was observed, indicating antiparallel coupling of Mn spin moments [35]. This agrees with our theoretical calculations. However, in Ref. [35] Mn2CuAl ribbons were prepared by meltspinning, which introduced huge atomic disorder in the sample. Then the saturation moment at 5 K is 1.44mB, much larger than our result and also result in Ref. [34]. Then, to realize the SGS character in Mn2CuAl, the atomic disorder in it should be considered carefully when preparing the samples. The spin projected total and partial DOS of Mn2CuAl have been shown in Fig. 5 (b). We can see that in majority spin band, there is a wide energy gap at EF, and in the minority spin band, the conduction and valence bands slightly touch each other at the Fermi level position, resulting in a zero-width gap. This is a typical character of SGSs. It can also be found that, the DOS structure around EF is mainly determined by the d-states of Mn (A) and Mn (B). The states of Cu are basically below 3.5 eV and quite symmetrical in both spin directions, which results in a very small spin moment on Cu site. The cases of Mn (A) and Mn (B) d-states are quite different,
The calculated total and partial spin moments of X2CuAl have been listed in Table 2. The variation of the total moments with different X elements has been presented in Fig. 6. In Table 2, the four X2CuAl alloys with L21 structure are all paramagnets except for Co2CuAl, which has a total moment of 1.14mB and is a ferromagnet. While the alloys with XA structure are all ferro/ferrimagnets. This difference can be understood in that way: in Heusler alloys X2CuAl, Cu is almost non-magnetic in both L21 and XA structures, so the magnetic properties of X2CuAl are mainly determined by the two X atoms. In the inverse XA structure, the two X atoms occupy nonequivalent A and B sites and are nearest neighbors. Here X (A) is tetrahedrally coordinated by four nn X (B) and four Al atoms, while X (B) has four Cu and four X (A) as nearest neighbors. In the conventional L21 structure, two X atoms occupy the equivalent A, C sites and are only next-nearest neighbors with octahedral coordination. Then the hybridization between the X atoms and the crystal field effect are strong in the XA structure, which result in obvious exchange splitting as well as large spin moments. In Fig. 6, the calculated total moments for X2CuAl Heusler alloys are also displayed as a function of the valence-electron concentration (VEC). It is clear that the total moment shows a increasing tendency with the increase of VEC first and reaches a maximum of 3.34mB at VEC ¼ 7.5 (Fe2CuAl), which agrees well with its saturated moment of 3.30mB at 5 K [36]. Then the total moment decreases rapidly and reaches zero at VEC ¼ 8.5 (Ni2CuAl). In Fig. 6, the only exception is Mn2CuAl, its total moment is zero with VEC ¼ 7. This is due to the fact that, it is a fully compensated ferrimagnetic SGS and following Slater-Pauling curve of M ¼ jZ 28j, where M is the total moment and Z is the number of valence electrons in Heusler alloys. In Mn2CuAl, the Mn (A) and Mn (B) moments are 1.76mB and 1.78mB, respectively, which compensate each other and determine the zero moment. In Fig. 6, the M ¼ jZ 28j curve was also presented by blue line. We can see that the total moment of Mn2CuAl is just at this curve. 3.5. Formation energy Finally, we discuss the phase stability of X2CuAl alloys based on the formation energies DEf (formation enthalpies at 0 K) calculation within density functional theory. This can help to predict whether these alloys can be prepared experimentally. Similar analyses on the phase stabilities of a large number of Heusler and inverse Heusler compounds have been reported [13,37]. Here the formation energy DEf is calculated by comparing the total energies of the X2CuAl Heusler phases with the sum of the total energies of the constituting elements. That is DEf ¼ EX2CuAl e (2EX þ ECu þ EAl), where EX2CuAl is the ground state total energy of Heusler alloy X2CuAl; EX, ECu and EAl are the total energies of X, Cu, and Al pure elements in bulk form. A negative formation energy suggests that a X2CuAl single Heusler phase is more favored energetically, while a positive DEf has the opposite effect. The calculated formation energies are shown in Table 1. We can see that X2CuAl all have a negative DEf except for V2CuAl and Cr2CuAl. This means most X2CuAl Heusler alloys are
