Substrate-induced antiferromagnetism of an Fe monolayer on the Ir(001) surface
Josef Kudrnovsky, Frantisek Maca, Ilja Turek, Josef Redinger
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J u l Substrate-induced antiferromagnetism of an Fe monolayer on the Ir(001) surface
Josef Kudrnovsk´y , , ∗ Frantiˇsek M´aca , , Ilja Turek , and Josef Redinger Institute of Physics ASCR, Na Slovance 2, CZ-182 21 Praha 8, Czech Republic Max-Planck Institut f¨ur Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany Institute of Physics of Materials ASCR, ˇZiˇzkova 22, CZ-616 62 Brno, Czech Republic Department of General Physics, Vienna University of Technology, Getreidemarkt 9/134, 1060 Vienna, Austria
We present detailed ab initio study of structural and magnetic stability of a Fe-monolayer on thefcc(001) surface of iridium. The Fe-monolayer has a strong tendency to order antiferromagneticallyfor the true relaxed geometry. On the contrary an unrelaxed Fe/Ir(001) sample has a ferromagneticground state. The antiferromagnetism is thus stabilized by the decreased Fe-Ir layer spacing instriking contrast to the recently experimentally observed antiferromagnetism of the Fe/W(001)system which exists also for an ideal bulk-truncated, unrelaxed geometry. The calculated layerrelaxations for Fe/Ir(001) agree reasonably well with recent experimental LEED data. The presentstudy centers around the evaluation of pair exchange interactions between Fe-atoms in the Fe-overlayer as a function of the Fe/Ir interlayer distance which allows for a detailed understanding ofthe antiferromagnetism of a Fe/Ir(001) overlayer. Furthermore, our calculations indicate that thenature of the true ground state could be more complex and display a spin spiral-like rather than ac(2 × PACS numbers: 75.30.-m,81.20.-nKeywords: surface magnetism, iron, iridium, density functional calculation
I. INTRODUCTION
Magnetic overlayers, i.e., the thin films of magneticmaterials on the nonmagnetic substrate are systemswith great technological potential. Magnetic overlay-ers are also a convenient system for a deeper under-standing of the origin of magnetism in the solid state.The prototypical system is a magnetic monolayer (ML)on a non-magnetic substrate which was the subjectof many theoretical and experimental studies in thepast . Yet, a technological prepara-tion, experimental study and detailed theoretical under-standing of the overlayer magnetism is still a challengeto solid state physics.There are a few important features which distinguishmagnetic overlayers from conventional magnetic materi-als. This is, first of all, the presence of an external agent,namely the presence of a non-magnetic substrate, whichcan strongly modify the magnetic state and propertiesof the overlayer system: (i) The reduced coordination onthe surface induces geometry as well as chemical bindingchanges. (ii) Magnetic atoms adapt to the underlyinglateral substrate lattice spacings, particularly true for amonolayer case. (iii) The substrate electronic structure,in particular the position of the substrate Fermi level isrelevant for overlayer magnetism. (iv) The position ofFermi level can be tuned by the substrate electron con-centration, e.g. by growing the overlayer on an alloysubstrate with varying concentration of the constituents.Alternatively, one could consider a substrate alloy whichcontains magnetic and non-magnetic species or only mag-netic species, and/or a partial coverage of the substrateto vary the properties of the magnetic overlayer. Theo-retical and experimental studies on the above trends help to establish a deeper understanding of the origin of sur-face magnetism.First-principles calculations represent a powerful toolfor such studies, as they allow to determine reliably theunderlying lattice structure (possible layer relaxations,surface reconstructions, etc.) which can be directly com-pared with experiment (LEED). They also allow to findout the underlying magnetic structure although in thisrespect the situation is much more complex. In addi-tion to collinear magnetic configurations (ferromagnetic(FM) and antiferromagnetic (AFM) ones) more complexconfigurations may exist (e.g. recently observed chi-ral structures in