Complex trend of magnetic order in Fe clusters on 4 d transition-metal surfaces
V. Sessi, F. Otte, S. Krotzky, C. Tieg, M. Wasniowska, P. Ferriani, S. Heinze, J. Honolka, K. Kern
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a r Complex trend of magnetic order in Fe clusters on 4 d transition-metal surfaces V. Sessi, F. Otte, S. Krotzky, C. Tieg, M. Wasniowska, P. Ferriani, S. Heinze, J. Honolka,
3, 4 and K. Kern
3, 5 European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP 220 38043 Grenoble Cedex 9, France Institute of Theoretical Physics and Astrophysics,University of Kiel, Leibnitzstr. 15, 24098 Kiel, Germany Max-Planck-Institut f¨ur Festk¨orperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany Institute of Physics of the ASCR v. v. i., Na Slovance 2, 182 21 Prague, Czech Republic Institut de Physique de la Mati`ere Condens´ee, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland (Dated: June 4, 2018)We demonstrate the occurrence of compensated spin configurations in Fe clusters and monolayerson Ru(0001) and Rh(111) by a combination of X-ray magnetic circular dichroism experiments andfirst-principles calculations. Our results reveal complex intra-cluster exchange interactions whichdepend strongly on the substrate 4 d -band filling, the cluster geometry as well as lateral and ver-tical structural relaxations. The importance of substrate 4 d -band filling manifests itself also insmall nearest-neighbor exchange interactions in Fe dimers and in an nearly inverted trend of theRuderman-Kittel-Kasuya-Yosida coupling constants for Fe adatoms on the Ru and Rh surface. PACS numbers: 75.20.Hr, 78.20.Ls, 78.70.Dm
I. INTRODUCTION
Today, there is a strive for a controlled fabrication ofnanomagnets in order to explore the concepts of spin-tronics at the atomic scale. Much progress was achievedin understanding direct intracluster exchange interac-tions in ferromagnetic few-atom clusters situated onmetal surfaces (see e.g. Ref.[1] and references therein), aswell as indirect surface-mediated magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions . A cen-tral challenge remains the increasing importance of ther-mal fluctuations in few-atom clusters, which leads to un-wanted destabilization of moments. As a consequence,in recent years the research focus has shifted towardsheavy 5 d transition-metal substrates, where large spin-orbit coupling (SOC) gives hope to enhance the mag-netic anisotropy and to counteract superparamagneticbehavior. Indeed, for ferromagnetic Co structures onPt(111) experiments show extraordinary large magneticanisotropies of up to 9 meV/atom . However, it hasbeen recently realized that in transition-metal nanostruc-tures on surfaces, SOC also induces the Dzyaloshinskii-Moriya (DM) interaction . It favors non-collinear mag-netic configurations and can destabilize ferromagnetismeven on the atomic scale .Less attention has been given to the lighter 4 d tran-sition metal substrates , where effects of relativis-tic origin such as the DM term and the magnetocrys-talline anisotropy are expected to be much smaller. Theexchange interaction, on the other hand, can dependcritically on the hybridization with the surface and itsband filling. Based on first-principles calculations it hasbeen predicted that the nearest-neighbor (NN) exchangecoupling changes from antiferromagnetic (AFM) to fer-romagnetic (FM) for Fe monolayers on Ru(0001) andRh(111), respectively . Since its magnitude is small,interactions beyond NNs as well as higher-order termsbeyond the pair-wise Heisenberg exchange, such as the four-spin and biquadratic interactions, can play a decisiverole for the magnetic order . Magnetic configurationsthat are surprising for Fe have been predicted for thosesubstrates, namely a N´eel state with angles of 120 ◦ be-tween adjacent spins for Fe monolayers on Ru(0001), anda collinear double row-wise AFM uudd -state on Rh(111).These two systems are thus ideal candidates to system-atically study the formation of complex magnetic phasesdriven by frustrated interactions beyond NN Heisenbergexchange.Here we show the essential importance of Fe 3 d stateitinerancy and hybridization with partially filled 4 d sub-strate bands in monatomic-height Fe clusters of differentatomic size N and various geometries. Randomly posi-tioned single Fe atom spins in the dilute regime ( N =1) indirectly interact via the RKKY mechanism whichshows inverted character on Ru(0001) and Rh(111). ForFe dimers ( N = 2) we prove the AFM (Ru) to FM (Rh)cross-over of the NN exchange coupling constant J , andfor larger clusters (2 < N ≤
4) the onset of cluster geom-etry dependent compensated magnetic structures, bothpredicted by our first-principles calculations. We demon-strate that compact clusters are ferromagnetic while openstructures exhibit compensated antiferromagnetic states.The origin of this unexpected trend arises from the com-petition of direct Fe-Fe exchange in the clusters and in-direct exchange mediated by the substrate. Finally, wepresent experimental evidence for the formation of com-pensated spin textures both for Ru(0001) and Rh(111)in fully ordered epitaxial Fe islands.