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Table 2 The total spin moment Mtotal and partial moments on A, B, C, D sites for Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). Alloys
Sc2CuAl
Ti2CuAl
V2CuAl
Cr2CuAl
Mn2CuAl
Fe2CuAl
Co2CuAl
Ni2CuAl
Mtotal (mB) MA (mB) MB (mB) MC (mB) MD (mB)
0.00 Sc 0.00 Cu 0.00 Sc 0.00 Al 0.00
0.00 Ti 0.00 Cu 0.00 Ti 0.00 Al 0.00
0.87 V 0.44 V 0.48 Cu 0.02 Al 0.02
1.14 Cr 1.66 Cr 2.72 Cu 0.04 Al 0.02
0.00 Mn 1.76 Mn 1.78 Cu 0.00 Al 0.02
3.34 Fe 1.48 Fe 2.10 Cu 0.16 Al 0.08
1.14 Co 0.60 Cu 0.02 Co 0.60 Al 0.08
0.00 Ni 0.00 Cu 0.00 Ni 0.00 Al 0.00
Foundation of Hebei Provincial Education Department in Grant No. BJ2014012 and also by Program for Changjiang Scholars and Innovative Research Team in University in Grant No. IRT13060.
References
Fig. 6. Variation of the total moments as functions of X elements and valence-electron concentration (VEC). VEC is marked below the elementary symbol and the blue line is the Slater-Pauling curve of M ¼ jZ - 28j (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
thermodynamically stable and may be prepared by conventional equilibrium methods like arc-melting. In fact, Fe2CuAl has been synthesized successfully [36]. V2CuAl and Cr2CuAl have a positive DEf, then some non-equilibrium methods like rapid quenching may be employed to prepare these metastable alloys. 4. Conclusion The site preference of Cu in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) has been investigated by first-principles calculations. A competition between the conventional L21 ordering and inverse XA ordering has been observed in these alloys. In X2CuAl, the site preference of Cu is strongly influenced by the crystal structure of pure X elements. When X element has a FCC or HCP structure (Sc, Ti, Co and Ni here), Cu prefers entering the ð14; 14; 14Þ position and forms the L21 structure, but when X element has a BCC structure (V, Cr, Mn, Fe here), Cu prefers entering the ð12; 12; 12Þ position and forms the XA structure. So the crystal structure as well as atomic radii of pure X element should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. In X2CuAl alloys, Mn2CuAl is found to be a spin gapless semiconductor in which 28 valence electrons occupy the spin-up and -down channel equally and result in a zero total moment, The Mn (A) and Mn (B) partial moments compensate each other. Finally, X2CuAl Heusler alloys all have a negative formation energy except for V2CuAl and Cr2CuAl. Acknowledgments This work is supported by the National Natural Science Foundation of China in Grant No. 11474343 and 51371075, the
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Competition of L21 and XA structural ordering in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) Hongzhi Luo a, b, *, Yuepeng Xin a, Bohua Liu a, Fanbin Meng a, Heyan Liu a, Enke Liu b, Guangheng Wu b a b
School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 17 November 2015 Accepted 26 November 2015 Available online 30 November 2015
A competition between the conventional L21 ordering and inverse XA ordering has been observed in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). In X2CuAl, the site preference of Cu is strongly X element has a close-packed FCC or HCP When influenced by the crystal structure of pure X elements. andforms the L21 structure, but structure (Sc, Ti, Co and Ni), Cu prefers entering the 14; 14; 14 position when X has a BCC structure (V, Cr, Mn, Fe), Cu prefers entering the 12; 12; 12 position and forms the XA structure. So the crystal structure of pure X element should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. Mn2CuAl is found to be a spin gapless semiconductor (SGS) with fully-compensated total moment. Based on this, a possible rule to design SGS has been discussed. Finally, X2CuAl alloys all have a negative formation energy except for V2CuAl and Cr2CuAl. © 2016 Published by Elsevier B.V.
