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Lattice constant changes leading to significant changes of the spin-gapless features and physical nature in a inverse Heusler compound Zr2MnGa
Journal of Magnetism and Magnetic Materials 444 (2017) 313–318
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Research articles
Lattice constant changes leading to significant changes of the spingapless features and physical nature in a inverse Heusler compound Zr2MnGa Xiaotian Wang a,b, Zhenxiang Cheng b,⇑, Rabah Khenata c, Yang Wu d, Liying Wang e, Guodong Liu e,⇑ a
School of Physical Science and Technology, Southwest University, Chongqing 400715, PR China Institute for Superconducting & Electronic Materials (ISEM), University of Wollongong, Wollongong 2500, Australia Laboratoire de Physique Quantique, de la Matière et de la Modélisation Mathématique (LPQ3M), Université de Mascara, Mascara 29000, Algeria d School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China e School of Material Sciences and Engineering, Hebei University of Technology, Tianjin 300130, PR China b c
a r t i c l e
i n f o
Article history: Received 12 July 2017 Received in revised form 13 August 2017 Accepted 14 August 2017 Available online 16 August 2017 Keywords: Magnetic materials Ab initio calculation Band structure Magnetic properties
a b s t r a c t The spin-gapless semiconductors with parabolic energy dispersions [1–3] have been recently proposed as a new class of materials for potential applications in spintronic devices. In this work, according to the Slater-Pauling rule, we report the fully-compensated ferrimagnetic (FCF) behavior and spin-gapless semiconducting (SGS) properties for a new inverse Heusler compound Zr2MnGa by means of the plane-wave pseudo-potential method based on density functional theory. With the help of GGA-PBE, the electronic structures and the magnetism of Zr2MnGa compound at its equilibrium and strained lattice constants are systematically studied. The calculated results show that the Zr2MnGa is a new SGS at its equilibrium lattice constant: there is an energy 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. Remarkably, not only a diverse physical nature transition, but also different types of spin-gapless features can be observed with the change of the lattice constants. Our calculated results of Zr2MnGa compound indicate that this material has great application potential in spintronic devices. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Very recently, spin-gapless semiconductors (SGSs) [1–10], such as Co-doped Pb-based oxide materials [1], have great potential applications for high performance electronic and spintronic devices. As shown in Fig. 1, four possible band-structure configurations with spin-gapless features have been given [11]. In the first case (see Fig. 1(a)), one spin direction is gapless, while the other spin direction is semiconducting. In the second case (see Fig. 1 (b)), one spin direction is gapless, and the other spin direction is semiconducting with the top of the valence band touches the Fermi level. In the third case (see Fig. 1(c)), one spin direction is gapless, and the other spin direction is semiconducting with bottom of the conduction band touches the Fermi level. In the fourth case (see Fig. 1(d)), there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap
⇑ Corresponding authors. E-mail addresses: [email protected] (Z. Cheng), [email protected] (G. Liu). http://dx.doi.org/10.1016/j.jmmm.2017.08.040 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
between the majority electrons in the valence band and the minority electrons in the conduction band. The SGS materials, such as Co-doped PbPdO2, was firstly presented theoretically by Wang in 2008 [1] and confirmed experimentally by Kim et al. later on [12]. After the Co-doped PbPdO2, several different classes of materials have been theoretically and experimentally reported to be new SGSs [2–11]. Among them, the compounds based on Heusler structure cannot be ignored due to their higher Curie temperatures (TC) and tunable electronic structures. Up to now, many Heusler based compounds (eg. Mn2CoAl, CoFeMnSi, and CoFeCrGa) [10,13–23] have been prepared and their SGS behaviors have been confirmed based on their novel magnetic and transport properties. Furthermore, several Heulser compounds have even been theoretically proposed and experimentally proved to be fully-compensated ferrimagnetic (FCF) SGSs [24–28]. Compared to the normal SGSs, FCF-SGSs will simultaneously own the properties of the spin-gapless semiconductivity and full-compensated ferrimagnetism. That is to say, besides the behavior of SGSs, FCF-SGSs also exhibit no net
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Fig. 1. Density of states (DOS) scheme of the four possible band structure configurations with spin-gapless behaviors: (a)–(d). Filled areas represent occupied states, and the arrows indicate majority (") and minority (;) spin.
