Stable half-metallic ferromagnetism in nonstoichiometric cubic binary chromium chalcogenides
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov epl draft Stable half-metallic ferromagnetism in nonstoichiometric cubic bi-nary chromium chalcogenides
San-Dong Guo and
Bang-Gui Liu (a)
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, ChinaBeijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
PACS – Intrinsic properties of magnetically ordered materials
PACS – General theory and models of magnetic ordering
PACS – Other topics in magnetic properties and materials
Abstract. - We find that three nonstoichiometric cubic binary chromium chalcogenides, namelyCr S , Cr Se , and Cr Te , are stable half-metallic ferromagnets with wide half-metallic gapson the basis of systematic state-of-the-arts first-principles calculations. We optimize their struc-tures, and then calculate their magnetic moments, electronic structures, formation heats, andelastic moduli and investigate their structural stability and robustness of ferromagnetism againstantiferromagnetic fluctuations. Our calculated results show that the three sulvanite phases arestructurally stable and ferromagnetically robust, and hence could be realized as epitaxial thinfilms. We attribute the structural and ferromagnetic stability and the better half-metallicity totheir special effective Cr valence 2 . It is believed that next-generation high-performancecomputers can be achieved through using the spin free-dom of electron in key materials and devices of currentsemiconductor technology [1, 2]. The half-metallic fer-romagnet, first discovered in NiMnSb by de Groot etal in 1983, has almost 100% spin polarization near theFermi level [3–5]. This feature of half-metallic ferromag-netism makes carriers have high spin-polarization nearthe Fermi level and avoid some spin-related scatteringprocesses that should exist otherwise. These are essen-tial to practical spintronic applications [1, 2, 5]. Half-metallic ferromagnetism has been found in many materi-als, such as Heusler alloys [3, 4, 6], transition-metal oxides[7–9], and even graphene nanoribbons under electric field[10]. The half-metallic ferromagnetic materials compatiblewith semiconductor technology is believed to be promis-ing candidates for achieving more powerful computers.For this purpose, many zincblende transition-metal pnic-tides and chalcogenides [11–18], regularly-doped semicon-ductors [19, 20], semiconductor super-structures [21, 22],and more related compounds have been proved to behalf-metallic. Although great advance has been achieved,better half-metallic ferromagnets compatible with cur- (a)
E-mail: [email protected] rent semiconductor technology are highly desirable for thenext-generation computers.Here we find three stable half-metallic ferromagnets,namely Cr S , Cr Se , and Cr Te , among nonstoichio-metric cubic binary transition-metal chalcogenides on thebasis of state-of-the-arts first-principles calculations. Weinvestigate their structural stability and ferromagnetic ro-bustness against antiferromagnetic fluctuations. Our cal-culated results show that the three nonstoichiometric sul-vanite phases have formation heats of down to -0.302 eVper formula unit with respect to corresponding zincblendephases and their half-metallic gaps can be up to 1.05 eV.We attribute the structural and ferromagnetic stabilityand the better half-metallicity to their special effective Crchemical valence 2 . Fig. 1: (color online). The crystal structures of zincblende Cr X (a) and sulvanite Cr X (b) phases, where X can be S, Se, orTe. The red (or black) ball denotes a Cr atom and the yellow(or gray) an X atom. and the scalar relativistic approximation is used for va-lence states. The spin-orbit coupling is neglected becauseit has little effect on our results. We use 2000 k pointsin the first Brillouin zone, make the harmonic expansionup to l max =10 in atomic spheres, and set R mt × K max to7.5. The radii of the atomic spheres of Cr and others arechosen so that as high accuracy as possible is obtained.The volumes are optimized in terms of total energy, andthe internal position parameters with a force standard of3 mRy/a.u. The simplest antiferromagnetic structures areconstructed by doubling the unit cells along the [100] and[110] directions. There are six Cr atoms in each of thesedoubled cells. We let three of the six Cr spins orient upand the other three down. All the spin values of the Cr,S, Se, and Te atoms are determined naturally by the self-consistent calculations. The structural stability is inves-tigated through deforming the structures (with the vol-umes fixed) along the three directions. The elastic moduliare calculated with the standard method implemented inWIEN2k [24, 25]. The formation heats of the cubic sul-vanite structures are calculated with respect to the crys-talline Cr phase and the corresponding zincblende struc-tures. The self-consistent calculations are considered tobe converged