Keywords: Heusler alloys First-principles calculations Site preference Spin gapless semiconductor
1. Introduction Heusler alloys are promising candidates in many technical fields. They crystallize in a highly-ordered cubic structure and have a stoichiometric composition of X2YZ, where X and Y are transition metal elements, and Z is a main group element. In Heusler alloys there are four Wyckoff-positions namely A (0, 0, 0), B ð14; 14; 14Þ, C ð12; 12; 12Þ and D ð34; 34; 34Þ, respectively. The transition metal elements X, Y enter A, B, C sites and main group element Z enters D sites. Now interesting physical properties like half-metallicity, ferromagnetic shape memory effect and topological insulator have been reported [1e5]. Many experimental and theoretical efforts have been made to design and prepare novel Heusler alloys and also to improve their properties [6e8]. The highly-ordered structure is essential for the physical properties of Heusler alloys. There are two possible atomic orderings in Heusler alloys if we consider the highly-ordered structures only: One is L21 (Cu2MnAl-type, space group No.225), in which two X atoms occupy A and C positions and Y, Z atoms enter B and D
* Corresponding author. School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China. E-mail address: [email protected] (H. Luo). http://dx.doi.org/10.1016/j.jallcom.2015.11.207 0925-8388/© 2016 Published by Elsevier B.V.
positions, respectively. The other is XA (Hg2CuTi-type, space group No.216), in which the two X atoms occupy A and B positions and Y, Z atoms locate at C and D positions, respectively. This structure is also called “inverse” Heusler alloy. In Heusler alloys, people usually believe that the site preferences of transition metal atoms X and Y are determined by the number of their valence electrons: atoms with more electrons tend to occupy the A and C positions while the atoms with fewer electrons prefer the B position [9,10]. This rule has been widely used in the design of new Heusler alloys and explanation of their properties. But now some exceptions like Ni2CuZ (Z ¼ Sn and Sb) [11] and Ti2VAl [12] have been reported, in which the atoms with more valence electrons enter the B site and form L21 structure rather than entering A, C sites. According to the studies in Fe2CuGa [13] and Fe2CoGa [14], the crystal structure of the pure X metal can have influence on the structural ordering in Heusler alloys. But now there are few reports about the effect of different X elements on the ordering in Heusler alloys. In this paper, we investigated the site preference of Cu in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). Influence of different X atoms on the relative stability of L21 and XA structures has been discussed. In Fig. 1, we presented the crystal structure model of Heusler alloys as an example, it can be seen that when Cu entering different positions, different ordered structures will be
H. Luo et al. / Journal of Alloys and Compounds 665 (2016) 180e185
Fig. 1. Crystal structure of Heusler alloys, the four Wyckoff-positions are A (0, 0, 0), B ð14; 14; 14Þ, C ð12; 12; 12Þ and D (343434), respectively.