II. EXPERIMENTAL
X-ray magnetic circular dichroism (XMCD) experi-ments were carried out at the ID08 beamline of the Euro-pean Synchrotron Radiation Facility (ESRF), where sam-ples can be prepared in-situ under UHV conditions.
FIG. 1: Quench-condensed deposition of Fe on Ru(0001) and Rh(111). (a) Examples of XAS and XMCD spectra in theimpurity limit. (b) and (c): Top Measured XAS L peak photon energy (stars). The dashed line is a guide to the eye. BottomAverage Fe magnetization R L versus Fe coverage. The full and dashed black lines are combined MC simulations with andwithout J RKKY between single adatoms, respectively. For comparison, dash-dotted curves represent simulations assuming FMand AFM trimers and tetramers. Triangles in magenta show values measured on epitaxial islands at θ = 0 . Ru(0001) and Rh(111) single crystal surfaces were pre-pared by cycles of Ar-sputtering and annealing at 900 ◦ C.A scanning tunneling microscope allows to verify thecleanliness of the single crystal surfaces. Fe of 99.99%purity was deposited onto Ru(0001) and Rh(111) froma rod by electron bombardment heating. A precise cali-bration of the evaporator was done with the help of thescanning tunneling microscope.During the X-ray measurements the pressure in the mag-net chamber was < × − mbar. Possible contamina-tions containing oxygen were excluded by monitoring theO K-edge signal at around 540eV. X-ray absorption spec-tra (XAS) were measured at the Fe L , -edges with 99%positive and negative circularly polarized light ( σ + and σ − ) using the surface sensitive total electron yield (TEY)mode. XMCD and XAS signals are then defined as thedifference ( σ + − σ − ) and the average ( σ + + σ − ) /
2, re-spectively. The Fe L , XAS contribution to the TEYis obtained by subtraction of a background signal mea-sured prior to Fe deposition. Spectroscopy was done attwo angles of incidence with respect to the sample sur-face: ϑ = 70 ◦ (in-plane) and ϑ = 0 ◦ (polar). Magneticfields up to B = 5 T are applied parallel to the X-raybeam direction. Both XAS and XMCD signals scale withthe iron coverage θ . Thus, all XMCD data shown in thiswork are normalized to the respective L peak amplitudein the non-dichroic Fe XAS. The L peak value R L ofthe normalized XMCD is then a good measure of the pro-jection of the average magnetization < M > on the fielddirection ˆ z : R L ∼ P ˆ z · < M > . III. RESULTS AND DISCUSSION
Using in-situ quench-condensed deposition of sub-monolayer amounts of Fe at low temperatures we achievea statistical distribution Γ(
N, g ) of cluster sizes N andtheir respective geometries g on both Rh(111) andRu(0001) due to suppression of diffusion of surfaceadatoms. Fig. 1(a) shows examples of XAS and XMCDspectra of impurities measured at B = 5T and T = 8K.A sharp, atomic-like dichroic signal corresponding to R L ∼ .