bcc-Fe/W(001) , magnetism of randomoverlayers , etc.). Consequently, an estimation and dis-cussion of exchange interactions is very useful to gain adeeper understanding of properties of both overlayer andbulk magnets and magnetic alloys, including the dilutedmagnetic semiconductors . Surprisingly and in con-trast to bulk systems, studies of exchange interactions formagnetic overlayers are still very rare despite of theirobvious importance. In particular, the distance depen-dence of exchange integrals can be very different fromthat in the bulk if, for example, adatoms can interact viathe host surface state as e.g. Co-adatoms on the fcc(111)faces on noble metals .Great emphasis, both theoretical and experimental,has been put recently on the study of the magnetic prop-erties of Fe-overlayers on the (001) and (110) faces ofbcc tungsten. An unusual AFM state was predictedtheoretically and confirmed experimentally for the bcc-Fe/W(001) system (in fact, the true ground state seemsto be a more complex one exhibiting a chiral state ).There is also evidence from theory that the ground stateof the Co/W(001) overlayer is AFM, whereas Mn and Croverlayers have a FM ground state . This means that a(Fe,Mn)-alloy overlayer on the bcc-W(001) should exhibita crossover from an AFM to a FM ground state . Fi-nally, a similar AFM- to FM-crossover was predicted forthe bcc-Fe/(Ta,W)(001) alloy substrate system , wherethe ground state of the bcc-Fe/Ta(001) is FM. However,only the leading exchange integrals were estimated in thelatter case .The (001)-faces of the fcc- and bcc-substrates exhibit asimple rectangular array of lattice sites and differ essen-tially by the d : a L -ratio, where a L is the lateral latticeconstant and d is the interlayer distance. Therefore aninvestigation of the magnetic properties of Fe-overlayerson the (001) faces of fcc transition metals poses an in-teresting problem. A particularly suitable system is thefcc-Fe/Ir(001) where very thin overlayers were grown suc-cessfully with negligible Fe-Ir intermixing . Further-more, there exist reliable LEED measurements eluci-dating the detailed geometry, while preliminary MOKE-studies indicate no magnetic signal in the limit ofa monolayer coverage; a situation similar to the bcc-Fe/W(001).The clean Ir(001) surface undergoes the (5 ×
1) quasi-hexagonal reconstruction. The finite Fe-coverage (largerthan 0.25 monolayer) lifts the reconstruction . In orderto avoid possible corrugation and Fe-Ir intermixing themetastable unreconstructed (1 × and VASP codes. In the next step we investigate themagnetic structure of the geometrically relaxed systemby comparing total energies of the non-magnetic (NM),FM-, and AFM-configurations ( c (2 × A strong indicator for a more com-plex magnetic state of the system under consideration isa lower total energy of the DLM state as compared to theNM and FM states. One should note, however, that ifsome specific magnetic state is the ground state, e.g., the c (2 × or in (Cu,Ni)MnSbHeusler alloys . The usefulness of the DLM concept wasdemonstrated recently for both overlayer studies anddisordered magnetic semiconductors . The DLM pic-ture may be straightforwardly implemented in the frame- work of the coherent-potential approximation (CPA) .Therefore in a third step, we perform studies based onthe Green function implementation of the TB-LMTO-CPA method in the framework of the surface Greenfunction (SGF) approach, in addition to the above men-tioned collinear WIEN2k and VASP calculations. TheTB-LMTO-SGF approach employs a realistic semiinfi-nite sample geometry (no slabs or periodic supercells)and allows to implement the DLM model. The one-electron potentials are treated within the atomic sphereapproximation (ASA); the dipole barrier due to the sam-ple electrons in the vacuum is included in the formal-ism. TB-LMTO-SGF even allows to include the effectof layer relaxations , provided, they are known eitherfrom full-potential calculations or from experiment. Animportant advantage of the TB-LMTO-SGF approach isthe possibility to estimate exchange interactions betweenmagnetic atoms in the overlayer by a straightforward gen-eralization of the well-approved bulk concept . Sum-marizing, the TB-LMTO-SGF approach is a very usefultool for a qualitative understanding of the results whilethe full-potential approaches are superior concerning thequantitative values and thus provide so to say the corner-stones. We will demonstrate that at least in the presentcase the results of both types of calculations are in a goodquantitative agreement which justifies our assumptionsand reinforces our conclusions. II. COMPUTATIONAL DETAILS