formed. In fact, Heusler alloy containing Cu itself is also interesting. In half-metallic Cu-based Heusler alloys like Mn2CuSb, the total spin moment M and number of valence electrons Z follow a SlaterPauling curve of M ¼ Z 28 rather than Z - 24 in many Heusler alloys [15]. Recently, a new ferromagnetic Heusler alloy V2CuAl has been reported, which is completely composed of non-magnetic elements V, Cu and Al, but the site occupation of Cu in which was only determined by the valence electrons rule and only XA structure was considered [16]. Our work can help to understand the ordering in Heusler alloys and to discover new functional materials in these alloys. 2. Computational methods The electronic structure was calculated by means of CASTEP code based on pseudopotential method with a plane-wave basis set [17,18]. The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudopotential [19]. The electronic exchangeecorrelation energy was treated under the local-density-approximation (LDA) [20,21]. For all cases, a planewave basis set cut-off of 500 eV was used. A mesh of 16 16 16 k-points was employed for Brillouin zone integrations for both L21 and XA structures. These parameters ensured good convergences for total energy. The convergence tolerance for the calculations was selected as a difference on total energy within 1 106 eV/atom. Structural optimization has been carried out to determine the stable structure of X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). In the calculations, we considered ferromagnetic (FM), non-magnetic (NM) and antiferromagnetic (AFM) states for X2CuAl alloys to determine the stable ground state. In the AFM state, antiparallel coupled spin moments between the two X atoms have been considered. 3. Results and discussions 3.1. Structural optimization In Fig. 2 we presented the calculated total energies of L21 and XA type X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) as functions of the lattice constants (E-a curve). For each structure, we gave the ground state E-a curve (relative to the lowest total energy) for visibility. The
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stable magnetic structure of these alloys can be found in Table 1. It is clear that the relative stability of the L21 and XA structures is different in these alloys and strongly related to the X atoms. At two ends of the 3d elements in the Periodic table, X ¼ Sc, Ti and Co, Ni, the L21 E-a curve locates below the XA curve and has lower total energy. But in the middle of 3d elements, X ¼ V, Cr, Mn and Fe, the XA curve has lower energy and is stabler. The detailed energy differences DE between XA and L21 structures for each alloy have been listed in Table 1 and presented as a function of X elements in Fig. 3. DE has the highest positive value (1.14 eV/cell) in Sc2CuAl, then decreases with increasing atomic number of the X atom, indicating that the site preference of Cu to the B site has been weakened. DE becomes negative in V2CuAl and decreases further till a minimum (0.61 eV/cell) in Mn2CuAl, then it begins to increase and becomes positive again in Co2CuAl. Finally, the DE in Ni2CuAl is þ0.32 eV/cell. Thus we can conclude that the L21 structure can also be stable in some X2CuAl Heusler alloys, especially in Sc2CuAl and Ti2CuAl, though Cu has more valence electrons than Sc or Ti. It should be noticed that, for the alloys with DE close to zero (V2CuAl and Co2CuAl), the stability of the XA and L21 structures are similar and may lead to an “inherent ” preference for disordered arrangements [13,22]. So in Ref. [16], it is not enough to consider only the ordered XA structure in the electronic structure calculation of V2CuAl. The equilibrium lattice constants of X2CuAl alloys were derived by minimizing the total energy and listed in Table 1. The variation of lattice constants with X atoms has been summarized in Fig. 3. It can be seen that for both L21 and XA structures, the equilibrium lattice constants of X2CuAl decrease with increasing atomic number of X atoms. Especially when X ¼ Sc, Ti and V, the lattice constants decrease rapidly. This coincides with the variation of atomic radii of 3d elements [23]. There is a little “jump” between the lattice constants of L21-type V2CuAl and Cr2CuAl, we think this is related to the change of magnetic ground state: V2CuAl is paramagnetic while Cr2CuAl is antiferromagnetic. 3.2. Electronic structure In order to discuss why the site preference rule depending on number of valence electrons does not work well in X2CuAl alloys, we compared the DOS structure of X2CuAl with L21 and XA structures in Fig. 4 first. The total DOSs of Sc2CuAl show rather localized character in both L21 and XA structures, due to the large lattice constant. The high-energy Sc d-states are basically above the Fermi level EF, while the d-states of Cu are far below EF and form a sharp DOS peak at 3.1 eV (L21) and 3.7 eV (XA). According to Ref. [13,14,24], the strong hybridization of the d states from the nearest neighbor (nn) atoms at B and C sites can be important for the stabilization of the XA structure. In the XA DOS of Sc2CuAl, the hybridization between Sc (B) and Cu (C) is weak and this can be a possible reason for the instability of this structure. In the L21 DOS, the Cu d-states are higher in energy and closer to the Sc d-states, this may help to enhance the hybridization between them. As X atom varies from Sc to V, the Cu states in the L21 DOS move to low energy and finally in the same energy region compared with the XA DOS. At the same time, the d-states of X atom also move from high energy above EF to low energy and finally locate below EF in Ni2CuAl. All this can have influence on the hybridization between the d-states of X atoms and Cu. In these alloys, the DOS of XA-type Mn2CuAl is particularly interesting: the DOS of which exhibits a bandgap in one spin direction and an energy valley approaching zero at the Fermi level in the other spin direction. This fulfills the requirements of spin gapless semiconductors (SGSs) and is worth further investigation. We will discuss the detailed electronic structure of Mn2CuAl in the next section.