25 is visible, as expected for a non-saturated,thermally fluctuating single Fe atom spin moment. Forcomparison, saturated Fe atoms on Pt(997) give en-hanced values of 0.6 under similar conditions .The impact of an increasing Fe coverage, and thus aver-age Fe-Fe coordination n Fe-Fe , is summarized in Fig. 1(b)and (c) for Ru(0001) and Rh(111), respectively. First wenote that the non-dichroic XAS L peak positions shiftby ∆ = 0 . d states, which leads to more efficientscreening of core-hole effects during X-ray absorption.The function ∆( n Fe-Fe ) is usually highly non-linear, sat-urating already at small values n Fe-Fe18 .At the bottom parts of Fig. 1(b) and (c) the evolu-tion of the magnetic signal with raising n Fe-Fe is shown.The trend of R L ( θ ) for Fe on Ru(0001) shows a steadydecay of the average magnetization with Fe coverage, in-dicating progressive magnetic compensation. Comparingthe R L values for ϑ = 70 ◦ and ϑ = 0 ◦ , we observe anin-plane magnetic anisotropy in the range θ < . R L with coverage and at low coverages anin-plane magnetic anisotropy. In contrast to Ru(0001), FIG. 2: Calculated exchange coupling constants J ( r ) as afunction of separation r between pairs of Fe adatoms. Opensymbols denote results for pure hcp adsorption sites and filledsymbols mark pure fcc sites and mixed dimers. The insetshows the position of the Fe atoms in the dimer. The fittinghas been performed with an RKKY-like function. at an intermediate coverage θ m ∼ .
25 ML the magne-tization reaches a minimum and increases monotonouslythereafter.In order to understand the observed trends of themagnetization with coverage, we have performed first-principles calculations based on density functional theory(DFT) for Fe clusters of different size and shape on bothsurfaces. We have applied the projector-augmented-wavemethod as implemented in the Vienna Ab-Initio Simula-tion Package (VASP) and used the generalized gra-dient approximation (GGA) to the exchange-correlationfunctional . We consider different collinear magneticconfigurations of the clusters and compare their total en-ergies taking vertical and lateral structural relaxationsinto account. Computational details can be found in theAppendix A.At low coverage there will be mostly a distribution ofsingle adatoms which can interact with each other via theexchange interaction mediated by the substrate. There-fore, we first focus on the exchange interaction betweentwo Fe adatoms as a function of their distance. The ex-change constants J ( r ) obtained from total energy calcu-lations are presented in Fig. 2. As expected we observean oscillatory behavior of J ( r ) changing from FM ( J >
J <
0) and a decay of its magnitude with in-creasing Fe-Fe separation. Interestingly, the trend foundfor Fe dimers on the Rh and Ru surface is almost per-fectly inverted. In contrast to the exchange interactionreported for substrates with a filled d -band we findthat the NN exchange constant J is reduced by aboutone order of magnitude and, thus, in competition withindirect exchange interactions J n with n >
1. The latterwill in the following be referred to as J RKKY .Our calculations for Fe trimers and tetramers onRh(111) and Ru(0001), shown in Fig. 3(a) and (b), re-spectively, display a complex dependence of the mag-netic order on the cluster geometry. For Rh(111) we find that compact trimers and tetramers possess a FM groundstate which is in accordance with the FM NN exchangecoupling from the dimer calculations (cf. Fig. 2) althoughthe energy differences are much larger than expectedfrom the exchange constants obtained from the dimers.However, Fe clusters in an open structure show a ten-dency to AFM order with compensated spin structures.This is surprising in view of the FM exchange interactionof the dimers. Interestingly, the open tetramers alreadydisplay the uudd state predicted for the full monolayer.These effects arise due to a competition of direct Fe-Feexchange and indirect exchange mediated by the sub-strate which are closely linked with the cluster geome-try and structural relaxations that differ for open andcompact structures . The impact of the structural re-laxation on the magnetic state is evident from Fig. 3(a)if one compares the energy differences obtained withouttaking structural relaxations into account. In the case ofa NN dimer on Rh(111) the exchange energy is reducedby one order of magnitude upon relaxation, leading to thevery low value of 6 meV/Fe-atom. A considerable reduc-tion of the energy difference occurs also for the compacttrimers and tetramers. For most of the open cluster con-figurations, the energetically favorable state even changesfrom a FM to a compensated state upon taking structuralrelaxations into account.A similar trend of magnetic order is found for Fetrimers and tetramers on Ru(0001) as shown in Fig. 3(b).For open structures, compensated AFM spin structuresare found which is expected from the AFM NN exchangein Fe dimers (cf. Fig. 2). Note, that the AFM NN ex-change is driven by the hybridization with the substrate.This can be seen by comparing the energy differences forthe Fe dimer without structural relaxation which prefersa FM state (see Fig. 3(b)). However, compact trimersand tetramers are in a FM ground state. The origin ofthis unexpected change of exchange coupling in the clus-ters is due to the enhanced direct FM Fe-Fe exchangeinteraction and a weakened effect of the Ru substrate.In order to obtain a quantitative interpretation ofour experimental data based on the magnetic config-urations calculated from first-principles we performedMonte-Carlo (MC) simulations. Knowing the magneticground states of all cluster configurations ( N, g ) with N ≤
