Ab intito study on some new spin-gapless semiconductors: The Zr-based quanternary Heusler alloys
Qiang Gao, Huan-huan Xie, Lei Li, Gang Lei, Jian-Bo Deng, Xian-Ru Hu
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Ab intito study on some new spin-gaplesssemiconductors: The Zr-based quanternary Heusleralloys
Qiang Gao a , Huan-Huan Xie a , Lei Li a , Gang Lei a , Ke Wang a , Jian-BoDeng a , Xian-Ru Hu a, ∗ a School of Physical Science and Technology, Lanzhou University, Lanzhou 730000,People’s Republic of China
Abstract
Employing ab intito electronic structure calculations, we have investigatedelectronic and magnetic properties of the Zr-based quanternary Heusler al-loys: ZrCoVIn, ZrFeVGe, ZrCoFeP, ZrCoCrBe and ZrFeCrZ (Z=In and Ga).Our ab intito calculation results show that all the alloys are (or nearly) spin-gapless semiconductors. All the alloys have large band gaps, indicating thestability of them at room temperature. The Slater-Pauling behaviours ofthese alloys are discussed as well. The values of Curie temperature of all thealloys are estimated. And it is found that the values of the Curie tempera-ture for all our calculated quanternary Heusler alloys are higher than that ofroom temperature. ∗ Corresponding author
Email address: [email protected] (Xian-Ru Hu)
Preprint submitted to Elsevier April 10, 2018 eywords:
A. intermetallic compounds, semiconductors; B. magneticproperties; D. electronic structure;
1. Introduction
Efficient spin injection from a ferromagnet to a semiconductor is verymeaningful for the development of the performance of spintronic devices [1].Since the prediction of HM ferromagnetism of Heusler alloy NiMnSb by abintito calculations in 1983 [2], half metallic ferromagnetism (HMF) has at-tracted great interest [3, 4, 5, 6]. And the half metallic ferromagnetic Heusleralloys are good candidates for the application of spintronic devices, as thesealloys often have high spin polarization, high Curie temperature compatiblelattice structure. The improvement of computer science makes it possible todesign materials on computers, which is efficient and less cost [7, 8, 9]. Espe-cially, computational material science enables the study of the new materials[8, 9], which is useful to the experiments and practical applications.Recent studies have shown that there is a new class of materials, namely,spin-gapless semiconductors (SGS) [10, 11, 12]. SGS was first predicted indiluted magnetic semiconductors PbPdO by ab intito calculations [10]. Theexcited carriers can be 100% spin polarized with tunable capabilities, andthe SGS may be more practical in the use of spintronic applications than2alf metals (HM). But there is a drawback that the Curie temperature (T C )of this material is almost 180 K [13, 14]. As is known the Heusler alloysoften have high T C , the Heusler alloys may be a realization of SGS. And theHeusler compound Mn CoAl was first predicted to be a SGS with a high T C of 720 K [11]. So the Heusler alloys are promising candidates for the futureSGS use.The Heuler alloys consist of Zr element have attracted great interest.There are many theoretical and experimental studies on the semi-Heusleralloy ZrNiSn recently[15, 16, 17, 18]. Some investigations have shown that theHeusler alloys Co ZrSn[19, 20], Ni ZrSn[19], Ni ZrAl[21], Co ZrGe[22] andZrCoSb[23] are half metals. And many other interesting properties have beenfound, for example, the alloy ZrPd Al is found to be superconductive[24].In recent reports[25, 26, 27, 28, 29, 30], some so-called LiMgPdSn orY-type structure Heusler alloys with a formula of X X YZ have been discov-ered to be HMs by density function theory (DFT). Among the new structureHeusler alloys, MnCrVAl, MnCrTiSi, CoFeCrAl, CoFeTiAs, CoMnCrSi, Mn-VTiAs, FeVTiAs, FeCrTiAl, CrVTiAl, CoVTiAl, CoFeMnSi, CoFeCrAl andCoFeVSi are (or nearly) SGSs [31, 32]. As reported in
Refs. [11, 33, 34, 35],the ternary Heusler alloys Ti MnZ (Z=Al, Ga and In), Mn CoAl, Ti CoSi3nd Ti VAs are (or nearly) also SGSs.The Zr-Ti coupling quanternary Heusler alloys, ZrFeTiZ (Z=Al, Si andGe) and ZrNiTiAl have been reported to be HMF very recently [36]. This isthe first prediction of HMF in the 4d-3d transition metal elements couplingquanternary Heusler alloys. As reported, these alloys have large half metallicband gaps and spin flip gaps. But they are just normal HMFs not SGSs.It is very interesting that the Zr-Ti coupling quanternary Heusler alloyshave large HM band gaps and spin flip gaps, which means these alloys maybe stable at room temperature. And there may be other Zr-based quan-ternary Heusler alloys with large HM band gaps, some probably being SGSs.Motivated by the above, we have designed the new Zr-based quanternaryHeusler alloys: ZrCoVIn, ZrFeVGe, ZrCoFeP, ZrCoCrBe and ZrFeCrZ (Z=Inand Ga). The electronic and magnetic properties of the alloys are investi-gated by ab intito calculations. ZrCoVIn, ZrCoCrBe, ZrCoFeP and ZrFeCrInalso have large band gaps of 0.98 eV, 0.71 eV, 0.41 eV and 0.80 eV. ZrFe-CrGa and ZrFeVGe are semiconductors. The calculation results show thatZrCoVIn, ZrCoCrBe, ZrFeVGe, ZrCoFeP, ZrFeCrIn and ZrFeCrGa are (ornearly) SGSs. The Slater-Pauling behaviours of these alloys are discussedin detail. The values of Curie temperature of all the alloys are estimated.4t is found that the values of the Curie temperature for all our calculatedquanternary Heusler alloys are higher than that of room temperature. Thismeans that all the calculated quanternary Heusler alloys keep being SGSs atroom temperature and they may be practical in the future SGS use.
