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Electronic structure and Magnetism in BaMn As and BaMn Sb 2 2 2 2 Jiming An Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6114 and Wuhan University of Technology, Wuhan, China A.S. Sefat, D.J. Singh, and Mao-Hua Du Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6114 (Dated: January 15, 2009) 9 We study the properties of ThCr2Si2 structure BaMn2As2 and BaMn2Sb2 using density func- 0 tional calculations of the electronic and magnetic as well experimental measurements on single 0 crystal samples of BaMn2As2. These materials are local moment magnets with moderate band 2 gap antiferromagnetic semiconducting ground states. The electronic structures show substantial n Mn-pnictogenhybridization,whichstabilizes anintermediatespinconfigurationforthenominally a d5 Mn. The results are discussed in the context of possible thermoelectric applications and the J relationship with the corresponding iron / cobalt / nickelcompounds Ba(Fe,Co,Ni)2As2. 5 1 PACSnumbers: 71.20.Lp,72.15.Jf,75.10.Lp ] i I. INTRODUCTION superconductivityisfoundforM=Fe,andanapparently c s different superconductivity for M=Ni.7,8,9 The M=Co - compound, BaCo As is near ferromagnetism,10 while l Requirements for a thermoelectric materialto be used 2 2 r CaCo P isreportedashavingferromagneticallyordered t in waste heat recovery include a high figure of merit, 2 2 m ZT =σS2T/κ,preferablyunity orhigher,andmaterials Coplanes,whicharestackedantiferromagnetically.11 In- terestingly,unconventionalsuperconductivityis foundin . cost compatible with the application. Here S is the See- at beckcoefficient(thermopower),σistheelectricalconduc- Ba(Fe1−xCox)2As2 for a substantial range of x around m 0.1.12 Turning to the electronic structures, the com- tivity,andκisthethermalconductivity. HighZT cannot - beobtainedwithouthighthermopower.1Currentmateri- pounds with M=Fe,Co and Ni show roughly similar d shapes of their densities of states, with the main dif- alsforintermediatetemperaturestypicalofrequirements n ference being the position of the Fermi energy, due to for automotiveexhaust heatconversioncontainsubstan- o the different electron counts. These electronic struc- tial amounts of Te, as in e.g. PbTe. However, Te is a c tures show moderate hybridization between the transi- [ rare element whose supply is mainly as a byproduct of tion metal d bands and the As p bands, with the main Cu production and whose cost is expected to sensitive 2 As p bands ∼ 2-3 eV below the Fermi energy, E and to usage. In particular, this may lead to difficulties in F v approximately ∼ 10-20% As characater in the d bands. 2 applicationsthat requirelargevolumesofTe basedther- Thus the As occurs nominally as As3−. Interestingly, 7 moelectricmaterial. Thereforeitisofinteresttoidentify eventhoughThCr Si isanverycommonstructuretype, 2 alternative materials based on common inexpensive ele- 2 2 0 ments. Among metals andmetalloids these include alka- the Pn=Sb compounds, namely BaFe2Sb2, BaCo2Sb2 1. line earths (Mg,Ca,Sr,Ba), mid-3 d transition elements, and BaNi2Sb2 are not reported. On the other hand, the Mn compounds, BaMn P , BaMn As and BaMn Sb 0 especiallyMnandFeandpnictogens(As,Sb). Wangand 2 2 2 2 2 2 9 co-workers2recentlyreportedmeasurementsofthetrans- are known phases as are the corresponding Ca, Sr and 0 port properties of single crystals of BaMn Sb grown Eumaterials,thoughwith structuraldistortionsin some : 2 2 cases.13,14,15,16,17 v from Sn flux. They report a room temperature ther- i mopowerof∼225µV/K,butaccompaniedbyalowelec- From a practical point of view, there are several re- X trical conductivity leading to low ZT. The conductivity ports of remarkably high thermopowers accompanied by ar increases with