First principle density functional theory calculationswere performed using both the all-electron full poten-tial linearized augmented plane wave (FP LAPW) codeWIEN2k and the Vienna ab initio simulation packageVASP , using the projector augmented wave scheme .In the FP LAPW calculations the Fe/Ir(001) systemswere modeled by the eleven-layer repeated slab with ≈
10 ˚A vacuum in between. All slabs were symmetric withrespect to the middle layer. We allowed the relaxationsfor top three layers, the remaining interlayer distanceswere fixed to the bulk values of 1.92 ˚A. For VASP re-peated asymmetric slabs with seven layers Ir and a singleFe mono-layer on one side and also symmetric slabs witheleven substrate layers and Fe mono-layers on both sideswere used, which were separated by at least 19 ˚A vacuum.All layer distances have been relaxed, and turned out tobe essentially the same for both setups. Two DFT poten-tial approximations have been employed: the local den-sity approximation (LDA) and the generalized gradientapproximation (GGA) for WIEN2k; the GGA accord-ing to Perdew and Wang (PW91) as well as the LDA asgiven by Perdew-Zunger (Ceperly-Alder) for VASP.We have tested NM-, FM-, and c (2 × c (2 × − . The to-tal force on single atoms was in every case smaller than1mRy/bohr.In all TB-LMTO-SGF calculations the LDA approxi-mation and experimental layer relaxations were used.The vacuum above the overlayer was simulated as usualby empty spheres (ES). Electronic relaxations were al-lowed in four empty spheres adjoining the overlayer, theoverlayer itself, and in five adjoining Ir substrate layers.This finite system was sandwiched selfconsistently be-tween an frozen semiinfinite fcc-Ir(001) bulk and the ESvacuum-space including the dipole surface barrier. Ad-ditionally to NM-, FM- and c (2 × J Fe , Fe i,j between sites i, j in the mag-netic overlayer may be expressed as follows J Fe , Fe i,j = 14 π Im Z C tr L h ∆ Fe i ( z ) g ↑ i,j ( z ) ∆ Fe j ( z ) g ↓ j,i ( z ) i d z . (1)Here, the trace extends over s − , p − , d − , f -basis set, thequantities ∆ Fe i are proportional to the calculated ex-change splittings, and the Green function g σi,j describesthe propagation of electrons of a given spin ( σ = ↑ , ↓ )between sites i, j . It should be noted that both the di-rect propagation of electrons in the magnetic overlayerand the indirect one via the Ir-substrate are included inEq. (1) on an equal footing. Finally, the energy inte-gration extends over all occupied valence states up theFermi energy E F which is technically performed by inte-grating over the contour C in the complex energy plane.For more details see Ref. 15. Once the exchange inter-actions were known, we constructed a two-dimensional(2D) classical Heisenberg Hamiltonian to describe themagnetic behavior of the Fe-overlayer on a non-magneticfcc-Ir(001) substrate H = − X i = j J Fe , Fe ij e i · e j . (2)In Eq. (2), e i denotes the orientation of the Fe-magneticmoment at the site i . By construction, the value of thecorresponding magnetic moment is included in the def-inition of J Fe , Fe ij , and positive (negative) values denoteFM (AFM) couplings. An early study of exchange inter-actions in fcc-Fe,Co/Cu(001) systems is found in Ref. 3,whereas some recent estimates of exchange integrals fora bcc-Fe/W(001) overlayer were obtained either by a su-percell approach or by an approach closely related tothe present one .A Green-function approach like the present one to cal-culate exchange interactions has a particular advantageover a supercell approach : Exchange interactions canbe evaluated easily and reliably even for disordered over-layers and partial coverages. III. RESULTS AND DISCUSSIONA. Structure and magnetism
The results of the total energy calculations are sum-marized in Tables I-IV.