2. Methods and details
The lattice optimization, electronic density of states (DOS), magneticmoment and band structure of the new Zr-based quanternary Heusler alloysare calculated by employing ab intito method. All our ab intito calculationsare performed by using the full-potential local-orbital minimum-basis bandstructure scheme (FPLO) [37, 38] with generalized gradient approximation(GGA)[39, 40, 41]. For the irreducible Brillouin zone, we use the k meshes of20 × ×
20 for all the calculations. The convergence criteria of self-consistentiterations is set to 10 − to the density and 10 − Hartree to the total energyper formula unit.As described in Refs. [25, 26], the quanternary Heusler alloys has a so-called LiMgPdSn or Y-type structure (space group No.216, F¯43m). So allour calculations are performed in this lattice structure.5 . Results and Discussions
In general, the quanternary Heusler alloys have a formula of X Y X Z . Inour calculations, the X atom is Zr atom and Z is a main group element atom.X and Y are the 3d transition metal element atoms, which the atomic num-ber X is smaller than that of Y. According to group theory, the LiMgPdSnor Y-type structure quanternary Heusler alloys have four Wychoff positions:4a (0, 0 ,0), 4b ( , , ), 4c ( , , ) and 4d ( , , ). The lattice structureis face centered cubic (FCC). In principle, the X , X , Y and Z atoms canoccupy one of the 4a, 4b, 4c and 4d positions. By interchanging the posi-tions of atoms in LiMgPdSn or Y-type structure quanternary Heusler alloys,three possible types of atom arrangement are formed: Y-type ( I ), Y-type( II ) and Y-type ( III ). Zr , Y, X and Z atoms are arranged at differentpositions Y-type ( I )=(4a, 4b, 4c, 4d), Y-type ( II )=(4a, 4b, 4c, 4d) andY-type ( III )=(4a, 4b, 4d, 4c). In order to get the equilibrium structuresof the Zr-based quanternary Heusler alloys, the geometry optimization arefirstly performed in their three different configurations by calculating the to-tal energies as a function of lattice constants. From the calculated resultsof total energies at equilibrium lattice constants, we find that Y-type ( I ) isthe most stable one of the three structures for both spin-polarization (FM6hase) and non-spin-polarization (NM phase). And FM phase is more stablethan NM phase in Y-type ( I ).This is in agreement with the previous papers[25, 26, 27, 28, 36]. The obtained equilibrium of lattice results in Y-type ( I )are presented in Table 1 for the FM phases. So we will only discuss thequanternary Heusler alloys in Y-type ( I ) structure for the FM phases. Table 2 shows the magnetic moment of all our calculated alloys underthe equilibrium lattice constants.All the calculated quaternary Heusler alloys have very large band gaps.It means they may keep their magnetic properties at room temperature.We will have a brief discussion of the Slater-Pauling behaviours basedon the values of total magnetic moment in
Table 2 . The calculated totalmagnetic moment per formula unit, 3 µ B , for the quanternary Heusler alloysZrCoVIn, ZrCoCrBe, ZrFeCrIn, ZrFeCrGa and ZrFeVGe, obeys the Slater-Pauling behaviour which can be expressed by, M tot = ( Z tot − µ B (1)here M tot and Z tot are the total magnetic moment per formula unit and7he number of total valence electrons in each the above alloys. Z tot is 21.The values of magnetic moment per formula unit is 2 µ B for the calculatedquanternary Heusler alloys ZrCoFeP. The Slater-Pauling behaviour which isobeyed by ZrCoFeP can be expressed by, M tot = ( Z tot − µ B (2)here M tot and Z tot have the same meaning as previous. The value of Z tot is26. The investigations of the Slater-Pauling behavours of usual full and in-verse Heusler alloys can be found in Refs. [42, 43]. Similar to the discussionsin Refs. [42, 43], we present the possible hybridizations between miority -spin d orbitals at different occupations in the case of 21 and 26 valence elec-trons in Figure 1 and
Figure 2 . As described in
Ref [42] for both figures,d ,..., orbitals correspond to the d xy , d yz , d zx , d z − r and d x − y orbitals,respectively. Figure 1 is in corresponding to the alloys ZrCoVIn, ZrCoCrBe, ZrFe-CrIn, ZrFeCrGa and ZrFeVGe. For these alloys, the 3d transition metallicelements X and Y sit at the sites with the same symmetry, so their 3d or-8itals hybridize similar to which described in Refs. [42, 43] . The 3d orbitalsof X and Y atoms hybride, creating five 3d bonding and nonbonding states.And the five X -Y bonding states hybride with the 4d orbitals of the Zr atom,creating again bonding and antibonding states. Similar to the Sc and Ti based inverse Heusler compounds[43], the triple-degeneration t u states andthe double-degeneration e u states are in very high energy level. So both the t u and e u states are empty. And the spin-down gap is created between