magnetization. Therefore, if these compounds were used in spintronic devices, there will be no stray magnetic fields generated. All the above-mentioned information motivated us to search for new FCF-SGSs based on full-Heusler structure. To identify SGSs among full-Heulser compounds, as we have summarized in our review article [3], the magnetic moments of these compounds should obey the generalized Slater-Pauling rule of Mt = Zt 24 (eg. Mn2CoAl) [13], Mt = Zt 28 (eg. Mn2CuAl) [25] or Mt = Zt 18 (eg. Ti2MnAl) [29] (where Mt is the total magnetic moment per unit cell and Zt is the total number of valence electrons). Then, to achieve the FCF property among the SGSs, the number of occupied electrons in both spin channels should be equal. That is, the total number of valence electrons of full-Heusler based FCF-SGSs should be 18 (9–9), 24 (12–12) or 28 (14–14). Recently, the electronic, magnetic, and half-metallic properties of many Zr-based fullHeusler compounds, such as Zr2CoGa [30], Zr2VGa [31], Zr2RhGa [32], and Zr2CrGa [33] have been investigated by us and other researchers. These half-metals contain 4 d transition metal elements Zr or Rh, which enlarge the scope of exploring new functional materials in compounds. Additionally, previous works show these half-metals Zr2YGa obey a Slater-Pauling rule: Mt = Zt 18 [31]. Therefore, in order to design a new FCF-SGS, the value of Mt must be 0, and the value of Zt must be 18. That is, Mn was chosen for doping into the Y site to form a new Heusler compound: Zr2MnGa with Zt = 18. In this paper, we will investigate the electronic structure, magnetic, and the FCF-SGS properties of newly designed Heusler compound Zr2MnGa by means of the firstprinciples calculation. Remarkably, a rather rare physical nature transition and different types of spin-gapless features can be observed if the lattice constant changes. 2. Computational details The electronic structures and the magnetic properties were performed by using the pseudo-potential method with a plane-wave basis set, implemented in the code of the Cambridge Serial Total Energy Package (CASTEP). The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudo-potential approach [34]. The generalized gradient approximation (GGA) [35,36] was adopted for the exchange-correction functional. For all cases, a plane-wave basis set cut-off of 450 eV was used. A k-points mesh of 15 15 15 was used in the Brillouin zone integrations for the Heusler structure. These parameters ensured good convergence for the total energy. The convergence tolerance for the calculations was selected as a difference in the
total energy within 1 106 eV/atom. In order to ensure the suitability of CASTEP for Heusler-type SGSs with relatively subtle band structures, the band structures of Mn2CoAl and CoFeMnSi compounds, which have been confirmed as SGSs were first calculated using the CASTEP code. The results are in line with previous studies. 3. Results and discussion Numerous investigations have pointed out that Heusler compounds X2YZ with Hg2CuTi-type structure (or named as XA/inverse-type) can be found when Y element has more electronegative than X one, such as many Sc2-, Zr2-, Ti2-, and Mn2-based Heusler compounds [37–42]. Especially, the Z2YGa (Y = Co, Rh, Cr, V, Mn, Ir) compounds are predicted to crystallize in XA-type structure due to the zirconium is less electronegative than Y elements. Therefore, for the Zr2MnGa compound in this work, it is supposed to exhibit the XA-type structure. That is, the Zr atoms occupy the A (0, 0, 0) and the B (0.25, 0.25, 0.25) sites, while the Mn and Ga atoms are located on the C (0.5, 0.5, 0.5) and the D (0.75, 0.75, 0.75) sites, respectively. Furthermore, to determine the ground state of Zr2MnGa compound, the geometry optimization [43–45] has been performed by calculating the total energies as functions of the lattice constant (cell volume). Three different magnetic states (AFM, FM and NM) have been taken into account. We observed that the AFM magnetic structure of Zr2MnGa compound is the most stable as the ground state, with an equilibrium lattice constant of 6.59 Å. Now, we calculate the electronic band structure for the Zr2MnGa compound with XA-type structure