TABLE I: Calculated ( LDA/GGA, WIEN and VASP, respec-tively) and experimental (LEED) interlayer distances d ij between top three sample layers (1-Fe overlayer, 2-top Ir layer,3-second Ir layer) for fcc-Fe/Ir(001) in the nonmagnetic (NM),ferromagnetic (FM), and c (2 × b -AFM displays the influence of 0.5 ML hydrogenadsorbed on favourable bridge positions. The interlayer (001)-distance in the bulk iridium is 1.92 ˚A. d ij d [˚A] d [˚A] d [˚A]LDA GGA LDA GGA LDA GGANM WIEN 1.52 1.61 1.95 2.00 1.86 1.93VASP 1.51 1.58 1.99 2.05 1.88 1.94FM WIEN 1.64 1.78 1.91 1.95 1.88 1.94VASP 1.60 1.76 1.94 1.98 1.89 1.97AFM WIEN 1.59 1.69 1.93 1.98 1.88 1.93VASP 1.55 1.66 1.97 2.02 1.88 1.94H b -AFM VASP 1.58 1.67 1.97 2.01 1.88 1.94LEED 1.69 1.96 1.91 In Table I we present results of the structural mini-mization and compare our results with experiment. Wefound that the ground state is antiferromagnetic and thatthe interlayer distances obtained for this order in GGAapproximation agree very well with the results of LEEDstructure analysis . For all calculations we used the ex-perimental lattice constant a=3.84 ˚A in layers, which liesbetween the calculated LDA bulk value (3.81 ˚A) belowand the GGA (3.87 ˚A) above. For this reason, the calcu-lated substrate interlayer distances are slightly underes-timated in LDA ( ≈ ≈ c (2 × ≈ .The first Ir-Ir distance is slightly expanded with re-spect to its bulk value, where one has to keep in mindthat the bulk spacing is enhanced for GGA and decreasedfor LDA. The next spacing is reduced leading to a os-cillatory pattern of interlayer distances found in manymetallic systems.The calculated work functions are presented in Table TABLE II: Calculated work functions Φ in eV for Ir(001) (ne-glecting a possible lateral reconstruction) and of Fe/Ir(001)in various magnetic states. Symbols Ir, NM, FM, AFM, DLMH b -AFM, and H b -FM denote respectively, the Ir(001) surface,and nonmagnetic, ferromagnetic, c (2 × for LMTO. Theexperimental value for the Ir(001) surface is 5.67 eV .Φ[eV] Ir NM FM AFM DLM H b -FM H b -AFMWIEN-GGA 5.65 4.86 4.38 4.45 − − − VASP-GGA 5.62 4.82 4.29 4.37 − − − − VASP-LDA 5.89 5.13 4.59 4.66 − − − TABLE III: Calculated stabilities (in mRy/Fe atom) of thevarious magnetic phases of Fe/Ir(001) as obtained by theWIEN, VASP, and LMTO codes for the unrelaxed geome-try ( d Fe − Ir =1.92 ˚A). The ferromagnetic ground state has thelowest energy and serves as the point of reference.∆[mRy] NM LDA
AFM
LDA
DLM
LDA NM GGA
AFM
GGA
WIEN 49.1 2.2 - 62.7 2.2VASP 44.5 3.8 - 60.4 3.9LMTO 42.5 5.1 2.1 − −
II. The experimental value of 5.7 eV for the fcc-Ir(001)is reasonably reproduced by the present calculations (nosurface reconstruction). Our calculations show that theiron overlayer reduces the sample work function by ≈ ≈ . Whilethe full potential VASP and WIEN codes agree very wellwith each other, the TB-LMTO-SGF approach slightlyoverestimates the values.The results of magnetic stability calculations are pre-sented in Tables III - V. Different theoretical approacheswere used and compared in Tables for the unrelaxed ge-ometry (Table III) as well as for the realistic, relaxed TABLE IV: Calculated stabilities (in mRy/Fe atom) of thevarious magnetic phases of Fe/Ir(001) as obtained by theWIEN, VASP, and LMTO codes for relaxed geometries. Thestabilities correspond to the respective calculated relaxed ge-ometries (see Table I) for WIEN/VASP, and to the experi-mental one for LMTO. The antiferromagnetic ground statehas the lowest energy and serves as the point of reference.∆[mRy] NM LDA FM LDA
DLM
LDA NM GGA FM GGA
WIEN 25.8 7.8 - 38.4 5.3VASP 22.1 8.6 - 38.7 5.5LMTO 27.7 5.0 0.8 − −
TABLE V: Influence of 0.5 ML adsorbed hydrogen on thecalculated stabilities (in mRy) of the various magnetic phasesof Fe/Ir(001) as obtained by VASP for relaxed geometries (seeTable I). The antiferromagnetic ground state has the lowestenergy and serves as the point of reference.∆[mRy] NM