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Fig. 2. The calculated total energies as functions of lattice constants for X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) with L21 and XA structures.
Table 1 The ground state structure, energy difference DE between XA and L21 structures, formation energy DEf, lattice constant a and magnetic structure for Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). The crystal structure of pure X element has also been presented. Here PM, FM and FIM are paramagnetic, ferromagnetic and ferrimagnetic, respectively. Alloys
Sc2CuAl
Ti2CuAl
V2CuAl
Cr2CuAl
Mn2CuAl
Fe2CuAl
Co2CuAl
Ni2CuAl
Stable structure Structure of X DE (eV/cell) DEf (eV/cell) a (Å) Magnetic structure
L21 HCP 1.14 1.47 6.52 PM
L21 HCP 0.80 0.93 6.13 PM
XA BCC 0.04 0.30 5.87 FM
XA BCC 0.54 0.32 5.74 FIM
XA BCC 0.61 0.44 5.65 FIM
XA BCC 0.24 0.91 5.58 FIM
L21 HCP 0.16 1.04 5.55 FM
L21 FCC 0.32 1.80 5.58 PM
Fig. 3. Energy differences DE between XA and L21 structures, lattice constants of X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) with L21 and XA structures, respectively. The crystal structure of pure X element has also been presented with DE.
It may be noticed that the DOS structure can not completely explain the site preference in X2CuAl. Usually, it is known that the DOS at EF (marked as N(EF)) is important for the phase stability of intermetallics. A lower N(EF) corresponds to a stabler structure [25,26]. But in the total DOS of X2CuAl, the inverse XA structure
does not specifically lower the DOS at EF compared with the conventional L21 one. This is quite obvious in the DOS of Cr2CuAl or Fe2CuAl. So further works are still necessary to find other possible factors which can influence the site preference in Heusler alloys. According to Refs. [13,14], the original crystal structure of the pure X metal will have influence on the structural ordering of the Heusler alloys X2YZ. When the X element prefers a close-packed FCC or HCP structure, it will stabilize the conventional L21 structure, while a X element with a BCC structure will stabilize the inverse XA structure. For example, in XA type Fe2CoGa, there are two different kinds of Fe, Fe (A) and Fe (B). Fe (B) occupies the ð14; 14; 14Þ position and is tetrahedrally coordinated by four nn Fe (A) and four nn Co, while Fe (A) occupies the (0, 0, 0) position and possesses Ga instead of Co as nearest neighbors. This introduces a strong FeeCo hybridization and stabilizes the XA structure [14]. Similar result has also been observed in Fe2CuGa by crystal orbital Hamilton population (COHP) calculation [13]. This inverse structure in Fe2CuGa has been confirmed by experimental observation though with some FeeCu disorder [27]. But now there is still lack of systematic works on the relation between different X elements and the site preference in Heusler alloys. Here, the investigation on X2CuAl can be a good example. In Fig. 3, we presented the crystal structure of pure X elements together with the energy difference DE. There is a clear correlation between the original structure of X element and the relative stability between L21 and XA ordering. When X element is Sc or Ti
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Fig. 4. Spin-projected total DOS for L21 and XA type X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni).