in the irreducible Brillouin zone (Fig. 2). Obviously, the calculated band structure of this compound is quite special. No matter in majority-spin or minority-spin channels, the Fermi level locates at an energy gap, which indicates that the Zr2MnGa compound is a semiconductive material. However, different from the conventional semiconductors, there is no gap between the majority electrons in the valence band (at a point along the W-L direction) and the minority electrons in the conduction band (at the X point). The closed band gap characteristic and the corresponding SlaterPauling rule suggest that this compound is a SGS (the fourth case) rather than a normal half-metal or semiconductor, and this deserves further experimental works to be confirmed. As mentioned above, there is an energy gap between the conduction and valence bands for both the majority and minority electrons, however, the origin of the two band gaps in the two spin
X. Wang et al. / Journal of Magnetism and Magnetic Materials 444 (2017) 313–318
Fig. 2. Zr2MnGa band structure at its equilibrium lattice constant. (The black and red lines denote the majority and minority spin bands, respectively.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
channels is different. To issue this problem, we further show in Fig. 3 the calculated total and main partial density of states (DOS) for Zr2MnGa compound at the equilibrium lattice constant. In the spin-up channel, the band gap is created by the separated C15 and C25 states, coming from the bonding t2g and antibonding
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t1u states (see Fig. 2). In detail, for Zr2MnGa, Mn and Zr atoms lie at sites with same symmetry in XA-type Heusler structure, and their ‘‘d” orbits hybridization created 5 bonding bands (3t2g and 2eg) and 5 non-bonding bands (2eu and 3t1u). Then, 5 Mn-Zr bonding ‘‘d” hybrids hybridize in turn with ‘‘d” orbitals of Zr and forming again bonding and anti-bonding bands, while the 5 nonbonding bands (2eu and 3t1u) still hold with no hybridizing. Finally, the distribution of the 15 ‘‘d” orbitals in the minority-spin direction can be determined, i.e., 3t2g, 2eg, 2eu, 3t1u, 3t2g, and 2eg, from highenergy level to low-energy level. Also, we cannot ignore that the Ga creates 1s band and 3p bands which are totally occupied in Zr2MnGa and are also below the above-mentioned 15 ‘‘d” orbitals. In the spin-down channel, we can observed that the hybridization between the lower-energy ‘‘d” states of the high-valence transition-metal Mn atom and the higher-energy ‘‘d” states of the lower-valence transition-metal Zr atoms leads to the formation of bonding and anti-bonding states (see Fig. 3). More information about the origin of the band gaps of Heusler-based compounds can be found in our previous studies [46,47]. The total and atomic magnetic moments of Zr2MnGa compound at its equilibrium and strained lattice constants are given in Fig. 4. The total magnetic moment of Zr2MnGa compound is 0.0 mB/fu (formula unit), obeying the Slater-Pauling rule, Mt = Zt 18 [48,49]. The following can account for this phenomenon: based on the generalized electron-filling rule [50,51] and our discussion above, for Zr2MnGa, the total number of occupied states is 9.0 and 9.0 in the spin-up and spin-down channels, respectively, and therefore, there is a total spin magnetic moment of 0.0 lB. The atomic magnetic moment of Zr (A), Zr (B), Mn, and Ga is 1.66 lB, 1.52 lB, 3.08 lB, and 0.10 lB, respectively. Next, we focus on the magnetic moment of Zr2MnGa compound in performing calculations with lattice constant between 6.20 and 7.10 Å. Obviously, the fully-compensated total magnetic moment of Zr2MnGa compound maintains (0.0 lB) from 6.25 Å to 6.74 Å, and therefore, the fully-compensated ferrimagnetism properties maintain unchanged in this range. As shown in Fig. 4, the atomic spin moments of Mn, Zr (A) and Zr (B) are quite sensitive to the value
Fig. 3. Calculated total and atom-projected DOS for XA-type Zr2MnGa compound at its equilibrium lattice constant.
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Fig. 4. The total and atomic magnetic moments as a function of the lattice constant for Zr2MnGa compound.
