Spin-dependence of Ce $4f$ hybridization in magnetically ordered systems A spin-resolved ph

a r X i v :0704.1254v 1 [c o n d -m a t .s t r -e l ] 10 A p r 2007Spin-dependence of Ce 4f hybridization in magnetically ordered systems:A spin-resolved photoemission study of Ce/Fe(110)

Yu.S.Dedkov,1,?M.Fonin,2Yu.Kucherenko,3

S.L.Molodtsov,1U.R¨u diger,2and https://www.sodocs.net/doc/1917705587.html,ubschat 1

1Institut f¨u r Festk¨o rperphysik,Technische Universit¨a t Dresden,01062Dresden,Germany 2Fachbereich Physik,Universit¨a t Konstanz,78457Konstanz,Germany 3Institute for Metal Physics,National Academy of Sciences of Ukraine,03142Kiev,Ukraine (Dated:February 5,2008)Abstract Spin-and angle-resolved resonant (Ce 4d →4f )photoemission spectra of a monolayer Ce on Fe(110)reveal spin-dependent changes of the Fermi-level peak intensities.That indicate a spin-dependence of 4f hybridization and,thus,of 4f occupancy and local moment.The phenomenon is described in the framework of the periodic Anderson model by 4f electron hopping into the exchange split Fe 3d derived bands that form a spin-gap at the Fermi energy around the

?Corresponding author.E-mail:dedkov@physik.phy.tu-dresden.de

As a function of chemical composition,the electronic properties of Ce4f states in in-termetallic compounds vary from localized4f1character over heavy-fermion behavior and mixed valence to the boarder of itinerant behavior[1].This fascinating variety of characters is already re?ected in Ce metal,where in the course of the famous isostructuralγ→αtransition a magnetic phase transforms into a nonmagnetic one depending on temperature and/or pressure accompanied by a volume collapse of15%[2].While in the promotion model this phenomenon was ascribed to a transition from a trivalent4f1(5d6s)3to a tetravalent 4f0(5d6s)4con?guration[3],later studies related the e?ect to a Mott-transition from local-ized to itinerant character of the4f state[4]or to a Kondo collapse[5].

The promotion model is clearly ruled out by photoemission(PE)that reveals only weak intensity changes of the total4f derived emission upon theγ→αtransition[6].Instead of a single4f0PE?nal state at about2eV binding energy(BE)as expected from a localized4f1 ground state a second4f-derived feature is observed at the Fermi energy,E F,that increases in intensity upon theγ→αtransition[6].An itinerant description based on the local density approximation(LDA)fails to explain this double-peak structure[7],it is,however, well reproduced in the framework of the single-impurity Anderson model(SIAM)considering electron hopping between localized4f1and valence-band(VB)states[8].A momentum dependence of the4f signal as recently observed by angle-resolved PE experiments[9,10,11] could be explained considering the translational symmetry of the solid within a simple approach to the periodic Anderson model(PAM)[10,11,12].

From both SIAM and PAM the Fermi-peak intensity may be taken as a direct measure for the hopping probability.The latter should increase with the VB density of states at E F,and in fact huge Fermi-level peaks are typically observed in PE spectra of Ce transition-metal compounds re?ectingα-like behavior of the Ce4f states due to hybridization with transition-metal d-bands[13].A spin-dependence of4f hopping may be expected for magnetically ordered systems where the exchange splitting of the VB leads to strong variations of the density of states at E F for di?erently oriented VB spins.Respective spin-dependentγ→αtransitions have not be observed so far,the e?ect,however,could be of high importance for the understanding of magnetic anomalies in these systems since the local magnetic properties of the Ce atoms may strongly vary as a function of4f spin orientation.

In this contribution we report for the?rst time on a spin-dependentγ→α?like transition observed by a spin-and angle-resolved resonant PE from an ordered Ce adlayer on Fe(110).

Although hybridization is expected to be relatively weak in the outermost surface layer due to the low coordination of the Ce atoms[14],the quasi two-dimensional structure of the system allows for a proper determination of the position in k space probed in the experiment as necessary for a quantitative description within PAM applied here.For Ce/Fe(110),our local spin density approximation(LSDA)slab calculations reveal at the

was in the upper10?11mbar range rising shortly to the upper10?10range during evaporation and annealing.

Fig.2shows spin-resolved PE data of Ce/Fe(110)taken on-and o?-resonance at121eV and112eV photon energies,respectively.The o?-resonance spectra are dominated by emis-sions from Fe3d-derived bands and are very similar to respective data of the pure Fe sub-strate(not shown here).The spectra re?ect clearly the exchange splitting of the Fe3d bands into a minority-spin component at E F(”spin down”:?lled triangles)and a majority-spin component shifted to higher BE(”spin up”:open triangles).While the spectra of the pure substrate remain almost unchanged when going from112eV to121eV photon energy,the on-resonance spectra of Ce/Fe(110)reveal an additional feature around2.2eV BE that is ascribed to the resonantly enhanced4f signal.