with a close-packed HCP structure, X2CuAl is in the L21-stable region. Beginning from V, the X element has a BCC structure, then the XA type X2CuAl has a lower ground state energy and is stabler. But when it comes to cobalt, which has a close-packed structure, the L21 structure becomes stable again. This picture agrees quite well with the conclusion in Refs. [13,14]. In Fig. 3 we can found that the atomic radii of the X atoms also have influence on the relative stability of the L21 and XA structures. Here Sc and Ti have quite large atomic radii compared with Cu [23], then large DE has been observed in Sc2CuAl and Ti2CuAl. So the crystal structure and atomic radius of pure X elements should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. 3.3. SGS character in Mn2CuAl In Section 3.2, XA-type Mn2CuAl has been predicted to be a SGS from its total DOS. SGS is an intermediate state between the well known half-metallic ferromagnets and gapless semiconductors. In the case of SGSs, one spin channel has an open band gap at EF like a half-metal but the other spin channel has a zero-width gap like a gapless semiconductor [28,29]. The SGS material can also be ferromagnetic when its two spin bands containing different number of electrons, though it is a semiconductor. This special band structure of SGS suggests some interesting transport properties and can have possible applications in spintronic devices, considering that the conducting electrons or holes are not only 100% spin polarized but also easily excited [29]. In Fig. 5 (a) the spin-projected band structure for Mn2CuAl at equilibrium lattice constant has been presented. In majority spin band, there is a wide energy gap around the Fermi level position, just like a half-metal. But in minority spin band, the valence and conduction bands overlap with each other and the Fermi level locates in a zero-width gap. This is an indirect gap with the maximum of the valence band at the W point and the minimum of the
conduction band at the X point. In Mn2CoAl, this gap is also an indirect gap [29], but in Ti2MnAl the gap is direct [30], so the detailed band structure of SGS Heusler alloys can be different and quite complicated. However, we can try to explain or predict the origin of SGS character in Heusler alloys from a simple picture based on the Slater-Pauling curve. It is known that there are several half-metallic energy gaps at EF in Heusler alloys, below this gap, there are 9, 12 or 14 valence electrons, respectively. This character is related to the origin of the half-metallic gap and can be traced back to the ded hybridization between X and Y atoms, the detail can be found in Ref. [31]. Then an easy way to realize energy gaps around EF in both spin-up and -down channels is that there are 9-9, 9e12, 12-12, 12e14 and 14-14 valence electrons filling in the two spin bands, respectively. So Heusler alloys with 18, 21, 24, 26 and 28 electrons are the most possible candidates for SGS character. Some information can also be found in Ref. [32]. It has been noticed that the appearance of a zero gap in one spin channel at EF is a rare phenomenon which is composition dependent and no exact rules have been observed [30]. But our findings can still help to make some on-demand designs of these alloys. Now, some SGS Heusler alloys Mn2CoAl [29], Ti2CoSi [30], Cr3Al [33] and Ti2MnAl [30] have 26, 21, 21 and 18 valence electrons, respectively. This agrees with our conclusion. In present work, Mn2CuAl has 28 valence electrons (7*2 from Mn, 11 from Cu and 3 from Al), they enter the spin-up and -down bands equally, so Mn2CuAl has a zero total moment and is a fully-compensated ferrimagnetic SGS. Till now, there are few reports on SGS character in other Heusler alloys containing 28 valence electrons. However, it should be mentioned that, the electronic structure of Mn2CuAl was reported by Li et al., in 2009. In their work, a quite large lattice constant of 5.855 Å and a total moment of 0.22mB were reported [34]. The large lattice constant can lead to a stronger exchange splitting effect and more localized partial moments. The Mn (A) and Mn (B) spin moments in Ref. [34] are about two times larger than ours, which is the cause of the non-zero total moment. But with the lattice constant decreasing to below 5.65 Å, the DOS structure and
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which locate mainly between 3.5 and þ1.5 eV and obvious exchange-splitting has been identified. Below 4 eV, Mn (A) and Mn (B) provide small d-peaks to hybridize with the huge DOS peak of Cu. It can also be found in Fig. 5(b) that, the contributions from Mn (A) and Mn (B) to the total DOS are opposite to each other. This implies an antiparallel alignment between the spin moments of Mn (A) and Mn (B). This is the main cause of the fully compensated total moment in Mn2CuAl. 3.4. Magnetism
Fig. 5. Band structure (a) and spin-projected total and partial DOS (b) for Mn2CuAl, the minority spin band is presented by dash line.