of the lattice constant. The absolute values of the atomic magnetic moments of Mn, Zr (A) and Zr (B) increase monotonously under lattice expansion. When the value of the lattice constant is greater than 6.75 Å, the magnetic state of Zr2MnGa compound changes from the FCF to the metallic ferrimagnet (MFi). When the value of the lattice constant is smaller than 6.25 Å, the FCF state of Zr2MnGa compound vanishes, and the NM state occurs. As a representative example, the band structures of Zr2MnGa compound at the lattice constants of 6.20 Å and 6.90 Å are given in Fig. 5. Finally, we study the calculated band structures of Zr2MnGa compound at its strained lattice constants. The findings demonstrate the band structures of Zr2MnGa compound undergo an interesting transition processes with respect to contraction and expansion of the lattice constant between 6.20 and 7.10 Å (see Fig. 5). In detail, as the lattice constant is compressed in the range of 6.51–6.58 Å (see the example of Zr2MnGa 6.52 Å -XA in Fig. 5), the conduction bands at the X-point in the spin-down channel move up, and a clear gap between the majority electrons in the valence band and the minority electrons in the conduction band appears, that is, Zr2MnGa compound becomes a
Fig. 5. S ? FCFS ? HM-FCF ? FCF-SGS ? FCFS ? FCF-SGS ? HM-FCF ? MFi transitions at different lattice constants. Zr2MnGa band structures at different lattice constants. (The black and red lines denote the majority and minority spin bands, respectively.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. Zr2MnGa band structures at different lattice constants (6.48 Å and 6.60 Å). (The black and red lines denote the majority and minority spin bands, respectively.) Obviously, different spin-gapless features can be found in this compound. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
fully-compensated ferrimagnetic semiconductor (FCF-S). With further decreasing of the lattice constants (6.48–6.50 Å), the conduction bands at the W-point in the spin-up channel move down and touch the Fermi level, and a new zero-gap can be found in the spinup channel (see the example of Zr2MnGa at the lattice constant of 6.48 Å in Fig. 6), and therefore, Zr2MnGa compound becomes a FCFSGS (the first case). Note that this is the first time that different types of spingapless features have been found in a Heusler compound. As shown in Fig. 6, the band structures of FCF-SGS Zr2MnGa compound can be different and quite complicated. Particularity, the appearance of a zero-width gap at the Fermi level is a rare phenomenon, and therefore, the Zr2MnGa compound with tunable spin-gapless features should be paid more attention to. In the lattice constant range from 6.41 Å to 6.47 Å, the FCF-SGS state of Zr2MnGa compound vanishes again due to the overlap between the bands and the Fermi level in the spin-up channel, and the half-metallic FCF state occurs (see the example of Zr2MnGa at the lattice constant of 6.45 Å in Fig. 5). In the lattice constant range from 6.25 Å to 6.40 Å, the HM-FCF Zr2MnGa becomes a FCF-S again. Here, we consider the case of lattice expansion, when the lattice constant increases to the range of 6.61 Å–6.70 Å, the band gap in the spin-up channel maintains and the Fermi level locates within the gap, while the energy bands show a metallic overlap (around the X point) with Fermi level in the spin-down channel, reflecting that Zr2MnGa becomes a HM-FCF. For a deeper understanding, by comparing the band structures in Figs. 5 and 6, the principal reason of changing of the physics nature has been given as below: (i) the changing of the spin splitting; (ii) the changing of the valence and conduction bands energies; (iii) the changing of the dispersion degree of the valence and conduction bands. In detail, the spin splitting changing is mainly due to the changing of the inter-atomic hybridization interaction and the intra-atomic exchange interaction between the transitions group elements Zr and Mn. The spin splitting changing may cause the asymmetrical distribution between the two spin channels, and therefore reshape the valence and conduction bands near the Fermi level and specifically the valence band maximum and
conduction band minimum. Due to the changing of the lattice constants, the energies and the dispersion degree of the valence and conduction bands can be affected in both spin channels, and these factors determine the physics nature of Zr2MnGa compound. 4. Summary In summary, based on the Slater-Pauling rule, the electronic, magnetic, origin of the band gaps of Zr2MnGa compound have been studied in this paper. Calculated results show that Zr2MnGa compound is a FCF-SGS at its equilibrium lattice constant. At strained lattice constants, Zr2MnGa undergoes an interesting physics change from S ? FCF-S ? HM-FCF ? FCF-SGS ? FCF-S ? FCFSGS ? HM-FCF ? MFi, which indicates that the electronic and magnetic structure could be highly tuned by external temperature or pressure. Importantly, tunable spin-gapless features have also been found in Zr2MnGa compound subjected to the strain engineering. For the diverse electronic and magnetic properties, the present work suggests that FCF-SGS Zr2MnGa compound is useful in spintronic applications. Acknowledgments Z.X. Cheng thanks the Australian Research Council for support. G.D. Liu acknowledges financial support from the Chongqing City Funds for Distinguished Young Scientists (No. cstc2014jcyjjq50003) and the Program for Leading Talents in Science and Technology Innovation of Chongqing City (No. cstckjcxljrc19). References [1] X.L. Wang, Proposal for a new class of materials: Spin gapless semiconductors, Phys. Rev. Lett. 100 (2008) 156404. [2] Xiao-Lin Wang, Shi Xue Dou, Chao Zhang, Zero-gap materials for future spintronics, electronics and optics, NPG Asia Mater. 2 (2010) 31–38. [3] Xiaotian Wang et al., Recent advances in the Heusler based spin-gapless semiconductors, J. Mater. Chem. C 4 (2016) 7176–7192. [4] S. Skaftouros et al., Search for spin gapless semiconductors: The case of inverse Heusler compounds, Appl. Phys. Lett. 102 (2013) 022402.