4, MC simulations of Γ(
N, g ) allows us to esti-mate the coverage dependent average magnetization ofthe ensemble in a magnetic field B = 5T. We assumeeach cluster to be magnetically independent and thateach single adatom interacts only with one closest sin-gle atom via the RKKY interaction as described in thesupplementary. The magnetic contribution of a certaincluster with ( N, g ) to the total signal R L is then givenby a Boltzmann statistics weighted according to Γ( N, g ),where also induced substrate moments enter the Zeemanenergy term (see Appendix B for further details).The low coverage behavior ( θ < . R L shownin Fig. 1 can be understood based on the RKKY interac-tions and the NN exchange constant J . In the simpler FIG. 3: Total energy differences between different magneticconfigurations for the Fe dimer, trimers and tetramers on (a)Rh(111) and (b) Ru(0001). Energy differences in meV perFe atom are given with respect to the FM state. Values inbrackets are energy differences without taking structural re-laxations into account. case of Ru(0001) the magnetization trend at low cover-ages is dominated by the AFM NN exchange constant J <
0. In Fig. 1(b) the result for magnetically inde-pendent clusters excluding RKKY interactions is shown,which reproduces the continuous decay of the magneti-zation well, considering that the modeling contains nofree parameter. At lowest coverage, R L corresponds toa single spin moment of 3.0 µ B as obtained from our DFTcalculations in the corresponding Zeeman field.Turning to the case of Fe clusters on Rh(111), we findthat R L at lowest coverages is larger compared to thevalues found for Ru(0001), which we attribute to (i) theenhanced spin moment 3.2 µ B of a single Fe atom onRh(111) and (ii) the about ten times larger magnetic sus-ceptibility of Rh(111) leading to larger induced substratemoments. The latter enter the Boltzmann statistics via FIG. 4: (a) and (b): STM topographies of Fe islands onRu(0001) and Rh(111), respectively. (c) R L vs temperaturemeasured at B = 5T and ϑ = 70 ◦ . Full and dotted lines areBoltzmann statistics of a superparamagnetic macrospin M Fe . the Zeeman term and stabilize the Fe spin moments. Itis evident that even a qualitative understanding of thetrend R L ( θ ) based on the NN exchange interaction isimpossible in the case of Rh. The steep decrease of R L at lowest coverages is surprising in view of the positiveNN exchange coupling J . Starting from single atomsthe increase of θ should thus enhance the average mag-netization per Fe atom due to FM dimer formation asseen by the dashed curve in Fig. 1(c). However, if wetake into account the RKKY coupling between single Featoms on Rh(111) we observe that the AFM exchangecoupling for separations of up to 6 ˚A overcompensate byfar the contribution of the FM NN dimer coupling andaccurately reproduces the steep decrease of the averagemagnetization below θ = 0 . R L in good agreement with our experimentaldata. According to statistics, trimer configurations startto play a role at coverages θ > . . R L start todecrease due to the increasing spectral weight of clusterswith N >
4, which in our MC simulations are assumedto have zero moment (see Appendix B). We attributethe rise of the experimental R L signal to the formationof three-dimensional FM clusters which are less coupledto the substrate and thus will be dominated by the FMdirect exchange between Fe moments.Finally, we present experimental evidence for compen-sated magnetic ground states of Fe MLs on the hexagonalsurfaces Ru(0001) and Rh(111). From the data discussedso far only the measurements on Ru(0001) are compat-ible with such a compensated ground state, since thevalues for R L reach very low values at high coverages θ = 0 . T = 300K. On Ru(0001) triangu-lar shaped islands with 5-10nm in diameter are formedon the terraces, and smaller islands decorate the terracestep edges. The onset of the 2nd layer formation on theislands is only visible on Ru(0001), but the ratio betweenbilayer and monolayer areas corresponds to less than 5%.On Rh(111), islands of mostly truncated triangular shapeare randomly distributed.Fig. 4(c) shows R L for the two systems measured at B = 5T and different temperatures. At T = 8 K only asmall Fe dichroic signal of R L = 0 .