temperature, but this is accompanied by metallic conduction in the Fe based superconducting a decreasing thermopower. This suggests intrinsic semi- phases.18,19,20,21,22 These materials have relatively nar- conducting behavior, which is consistent with activated row manifolds of Fe d bands near the Fermi energy. fits of the conductivity. Interestingly, a transition was These result from the combination of moderate Fe-As found from a low activation energy of ∼ 0.1 eV (T <470 hybridization and expanded Fe-Fe distance as compared K) to a higher activation energy region (∼ 1.1 eV) at withbulk Fe. Inanycase,the values ofS inthe Fe com- T >650 K, possibly reflecting a cross-over from an ex- pounds are too low by a factor of ∼ two compared with trinsic to an intrinsic regime. However, doping studies practical thermoelectrics, and are high at low tempera- have not yet been reported. tures,inapplicabletowasteheatrecovery. Asmentioned, Recentdiscoveriesofsuperconductivity3,4 inThCr Si BaMn Sb isreportedtobeasemiconductor.2,17Wenote 2 2 2 2 structure pnictides has led to renewed interest in this thatBaMn Sb ,BaMn As andBaFe As arecomposed 2 2 2 2 2 2 large class of compounds.5,6 Among the compounds of common,inexpensive elements, whichas mentionedis AM Pn , A=Ca,Sr,Ba,Eu, Pn=As, high temperature an important consideration for some thermoelectric ap- 2 2 2 plications. Key questions concern the relationship be- within the LDA with the LAPW method, but we note tween BaMn As and BaMn Sb , and that between the that the conclusions are robust with very similar results 2 2 2 2 Mn and Fe compounds, as well as the related issue of and conclusions emerging from the GGA planewave cal- whether the conductivity in the Mn compounds can be culations. We also note that our electronic structure for improvedbydoping, while atthe same time maintaining BaMn Sb isquitesimilartothatreportedpreviouslyby 2 2 high thermopowers. Xia and co-workers.17 II. THEORETICAL METHODS III. SYNTHESIS The purpose of this paper is to further elucidate the Experimental characterization of BaMn2As2 was per- electronic properties of these Mn compounds in relation formed using single crystals. These were grown out of to the Fe phases, in particular by comparing BaMn As MnAs flux. The typical crystal sizes were ∼ 5x3x0.2 2 2 withBaFe As ,andwithBaMn Sb ,whichwasrecently mm3. High purity elements (> 99.9%) were used in the 2 2 2 2 studied by Xia and co-workers.17 We find that the Mn preparation of the samples. The source was Alfa Aesar. compounds are rather different from the Fe, Co and Ni First, MnAs binary was preparedby placing mixtures of compounds in that there is much stronger hybridization As,Mnpiecesinasilicatube. Thesewerereactedslowly ◦ ◦ with the pnictogen p states. This leads to an electronic by heating to 300 C (25 C/hour, dwell 10 hours), and ◦ ◦ structure that cannot be regarded as derived from that to 600 C (15 C/hour, dwell 75 hours). Then a ratio of ofthe Fe compoundwithadifferentelectroncount. Fur- Ba:MnAs= 1:5washeatedinanalumina cruciblefor15 ◦ thermore, in contrast to the metallic character and itin- hoursat1230 Cunderpartialatmargon. Thisreaction ◦ erant magnetism in the Fe phases, we find local mo- wascooledattherateof2 /hour,followedbydecanting ◦ ment, semiconducting behavior in both BaMn Sb and of the MnAs flux at 1120 C. 2 2 BaMn As . 