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Research articles
Lattice constant changes leading to significant changes of the spingapless features and physical nature in a inverse Heusler compound Zr2MnGa Xiaotian Wang a,b, Zhenxiang Cheng b,⇑, Rabah Khenata c, Yang Wu d, Liying Wang e, Guodong Liu e,⇑ a
School of Physical Science and Technology, Southwest University, Chongqing 400715, PR China Institute for Superconducting & Electronic Materials (ISEM), University of Wollongong, Wollongong 2500, Australia Laboratoire de Physique Quantique, de la Matière et de la Modélisation Mathématique (LPQ3M), Université de Mascara, Mascara 29000, Algeria d School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China e School of Material Sciences and Engineering, Hebei University of Technology, Tianjin 300130, PR China b c
a r t i c l e
i n f o
Article history: Received 12 July 2017 Received in revised form 13 August 2017 Accepted 14 August 2017 Available online 16 August 2017 Keywords: Magnetic materials Ab initio calculation Band structure Magnetic properties
a b s t r a c t The spin-gapless semiconductors with parabolic energy dispersions [1–3] have been recently proposed as a new class of materials for potential applications in spintronic devices. In this work, according to the Slater-Pauling rule, we report the fully-compensated ferrimagnetic (FCF) behavior and spin-gapless semiconducting (SGS) properties for a new inverse Heusler compound Zr2MnGa by means of the plane-wave pseudo-potential method based on density functional theory. With the help of GGA-PBE, the electronic structures and the magnetism of Zr2MnGa compound at its equilibrium and strained lattice constants are systematically studied. The calculated results show that the Zr2MnGa is a new SGS at its equilibrium lattice constant: there is an energy 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. Remarkably, not only a diverse physical nature transition, but also different types of spin-gapless features can be observed with the change of the lattice constants. Our calculated results of Zr2MnGa compound indicate that this material has great application potential in spintronic devices. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Very recently, spin-gapless semiconductors (SGSs) [1–10], such as Co-doped Pb-based oxide materials [1], have great potential applications for high performance electronic and spintronic devices. As shown in Fig. 1, four possible band-structure configurations with spin-gapless features have been given [11]. In the first case (see Fig. 1(a)), one spin direction is gapless, while the other spin direction is semiconducting. In the second case (see Fig. 1 (b)), one spin direction is gapless, and the other spin direction is semiconducting with the top of the valence band touches the Fermi level. In the third case (see Fig. 1(c)), one spin direction is gapless, and the other spin direction is semiconducting with bottom of the conduction band touches the Fermi level. In the fourth case (see Fig. 1(d)), there is a gap between the conduction and valence bands for both the majority and minority electrons, while there is no gap
⇑ Corresponding authors. E-mail addresses: [email protected] (Z. Cheng), [email protected] (G. Liu). http://dx.doi.org/10.1016/j.jmmm.2017.08.040 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
between the majority electrons in the valence band and the minority electrons in the conduction band. The SGS materials, such as Co-doped PbPdO2, was firstly presented theoretically by Wang in 2008 [1] and confirmed experimentally by Kim et al. later on [12]. After the Co-doped PbPdO2, several different classes of materials have been theoretically and experimentally reported to be new SGSs [2–11]. Among them, the compounds based on Heusler structure cannot be ignored due to their higher Curie temperatures (TC) and tunable electronic structures. Up to now, many Heusler based compounds (eg. Mn2CoAl, CoFeMnSi, and CoFeCrGa) [10,13–23] have been prepared and their SGS behaviors have been confirmed based on their novel magnetic and transport properties. Furthermore, several Heulser compounds have even been theoretically proposed and experimentally proved to be fully-compensated ferrimagnetic (FCF) SGSs [24–28]. Compared to the normal SGSs, FCF-SGSs will simultaneously own the properties of the spin-gapless semiconductivity and full-compensated ferrimagnetism. That is to say, besides the behavior of SGSs, FCF-SGSs also exhibit no net
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Fig. 1. Density of states (DOS) scheme of the four possible band structure configurations with spin-gapless behaviors: (a)–(d). Filled areas represent occupied states, and the arrows indicate majority (") and minority (;) spin.