In order to extract the Ce4f contributions from these spectra,the o?-resonance data were subtracted from the on-resonance spectra after proper normalization of the intensities with respect to the photon?ux and the slowly varying Fe3d photoionization cross section. The resulting spin-resolved4f spectra are shown in the upper part of Fig.3together with the corresponding spin polarization P(inset)de?ned as P=(I↑?I↓)/(I↑+I↓),where I↑and I↓denote the intensities of the majority-and minority-spin channels,respectively.The spectra reveal the well-known double-peak structure of the Ce4f emission consisting of a main maximum at2.2eV corresponding to the ionization peak expected for an unhybridized 4f1ground state and the hybridization peak at E F.From the weak intensity of the latter relative to the ionization-peak signal,a weak hybridization similar to the one inγ-Ce can be concluded as it is expected for a Ce surface layer[18].The most important observation is,however,that the intensity of the hybridization peak is larger for the minority-than for the majority-spin component(Fig.3)indicating larger4f-hybridization of the former.The spin polarization of both,the ionization and the hybridization peaks,gives a negative sign indicating that the preferred orientation of the Ce4f spins is opposite to the magnetization direction of the Fe layers.In addition to the double-peak structure another feature is visible around1eV BE(Fig.3),that is weaker in intensity and shifts to lower BE when going from the minority-to the majority-spin component.

In order to understand the ground-state magnetic properties of Ce/Fe(110),as a?rst step fully relativistic spin-polarized band-structure calculations were performed by means of the linear mu?n-tin orbital(LMTO)method.A pure Fe surface and the Ce/Fe(110)

system were considered using the structural model shown in Fig.1(c).The Fe substrate was simulated by a?ve-layer slab of Fe atoms with(110)orientation of the surface.The results were compared to data calculated for the isostructural non-f system La/Fe(110).

For the atoms in the middle layer of the Fe slab the calculations give a local electronic structure close to that obtained for Fe bulk[19].The calculated Fe3d spin moment value lies between2.35μB and2.40μB.At the surface it increases to2.60μB.In all cases contributions of s and p electrons to magnetic moment are negligible.

By the presence of a Ce overlayer the Fe3d spin moments of the surface atoms are reduced to2.14μB and2.50μB,respectively,depending on whether the Fe atoms are nearest neighbors of Ce atoms or not.Replacing in the calculation Ce by La atoms give very similar results indicating that the electronic structure of the Fe atoms is perturbed by interactions with extended valence states(mainly5d)of the overlayer.

The calculations yield for a La atom on the Fe(110)surface a local spin moment of ?0.24μB,determined mainly by the5d electrons(?0.20μB).The negative sign stands for an antiparallel orientation with respect to the Fe3d spin moment.For the Ce atom the local spin moment is equal to?1.12μB,with5d and4f contributions of?0.28μB and?0.82μB, respectively.Thus,like in other Ce-Fe systems[20,21,22],the Ce4f electrons reveal a spin orientation opposite to Fe3d majority spin in agreement with the PE experiment. Since the4f electrons have additionally a large positive orbital momentum of2.80μB due to their reduced atomic coordination at the surface the total moment equals to1.70μB and corresponds,thus,to ferromagnetic coupling with respect to the Fe3d spins.At?nite temperatures magnetic disorder leads to the situation encountered in the experiment where a part of the4f spins are?ipped into the opposite direction.

In order to describe the observed variation of4f hybridization as a function of spin orientation,we used the simpli?ed periodic Anderson model that was recently successfully applied to explain the angle-resolved PE spectra of CePd3[10]and Ce/W(110)[11].In this approach the double occupation of the4f states is ignored(on-site f?f Coulomb interaction energy,U ff→∞)and k vector conservation upon hybridization is assumed.In

this case a simpli?ed(without U ff term)Anderson Hamiltonian can be written as follows

H=

k,σεσ(k)d+

kσ

d kσ+

k,σ

εσf(k)f+

kσ

f kσ

+

k,σ

Vσk(E) d+kσf kσ+f+kσd kσ ,

where the VB states|kσ have a dispersionεσ(k)and are described by creation(annihilation)

operators d+

kσ(d kσ).The operator f+

kσ

creates a f electron with momentum k,spinσ,

and energyεσf(k).We assume that a non-hybridized f band has no dispersion:εσf(k)=εσf allowing,however,a possible small di?erence in the energy positions of4f levels with di?erent spinσdue to exchange interaction.The two electron subsystems(VB and4f states)are coupled via a hybridization Vσk(E)that leaves the electron spin una?ected,i.e. spin-?ips upon electron hopping are excluded.E denotes the BE with respect to E F.This form of the Hamiltonian allows us to diagonalize it for each particular k point of the surface Brillouin zone(BZ)and for each spin stateσ.