thenon-bonding t u states and the bonding t g state. As can be seen in Figure 1 ,one bonding t g state and e g state are below the Fermi level in the hybridiza-tion schematic. The un-shown 1 × s state and 3 × p state are also below theFermi level. In total there are 9 states below Fermi level. The total magneticmoment M tot (in µ B ) is just the difference between the number of occupiedspin-up states and occupied spin-down states. We can directly deduce thenumber of occupied spin-up states: N ↑ = Z tot − N ↓ . So the total magneticmoment: M tot = ( N ↑ − N ↓ ) µ B = ( Z tot − × N ↓ ) µ B = ( Z tot − µ B . Sothe Heusler alloys ZrCoVIn, ZrCoCrBe, ZrFeCrIn, ZrFeCrGa and ZrFeVGeobey the Slater-Pauling behaviour expressed by Equation(1) .As for ZrCoFeP, we should focus on the hybridization schematic in
Figure2 . X , Y and Z are Fe, Co and P, respectively. This case is similar to the full-9eusler alloys.[42] As can be seen in Figure 2 , the t u state is below Fermilevel and e u state is above Fermi level. The the spin-down gap is createdbetween the nonbonding t u and e u states. From Figure 2 , we can get that t g and e g states are below Fermi level. Considering the 1 × s and 3 × p states,there are 12 states below Fermi level in total. We can directly deduce thetotal magnetic moment: M tot = ( N ↑ − N ↓ ) µ B = ( Z tot − × N ↓ ) µ B =( Z tot − µ B . That is why ZrCoFeP obeys the Slater-Pauling behaviourexpressed by Equation(2) .It is very interesting that the number of the valence electrons for ourcalculated spin-gapless semiconductors (SGS) is either 21 or 26, which issimilar to the results described in
Ref [31] . And the Slater-Pauling be-haviours obeyed by our calculated SGSs are also similar to the discussions in
Ref [31] . In this section, we will discuss the properties of spin-gapless semicon-ductors (SGS).
Figure 3 shows the total density of states of all the calcu-lated alloys. And
Figure 4 shows the partial density of states (PDOS) ofZrCoVIn under the equilibrium lattice constants of all our calculated quan-ternary Heusler alloys. 10irstly, we focus on the total DOS. In each of the cases, there is a largegap in the spin down band structure and the Fermi level falls within thisgap. In the spin up band structure, for ZrCoVIn and ZrFeCrIn, the valenceand conduction bands touch each other and the Fermi level falls within azero-energy gap, which forms a valley in the spin up band structure. Asdescribed in
Refs. [10], ZrCoVIn and ZrFeCrIn can be classified as SGSs.So no energy is required to excite electrons from the valence band to theconduction band, which is the same phenomenon that can be seen for theHg-based gapless semiconductors and graphene [10]. And more interesting isthat for an excitation energy up to the band gap energy of the spin channeland the holes can also be 100% spin polarized. So the carriers two canbe possible fully polarized in the two SGSs. Therefore they can be usedas spintronic materials with superior performance to half metals and dilutedmagnetic semiconductors [10, 11]. In the cases of ZrCoCrBe and ZrCoFeP, inthe spin up band structure, there is a small overlap of the band being locatedand above and below the Fermi level although no band-crossing occurs. Sothe quanternary Heusler alloys ZrCoCrBe and ZrCoFeP are almost SGSs.In the case of ZrFeCrGa, it is clear to see there is a large band gap in thespin-down channel. And a close look at the band structure reveals that11here is a very narrow band gap of 0.02 eV. In the spin up band structure,the valence and conduction bands touch each other but the Fermi level fallswithin a narrow band gap. So ZrFeCrGa is very close to a SGS. In the caseof ZrFeVGe, there is a large band gap in both spin down and up channelsbut the two gaps are not located at the same energy region. And a close lookat the band structure reveals that there is a band gap below the Fermi levelin the spin up band which touches the Fermi level resulting in an almostvanishing DOS below the Fermi level. So the Fermi level slightly crossesthe spin-down conduction band and the spin-up valence band. As a result,the quanternary Heusler alloy ZrFeVGe can be classified as an indirect spin-gapless semiconductor.Next the partial density of states (PDOS) will be discussed. From
Figure4 , we can get that for the quanternary Heusler alloy ZrCoVIn, the 3d statesof V and Co atoms make the most contributions to the total DOS near theFermi levels. The 4d states of Zr make the most contributions to the totalDOS of the Zr states near the Fermi levels. And the 5p states of In statesmake the most contributions to the total DOS near the Fermi levels of theZ states. From the PDOS, it can be seen there are hybridizations betweenV-3d, Zr-4d and Co-3d states around the Fermi levels. We can get similar12onclusions for the other calculated alloys.