magnetization. Therefore, if these compounds were used in spintronic devices, there will be no stray magnetic fields generated. All the above-mentioned information motivated us to search for new FCF-SGSs based on full-Heusler structure. To identify SGSs among full-Heulser compounds, as we have summarized in our review article [3], the magnetic moments of these compounds should obey the generalized Slater-Pauling rule of Mt = Zt 24 (eg. Mn2CoAl) [13], Mt = Zt 28 (eg. Mn2CuAl) [25] or Mt = Zt 18 (eg. Ti2MnAl) [29] (where Mt is the total magnetic moment per unit cell and Zt is the total number of valence electrons). Then, to achieve the FCF property among the SGSs, the number of occupied electrons in both spin channels should be equal. That is, the total number of valence electrons of full-Heusler based FCF-SGSs should be 18 (9–9), 24 (12–12) or 28 (14–14). Recently, the electronic, magnetic, and half-metallic properties of many Zr-based fullHeusler compounds, such as Zr2CoGa [30], Zr2VGa [31], Zr2RhGa [32], and Zr2CrGa [33] have been investigated by us and other researchers. These half-metals contain 4 d transition metal elements Zr or Rh, which enlarge the scope of exploring new functional materials in compounds. Additionally, previous works show these half-metals Zr2YGa obey a Slater-Pauling rule: Mt = Zt 18 [31]. Therefore, in order to design a new FCF-SGS, the value of Mt must be 0, and the value of Zt must be 18. That is, Mn was chosen for doping into the Y site to form a new Heusler compound: Zr2MnGa with Zt = 18. In this paper, we will investigate the electronic structure, magnetic, and the FCF-SGS properties of newly designed Heusler compound Zr2MnGa by means of the firstprinciples calculation. Remarkably, a rather rare physical nature transition and different types of spin-gapless features can be observed if the lattice constant changes. 2. Computational details The electronic structures and the magnetic properties were performed by using the pseudo-potential method with a plane-wave basis set, implemented in the code of the Cambridge Serial Total Energy Package (CASTEP). The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudo-potential approach [34]. The generalized gradient approximation (GGA) [35,36] was adopted for the exchange-correction functional. For all cases, a plane-wave basis set cut-off of 450 eV was used. A k-points mesh of 15 15 15 was used in the Brillouin zone integrations for the Heusler structure. These parameters ensured good convergence for the total energy. The convergence tolerance for the calculations was selected as a difference in the
total energy within 1 106 eV/atom. In order to ensure the suitability of CASTEP for Heusler-type SGSs with relatively subtle band structures, the band structures of Mn2CoAl and CoFeMnSi compounds, which have been confirmed as SGSs were first calculated using the CASTEP code. The results are in line with previous studies. 3. Results and discussion Numerous investigations have pointed out that Heusler compounds X2YZ with Hg2CuTi-type structure (or named as XA/inverse-type) can be found when Y element has more electronegative than X one, such as many Sc2-, Zr2-, Ti2-, and Mn2-based Heusler compounds [37–42]. Especially, the Z2YGa (Y = Co, Rh, Cr, V, Mn, Ir) compounds are predicted to crystallize in XA-type structure due to the zirconium is less electronegative than Y elements. Therefore, for the Zr2MnGa compound in this work, it is supposed to exhibit the XA-type structure. That is, the Zr atoms occupy the A (0, 0, 0) and the B (0.25, 0.25, 0.25) sites, while the Mn and Ga atoms are located on the C (0.5, 0.5, 0.5) and the D (0.75, 0.75, 0.75) sites, respectively. Furthermore, to determine the ground state of Zr2MnGa compound, the geometry optimization [43–45] has been performed by calculating the total energies as functions of the lattice constant (cell volume). Three different magnetic states (AFM, FM and NM) have been taken into account. We observed that the AFM magnetic structure of Zr2MnGa compound is the most stable as the ground state, with an equilibrium lattice constant of 6.59 Å. Now, we calculate the electronic band structure for the Zr2MnGa compound with