magnetism will become quite similar to ours. Considering their calculations were also base on the LDA functional, this difference is quite interesting. In calculations, we used a much preciser k-point set compared with Ref. [34]. This may be a possible reason. However, additional works are still necessary to find the exact reasons. In Ref. [35], Mn2CuAl ribbons have been prepared and its magnetic properties were investigated. In the M-T curve of Mn2CuAl a compensated point was observed, indicating antiparallel coupling of Mn spin moments [35]. This agrees with our theoretical calculations. However, in Ref. [35] Mn2CuAl ribbons were prepared by meltspinning, which introduced huge atomic disorder in the sample. Then the saturation moment at 5 K is 1.44mB, much larger than our result and also result in Ref. [34]. Then, to realize the SGS character in Mn2CuAl, the atomic disorder in it should be considered carefully when preparing the samples. The spin projected total and partial DOS of Mn2CuAl have been shown in Fig. 5 (b). We can see that in majority spin band, there is a wide energy gap at EF, and in the minority spin band, the conduction and valence bands slightly touch each other at the Fermi level position, resulting in a zero-width gap. This is a typical character of SGSs. It can also be found that, the DOS structure around EF is mainly determined by the d-states of Mn (A) and Mn (B). The states of Cu are basically below 3.5 eV and quite symmetrical in both spin directions, which results in a very small spin moment on Cu site. The cases of Mn (A) and Mn (B) d-states are quite different,
The calculated total and partial spin moments of X2CuAl have been listed in Table 2. The variation of the total moments with different X elements has been presented in Fig. 6. In Table 2, the four X2CuAl alloys with L21 structure are all paramagnets except for Co2CuAl, which has a total moment of 1.14mB and is a ferromagnet. While the alloys with XA structure are all ferro/ferrimagnets. This difference can be understood in that way: in Heusler alloys X2CuAl, Cu is almost non-magnetic in both L21 and XA structures, so the magnetic properties of X2CuAl are mainly determined by the two X atoms. In the inverse XA structure, the two X atoms occupy nonequivalent A and B sites and are nearest neighbors. Here X (A) is tetrahedrally coordinated by four nn X (B) and four Al atoms, while X (B) has four Cu and four X (A) as nearest neighbors. In the conventional L21 structure, two X atoms occupy the equivalent A, C sites and are only next-nearest neighbors with octahedral coordination. Then the hybridization between the X atoms and the crystal field effect are strong in the XA structure, which result in obvious exchange splitting as well as large spin moments. In Fig. 6, the calculated total moments for X2CuAl Heusler alloys are also displayed as a function of the valence-electron concentration (VEC). It is clear that the total moment shows a increasing tendency with the increase of VEC first and reaches a maximum of 3.34mB at VEC ¼ 7.5 (Fe2CuAl), which agrees well with its saturated moment of 3.30mB at 5 K [36]. Then the total moment decreases rapidly and reaches zero at VEC ¼ 8.5 (Ni2CuAl). In Fig. 6, the only exception is Mn2CuAl, its total moment is zero with VEC ¼ 7. This is due to the fact that, it is a fully compensated ferrimagnetic SGS and following Slater-Pauling curve of M ¼ jZ 28j, where M is the total moment and Z is the number of valence electrons in Heusler alloys. In Mn2CuAl, the Mn (A) and Mn (B) moments are 1.76mB and 1.78mB, respectively, which compensate each other and determine the zero moment. In Fig. 6, the M ¼ jZ 28j curve was also presented by blue line. We can see that the total moment of Mn2CuAl is just at this curve. 