2 2 Electronic structure calculations were performed within density functional theory. We did calculations IV. CRYSTAL STRUCTURE, TRANSPORT using both the local density approximation (LDA) and AND SPECIFIC HEAT thegeneralizedgradientapproximation(GGA)ofPerdew andco-workers,23 andalsousing boththe generalpoten- The crystals were malleable but well-formed plates tial linearized augmented planewave (LAPW) method24 with the [001]direction perpendicular to the large faces. similar to our earlier calculations for the Fe-based The structural identification was made via powder x-ray materials,25,26 and an ultrasoft pseudopotential method diffractionusingaScintagXDS2000Θ-Θdiffractometer implemented in the Quantum Espresso package.27 For (Cu K radiation). The cell parameters were refined us- α the LAPW calculations, we used two different codes, ing least squres fitting of the measuredpeak positions in an in-house code and the Wien2k code,28 and com- the range 2Θ = 10−90◦ using the Jade 6.1 MDI pack- pared results, finding no significant differences. We used age. The resulting lattice parametersofBaMn As were 2 2 LAPW sphere radii of 2.1 Bohr for the elements other a=4.1633(9) ˚A, c=13.448(4) ˚A, in the ThCr Si struc- 2 2 than Ba in BaMn As and 2.2 Bohr for all elements in ture(I4/mmm,Z=2). ThecellvolumeforBaMn As is 2 2 2 2 BaMn Sb . Two different sphere radii were used for Ba then233.087(4)˚A3,whichisinaccordwithpriorreports 2 2 in BaMn As : 2.35 Bohr with Wien2k and 2.2 Bohr in and much larger than BaFe As (204.567(2) ˚A3) (Ref. 2 2 2 2 theotherLAPWcalculations. Inallcases,convergedba- 12) or BaCo As (197.784(1) ˚A3) (Ref. 10). 2 2 sis sets, corresponding to R k =9 with additional Temperature dependent electrical resistivity measure- min max local orbitals29 were used, where R is the minimum ments were performed on a Quantum Design Physical min LAPW sphere radius and k is the planewave cut- PropertyMeasurementSystem(PPMS),measuredinthe max off. Convergence of the Brilloiun zone sampling was ab-planeabove5 K.For BaMn As ,the resistivity,ρ de- 2 2 checked by directly calculating results using different creaseswithincreasingtemperatureupto∼150K,above grids. Weusedtheliteraturevaluesofthelatticeparame- whichitgivesadecreasing,metallic-likedependence(Fig. ters,a=4.418˚A,c=14.200˚A,forBaMn2Sb2anda=4.15˚A, 1). The resistivity at room temperature is 165 mΩ cm. c=13.47˚A, for BaMn2As2 with internal parameters, zAs Specificheatdata,Cp(T),werealsoobtainedusingthe and zSb determined by LDA total energy minimization PPMS via the relaxation method. Fig. 2 gives the tem- in the low energy antiferromagnetic state. The resulting perature dependence of the specific heat. There are no values were zSb=0.3594 for BaMn2Sb2 and zAs=0.3524 featuressuggestingaphasetransitioninthespecificheat for BaMn2As2. The value obtained for BaMn2Sb2 is up to 200 K. Below ∼ 6 K, C/T has a linear T2 depen- in reasonable accord with the experimental value17 of dence(insetofFig. 2). ThefittedSommerfeldcoefficient, 0.3663. γ=0.79(2) mJ/(K2 mol), or ∼ 0.4 mJ/(K2 mol Mn) is Transportcalculationswereperformedwithinthecon- near zero. For comparisonthe value fo BaFe As , which 2 2 stantscatteringtimeapproximationusingtheBoltzTraP has a spin density wave instability gapping most of the code.30 Forconsistencywefocushereonresultsobtained Fermisurfaceis 3.0mJ/(K2 molFe),12 andthe value for 3 4 10 100 BaMn As 2 2 ) 1 - l o m ρΩ ( cm)ab 102 BaMn2As2 -1 C (J K 50 -2-1 T (mJ K mol)105 0 C/ 0 10 0 20 40 2 2 T ( K) 0 0 100 200 -2 T (K) 10 0 100 200 300 400 FIG. 2: Temperature dependence of the specific heat for T (K) BaMn2As2. The inset shows C/T vs. T2 and a linear fit between 1.8 K and 3.5 K FIG. 1: Temperature dependence of the in-plane resistivity of BaMn2As2 betrween 1.8 K and 380 K. ing. The energetics are summarized along with those of BaMn As in Table I. We find a strong tendency to- BaCo As is20.8mJ/(K2 molCo).10. Infact,itis likely 2 2 2 2 wards moment formation, which results from the strong that the small observed γ arises from a small amount of Hund’s rule coupling on the nominal Mn2+ ions in the MnAs flux included in the sample and is therefore not compound,withstablemomentsindependentofthemag- intrinsic to BaMn As . This is based on squid measure- 2 2 netic order. Integrating within the Mn LAPW sphere ments,wherewefindasmallsignalat310K,correspond- (radius 2.2 Bohr) we obtain moments of 3.47 µ for the B ing to the ordering temperature of MnAs. The value for ferromagnetic (F) ordering and 3.55 µ for the G-type the Debye temperature is Θ ∼ 280 K, estimated above B D checkerboard AF-C ordering, which is the lowest energy 150 K, using the calculated values of the T/Θ depen- D state (n.b. G-type ordering is the experimental ground dence of the Debye specific heat model. Thus our trans- state at least for the phosphide).16 Including contribu- port and specific heat measurements are consistent with tions from all atoms in the unit cell, the F ordered spin asmallbandgapsemiconductor. Theyarenotconsistent magnetization is 3.76 µ on a per Mn basis, reflecting B with either a large gap insulator (e.g. a Mott insulator) a small parallel contribution from the Sb. Significantly, or a metal with significant carrier density. this is considerably reduced from the nominal 5 µ ex- M pectedforhighspinMn2+. Thisreductionreflectsstrong hybridizationbetweenMn dandSb pstates inthis com- V. ELECTRONIC STRUCTURE AND pound. Ingeneral,verystronghybridizationisneededto MAGNETISM effectivelycompete againstthe verystrongHund’s interaction in the half-filled d shell of Mn2+ though we note We begin the discussion of the density functional in- thatstronghybridizationwaspreviouslyidentifiedinthe vestigation with a summary of our calculated results phosphides by Hoffmann and Zheng and by Gustenau for BaMn Sb , which as mentioned are similar to those and co-workers.31,32,33 Also, associated with the strong 2 2 obtained previously by Xia and co-workers,17 although hybridization we find a very large energy difference be- in general the LAPW method is more accurate than tweentheferromagneticandantiferromagneticorderings. the linear muffin tin orbital method employed in that This amountstomorethan0.29eV/Mninthe LDAand work. Calculations were performed for a checkerboard implies a very high magnetic ordering temperature well antiferromagnetic ordering (AF-C), which is the lowest above room temperature. This would be similar to the energy state, as well as a ferromagnetic ordering (F), phosphide,whichisreportedtohaveanorderingtemper- and zone boundary antiferromagnetic orders alternating ature above 750K.16 For comparison the corresponding chains of like spin Mn (as in the spin density wave state energyfor bcc Fe (Curie temperature, TC=1043K)is 0.4 ofBaFe As ),andanon-spin-polarized(NSP)case. The eV, with opposite (ferromagnetic) sign.34 2 2 two cells with chain ordering are denoted AF-S1, which In fact, strong, spin dependent hybridization is seen consistsofchainsstackedantiferromagneticallyalongthe in the electronic structure, represented by the electronic c-axis direction, and AF-S2, with ferromagnetic stack- density of states and projections (Fig. 3). As may be 4 notaslowcomparedwiththenon-spin-polarizedcase,as TABLE I: Magnetic energies in eV of BaMn2Sb2 and thoseintheantimonide. Thisreflectslowermomentsdue BaMn2As2 asobtainedwithintheLDAonaperformulaunit toevenstrongerhybridization. TheLDAtotalspinmag- (twoMn)basis. Thenon-spin-polarizedcase,denotedNSP,is netizationfortheForderingis2.9µ /Mn,i.e. ∼0.9µ setaszero. Fdenotesferromagneticorder,whileAF-Cisthe B B lowerthanintheantimonide. Themomentinsidethe2.1 checkerboard G-type antiferromagnetic ordering, and AF-S1 and AF-S2are stripe-like orders (see text). Bohr LAPW sphere is 3.20 µB for the AF ordering and 2.74 µ for the F ordering. Nonetheless, the ordering B BaMn2Sb2 BaMn2As2 energy remains very high, again reflecting strong spin- NSP 0 0 dependent hybridization. The energy difference between F -1.55 -0.66 the AF and F orderings is 0.33 eV / Mn in the LDA. AF-S1 -1.94 -1.03 The corresponding GGA value of 0.38 eV is similar, the AF-S2 -1.91 -1.01 main difference between the LDA and GGA results be- AF-C -2.14 -1.32 ing that the moment formation is stronger in the GGA, leading to moments in the LAPWspheres of 3.07 µ for B F ordering and 3.35 µ for AF ordering. Turning to the B AF-S1 and AF-S2 orders, the energies are slightly lower 15 total Mn d than the average of the F and AF-C states. A simple 10 nearestandnextnearestneighborsuperexchangepicture is probably an oversimplification for these narrow gap 5 semiconductors. However, the results indicate that the N(E) 0 nteeraarcetsitonnseiagnhdbotrhaintttehraecct-iaoxnisisindtoemrainctainotnoivsecrofnusritdheerrabinly- -5 weaker than the in-plane interaction and that it is antiferromagnetic. -10 The calculated LDA electronic density of states of BaMn As is shown in Fig. 4 for both F and AF order- -15 2 2 ings. The low energy AF state again has a small semi- -5 -4 -3 -2 -1 0 1 2 3 4 conducting gap of 0.1 eV in the LDA and 0.2 eV in our E (eV) GGA calculations. These low values are consistent with FIG. 3: (color online) Electronic DOS and projections onto the activationenergiesfromresistivitydata below 470K the LAPW spheres for antiferromagnetic BaMn2Sb2. The obtained by Wang and co-workers.2 Thus we interpret plot shows the total DOS above and below the axis, the Mn their low temperature value of ∼ 0.1 eV as the intrinsic majorityspinprojectionaboveandtheMnminorityspinpro- bulk gap for the AF orderedstate. Within this scenario, jection below. The remaining (non-Mn) contribution to the the larger activation gap at high T would be associated valence bandsis mainly from Sbp states. with Anderson localization arising from magnetic disor- der above the AF ordering temperature. Strong spin-dependent hybridization is seen, and in noted, the antiferromagnetic structure is found to be a particular there is even more minority spin Mn charac- smallband gapsemiconductor,E =0.21eVin the LDA. g termixedwiththepnictogenderivedvalencebandsthan The majority spin Mn d states overlap in energy with in the antimonide. This stronger hybridization is consis- the Sb p states and are strongly mixed with them. The tent with the general trend that As has a greater ten- minorityspinMndstatesareabovethe mainSbpDOS, dency towards bond formation with transition elements and are therefore less strongly mixed with the Sb states. than Sb and is reflected in the higher energy difference Nonetheless,thereissufficientminorityspinMnd-Sbp between the F and AF magnetic orderingsin BaMn As hybridizationtoleadtonoticeableMndcharacterinthe 2 2 than in BaMn Sb . We emphasize that this behavior is occupied valence band states. This is the main source of 2 2 very different from that found in BaFe As , BaCo As the momentreduction,correspondingto aMndelectron 2 2 2 2 count closer to Mn1+ than Mn2+. Finally we note that andBaNi2As2,whichhavesomed-phybridization,asin anoxide,butaremuchmoreionic.9,10,26 ThedistinctMn suchstrongspindependenthybridizationwhileleadingto - As bonding in this structure also explains why Mn is strong superexchange interactions is highly unfavorable for carriermobility in an antiferromagnet,35 since at low notaneffectivedopantforthe Fe-basedsuperconducting compounds, while Co and Ni are.36 T hopping between nearest neighbor sites with opposite spinwillbesuppressedandathigherT spindisorderwill lead to strong scattering. VI. THERMOPOWER We now discuss our experimental and calculated results for BaMn As . The calculated magnetic energies 2 2 (Table I) show strong local moment magnetism with a As noted, antiferromagnetism with strong spin de- largeexchange,similartoBaMn Sb ,withtheexception pendent hybridization is not favorable for high mobility 2 2 that the energies of the magnetically ordered states are conduction. Nonetheless, the chemical flexibility of the 5 15 total 300 Mn d 10 200 100 5 0 N(E) 0 µV/K) -100 S( -5 -200 n=0.030 n=0.020 n=0.010 -10 -300 n=0.005 p=0.005 -400 p=0.010 -15 p=0.020 p=0.030 -5 -4 -3 -2 -1 0 1 2 3 4 -500 100 150 200 250 300 350 400 E (eV) T(K) 15 total FIG. 6: (color online) LDA constant scattering time approx- Mn d imation c-axis Seebeck coefficient of AF ordered BaMn2As2. 10 The dopinglevels are in carriers per formula unit. 5 N(E) 0 ThCr2Si2 structuresuggeststhathighdoping levelsmay be achievable. In that case, if the thermopower remains -5 high, as in the oxide thermoelectric Na CoO , high ZT x 2 mayresultinspiteoflowmobility.37 Thereforewecalcu- -10 lated the Seebeck coefficients from the LDA band struc- -15 tureasafunctionofdopinglevelandtemperatureinthe -5 -4 -3 -2 -1 0 1 2 3 4 constant scattering time approximation. The results are E (eV) showninFigs. 5and6. Theanisotropiesaredifferentfor thevalenceandconductionbands. Inthebasalplane,the FIG. 4: (color online) Electronic DOS and projections onto hole doping yields higher S than electron doping, while theLAPW spheresfor ferromagnetic ordered (top) and anti- anoppositetrendisfoundintheconductionbands. This ferromagneticBaMn2As2 (bottom). Theplotsshowmajority difference is due to differentbandanisotropies. The con- spin above the axis and minority spin below. The remaining stant scattering time transport anisotropy σ /σ esti- (non-Mn) contribution to the valence bands is mainly from zz xx Asp states. mated from the band anisotropy is 1.9 for the valence bands (p-type doping) and 0.5 for the conduction bands (ntype). Thesemodestanisotropiesmeanthatthemate- rial is effectively a three dimensional intermetallic compound rather than a quasi-2D system. Turning to the values of S we observe that high values compatible with highZT areonlyfoundformodestdopinglevelsandnot 300 forhighmetallicdopinglevelssuchasthoseinNa CoO x 2 200 (0.01carriersperformulaunitis 8.6x1019 cm−3; the carrier concentration in thermoelectric Na CoO is more 100 x 2 than one order of magnitude higher).38 Considering the K) 0 likelihood of carrier localization in this magnetic mate- µV/ -100 rial, this would initially seem not favorable for applica- S( tion of BaMn As as a thermoelectric for waste heat re- -200 n=0.030 2 2 n=0.020 covery. n=0.010 -300 n=0.005 p=0.005 -400 p=0.010 p=0.020 p=0.030 -500 VII. SUMMARY AND CONCLUSIONS 100 150 200 250 300 350 400 T(K) To summarize, we characterize BaMn As and FIG. 5: (color online) LDA constant scattering time approx- 2 2 BaMn Sb as small band-gap, local moment antiferro- imation Seebeck coefficient in the basal plane of AF ordered 2 2 BaMn2As2. Thedopinglevelsareincarriersperformulaunit magnetic semiconductors. We find a very strong spin (2 Mn). dependent hyridization. This leads to high exchange energies, which are consistent with high magnetic ordering temperatures. The lowest energy state found is the G- 6 type checkerboardantiferromagneticstate for both com- Acknowledgments pounds. We note that the bonding, electronic structure and magnetic properties are very distinct from those of the correspondingFe,Co andNicompounds,whichmay explain why Mn leads to carrier localization rather than effective doping in BaFe As and related materials. We are gratefulfor helpful discussions with B.C. Sales 2 2 The strong spin dependent hybridization is not favor- and D. Mandrus. This work was supported by the De- ableforhighcarriermobility. 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