XA-type structure in the irreducible Brillouin zone (Fig. 2). Obviously, the calculated band structure of this compound is quite special. No matter in majority-spin or minority-spin channels, the Fermi level locates at an energy gap, which indicates that the Zr2MnGa compound is a semiconductive material. However, different from the conventional semiconductors, there is no gap between the majority electrons in the valence band (at a point along the W-L direction) and the minority electrons in the conduction band (at the X point). The closed band gap characteristic and the corresponding SlaterPauling rule suggest that this compound is a SGS (the fourth case) rather than a normal half-metal or semiconductor, and this deserves further experimental works to be confirmed. As mentioned above, there is an energy gap between the conduction and valence bands for both the majority and minority electrons, however, the origin of the two band gaps in the two spin
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Fig. 2. Zr2MnGa band structure at its equilibrium lattice constant. (The black and red lines denote the majority and minority spin bands, respectively.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
channels is different. To issue this problem, we further show in Fig. 3 the calculated total and main partial density of states (DOS) for Zr2MnGa compound at the equilibrium lattice constant. In the spin-up channel, the band gap is created by the separated C15 and C25 states, coming from the bonding t2g and antibonding
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t1u states (see Fig. 2). In detail, for Zr2MnGa, Mn and Zr atoms lie at sites with same symmetry in XA-type Heusler structure, and their ‘‘d” orbits hybridization created 5 bonding bands (3t2g and 2eg) and 5 non-bonding bands (2eu and 3t1u). Then, 5 Mn-Zr bonding ‘‘d” hybrids hybridize in turn with ‘‘d” orbitals of Zr and forming again bonding and anti-bonding bands, while the 5 nonbonding bands (2eu and 3t1u) still hold with no hybridizing. Finally, the distribution of the 15 ‘‘d” orbitals in the minority-spin direction can be determined, i.e., 3t2g, 2eg, 2eu, 3t1u, 3t2g, and 2eg, from highenergy level to low-energy level. Also, we cannot ignore that the Ga creates 1s band and 3p bands which are totally occupied in Zr2MnGa and are also below the above-mentioned 15 ‘‘d” orbitals. In the spin-down channel, we can observed that the hybridization between the lower-energy ‘‘d” states of the high-valence transition-metal Mn atom and the higher-energy ‘‘d” states of the lower-valence transition-metal Zr atoms leads to the formation of bonding and anti-bonding states (see Fig. 3). More information about the origin of the band gaps of Heusler-based compounds can be found in our previous studies [46,47]. The total and atomic magnetic moments of Zr2MnGa compound at its equilibrium and strained lattice constants are given in Fig. 4. The total magnetic moment of Zr2MnGa compound is 0.0 mB/fu (formula unit), obeying the Slater-Pauling rule, Mt = Zt 18 [48,49]. The following can account for this phenomenon: based on the generalized electron-filling rule [50,51] and our discussion above, for Zr2MnGa, the total number of occupied states is 9.0 and 9.0 in the spin-up and spin-down channels, respectively, and therefore, there is a total spin magnetic moment of 0.0 lB. The atomic magnetic moment of Zr (A), Zr (B), Mn, and Ga is 1.66 lB, 1.52 lB, 3.08 lB, and 0.10 lB, respectively. Next, we focus on the magnetic moment of Zr2MnGa compound in performing calculations with lattice constant between 6.20 and 7.10 Å. Obviously, the fully-compensated total magnetic moment of Zr2MnGa compound maintains (0.0 lB) from 6.25 Å to 6.74 Å, and therefore, the fully-compensated ferrimagnetism properties maintain unchanged in this range. As shown in Fig. 4, the atomic spin moments of Mn, Zr (A) and Zr (B) are quite sensitive to the value
Fig. 3. Calculated total and atom-projected DOS for XA-type Zr2MnGa compound at its equilibrium lattice constant.
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Fig. 4. The total and atomic magnetic moments as a function of the lattice constant for Zr2MnGa compound.