LDA FM LDA NM GGA FM GGA clean 22.1 8.6 38.7 5.5bridge-H 14.4 3.7 29.5 2.4 case (Table IV) including the possibility of residual ad-sorbed hydrogen (Table V). It should be noted that onemay only compare different LDA or GGA energies di-rectly to each to other. Our calculations clearly show,that the nonmagnetic case can be safely excluded. Allmodels with local magnetic moments have a substan-tially lower total energy. The most striking result, ob-tained by all methods, is the fact that while the FM isthe ground state for an unrelaxed geometry, the layerrelaxations stabilize the c (2 × where the antiferromagnetism of bcc-Fe/W(001)is robust with respect to the structural relaxations. In-terestingly adsorbed hydrogen also does not change thepicture as evident from Table V. Differences only getsmaller, but the general trend is preserved. However,strictly speaking, the c (2 × p (2 × . To shed some light onthis issue we included in Tables III and IV the resultsof DLM calculations as performed in the framework ofthe TB-LMTO-SGF approach. The sufficient reliabilityof the TB-LMTO-SGF approach for the present purposeis confirmed by a comparison with accurate full potentialcalculations for NM-, FM-, and c (2 × d : a L , where a L is the lateral lattice constant and d is the layer spac-ing. For bcc(001) we have d = a L / a/ a isthe bulk lattice constant) while for fcc(001) d = a/ a L = a/ √ d : a L . The reductionof the d : a L ratio stabilizes the AFM-/DLM-state forthis fcc(001) surface. This ratio is sufficiently small forcomparable bcc(001) surfaces even in the unrelaxed ge-ometry (see e.g. Fe/W(001) ). It is well-known that theexchange interaction between Mn spins becomes antifer-romagnetic for smaller distances, a trend we observe herefor exchange interactions in the Fe-overlayer as detailedbelow. This is a first strong indication that indirect inter-actions of Fe-spins via the Ir-substrate play an essentialrole for the fcc-Fe/Ir(001) magnetism. A dominant char-acter of indirect interactions as compared to direct onesbetween Fe-spins in the overlayer will result in a strongdependence of exchange interactions on the Fe-Ir inter-layer distance as we shall see below. B. Densities of states and exchange interactions T o t a l d e n s it y o f s t a t e s ( s t a t e s / s p i n / R y ) Energy (Ry)maj minx10 -0.8 -0.6 -0.4 -0.2 0 0.2Energy (Ry)Fe + : maj minx10 -0.8 -0.6 -0.4 -0.2 0 0.2Energy (Ry)Fe + : maj min Vacx10 FeSS-1S-2bulk FIG. 1: Total layer-resolved densities of states (DOS) for thefcc-Fe/Ir(001) overlayer and experimental layer relaxations based on the LMTO approach. In the case of the Fe-overlayerthe total DOSs are additionally split into majority (dashedlines) and minority (dotted lines) contributions: (a) the FMcase, (b) the DLM case, and (c) the c (2 × + ) is plotted for the DLMand AFM cases. Symbols Vac, Fe, S-1, S-2, and bulk denotethe first vacuum layer, Fe-overlayer, first and second substrateIr-layers, and the fcc bulk Ir host DOSs, respectively. TheFermi energy is shifted to the energy zero. In Fig 1 we present the layer-resolved densities of states(DOS) for the various magnetic states. Compared to theIr bulk, the most important feature observed for all casesis an extra contribution to the overlayer DOS around theFermi energy due to the minority Fe-states. The largeexchange splitting of majority and minority Fe-states isdue to the enhanced overlayer magnetic moment (about2.65 µ B in all cases) which illustrates the rigidity of the Fe-moment with respect to changing spin-orientations.The large Fe moment is due to the large lateral overlayerlattice constant as given by the Ir-substrate as well asto the reduction of coordination number at the surfacetypical for overlayer systems. There is also a relevantextra peak in the DOS in the vacuum close to the sam-ple surface which gives a possibility to detect it in STMmeasurements. We also observe a strong reduction of theFe-overlayer imprint on the deeper Ir-substrate layers:already the second Ir-substrate layer is almost bulk like.There is a small induced moment on the first-substrateIr-layer of the order of 0.1 µ B while other induced mo-ments are strongly damped in an oscillatory manner (theFriedel-like oscillations) into the