Semiconducting (Half-Metallic) Ferromagnetism in Mn(Fe) Substituted Pt and Pd Nitrides
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Semiconducting (Half-Metallic) Ferromagnetism in Mn(Fe) Substituted Pt and PdNitrides
Abdesalem Houari ∗ Laboratoire de Physique Th´eorique, D´epartement de Physique, Universit´e de B´ejaia, B´ejaia, Alg´erie
Samir F. Matar
CNRS, Universit´e de Bordeaux, ICMCB, 87 avenue du Docteur Albert Schweitzer, 33600 Pessac, France
Volker Eyert † Center for Electronic Correlations and Magnetism,Institut f¨ur Physik, Universit¨at Augsburg, 86135 Augsburg, Germany (Dated: July 11, 2018)Using first principles calculations as based on density functional theory, we propose a class of sofar unexplored diluted ferromagnetic semiconductors and half-metals. Here, we study the electronicproperties of recently synthesized 4 d and 5 d transition metal dinitrides. In particular, we addressMn- and Fe-substitution in PtN and PdN . Structural relaxation shows that the resulting orderedcompounds, Pt . (Mn,Fe) . N and Pd . (Mn,Fe) . N , maintain the cubic crystal symmetryof the parent compounds. On substitution, all compounds exhibit long-range ferromagnetic order.While both Pt . Mn . N and Pd . Mn . N are semiconducting, Fe-substitution causes half-metallic behavior for both parent materials. PACS numbers: 71.15.Mb, 71.15.Nc, 71.20-b, 75.10.Lp, 74.25.Ha, 73.43.CdKeywords:
Being known since the beginning of the 20th century,transition metal nitrides are considered as an excitingclass of materials due to a wide range of technologi-cal applications. Traditionally, the great advantages ofthese compounds concern their hardness and refractorynature . However, much attention is currently directedtowards their electronic, magnetic, and optical proper-ties, where fascinating applications are expected. Manyefforts, experimental as well as theoretical, have beenmade to study the transition metal nitrides . Untilrecently none of the noble metal nitrides or the platinumgroup nitrides were known. The first synthesis of plat-inum nitride (Pt-N), under extreme conditions of pres-sure and temperature, was reported only few years ago .Lateron, several other nitrides of different elements (Ir,Os, Ru and Pd) were also obtained .There was a debate about the crystal structure and thestoichiometry of platinum nitride. While a zinc-blendestructure was first proposed, Crowhurst et al. demon-strated that this nitride crystallizes neither in zinc-blende(PtN: mononitride) nor in fluorite (PtN : dinitride) typestructures, which are highly unstable at the synthesisconditions ( P = 50 GPa and T = 2000 K) . Instead, theauthors revealed that the coumpound is a dinitride, hencePtN , and the ground state structure is a cubic pyritestructure. Lateron, these authors succeeded in synthe-sizing IrN and PdN , where the first one is found tobe in the monoclinic baddeleyite structure . Yet, PdN ,which could by synthesized at high pressures but wasnot stable at ambient conditions, was proposed to alsocrystallize in the pyrite structure. In a recent theoreti-cal investigation it was shown that tetragonal distortionsmay stabilize PdN at ambient pressure . Other nitrides (OsN , RuN and RhN ) have been also obtained and areshown to crystallize in marcasite type structure .Platinum dinitride has been predicted to have excellentmechanical properties. The calculated hardness (bulkmodulus, shear modulus and other elastic constants)shows that it is harder than many known hard mate-rials like TiN and SiC . The electronic properties ofPtN are also very interesting. Contrary to other transi-tion metal nitrides, which are almost all metallic, PtN is found to be semiconducting, and this could make it animportant material for optoelectronic applications. Bandstructure calculations as based on density functional the-ory and the local density approximation (LDA) show anindirect band gap of ∼ .In general, pyrite-type compounds have attracted at-tention since long. The dinitrides AN (A=C,Si,Ge)were devised in assumed pyrite-type structures leadingto compounds with peculiar properties, such as the ex-treme hardness obtained for CN with a bulk modulusof 405 GPa. For these systems characterized as wideband gap semiconductors, strong hybridization of theN 2 p states with the A p states results in a depressionof the optical band gap along the C, Si, Ge series .Pyrite-type disulfides have also been of considerable in-terest for different reasons . Semiconducting FeS hasfound widespread attention for its application in photo-voltaic energy conversion . ZnS is a diamagnetic insu-lator. Substitution of Zn for Fe in iron pyrite has thusbeen used to tune the optical band gap in order to en-hance the response to the solar spectrum . While FeS is a van Vleck paramagnet, metallic CoS displays long-range ferromagnetic order. In contrast, NiS is an anti-ferromagnetic insulator, where the insulating behaviourhas been attributed to the presence of strong electroniccorrelations.Our present work is focused especially on the electronicand magnetic properties of substituted PtN and PdN .We demonstrate that substitution of the non-magnetic4 d - and 5 d -transition metal ions by the magnetic 3 d -ionsMn and Fe may lead to semiconducting and half-metallicferromagnetism, respectively.In our investigation, we first consider Mn-substitutionin PtN and PdN . For the latter compound, we as-sumed a cubic pyrite crystal structure as for PtN . Thisassumption is based on the fact that experimentallyPdN is actually synthesized in cubic pyrite structureat high pressure conditions, even though it is not sta-ble at ambient pressure . Replacing one of the fourPt and Pd by magnetic Mn leads to Pt . Mn . N and Pd . Mn . N , respectively. To check if the cu-bic symmetry is maintained on Mn-substitution, a quan-tum molecular dynamics relaxation has been performedusing the Siesta ab initio simulation package with norm-conserving pseudopotentials . Both atomic positionsand cell shape were included in the relaxation process. Asa result, neither Pt . Mn . N nor Pd . Mn . N dis-play any deviations from cubic symmetry and the atomsremain nearly at the positions of the pure compound.In particular, the internal nitrogen parameters are al-most unchanged after Mn-substitution in both PtN andPdN . The changes in the nitrogen positions are within0.07 ˚A. To be specific, in PtN the internal nitrogen pa-rameter changes from 0.415 (as given in Ref. 8) to 0.416after the relaxation of the substituted system.In a second step, full potential augmented sphericalwave (FPASW) calculations were carried out in orderto address the electronic properties of all compounds un-der study. To start with, we recalculated the equilibriumlattice constant. From non-spin polarized LDA calcula-tions, we obtained a lattice parameter of a NM = 4 .
79 ˚Afor Pt . Mn . N . Taking into account spin polariza-tion led to a slightly larger value of a F M = 4 .
82 ˚A, withthe ferromagnetic state being more stable than the non-magnetic one. It is important to note that the valuesobtained for the lattice constant of Pt . Mn . N re-semble that of PtN , which is a = 4 .
80 ˚A, and confirmthe molecular dynamics result. To conclude from bothsets of calculations, not only the cubic symmetry is pre-served after Mn-substitution, but even the lattice con-stant is almost not affected. The negligible changes ofthe structure can be understood from the fact that onlyone out of four Pt atoms is replaced and thus the plat-inum network is affected by the substitution only to asmall degree. Motivated by these findings, we decidedto perform the calculations for Pd . Mn . N using thesame lattice constant as for PdN , i.e. a = 4 .
75 ˚A (seealso the discussion below).Subsequently, the electronic structures of the Mn-substituted compounds were analyzed in terms of the projected densities of states as arising from the FPASWcalculations. However, for the Mn-substituted systemsthe LDA results bear some ambiguity. To be specific,we obtain semiconducting behavior for Pd . Mn . N ,whereas Pt . Mn . N is at the verge of being a semi-conductor but displays a small band overlap. In order tocheck these findings, we additionally performed a set ofcalculations based on the GGA . They resulted in semi-conducting ferromagnetic ground states for both com-pounds with indirect band gaps of 0.17 eV and 0.42 eV forPt . Mn . N and Pd . Mn . N , respectively. Thecorresponding partial densities of states (DOS) are illus-trated in Figs. 1 and 2. The spectrum falls essentially -8-6-4-2 0 2 4-10 -8 -6 -4 -2 0 2 4 6 DO S ( / e V ) (E - E V ) (eV)Mn-3d-t Mn-3d-e g Pt-5dN
FIG. 1: (Color online) Partial DOS of Pt . Mn . N . Hereand in all subsequent figures, t g and e g orbitals are referred toa rotated coordinate system with the Cartesian axes pointingalong the metal-nitrogen bonds. -5-4-3-2-1 0 1 2 3-10 -8 -6 -4 -2 0 2 4 6 DO S ( / e V ) (E - E V ) (eV)Mn-3d-t2gMn-3d-egPd-4dN FIG. 2: (Color online) Partial DOS of Pd . Mn . N . in four parts. While the low-energy range from − − − − . Mn . N andPd . Mn . N , respectively, is dominated by the N 2 p states, the upper valence band is formed mainly by the t g manifolds of the transition metal d states. For thespin-minority bands, the situation is slightly more com-plicated. Whereas the Pd 4 d and Pt 5 d states are fully oc-cupied and found in the same energy range as their spin-majority counterparts, the Mn 3 d t g states experiencestrong exchange splitting. As a result, the Mn 3 d t g spin-down states form the lower conduction band of this spinchannel and a magnetic moment of 3 µ B is found at theseatoms. In contrast, spin polarizations of Pd, Pt, and Nare negligible. Finally, the remaining conduction bandstates can be attributed to the transition metal d statesof e g symmetry. Since the latter form σ -type bonds withthe N 2 p states, we find a considerable admixture of bothtypes of states in the lower valence and upper conduc-tion band. This admixture is much smaller for the bandsbetween − − t g symmetry and form less strong π bonds.In passing we mention the albeit small band gaps, whichmake both Mn-substituted compounds semiconducting.Yet, we note that LDA and GGA underestimate the opti-cal band gap, which might thus be considerably larger inreality. In order to check this, we performed additionalGGA+ U calculations for Pt . Mn . N . While therewere no qualitative changes, both the exchange splittingof the Mn 3 d t g states and the optical band gap increasedconsiderably.The second substitution that we considered was thereplacement of Pt and Pd by iron, leading to the orderedcompounds Pt . Fe . N and Pd . Fe . N . Our pro-cedure was the same as for Mn-substitution. Molecu-lar dynamics relaxations using the Siesta code (with thesame calculations details cited above)w were performedincluding relaxation of both the atomic positions and thecell shape. As in the Mn-case we found that the cubicsymmetry is not broken on Fe-substitution and that eventhe internal nitrogen parameter remained essentially un-changed.For the FPASW calculations performed in a secondstep in order to address the electronic and magnetic prop-erties, we followed the procedure already adopted forPdN and used the lattice constants of the pure systemsalso for the substituted materials. In this case, our pro-cedure was justified by an additional recalculation of theequilibrium lattice constant for Pd . Fe . N . As a re-sult, values of a NM = 4 .