of the lattice constant. The absolute values of the atomic magnetic moments of Mn, Zr (A) and Zr (B) increase monotonously under lattice expansion. When the value of the lattice constant is greater than 6.75 Å, the magnetic state of Zr2MnGa compound changes from the FCF to the metallic ferrimagnet (MFi). When the value of the lattice constant is smaller than 6.25 Å, the FCF state of Zr2MnGa compound vanishes, and the NM state occurs. As a representative example, the band structures of Zr2MnGa compound at the lattice constants of 6.20 Å and 6.90 Å are given in Fig. 5. Finally, we study the calculated band structures of Zr2MnGa compound at its strained lattice constants. The findings demonstrate the band structures of Zr2MnGa compound undergo an interesting transition processes with respect to contraction and expansion of the lattice constant between 6.20 and 7.10 Å (see Fig. 5). In detail, as the lattice constant is compressed in the range of 6.51–6.58 Å (see the example of Zr2MnGa 6.52 Å -XA in Fig. 5), the conduction bands at the X-point in the spin-down channel move up, and a clear gap between the majority electrons in the valence band and the minority electrons in the conduction band appears, that is, Zr2MnGa compound becomes a
Fig. 5. S ? FCFS ? HM-FCF ? FCF-SGS ? FCFS ? FCF-SGS ? HM-FCF ? MFi transitions at different lattice constants. Zr2MnGa band structures at different lattice constants. (The black and red lines denote the majority and minority spin bands, respectively.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. Zr2MnGa band structures at different lattice constants (6.48 Å and 6.60 Å). (The black and red lines denote the majority and minority spin bands, respectively.) Obviously, different spin-gapless features can be found in this compound. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
fully-compensated ferrimagnetic semiconductor (FCF-S). With further decreasing of the lattice constants (6.48–6.50 Å), the conduction bands at the W-point in the spin-up channel move down and touch the Fermi level, and a new zero-gap can be found in the spinup channel (see the example of Zr2MnGa at the lattice constant of 6.48 Å in Fig. 6), and therefore, Zr2MnGa compound becomes a FCFSGS (the first case). Note that this is the first time that different types of spingapless features have been found in a Heusler compound. As shown in Fig. 6, the band structures of FCF-SGS Zr2MnGa compound can be different and quite complicated. Particularity, the appearance of a zero-width gap at the Fermi level is a rare phenomenon, and therefore, the Zr2MnGa compound with tunable spin-gapless features should be paid more attention to. In the lattice constant range from 6.41 Å to 6.47 Å, the FCF-SGS state of Zr2MnGa compound vanishes again due to the overlap between the bands and the Fermi level in the spin-up channel, and the half-metallic FCF state occurs (see the example of Zr2MnGa at the lattice constant of 6.45 Å in Fig. 5). In the lattice constant range from 6.25 Å to 6.40 Å, the HM-FCF Zr2MnGa becomes a FCF-S again. Here, we consider the case of lattice expansion, when the lattice constant increases to the range of 6.61 Å–6.70 Å, the band gap in the spin-up channel maintains and the Fermi level locates within the gap, while the energy bands show a metallic overlap (around the X point) with Fermi level in the spin-down channel, reflecting that Zr2MnGa becomes a HM-FCF. For a deeper understanding, by comparing the band structures in Figs. 5 and 6, the principal reason of changing of the physics nature has been given as below: (i) the changing of the spin splitting; (ii) the changing of the valence and conduction bands energies; (iii) the changing of the dispersion degree of the valence and conduction bands. In detail, the spin splitting changing is mainly due to the changing of the inter-atomic hybridization interaction and the intra-atomic exchange interaction between the transitions group elements Zr and Mn. The spin splitting changing may cause the asymmetrical distribution between the two spin channels, and therefore reshape the valence and conduction bands near the Fermi level and specifically the valence band maximum and
conduction band minimum. Due to the changing of the lattice constants, the energies and the dispersion degree of the valence and conduction bands can be affected in both spin channels, and these factors determine the physics nature of Zr2MnGa compound. 4. Summary In summary, based on the Slater-Pauling rule, the electronic, magnetic, origin of the band gaps of Zr2MnGa compound have been studied in this paper. Calculated results show that Zr2MnGa compound is a FCF-SGS at its equilibrium lattice constant. At strained lattice constants, Zr2MnGa undergoes an interesting physics change from S ? FCF-S ? HM-FCF ? FCF-SGS ? FCF-S ? FCFSGS ? HM-FCF ? MFi, which indicates that the electronic and magnetic structure could be highly tuned by external temperature or pressure. Importantly, tunable spin-gapless features have also been found in Zr2MnGa compound subjected to the strain engineering. For the diverse electronic and magnetic properties, the present work suggests that FCF-SGS Zr2MnGa compound is useful in spintronic applications. Acknowledgments Z.X. Cheng thanks the Australian Research Council for support. G.D. Liu acknowledges financial support from the Chongqing City Funds for Distinguished Young Scientists (No. cstc2014jcyjjq50003) and the Program for Leading Talents in Science and Technology Innovation of Chongqing City (No. cstckjcxljrc19). References [1] X.L. Wang, Proposal for a new class of materials: Spin gapless semiconductors, Phys. Rev. Lett. 100 (2008) 156404. [2] Xiao-Lin Wang, Shi Xue Dou, Chao Zhang, Zero-gap materials for future spintronics, electronics and optics, NPG Asia Mater. 2 (2010) 31–38. [3] Xiaotian Wang et al., Recent advances in the Heusler based spin-gapless semiconductors, J. Mater. Chem. C 4 (2016) 7176–7192. [4] S. Skaftouros et al., Search for spin gapless semiconductors: The case of inverse Heusler compounds, Appl. Phys. Lett. 102 (2013) 022402.
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