07 and R L = 0 .
09 ispresent for θ = 0 . T = 300 K can be fitted by a classical Boltzmann statis-tics of a constant superparamagnetic macrospin M Fe26 ,suggesting stable ground states up to energy scales be-yond 25meV. As in the quench-condensed samples a faintin-plane magnetic easy direction is observed for both sub-strates (see Fig. 1(b) and (c), where open/full trianglescorrespond to ϑ = 0 ◦ and ϑ = 70 ◦ ).The difference of the island results compared to thoseobtained by quench-condensed deposition underlines theimportance of the structure on the magnetic state. Thestabilization of a compensated magnetic configuration onRh(111) against a FM exchange term J > d states over larger distances.Increased hybridization in the ordered case is also di-rectly visible in the measured XAS L peak photon en-ergy, which remains ∼ . IV. CONCLUSIONS
In conclusion, we have shown a complex trend of mag-netic order in Fe nanostructures on 4 d transition-metalsurfaces due to the hybridization of Fe 3 d -states withthe partly filled substrate 4 d -band. For Fe dimers thenearest-neighbor exchange is very small and of oppositesign on the Ru and Rh surface. For larger clusters thecompetition of direct FM Fe-Fe exchange with the indi-rect exchange mediated by the substrate determines themagnetic order. Finally, we have presented first exper- imental evidence for the formation of compensated spintextures in epitaxial Fe islands on both for Ru(0001) andRh(111) as predicted by theory. Acknowledgments
F. O., P. F., and S. H. acknowledge financial supportby the Deutsche Forschungsgemeinschaft within the SFB677 and thank the HLRN for providing high-performancecomputing resources. J. H. acknowledges the CzechPurkynˇe fellowship program.
Appendix A: Computational details
Fe clusters on Rh(111) and Ru(0001) have been stud-ied based on density functional theory calculations inthe generalized gradient approximation (GGA) to theexchange-correlation functional , using the projecter-augmented-wave method as implemented in the ViennaAb-Initio Simulation Package (VASP) . All calcula-tions have been performed in the scalar-relativistic ap-proximation, i.e. neglecting the effect of spin-orbit cou-pling. To model the Fe clusters we have used the p (4 × p (5 ×
5) surface unit cells for clusters with
N < N = 4, respectively. To model the Rh(111) or Ru(0001)surface eight layers have been used. The adatoms as wellas the two upmost surface layers have been structurallyrelaxed until the forces were smaller than 0.005 eV/˚A.A (5 × ×
1) and (3 × ×
1) Γ-centered k-point meshhas been used for the p (4 ×
4) and p (5 ×
5) surface unitcell, respectively. The experimental lattice constant of3.8034 ˚A for Rh and lattice parameters of 2.7059 ˚A and4.2815 ˚A for Ru have been chosen. The energy cutoffparameter for the plane wave expansion was 390 eV anda Gaussian smearing of σ = 0 .
07 eV has been applied.An important aspect of our approach to calculate theexchange constants is the possible interaction of theclusters with those in adjacent cells due to the two-dimensional (2D) periodic boundary conditions. In orderto estimate the influence of atoms in neighboring cells wehave performed test calculations in the p (3 × p (4 × p (5 ×
5) unit cells. We found that the p (4 ×
4) unitcell size is sufficiently large to avoid spurious interactioneffects for compact clusters and to determine their mag-netic ground state. However, if the distance between theadatoms within the unit cell is large as for dimers withlarge separation, the influence of atoms in the adjacentunit cells also becomes important. We have taken suchinteractions into account when determining the RKKYexchange constants. More detailed information can befound in Ref. [33].