3.5. Formation energy Finally, we discuss the phase stability of X2CuAl alloys based on the formation energies DEf (formation enthalpies at 0 K) calculation within density functional theory. This can help to predict whether these alloys can be prepared experimentally. Similar analyses on the phase stabilities of a large number of Heusler and inverse Heusler compounds have been reported [13,37]. Here the formation energy DEf is calculated by comparing the total energies of the X2CuAl Heusler phases with the sum of the total energies of the constituting elements. That is DEf ¼ EX2CuAl e (2EX þ ECu þ EAl), where EX2CuAl is the ground state total energy of Heusler alloy X2CuAl; EX, ECu and EAl are the total energies of X, Cu, and Al pure elements in bulk form. A negative formation energy suggests that a X2CuAl single Heusler phase is more favored energetically, while a positive DEf has the opposite effect. The calculated formation energies are shown in Table 1. We can see that X2CuAl all have a negative DEf except for V2CuAl and Cr2CuAl. This means most X2CuAl Heusler alloys are
H. Luo et al. / Journal of Alloys and Compounds 665 (2016) 180e185
185
Table 2 The total spin moment Mtotal and partial moments on A, B, C, D sites for Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni). Alloys
Sc2CuAl
Ti2CuAl
V2CuAl
Cr2CuAl
Mn2CuAl
Fe2CuAl
Co2CuAl
Ni2CuAl
Mtotal (mB) MA (mB) MB (mB) MC (mB) MD (mB)
0.00 Sc 0.00 Cu 0.00 Sc 0.00 Al 0.00
0.00 Ti 0.00 Cu 0.00 Ti 0.00 Al 0.00
0.87 V 0.44 V 0.48 Cu 0.02 Al 0.02
1.14 Cr 1.66 Cr 2.72 Cu 0.04 Al 0.02
0.00 Mn 1.76 Mn 1.78 Cu 0.00 Al 0.02
3.34 Fe 1.48 Fe 2.10 Cu 0.16 Al 0.08
1.14 Co 0.60 Cu 0.02 Co 0.60 Al 0.08
0.00 Ni 0.00 Cu 0.00 Ni 0.00 Al 0.00
Foundation of Hebei Provincial Education Department in Grant No. BJ2014012 and also by Program for Changjiang Scholars and Innovative Research Team in University in Grant No. IRT13060.
References
Fig. 6. Variation of the total moments as functions of X elements and valence-electron concentration (VEC). VEC is marked below the elementary symbol and the blue line is the Slater-Pauling curve of M ¼ jZ - 28j (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
thermodynamically stable and may be prepared by conventional equilibrium methods like arc-melting. In fact, Fe2CuAl has been synthesized successfully [36]. V2CuAl and Cr2CuAl have a positive DEf, then some non-equilibrium methods like rapid quenching may be employed to prepare these metastable alloys. 4. Conclusion The site preference of Cu in Heusler alloys X2CuAl (X ¼ Sc, Ti, V, Cr, Mn, Fe, Co, Ni) has been investigated by first-principles calculations. A competition between the conventional L21 ordering and inverse XA ordering has been observed in these alloys. In X2CuAl, the site preference of Cu is strongly influenced by the crystal structure of pure X elements. When X element has a FCC or HCP structure (Sc, Ti, Co and Ni here), Cu prefers entering the ð14; 14; 14Þ position and forms the L21 structure, but when X element has a BCC structure (V, Cr, Mn, Fe here), Cu prefers entering the ð12; 12; 12Þ position and forms the XA structure. So the crystal structure as well as atomic radii of pure X element should also be considered together with number of valence electrons when discussing the site preference in Heusler alloys. In X2CuAl alloys, Mn2CuAl is found to be a spin gapless semiconductor in which 28 valence electrons occupy the spin-up and -down channel equally and result in a zero total moment, The Mn (A) and Mn (B) partial moments compensate each other. Finally, X2CuAl Heusler alloys all have a negative formation energy except for V2CuAl and Cr2CuAl. Acknowledgments This work is supported by the National Natural Science Foundation of China in Grant No. 11474343 and 51371075, the
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