Ir-substrates and theirvalues are of the order of 0.01 µ B and smaller. It shouldbe noted that induced moments in the Ir-substrate and inthe vacuum are much smaller and more strongly dampedin both substrate and vacuum for the c (2 × . The above results areconfirmed by full-potential slab-model calculations usingboth WIEN and VASP codes.Exchange interactions J Fe , Fe ( d ) have been determinedby the TB-LMTO-SGF method for Fe/Ir(001) as a func-tion of the interatomic Fe-Fe distance d for both un-relaxed and relaxed geometries, and FM-, DLM-, andAFM-reference states. Additionally we present results inthe DLM state for a simple layer-relaxation model whereonly the Fe-Ir interlayer distance is reduced from the un-relaxed value (1.92 ˚A) to values of 1.82 ˚A, 1.72 ˚A, and1.62 ˚A corresponding to a reduction of 5 %, 10.5 %, and16 %. These results are shown in Fig. 2.Calculated exchange integrals are rather similar, e.g.,all leading to the AFM interactions for the relaxed caseirrespective of the reference state. The problem of thechoice of reference state for estimate of exchange inte-grals in the present context was also addressed in Ref. 34.We have chosen the DLM reference state (with self-consistently calculated spin-polarized potentials and withcorresponding modification of Eq. (1)) for the magneticstability study below as it assumes no magnetic orderingand for our purposes is thus most suitable. We admit thatto estimate e.g. the critical temperatures other choicesmay be more suitable.With increasing layer relaxations we observe a cleartendency towards dominating AFM interactions whichstabilize the AFM-like state in the overlayer. The domi-nating role of indirect interactions between Fe-atoms viathe Ir-substrate is obvious: the only varying quantity isthe Fe-Ir distance and thus the Fe-Ir hybridization. Re-sults for experimental layer relaxations (inset in Fig. 2)are between model cases of 1.72 ˚A, and 1.62 ˚A. The factthat strong AFM coupling in the layer-relaxed case wereobtained from a reference FM state indicates the robust-ness of the AFM order (more precisely, of a more complexmagnetic state) for the relaxed Fe/Ir(001) overlayer. -1.25-1-0.75-0.5-0.25 0 0.25 0.5 0.75 0.5 1 1.5 2 2.5 3 J F e , F e ( d ) ( m R y ) (d/a) unrelaxed-5%-10.5%-16% -1.25-1-0.75-0.5-0.25 0 0.25 0.5 0.75 0.5 1 1.5 2 2.5 3 J F e , F e ( d ) ( m R y ) experimentalrelaxation DLM c(2x2)-AFM
FIG. 2: Exchange interactions among Fe-atoms in theFe/Ir(001) overlayer for the unrelaxed case and model layerrelaxations evaluated as a function of the reduced interatomicdistance ( d/a ), where a denotes the lattice constant. Num-bers attached to symbols indicate the reduction of the Fe-Irinterlayer distances in % as compared to the bulk value of1.92 ˚A. The inset shows exchange interactions for AFM andDLM state for the experimental layer relaxations . All re-sults were obtained assuming the DLM-reference state. -4-2 0 2 4 J F e , F e ( q ) ( m R y ) − X −Γ − M − XFe|Ir(001)unrelaxedexperimentalrelaxation -5%-10.5%-16%
FIG. 3: Lattice Fourier transformation of the real-space ex-change interactions J Fe , Fe ij , J( q k ), for the ideal unrelaxed ge-ometry, the experimental layer relaxations as well as forthree model Fe-Ir layer relaxations (same as in Fig. 2) whichwere obtained for the reference DLM state of the Fe/Ir(001)overlayer. Here, q k = ¯X=2 π/a L (1 / , / q k =¯Γ=2 π/a L (0 , q k = ¯M=2 π/a L (1 , To further investigate this point we present in Fig. 3the result of the lattice Fourier transformation of ex-change integrals (1) as obtained for the DLM referencestate. It should be noted that the DLM state is neitherthe ground state for the ideal geometry nor for the exper-imental layer-relaxed model. On the other hand, possiblemagnetic phases of the 2D-Heisenberg model (2) can beobtained by studying its stability with respect to the pe-riodic excitations. A similar approach was successfullyused in the study of the complex magnetic stability ofbcc-Eu: starting from the FM reference state, a properspin-spiral ground state was obtained in good agreementwith the experiment . Due to the sign convention ineqaution (2) the maximum of J( q k ) corresponds to theground state (the energy minimum). It is obvious thatthe ground state for the unrelaxed model is the ferromag-netic state (the maximum of J( q k ) is obtained for q k =2 π/a L (0 , q k =2 π/a L (1 / , /
2) which corresponds to the c (2 × d =1.82 ˚A orreduced by 5%). If the Fe-Ir interlayer distance furtherdecreases (by 10.5% and 16%) the stability of the FMstate further decreases and a new, complex spin-spirallike magnetic state becomes more stable as comparedto the c (2 × c (2 × and for the modelwith the largest reduction of the Fe-Ir interlayer distance(by 16%) the p (2 × q k =2 π/a L (1 , c (2 × d substrate would be beneficial. Rhodiumcrystallizes also in the fcc structure, has the same numberof valence electrons (9) as iridium and a similar latticeconstant (3.80 ˚A), while the value of the work function,5.11 eV , is smaller as well as the spatial extent of the4 d -wave functions of Rh as compared to 5 d -wave func-tions of Ir. The results of a similar study of the mag-netic stability for fcc-Fe/Rh(001) overlayer as a functionof the Fe-Rh interlayer distance will be presented in thefollowing. The same relative interlayer reductions as forfcc-Fe/Ir(001), namely by 5 %, 10.5 %, and 16 % will beused.The results are summarized in Fig. 4. The FM stateis again the ground state for the unrelaxed case, and weobserve a similar Fe-Rh interlayer distance reduction ef-fect on the magnetic stability as for fcc-Fe/Ir(001). Thereduction of the Fe-Rh interlayer distance by about 5 %seems to be the point where the FM state is no longer theground state and the c (2 × q k =2 π/a L (1 / , / -4-2 0 2 4 J F e , F e ( q ) ( m R y ) − X −Γ − M − XFe|Rh(001) unrelaxed -5% -10.5% -16%
FIG. 4: Lattice Fourier transformation of real-space ex-change interactions J Fe , Fe ij , J ( q k ), for the unrelaxed geome-try, and three model Fe-Rh interlayer relaxations for the fcc-Fe/Rh(001) system. The identical relative interlayer distanceswere used for both the fcc-Fe/Ir(001) system and for the DLMreference state. creasing reduction of the Fe-Rh distance the more com-plex AFM state is stabilized until for an interlayer re-duction of 16 % this state become the ground state (seean indication of this case in the Fig. 4: maximum in theneighborhood of the q k =2 π/a L (1 ,
0) ordering vector rep-resenting the p (2 × . IV. CONCLUSIONS
We have investigated the experimentally preparedFe/Ir(001) system by a combination of different first-principles methods for both supercell slab geometries(WIEN and VASP codes) and semi-infinite boundaryconditions (TB-LMTO-SGF codes). Using the latter ap-proach we investigated the magnetic phase stability ofthe system by calculating the exchange interactions be-tween Fe-atoms in the overlayer. The following conclu-sions can be drawn: (i) Calculated relaxed geometriesagree well with available experimental data. A betteragreement is obtained for the Fe-Ir distance using GGArather than LDA potentials. The calculated geometriesdepend on the magnetic state (non-magnetic, FM, andAFM states) but the most important result is the re-duction of the Fe-Ir interlayer distance as compared tothe bulk value by about 12 % for the AFM order. A possible residual H contamination on the overlayer haspractically no effect on the distances; (ii) The local Fe-moment is enhanced to about 2.65 µ B as compared toits canonical value of 2.15 µ B in the bcc Fe-metal. Theenhancement is due to both the enlarged lateral latticeconstant of the Fe-overlayer on fcc-Ir(001) and the re-duction of nearest-neighbors there. The work function ofthe system with Fe-overlayer is reduced more than 1 eVas compared to the value found for pure Ir-surface. Hy-drogen on the overlayer increases the work function by ≈ c (2 × p (2 × c (2 × ), and can lead to chiral magnetic order inducedby Dzyaloshinskii-Moriya interaction; and (vi) We haveshown that increasing Fe-Ir hybridization stabilizes theAFM state. This seems to be a robust effect to war-rant similar stabilization on a much more complex re-constructed Ir(001) surface. However, such a study goesbeyond the subject of the present paper.Experimentally no-magnetization was found for ironoverlayers thinner than ≈ and ≈ . Our study indi-cates that this is not the result due to disappearing of thelocal iron magnetic moments in the top surface layers butrather due to a more complex ”antiferromagnetic-like”order in the fcc-iron overlayer. Acknowledgements