742 ˚A and a F M = 4 .
749 ˚A wereobtained as arising from non-spin polarized and spin po-larized calculations, respectively. The latter value is al-most identical to the value of a = 4 .
75 ˚A of pure PdN .Again, the LDA results bear some ambiguity as theyled to half-metallic behavior for Pd . Fe . N butmetallicity of both spin channels for Pt . Fe . N . Yet,the spin-majority density of states at the Fermi energywas found to be very small. The problem could again beresolved by GGA calculations, which render both substi-tuted materials half-metallic. Both compounds exhibitstable magnetic order with magnetic moments of 2.0 µ B located almost completely at the iron atoms.The electronic structure and partial DOS of the twocompounds as arising from the spin-polarized ferromag- netic calculations are illustrated in Figs. 3 and 4. The -8-6-4-2 0 2 4 6-10 -8 -6 -4 -2 0 2 4 6 DO S ( / e V ) (E - E F ) (eV)Fe-3d-t Fe-3d-e g Pt-5dN
FIG. 3: (Color online) Partial DOS of Pt . Fe . N . -6-4-2 0 2 4-10 -8 -6 -4 -2 0 2 4 6 DO S ( / e V ) (E - E F ) (eV)Fe-3d-t Fe-3d-e g Pd-4dN
FIG. 4: (Color online) Partial DOS of Pd . Fe . N . gross features of the partial densities of states are thesame as for the Mn-substituted compounds. Differencesare due to the smaller magnetic moments of the Fe atoms,which lead to reduced exchange splittings of the 3 d t g states. As a consequence, the respective spin-majoritybands are shifted to higher energies as compared to the d states of the Pt and Pd matrix. In addition, the Fespin-minority bands are shifted to lower energies as com-pared to the Mn-systems due to the increased electroncount. As a result, the semiconducting behavior is lostand a metallic spin-down channel found. Again, these re-sults were qualitatively confirmed by additional GGA+ U calculations, which revealed an increase of the exchangesplitting of the Fe 3 d t g states as well as the band gapof the spin-majority channel.In passing, we mention additional spin polarized calcu-lations, which were performed Pt . Mn . N in order tocheck for long range antiferromagnetic order. For thesecalculations, we used a tetragonal structure arising fromdoubling the cubic cell along the c axis. As a result,an antiferromagnetic and again semiconducting solutionwas found albeit with a total energy, which by about 7mRy/f.u. higher than that of the ferromagnetic groundstate.In summary, based on our first principles investigationwe propose the existence of so far unexplored diluted fer-romagnetic semiconductors and half-metals. These ma-terials arise from substituting magnetic 3 d ions (Mn, Fe)in the non-magnetic dinitrides PtN and PdN . Accord-ing to molecular dynamics calculations, the ordered com-pounds A . B . N , where A = Pt , Pd and B = Mn , Fe,preserve the cubic pyrite structure of their parent com-pounds. On substitution, stable long-range ferromag- netic order results with magnetic moments of 3 µ B and2 µ B , which are well localized at the Mn- and Fe-sites, re-spectievly. While Mn-substitution leads to semiconduct-ing behavior, introduction of iron causes the substitutedcompounds to be half-metallic. Our results still awaitexperimental confirmation. Acknowledgments
This work was supported by the Deutsche Forschungs-gemeinschaft through TRR 80. ∗ Corresponding authors:[email protected] † [email protected] S. T. Oyama,
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