Exploring small energy scales with x-ray absorption and dichroism C. Praetorius,1 M. Zinner,1 P. Hansmann,2 M. W. Haverkort,3 and K. Fauth1,4,∗ 1Physikalisches Institut, Universita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany 2Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany 3Max Planck Institute for Chemical Physics of Solids, No¨thnizer Straße 40, 01187 Dresden, Germany 4Wilhelm Conrad Ro¨ntgen-Center for Complex Material Systems (RCCM), Universita¨t Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany (Dated: January 28, 2016) Softx-raylinearandcirculardichroism(XLD,XMCD)experimentsattheCeM edgesarebeing 4,5 used to determine the energy scales characterizing the Ce 4f degrees of freedom in the ultrathin ordered surface intermetallic CeAg /Ag(111). We find that all relevant interactions, i. e. Kondo x 6 scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study 1 demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular 0 dichroism owing to their strong sensitivity for anisotropies in both charge distribution and para- 2 magnetic response, respectively. n a J Rareearthintermetalliccompoundsdisplayarichphe- 7 nomenology of physical properties, encompassing very 2 different kinds of ground states, such as magnetic or- der,unconventionalsuperconductivityandparamagnetic ] l heavy fermion liquids [1, 2]. The interaction of localized e 4f electrons with itinerant electronic degrees of freedom - r may result in the emergence of small characteristic en- t s ergy scales which produce nontrivial macroscopic behav- . t ioratlowtemperatureandcomplexphasediagramswith a m competing interactions and orders [1–5]. In a solid en- vironment, the degeneracy of the rare earth 4f ground - d configurationisliftedbythecrystalfieldingeneral,caus- n ing both an anisotropic 4f charge distribution and, in FIG.1. LEEDpatternsrecordedatanelectronkineticenergy o of70eVfromAg(111)(left)andCeAg (right). Thesatellite conjunction with spin orbit coupling, (single ion) mag- x √ c reflections in the latter indicate the formation of a (2 3× netic anisotropy. Unraveling the crystal field induced √ [ 2 3)R30◦ superstructureasinCePt /Pt(111)atcomparable level structure thus constitutes an essential part of un- 5 Ce dose [21, 23]. Ag(111) reflections merge with one of the 1 derstanding the low temperature physics and of estab- satellite reflections around (cid:104)2 1(cid:105) (indicated by arrows), v √ √ CeAgx 0 lishing correlations between local 4f symmetry at low yielding a (190 3× 190 3)R30◦ relation between CeAgx and 4 temperature on the one hand and macroscopic ground substrate unit cells, respectively. 2 state properties on the other. 7 In this respect, the usefulness of probing the 4f con- 0 figuration with linear polarized soft x-rays [6] has been the same installation and therefore can be performed in . 1 demonstrated for a variety of Ce compounds in recent situ within a single experimental run. Second, the split- 0 years[7–14], allowingtosettleseveralopenissues, where tings turn out to be of the order of 1 meV only, making 6 otherexperimentsleftroomfordiverginginterpretations. their discrimination from quasi-elastic scattering a diffi- 1 : Its magnetic variants, x-ray magnetic linear and circu- cult task. Last but not least, the sample volume is so v lar dichroism (XMLD, XMCD) constitute sensitive ele- small that most alternative methods would face serious i X mentandorbitalspecificprobesofmagneticpolarization sensitivity challenges. r and anisotropy [15–20]. XMCD was successfully utilized The formation of an ordered intermetallic phase upon a to reveal the presence of magnetic Kondo screening in depositingminuteamountsofCeontoAg(111)heldatel- CePt /Pt(111) [21]. evatedtemperaturehasbeenreportedbefore[22]. Inthe 5 Inthepresentletterwedemonstratethatthecombined preparation of our specimens we have adopted a similar use of linear and magnetic circular dichroism allows us procedure. In brief, clean Ag(111) was prepared by cy- to determine the crystal field structure without recourse cles of Ar+ ion sputtering (Ekin: 1 keV) and subsequent to e. g. inelastic neutron scattering, as in some previous annealing to 920 K. The crystal was then held at 840 K work [7–9]. Our chosen example of an ultrathin Ce-Ag while a Ce dose of approx. 1×1015 atoms/cm2 was de- surface intermetallic furthermore highlights a threefold posited onto it from a thoroughly outgassed W crucible advantage of this approach. First, linear and circular mounted in a commercial electron beam evaporator. dichroism experiments are frequently both feasible with Fig. 1 displays a LEED pattern of a CeAg specimen x 2 characteristic of this range of Ce coverage next to the one of pristine Ag(111), taken at the same electron ki- netic energy. The diffraction pattern is very much remi- niscent of our earlier observations for CePt /Pt(111) at 5 similar Ce dose [21, 23]. It reveals a combination of two superstructures on two different length scales. The main diffraction features may be attributed to an intermetal- √ √ lic (1.1 3×1.1 3)R30◦ surface reconstruction, whereas the satellites indicate the formation of a longer range √ √ surface corrugation of (3 3×3 3)R30◦ character with respect to this intermetallic phase. This corresponds to a hexagonal surface corrugation in rotational alignment withthesubstratelatticeandaperiodicityofapprox.15 nm. As indicated by arrows in Fig. 1 the Ag(111) first order diffraction beams superimpose with the outermost satellitereflectionssurroundingthe(cid:104)21(cid:105)spotsofthesur- face intermetallic. Like in CePt the satellite intensities 5 strongly loose intensity as the initial Ce coverage is in- creased[22,24]. Despitetheobvioussimilaritiesbetween FIG.2. SelectionofexperimentalandsimulatedCeM XA