This work has been done within the project AV0Z1-010-0520 and AV0Z2-041-0507 of the ASCR. The au-thors acknowledge fruitful discussions with J. Kirschner,D. Sander and Z. Tian and the support from theGrant Agency of the Czech Republic, Contract No.202/07/0456, 202/09/0775 and COST P19-OC-09028project. ∗ Electronic address: [email protected] P. Ferriani, K. von Bergmann, E. Y. Vedmedenko, S.Heinze, M. Bode, M. Heide, G. Bihlmayer, S. Bl¨ugel, andR. Wiesendanger, Phys. Rev. Lett. , 027201 (2008). M. Ondr´aˇcek, J. Kudrnovsk´y, and F. M´aca, Surf. Sci. ,4261 (2007). M. Pajda, J. Kudrnovsk´y, I. Turek, V. Drchal, and P.Bruno, Phys. Rev. Lett. , 5424 (2000). V.S. Stepanyuk, A.N. Baranov, D.V. Tsivlin, W. Hergert,P. Bruno, N. Knorr, M.A. Schneider, and K. Kern, Phys.Rev. B , 205410 (2003). P. Hylgaard and M. Persson, J. Phys.: Condens. Matter , L13 (2000). R. Wu and A.J. Freeman, Phys. Rev. B , 7532 (1992). D. Spiˇs´ak and J. Hafner, Phys. Rev. B , 195426 (2004). A. Kubetzka, P. Ferriani, M. Bode, S. Heinze, G.Bihlmayer, K. von Bergmann, O. Pietzsch, S. Bl¨ugel, andR. Wiesendanger, Phys. Rev. Lett. , 087204 (2005). P. Ferriani, S. Heinze, G. Bihlmayer, and S. Bl¨ugel, Phys.Rev. B , 024452 (2005). P. Ferriani, I. Turek, S. Heinze, G. Bihlmayer, and S.Bl¨ugel, Phys. Rev. Lett. , 187203 (2007). V. Martin, W. Meyer, C. Giovanardi, L. Hammer, K.Heinz, Z. Tian, D. Sander, and J. Kirschner, Phys. Rev. B , 205418 (2007). Z. Tian, D. Sander, and J. Kirschner, Phys. Rev. B ,024432 (2009). C. Hwang, A.K. Swan, and S.C. Hong, Phys. Rev. B ,14429 (1999). J. Kudrnovsk´y, I. Turek, V. Drchal, F. M´aca, P. Wein-berger, and P. Bruno, Phys. Rev. B , 115208 (2004). I. Turek, J. Kudrnovsk´y, V. Drchal, and P. Bruno, Phil.Mag. , 1713 (2006). P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka andJ. Luitz,
WIEN2k, An Augmented Plane Wave + LocalOrbitals Program for Calculating Crystal Properties , Karl-heinz Schwarz, Techn. Universit¨at, Wien, 2001. G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996); URL:http://cms.mpi.univie.ac.at/vasp/ G. Kresse and D. Joubert, Phys. Rev. B , 1758 (1999). J. Staunton, B.L. Gyorffy, A.J. Pindor, G.M. Stocks, andH. Winter, J. Phys. F - Metal Physics , 1387 (1985). H. Akai and P.H. Dederichs, Phys. Rev. B , 8739 (1993). J. Kudrnovsk´y, V. Drchal, I. Turek, and P. Weinberger,Phys. Rev. B , 054441 (2008). H. Akai, Phys. Rev. Lett. , 3002 (1998). I. Turek, V. Drchal, J. Kudrnovsk´y, M. ˇSob, and P. Wein-berger,
Electronic Structure of Disordered Alloys, Surfacesand Interfaces (Kluwer, Boston, 1997); I. Turek, J. Ku-drnovsk´y and V. Drchal, in
Electronic Structure and Phys-ical Properties of Solids , edited by H. Dreyss´e, LectureNotes in Physics, Vol. (Springer, Berlin, 2000), p. 349. A.I. Liechtenstein, M.I. Katsnelson, V.P. Antropov, andV.A. Gubanov, J. Magn. Magn. Mater. , 65 (1987). J.P. Perdew and Y. Wang, Phys. Rev. B , 13244 (1992). J.P. Perdew et al., Phys. Rev. Lett. , 136406 (2008). Y. Wang and J.P. Perdew, Phys. Rev. B , 13298 (1991). J.P. Perdew and A. Zunger, Phys. Rev. B , 5048 (1981). D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. , 566(1980). M. Hortamani, L. Sandratskii, P. Kratzer, I. Mertig, andM. Scheffler, Phys. Rev. B , 104402 (2008). L. Udvardi, A. Antal, L. Szunyogh, ´A. Buruzs, P. Wein-berger, Physica B , 402 (2008). A.B. Shick, F. M´aca, M. Ondr´aˇcek, O.N. Mryasov, and T.Jungwirth, Phys. Rev. B , 054413 (2008). H.L. Skriver and N.M. Rosengaard, Phys. Rev. B , 7157(1992). L. Szunyogh and L. Udvardi, Philos. Mag. B , 617(1998). I. Turek, J. Kudrnovsky, M. Divis, P. Franek, G.Bihlmayer, and S. Bl¨ugel, Phys. Rev. B , 224431 (2003). K. Christmann, Surf. Sci. Rep.9