As is known, the Curie temperature, T C , of the magnetic materials iscrucial for the practical applications. So in this section, we would commenton the expected Curie temperature.The previous investigations on multi-sublattice half-metallic Heusler com-pounds have shown that Curie temperature is more or less proportional tototal spin magnetic moment (or the sum of the absolute values of the atomicspin magnetic moments in the case of ferrimagnets) since Curie tempera-ture is mainly determined by the nearest neighbor inter-sublattice exchangeinteractions [44, 45, 46, 47, 48, 49]. As described in Refs. [11, 33], it isfound experimentally that the T C of Mn CoAl is 720 K and the the sum ofthe absolute values of the spin moments is 5.47 µ B . Based on the empiricalvalue and according to Table 2 , we can estimate that the value of T C forthe quanternary Heusler alloy ZrCoFeP is 320 K. As the sum of the absolutevalues of the atomic spin magnetic moments for ZrCoFeP is the lowest of allour calculated quanternary Heusler alloys, the values of T C for all our calcu-lated quanternary Heusler alloys are higher than that of room temperature.So the SGSs may probably be stable at room temperature. And they may13e candidates for the future spin-gapless semiconductors applications.
4. Conclusions
In conclusion, we have investigated some Zr-based quanternary Heusleralloys by employing ab intito calculations. It is found that the Zr-basedquanternary Heusler alloys ZrCoVIn, ZrCoCrBe, ZrFeVGe, ZrCoFeP, ZrFe-CrIn and ZrFeCrGa are (or nearly) SGSs with large band gaps by studyingthe DOS. The Slater-Pauling behaviours of these alloys are discussed as well.The Curie temperature for these alloys have also been estimated, and theresults show that the values of the Curie temperature for these alloys arehigher than that of room temperature. So these alloys can be the potentialcandidates for the future SGS applications.14 eferences [1] I. uti, J. Fabian, S. Das Sarma,Spintronics: Fundamentals and applications, Reviews of ModernPhysics 76 (2) (2004) 323–410. doi:10.1103/RevModPhys.76.323 .URL http://link.aps.org/doi/10.1103/RevModPhys.76.323 [2] R. A. de Groot, F. M. Mueller, P. G. v. Engen, K. H. J. 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ZrYX Z M X ( µ B ) M Zr ( µ B ) M Y ( µ B ) M Z ( µ B ) M tot ( µ B ) M abs ( µ B )ZrCoVIn 2.89 0.19 0.04 -0.12 3.00 3.25ZrCoCrBe 3.21 -0.17 0.14 -0.18 3.00 3.72ZrFeCrIn 3.45 -0.27 -0.03 -0.15 3.00 3.91ZrFeCrGa 3.12 -0.29 0.32 -0.15 3.00 3.88ZrFeVGe 2.58 0.00 0.57 -0.15 3.00 3.32ZrCoFeP 1.19 -0.24 0.99 0.06 2.00 2.49 Figure captionsFigure 1:
Possible hybridizations between spin-down orbitals siting atdifferent sites in the case of 21 valence electrons for our calculated quaternaryHeusler alloys.
Figure 2:
Possible hybridizations between spin-down orbitals siting atdifferent sites in the case of ZrCoFeP.
Figure 3:
The total density of states (DOS) for all our calculated qua-ternary Heusler alloys.
Figure 4:
The partial density of states (PDOS) for ZrCoVIn.29 xt g u X Y3xt ZrX - Y 2xe u u g u E F g u g d , d d , d , d d , d , d d , d d , d d , d , d Figure 1: