Spin injection efficiency based on conventional ferromagnet (or half-metallic ferromagnet). /semiconductor is greatly .... re plotted wit f the spin gap f our calculat.
Spin injection based on the spin gapless semiconductor(SGS)/semiconductor heterostructures G. Z. Xu, W. H. Wanga), X. M. Zhang, Y. Wang, E. K. Liu, X. K. Xi, and G. H. Wu State Key Laboratory for Magnetism, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Spin injection efficiency based on conventional ferromagnet (or half-metallic ferromagnet) /semiconductor is greatly limited by the Schmidt obstacle1 due to conductivity mismatch, here we proposed that by replacing the metallic injectors with spin gapless semiconductors can significantly reduce the conductive mismatch while conserve high spin polarization. By performing first principles calculations based on superlattice structure, we have studied the representative system of Mn2CoAl/semiconductor spin injector scheme. The results showed that high spin polarization were maintained at the interface in systems of Mn2CoAl/Fe2VAl constructed with (100) interface and Mn2CoAl/GaAs with (110) interface, and the latter is expected to possess long spin diffusion length. Inherited from the spin gapless feature of Mn2CoAl, a pronounced dip was observed around the Fermi level in the majority-spin DOS in both systems, suggesting fast transport of the low-density carriers.
Introduction.―The rapid development of spintronics requires large sources of spin-polarized charge carriers, turning spin injection into a field of growing interest in recent decades. Conventionally, the spin injection utilized the ferromagnet/semiconductor (SC) interface2, for which the injection efficiency was greatly limited due to the conductivity mismatch (theoretically modeled by Schmidt et al1) and low spin polarization degree of the magnetic source. Subsequently, with the emerging of half-metallic ferromagnets (HMF) that possess nearly 100% spin polarization, the HMF/SC heterostructures were proposed for enhancing the spin injection efficiency3, 4. Nevertheless, the conductivity mismatch between the metal and semiconductor still exists. The tunnel contacts were raised as one way to circumvent this obstacle5, 6. Usually with an oxide layer between the metal and semiconductor to form tunneling barriers, such as FM/MgO/SC heterostrucutre7, the fabrication process became more stringent and complicated. On the other hand, magnetic semiconductors were also tried to realize high spin polarization injection8, 9 , but they are restricted to low temperatures and sometimes need large field bias. Here we proposed another spin injector scheme that not only keep a high spin polarization of the injection source like HMF, but also can effectively overcome the conductivity mismatch. The scheme we considered is the spin gapless semiconductors (SGS), a kind of gapless semiconductor accompanying with fully spin polarized charge carriers10 (see in Fig.1 for the band schetch of SGS comparing with a normal semiconductor). In addition, the Heusler type SGS we mentioned in the following possess the advantage of high Curie temperature and compatibility to the industrial semiconductor from both structure and lattice constant. Heusler alloy Mn2CoAl has been predicted to be a spin gapless semiconductor both theoretically and experimentally11. The reported data for the conductivity of Mn2CoAl is in the order of 103 S cm-1, about two orders lower than the traditional HMF (for example, Co2MnSi12 is ~105 S cm-1). Considering that the electronic states of SGS are extremely sensitive to the atomic order, we evaluated the conductivity of fully ordered Mn2CoAl by employing BoltzTraP code13 based on semiclassical Boltzmann transport theory. The calculated room temperature conductivity (with respect to a constant relaxation time) for the three typical systems of Co2MnSi, Mn2CoAl and GaAs were presented in the right panel of Fig.1. It can be seen that the conductivity of perfect Mn2CoAl is much lower (nearly ten times) than that of Co2MnSi, while very close to that of GaAs. The small conductivity mismatch between SGS and SC is promising to enhance the degree of spin polarization in SC region according to the Schmidt model1. As done in most systems of HMF/SC, the interface spin polarization can be evaluated by building heterostructure model using first principles method3,
14
. In the present letter we
investigated the layer-by-layer electronic structure of SGS/SC (SGS=Mn2CoAl, SC=Fe2VAl, GaAs) heterostructures. We found that high spin polarization can be preserved for certain interface configurations.
Fig. 1 (color onliine) Left: DO OS scheme of the spin gap pless semiconductor (up) and conventtional semiiconductor (ddown). Middlle: a sketch of our calculattion model off SGS/SC hetterostruture. Right: R the calculated c rooom temperatture conductiivity with respect to a coonstant relaxaation time () for
Co2MnSi, M Mn2CooAl and GaA As, plotted as a function off chemical pootential. The ggreen bar cen ntered on thhe Fermi leveel marks regim me without doping. d
Calculationn details.―T The first-princciple calculattions were peerformed withhin the framew work of deensity functioonal theory by pseudopoteential method d implemented in the CAS STEP packagee 15,16. The exchange correlation enerrgy were treaated under thee generalized gradient approximation (G GGA) 17
. Theoretically, T the spin injeected system can be simu ulated with suuperlattice strructure as lon ng as
the constitute layyers are thickker enough to t restore thee bulk propeerties in the ccenter part of o the p studyy, we investiigated the heterostructur h re propertiess by constru ucting slabs4. In the present supeercells contaaining severaal unit cells of the con nstituent matterial. Two typical kind ds of semiiconductor suubstrates werre chosen: onne is the non--magnetic Heeusler alloy F Fe2VAl, which h has expeerimentally been proved to exhibit sem miconductor-llike propertiees18; the otherr is the stereo otype semiiconductor of o GaAs. In I Fig. 2, the Mn2CoAl/Fe2VAl constructed c with (100) and Mn2CoAl/GaAs with w (110) innterface were presented sep parately. Thee in-plane latttice parameters (a, b) of o the superccells were determined d too be in acco ordance withh the bulk substrate, and d the paraameter c alonng the stackiing direction was manually optimizedd. Based on the experim mental valuue of aFe2VAl = 5.76Å and a aGaAs = 5.65Å, the lattice consttant set for the superceell is
a = b = a Fe2 VAl / 2 for the (1100) geometryy, and a = a GaAs , b = a GaAss / 2 for thhe (110) geom metry. G The lattice mism match betweenn Mn2CoAl (a=5.8Å) ( and d these two substrates s aree 0.7% and 2.7%, 2 respectively. For all cases we apply a planne-wave basiss set cut-off energy e of 500 eV for ensu uring ( goodd convergencce and a mesh of 12×12×4 k-points for (100) intterface and 112×8×4 for (110) interrface. All DO OS curves werre plotted witth a smearing g width of 0.005eV.
Fig.22 (color online) The supeerlattice prim mitive cells of [Mn2CoAl//Fe2VAl]2 witth (100) inteerface (leftt) and [Mn2CoAl/GaAs]4 with w (110) innterface (rightt) for the firsst principles ccalculations. Both of thhem contain eight atomicc layers. The crystal latticce of Mn2CoA Al and GaAss are given in n the midddle panel for better undersstanding of thhe stacking paattern. Mn2CoAl/Fee2VAl heterosstructures.― ―As seen in Fig.2, Mn2CoAl/Fe C ctures 2VAll heterostruc consstructed alonng [001] direection consistt of alternatee Co-Mn, Mn-Al M and Fe-Fe,V-Al attomic layers. The inteerfacial layerrs that combbine the two o compoundss can be eitther Co-Mn//V-Al (Mnn-Al/Fe-Fe, thhe other side)) or Co-Mn/F Fe-Fe (Mn-A Al/V-Al, the other o side). W We calculated both of thhem and founnd that the suuperlattice witth Co-Mn/Fee-Fe (Mn-Al/V V-Al) interface exhibit no o spin polaarization at alll. As also discussed in reef [4], the fin nal spin polarrization of the heterostrucctures can be simply anticipated a byy examiningg the junction n componentts. The so-caalled constru uctive juncction layers are a usually thhose being seemiconductin ng or ferromaagnetic phasee that bridge their bulkk neighbors, like Co-Mn//V-Al (Mn-A Al/Fe-Fe) heree. Therefore,, we studiedd in detail fo or the supeerlattices of [M Mn2CoAl/Fe2VAl]4 with Co-Mn/V-Al C (Mn-Al/Fe-F Fe) interface. As shown in n Fig. 3 for the [100] projected p lattiice, this struccture includess 32 nonequiivalent atomss distributed in i 16 atom mic planes. The T layer-ressolved magnnetic momentt and local spin polarizaation (defineed as P
N (EF ) N (EF ) N ( EF ) N ( EF )
, N(EF) is thhe density of states at the Fermi level) were both prresented. It caan be
seenn that in the middle m of eachh slab, the buulk moment was w well reprroduced, withh the total mo oment
to bee 8.09B, devviating little from the bullk values of Mn M 2CoAl (2 B 4). Whenn approaching the interrface (in the middle m and boundary b of the t figure), th he moment off the magnetiic layer decreeased and small moment was inducced in the sem miconductor layer. Corresspondingly, tthe degree off spin polaarization in Mn M 2CoAl sidee maintained high, but drropped quicklly in the sem miconductor layer, l impllying a short spin diffusionn length in thhis heterostruccture. n of the DOS S within separrate layers arround The right paanel of Fig. 3 shows detaiiled evolution the interface. In the minorityy spin, a largge gap was observed forr all layers. T The overall DOS g weak interfface scatterinng in this sysstem, patteern varied noot much withh layer changge indicating whicch may attriibuted to thhe high struccture similarrities. Still, comparing tthe same attomic
com mposited layerr, for examplle 7th and 9tth ones (both h Co-Mn layyer), the DOS S of the 9th layer reveealed less proonounced excchange splittinng due to interface bondinng states. The spin splittin ng of the semiconductting layer (10th to 13th)) reduced wiith increasedd distance froom the interrface, indiccating by the symmetry chhange of the spin-resolved d DOS. Notabbly, the Ferm mi level locatee near to a valley in the majority spinn, inherited from f the gaplless feature off SGS (DOS scheme in Fiig.1), makking it advantageous with lower carrierr densities com mparing to thhe traditional metallic injeection sourrce.
Fig.33 (color onlinne) Left paneel: the structuure of [Mn2CoAl/Fe C e projected in n one 2VAl]]4 superlattice [1000] direction annd the corressponding layeer-resolved magnetic m mom ment and spinn polarization. The dotteed line markks the junctioon position off the two com mpound layeers. Right pannel: spin reso olved DOS S of different layers arounnd the interfacce. The numb ber correspondds to the left indicated onees. s thee heterostructuure constructted in Mn2CoAl/GaaAs heterostrructures.―Foor the GaAs substrate, [0011] direction lost l its polarrization at thhe interface according too our calculaation. Studiees on Mn2CoAl (001)) surface reevealed that while Mn n-Al terminaated surface maintained d the half--metallicity of o the bulk, Co-Mn termination destroy yed it19. In conntact with Gaa or As in ourr case, Mn--Al also lost its high spin polarization,, with overall moment alm most vanished. For the (110) ( interrface, as seenn in Fig. 4 ([110] projectionn of the latticce), each (1100) plane contaains a full forrmula unit of the cubic phase, so theey are expectted to restore the propertiees of the bulkk form. Consiistent withh our result, high spin poolarization haas been reporrted in other (110) conneected full Heeusler alloyy and GaAs systems14, 200. There are also two kin nds of atom-cconnected w ways for the (110) ( interrface, which can be denooted as Co-Ga (Al-As) or Co-As (Al-G Ga) considerring their bon nding ways. As the atom mic magneticc moments off the latter deecreased much in the interrface, we focu us on the former f condittion in the succceeding disccussion. The magneetic moment and spin poolarization with w respect to t different [[Mn2CoAl/GaaAs]4 plannes were giveen in Fig. 4 inn the same manner m with Mn M 2CoAl/Fe2VAl. V In the M Mn2CoAl sidee, the mom ment of eachh layer remaained almostt unchanged with the buulk value off 2B, whilee the
correesponding sppin polarizatioon was largelly reduced co omparing witth the bulk off 100%. From m the DOS S of the 3rd and a 4th layerr, small statess emerged in the minorityy spin when ggetting near to t the bounndary, since the t majority DOS D is also very v small, th he spin polariization can bee easily destrroyed due to the comppensation of the states att Fermi levell. Prominentlly, high spin polarization n was w is mosst desirable iin designing spin obseerved for all layers in thhe semiconduucting side, which injecctor system. The DOS off the 5th andd 6th still preesent strong exchange spplitting, indiccating probbable long sppin diffusion length l in thiss system. Lik ke in the casee of Fe2VAl, a pronounced d dip was also found inn the majorityy-spin DOS, suggesting lo ow carrier cooncentration tthat may faciilitate fast transport of electrons. e
Fig.44 (color online) The description d iss the same to Fig.3 exxcept that thhe lattice iss for [Mnn2CoAl/GaAs]4 projected inn [110] directtion. Prospect.―To realize the applicationn of the abovee scheme, thee first step is to fabricate good ordeered SGS film ms. Recentlyy, Mn2CoAl films orienteed in (100) direction d werre deposited on a silicon and GaA As substrate, both exhibbiting ferrom magnetism and a semicondducting tran nsport propperties21, 22. Future F work will concenntrate on enh hancing the structure s ordering and fu urther conttrolling the fiilm growth diirection and terminated t laayers, which greatly g affectt the injected d spin polaarization degrree according to above disccussions. Summary.― ―Using first-pprinciples dennsity functional calculatioons, we havee investigated d the spinn injection in two represeentative systeem of Mn2Co oAl/SC (SC= =Fe2VAl, GaA As), based on n the assuumption that SGS/SC cann reasonably enhance the spin injectioon efficiencyy by reducing g the condductivity mismatch. Thee computed results sho owed that systems s of Mn2CoAl/Fee2VAl consstructed withh (100) interrface and Mn M 2CoAl/GaA As with (1100) interface w were favored d for mainntaining highh spin polarizzation. Particuularly, in Mn n2CoAl/GaAs system, a hiigh degree off spin polaarization was achieved in the semiconnducting region, implyingg a long spinn diffusion length. Prom minently, in both b systems, the layeredd DOS reveall the spin gappless feature with a dip in n the majoority spin, whhich means thhat the transpport carriers should s be relaatively low. T This may givee rise
to higher mobility of the carriers comparing to traditional metallic injection system.
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