Appendix B: Monte Carlo Simulations
During the Monte Carlo (MC) simulation iron atomsare randomly deposited onto two hexagonal hcp and fccsublattices, each of which have a size of 500 × T = 8 K no thermal activated hopping of atomsis included in the simulation. However, we do take intoaccount random tip-over processes onto neighboring freeadsorption sites, if the initial MC step chooses a landingsite which is already occupied by an iron atom. Dur-ing one MC deposition cycle the sum of the number ofatoms on both sublattices is increased by 0.02% of a fullmonolayer (ML).After every MC deposition cycle the program countsthe different types of clusters: an atom is evaluated asa monomer if it has no nearest neighbor (NN) on thesame lattice, two atoms are evaluated as a dimer if theyhave just themselves as NNs, and so on. Moreover, theprogram distinguishes between different geometries g forone and the same cluster size N , e.g. between lineartrimers and trimers with an angle. The MC simula-tion thus gives access to the distribution Γ( N, g ) of alldifferent cluster configurations (
N, g ) from monomers totetramers (
N <
5) both on hcp or fcc sublattices. Fig-ure 5(a) reflects the statistics of cluster counts with size
N <
N, g ) with cov-erage. Figure 5(a) shows the statistics of cluster countswith size N versus coverage, while Fig. 5(b) translatesthis statistics into spectral weights contributing to theX-ray absorption signal. The spectral weight ω ( N ) ishereby defined as: ω ( N ) = P g N · Γ( N, g ) P ˜ N, ˜ g ˜ N · Γ( ˜
N , ˜ g ) (B1)The degree of magnetic alignment of a given Fe clus-ter ( N , g ) (including RKKY-coupled pairs of monomers)with an applied field of B = B · ˆ z is estimated usinga Zeeman energy term of the form E ( M N,g tot , B,
Θ) = − B · M N,g tot · cos(Θ), where the absolute value of the totalmoment vector M N,g tot in units µ B is defined as the sumof total Fe moment M Fe and induced substrate moments M : M N,g tot = M Fe + M . Θ is the angle between themoment vector and the field direction ˆ z . All momentsare readily taken from DFT results. The contribution R N,gL ( B, T ) of a certain cluster with (
N, g ) to the totalsignal R L is then given by a Boltzmann statistics, al-lowing M N,g tot to point in all directions in space: R N,gL ( B, T ) = R sat L N · µ B 2 π Z π Z M N,g Fe · cos(Θ) · sin(Θ) · e − E ( M N,g tot ,B, Θ) /k B T d Θ dϕ/Z, (B2)where Z is the partition function. The term M N,g Fe · cos(Θ) projects the Fe cluster moments M N,g Fe onto theˆ z direction, which accounts for the fact that the XMCDtechnique measures Fe moment components along the X-ray beam direction. The calibration factor in front of theintegral contains R sat L = (0 . ± . R L expected for low coordinated Fe spin moments of(3 . ± . µ B in a saturating magnetic field . In oursimulation we thus make the assumption that the value R sat L is a Fe moment dependent constant value whichdoes not change significantly if the coordination state ofthe Fe changes. This assumption is not generally validbut is a good approximation for Fe atoms in metallicenvironments. For a comparison with the experimentalspectroscopy data, the total simulated signal R L is de- fined as the sum of all components R N,gL ( B, T ) of clusters(
N, g ) at experimental conditions T = 8 K and B = 5 T,scaled to their respective spectral weights determined byΓ( N, g ).The coverage dependent spectral weight of clusters N = 1 , , , θ = 0 . θ = 0 . N = 2 are com-parable to those of monomers. At the same time alsoclusters with N = 3 gain a spectral weight of more than10%, indicating the onset of larger cluster contributions.At coverages θ = 0 .
25 ML the spectral weight of allcluster contributions with
N >
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