For the hybridization matrix element Vσk(E)we use calculated f-projected local expansion coe?cients cσf(E,k)of the Bloch functions around the rare-earth sites:Vσk(E)=?·cσf(E,k), where?is a constant,adjustable parameter.Expansion coe?cients cσf(E,k)that charac-terize the local f character of VB states were taken from the results of the band-structure calculations of the La/Fe(110)system,in order to exclude the contribution of localized Ce 4f orbitals.For normal emission of the photoelectrons we have to consider VB states at theΓpoint of the surface BZ.The calculated values of cσf(E,Γ) 2are shown in the bottom

part of Fig.2.The energy distributions of the VB states of local f character are quite di?erent for majority-and minority-spin electrons.Since these states are formed by linear combination of wave functions of the neighboring atoms(mainly Fe3d)penetrating into the La atomic spheres,they re?ect to some extent the energy and spin distribution of the latter(see o?-resonance spectra in Fig.2).Their di?erent amplitude and energy distribution for majority-and minority-spin states causes strong di?erences in the respective hybridiza-tion matrix elements and results in di?erent shape of the4f PE spectra for the two spin directions.

The spectral functions of the Ce4f emission were calculated using the parametersε↑

f

=

?1.9eV,ε↓

f

=?1.7eV,and?=0.85eV.These values deviate from those used in Ref.[11] for Ce/W(110)only by slightly higher BE of the non-hybridized4f level resulting from the

lower coordination of the Ce atoms.An energy-dependent life-time broadening of the form ΓL=0.030eV+0.085E was considered.The calculated spectral functions were additionally broadened with a Gaussian(ΓG=100meV)to simulate?nite instrumental resolution and an integral background was added to take into account inelastic scattering.

The calculated spin-resolved Ce4f PE spectra are presented in Fig.3(lower part).The energy distribution of the PE intensity agrees well with that of the experimental spectra (Fig.3,upper part).The minority-spin spectrum reveals high intensity of the hybridization peak due to large density of the minority-spin VB states close to E F.A shoulder near1eV BE is formed by hybridization with VB peaks at0.9eV and1.3eV BE(Fig.1).In accordance with the experiment,in the calculated majority-spin spectrum the ionization peak is split into three components(maxima at0.9eV,2.1eV,and shoulder at3eV BE)as a result of hybridization with the VB states(at1.4eV and between2eV and3eV BE).No majority-spin hybridization peak is obtained in the calculation due to the negligibly small density of VB states for this spin direction at the Fermi level.This theoretical result deviate from the experiment where a reduced but?nite hybridization peak was observed.The latter may be ascribed to the?nite angle resolution of the experiment that samples also regions in the k space where majority-spin bands cross E F.The calculated spin polarization(Fig.3,inset in the lower part)reproduces qualitatively the energy dependence of the measured polarization. Particularly good agreement is obtained for the points where the spin polarization changes its sign.

In summary,we have shown that the observed spin-dependence of the shape of the Ce4f emission in Ce/Fe(110)system may be explained by a spin-dependence of4f-hybridization. From this result4f-occupancy as well as e?ective magnetic moment are generally expected to vary with spin-orientation,an e?ect that may be of crucial importance for the understanding of many-body e?ects and magnetic anomalies in RE systems.

This work was funded by the Deutsche Forschungsgemeinschaft,SFB463,Projects TP B4and TP B16as well as SFB513.We would like to acknowledge BESSY sta?for technical support during experiment.

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FIG.1:(Color online)LEED images obtained from(a)Fe(110)and(b)Ce/Fe(110);assumed surface crystallographic structure of the Ce/Fe(110)system(c)and simulation of the LEED-image (d).The shaded rectangle in(c)visualizes the fcc Ce(110)plane expanded by11%.

FIG.2:(Color online)Spin-resolved PE spectra of Ce/Fe(110)system measured in on-and o?-resonance at the4d→4f absorption threshold.Open/?lled triangles denote contributions of majority/minority spin directions,respectively.Bottom part:Calculated local4f character of the VB states(|cσf(E,Γ)|2)at the La site in theΓpoint of the surface BZ for La/Fe(110)system for majority-(solid line)and minority-spin(shaded area)direction.

FIG.3:(Color online)Spin-resolved experimental(upper part)and calculated(lower part)Ce 4f emission for Ce/Fe(110).Majority-and minority-spin emissions are shown by open and solid triangles,respectively.The insets show the corresponding spin polarization P.