only when the absolute integrated charge-density difference per formula unit between the two suc-cessive loops is less than 0.0001 | e | , where e is the electroncharge.The ground-state phases for three stoichiometric Cr X ( X =S, Se, and Te) compounds are of nickel-arsenide (na)structure, but the zincblende (zb) structures of the Cr X have been shown to be higher only by 0.28-0.36 eV performula unit than the corresponding na ones [15], andtherefore have very good stability. This actually stim-ulated experimental synthesis of zb-CrTe epitaxial thinfilms with a thickness up to 100 nm [16]. The sulvanitestructure of Cr X still has cubic symmetry with spacegroup No. 215. Each of the cations has four anionic neigh-bors, but each of the anions three cationic neighbors. Withthe cations being at the ( ,0,0) sites, the anions occupythe ( z X , z X , z X ) sites. The two cubic structures are shownin Fig. 1. For all the sulvanite Cr X compounds, the Table 1: The lattice constants a , the internal atomic parame-ters z X , and the Cr- X bond lengths l v of the three sulvaniteCr X phases. Presented in parentheses are those of the cor-responding zb-Cr X phases. Name Cr S (CrS) Cr Se (CrSe) Cr Te (CrTe) a (˚A) 5.344 (5.469) 5.679 (5.833) 6.117 (6.292) z X l v (˚A) 2.315 (2.368) 2.460 (2.526) 2.686 (2.725) D -5 -4 -3 -2 -1 0 1 2 3128404812 D en s i t y o f S t a t e s tot Cr S int (a) A BC D -5 -4 -3 -2 -1 0 1 2 3128404812 D en s i t y o f S t a t e s tot Cr Se int (b) A BC D -4 -3 -2 -1 0 1 2 3128404812 D en s i t y o f S t a t e s Energy (eV) tot Cr Te int (c) A BC
Fig. 2: (color online). Spin-dependent densities of states(DOSs) of the three sulvanite Cr X phases for X = S (a),Se (b), and Te (c). The upper part in each of the three panelsis the majority-spin DOS and the lower part the minority spin.The solid thick line represents the total DOS; the red (or gray)dash, blue (or light gray) dot, and black thin lines describethe partial DOSs projected in Cr and X atom spheres and theinterstitial region, respectively. p-2table half-metallic ferromagnetism in chromium chalcogenideslattice constant a and the internal structural parameter z X are optimized fully in terms of usual total energy andforce standards, and then the Cr- X bond lengths l v arecalculated with the optimized structures. We present ourcalculated a , z X , and l v results for all the three sulvaniteCr X in Table 1. Those of the corresponding zb Cr X phases are shown in parentheses for comparison. Cr S and Cr Se almost keep the same z X =0.25 as zb-CrS andzb-CrSe, and Cr Te has z X =0.260, a little larger thanthat of zb-CrTe. The sulvanite structures have smaller lat-tice constants than the zb ones by 1.6-2.6% and smallerCr- X bond lengths by 1.4-2.6%. In the following, spin-dependent densities of states (DOSs), energy bands, andcharge and moment density distributions are calculated interms of the optimized structures. Fig. 3: Spin-dependent energy band structures (EBs) of thethree sulvanite Cr X phases for X = S (a), Se (b), and Te(c). The left part in each of the three cases is the majority-spin bands and the right part the minority spin. The solid linewith dots describes the EB structure along the high-symmetrypoints and the dot diameter is proportional to the Cr d weightat that point. The spin-dependent DOSs of the three sulvanite Cr X ( X =S, Se, and Te) phases are presented in Fig. 2. For theconvenience of description, we label the four different setsof the energy bands as A, B, C, and D, respectively. Foreach of the three X cases, there is a narrow gap betweenA and B in the majority-spin (MAS) channel and a widegap between C and D in the minority-spin (MIS). It isclear that there is a gap across the Fermi level in the MISchannel for each of all the three cases and therefore allthe three are half-metallic ferromagnets. In addition tothe total DOS, partial DOSs projected in the muffin-tinspheres of Cr and X atoms and in the interstitial regionare presented too. It is clear that the B and D bands areoriginated from Cr-d states and the A and C bands mainlyhave the X -p (S, Se, or Te) character.Presented in Fig. 3 are the spin-dependent energybands, according to the corresponding DOS plots in Fig.2, for X =S, Se, and Te. There are twelve bands in bothA and C. They result from the fact that we have four X (S, Se, or Te) atoms in the sulvanite Cr X unit cell andeach of the four has three p orbitals. There are fifteenbands in both B and D because we have three Cr atomshere and each of the three has five d orbitals. The e g bands are lower than the t g ones. The Cr-s state is putto higher energy than the B and D bands in both of theMAS and MIS channels. This is in contrast with zb-Cr X phases whose Cr-s states are merged with the Cr-d t g states. We have also calculated charge and spin densitiesin three typical planes. Our results show that the chargedensity from the A and C bands is distributed mainly inthe neighborhoods of the X and Cr atoms, but the spindensity is almost limited to Cr and X atoms only. Thefilled part of the B bands are substantially localized nearCr and X atoms. When X changes from S to Te, the X -p character becomes less and less in the electron densityfrom the filled B bands because the ionic radius becomeslarger and larger. Table 2: The magnetic moments ( M ), half-metallic gaps( G HM ), magnetic energy differences (∆ E ), formation heats( H Form ), and the elastic moduli ( B , C ′ , and C ) of the threeCr X phases, compared with the zb-Cr X phases (in paren-theses). Name Cr S (CrS) Cr Se (CrSe) Cr Te (CrTe) M ( µ B ) 10 (4) 10 (4) 10 (4) G HM (eV) 0.50 (0.07) 0.83 (0.61) 1.05 (1.00)∆ E (eV) 0.57 0.56 0.11 H Form (eV) -0.148 -0.114 -0.302 B (GPa) 72.9 (63.2) 57.7 (59.5) 44.1 (45.9) C ′ (GPa) 8.8 5.9 (5.6) 4.8 (5.5) C (GPa) 34.2 35.9 (50.7) 32.9 (36.4)We summarize in Table 2 the total moments per for-mula unit ( M ), half-metallic gaps ( G HM ) [27], and theenergy differences per formula unit (∆ E = E AF − E FM )p-3an-Dong Guo and Bang-Gui Liufor all the three sulvanite Cr X phases ( X =S, Se, andTe), where E AF and E FM are the total energies for theAF and FM spin configurations. Here we define G HM asthe smaller of E cb and E vt , where E cb is the bottom energyof the minority-spin conduction bands with respect to theFermi level and E vt the absolute value of the top energy ofthe minority-spin valence bands. Our GGA G HM valuesshould be rough estimates for the minimal energies for spinflip excitations. We obtain 10 µ B for the magnetic momentper formula unit in all the three cases. This is because wehave ten Cr d electrons to contribute to the moment aftereight of the eighteen Cr electrons of the three Cr atomsare bonding with the sixteen X p electrons of the four X atoms. The half-metallic gaps are larger than the corre-sponding zb-Cr X phases because the Fermi levels movetoward lower energy level due to the fact that there areone less Cr atom for Cr X , compared with the cubic zbunit cell including four Cr and X atoms. The ∆ E results,from 0.11 to 0.57 eV, show that our FM solutions are veryrobust against possible AF fluctuations.In addition, we present the formation heats per formulaunit ( H Form ), the elastic moduli ( B , C ′ , and C ) of thethe three Cr X phases in Table 2. We calculate the for-mation heats to investigate the stability of the Cr X withrespect to the zb-Cr X phases. For this reason, H Form isdefined as E (Cr X ) − E (zb − Cr X )+ E (Cr), where E ( f )is the total energy of the formula f . The negative valuesof H Form for all the three cases mean that the sulvaniteCr X phases can be synthesized more easily than thecorresponding zb phases, since zincblende CrTe has beensynthesized in the form of epitaxial thin films [16]. The B and C values of the sulvanite phases are similar to thoseof the corresponding zincblende phases. The key tetrag-onal moduli, C ′ , are 8.8, 5.9, and 4.8 GPa for the threecases. The latter two C ′ values are comparable with thoseof the corresponding zincblende phases. Therefore, thesecalculated results show that the three sulvanite phases aremechanically stable.The nonstoichiometry plays key roles in the sulvaniteCr X . A Cr atom in the zb-Cr X contributes a momentof 4 µ B , but three Cr atoms yield 10 µ B , not 12 µ B , in thesulvanite Cr X because two more Cr electrons are neededto fill all the p orbitals of four X atoms. Effectively, theaverage valence of a Cr atom is equivalent to + (higherthan 2+) and the enhanced Cr valence makes the forma-tion heat negative and hence enhances the stability of theCr X with respect to the zb-Cr X . In zb-Cr X , Cr-d t g states are hybridized substantially with X p ones, and Cr-d eg are quite isolated. For the Cr X , Cr-d x − y statesremain isolated, and the other Cr d states are hybridizedmore strongly with the X p ones, which makes Cr s statehigher in energy.In summary, we show that the three nonstoichiomet-ric cubic binary chromium chalcogenides are stable half-metallic ferromagnets with wide half-metallic gaps onthe basis of systematic state-of-the-arts DFT calculations.Our calculated results indicate that the sulvanite Cr S , Cr Se , and Cr Te are better than or approximatelyequal in both structural and ferromagnetic stability thanzincblende CrS, CrSe, and CrTe, respectively. The struc-tural stability against crystal deformations and the nega-tive formation heats (-0.114 ∼ -0.302 eV per formula unit)mean that they can be synthesized, at least as epitaxialthin films, more easily than the corresponding zincblendephases. We attribute the structural and ferromagneticstability and the better half-metallicity to the higher Crchemical valence, 2 . ∗ ∗ ∗ This work is supported by Nature Science Foundation ofChina (Grant Nos. 10874232 and 10774180), by the Chi-nese Academy of Sciences (Grant No. KJCX2.YW.W09-5), and by Chinese Department of Science and Technology(Grant No. 2005CB623602).
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