bothsystems,therearealsosomedifferences. Wehaveso 4,5 spectra for CeAg /Ag(111). a) Experimental low tempera- far been unable to determine the exact composition and x ture(T =15K)isotropicandhightemperature(T =250K) structure of this ordered Ce-Ag phase which we there- normal incidence spectrum b) Simulated isotropic spectrum fore label as CeAgx. A more extensive account of the and normal incidence spectra for pure |mj(cid:105) initial states c) properties of CeAgx/Ag(111) and their dependence on Experimental normal incidence spectra at various tempera- Ce coverage shall be given in a separate publication [24]. tures d) Zoom-in on the main spectral features of both ex- Forthepurposeofthisletteritissufficienttorecognize perimental and simulated normal incidence spectra for three temperatures (see text for details). In each panel, individual theformationofahexagonalstructureandweshallthere- spectra were displaced along the ordinate for clarity. fore analyze our results by assuming sixfold rotational symmetry about the Ce sites. It is a fundamental prop- erty of hexagonal crystal fields (CF) to split the atomic given by Ce 4f1 configuration (j = 5/2) into three Kramers dou- (cid:16) (cid:17) blets of pure mj character. Unlike in cubic or tetragonal INI(T)=Z−1 I|N1/I2(cid:105)+p1I|N3/I2(cid:105)+p2I|N5/I2(cid:105) , (1) symmetry [7, 11, 12] the CF is therefore fully specified by |mj(cid:105) level splittings and ordering. We denote the CF whereZ =1+p1+p2isthepartitionfunction. Evidently, splittingsas∆1 =E3/2−E1/2 and∆2 =E5/2−E1/2 and inthelimitkBT (cid:29)∆1,∆2 thelineshapeobservedatNI determinetheirmagnitudeandsignfromlinearandmag- converges to the isotropic one. The two experimental netic circular dichroism measurements at the soft x-ray spectra displayed in Fig. 2a) demonstrate that this con- Ce M4,5 edges in what follows. dition is fulfilled in our CeAgx/Ag(111) specimens. The All soft x-ray absorption experiments were carried out NIspectrum(θ =0◦)measuredatT =250Kishardly X at the PM3 bending magnet beamline of BESSY-II, distinguishable from the isotropic spectrum. Berlin, using circular polarization (p ≈ 0.93) [25]. X- In our analysis we make use of simulated absorption ray absorption was measured in the total electron yield spectra to trace the experimental temperature depen- (TEY) mode and normalized by the TEY captured from dences. Thesesimulationswereobtainedfromfullatomic a gold mesh. Although with reduced amplitude, lin- multiplet calculations as implemented in the Quanty ear dichroism can nevertheless be observed by variation Package [26, 27]. To obtain the best match between of the x-ray angle of incidence θ . The polarization calculated and experimental isotropic spectra, the ff X averaged, so-called isotropic spectrum is well approxi- (df)SlaterIntegralswerereducedby42.5%(17.5%)from mated by oblique incidence data taken at θ = 60◦ in their respective Hartree-Fock values, well in accordance X the present work. Its line shape is independent of the with previous work [7, 9, 11, 14, 28]. In addition, the Ce thermal occupation of the CF states, since it is identi- 3dcoreholespinorbitcouplingconstantζ wasslightly 3d cal for all |m (cid:105) initial states. In contrast, spectra mea- readjusted to reproduce the experimental separation be- j sured at normal incidence (NI, i.e. along the hexagonal tween the M and M edges. Theoretical line spectra 4 5 symmetry axis) do exhibit temperature dependent line were convoluted with a Gaussian (FWHM 0.2 eV) rep- shapes, determined by the fractional occupation of the resenting the experimental energy resolution as well as CFsplit|m (cid:105)states. IntroducingtheBoltzmannweights with Lorentzian contributions to account for the lifetime j p = exp(−∆ /k T), the NI spectrum INI(T) is of the core excited states. Since the spectral shape of 1,2 1,2 B 3 the M edge is affected by autoionization decay [29], its 4 lifetimebroadeningwascalculatedbyconvolutionwitha Fano profile (q ≈16) [30] rather than a Lorentzian. TheresultingCeM absorptionspectraaredisplayed 4,5 in Fig. 2b). While the overall agreement of the isotropic spectrum with measured data is very good we note that not all multiplet terms can simultaneously be made to coincide with the experimental features when applying universal scaling factors to the Slater Integrals. This is most apparent for the weak shoulder at 903 eV, which is not discernible in the calculated spectra since its separa- tion from the main M peak (feature C) is too small. 4 TheremainingspectrainFig.2b)demonstratethedif- ferent spectral shapes owing to the anisotropic charge distribution in the |m (cid:105) states. In particular, their most j prominent peaks (A, B & C) feature considerable varia- tions in their relative intensities. Experimental NI data acquired at T >∼ 100 K dis- play variations which cannot be resolved on the scale FIG. 3. Selection of experimental and simulated XMCD of Fig. 2c). In comparison to the isotropic spectra, they spectra. a) low temperature XMCD obtained at θ = neverthelesssystematicallyexhibitaslightlylarger(≈1- X 60◦ (“isotropic” configuration) alongside with the calculated 2%)C/Bpeakintensityratio. Referringtothe|m (cid:105)spe- j XMCD spectrum, scaled such as to match the magnitude of cific spectra of Fig. 2b) this observation immediately re- the experimental data. b) temperature dependent Ce M 4 vealsthat|5/2(cid:105)mustbeanexcitedstate. Asthetemper- XMCD in NI geometry c) same as in b) but for θ =60◦. X ature is lowered, the C/B peak intensity ratio is further enhanced, but in addition the M line shape now ac- 5 quires a noticeable change in spectral appearance. The atomic relation mS = −mL/4 between spin and orbital observed spectral variations restrict the parameter ∆ contributions to the total 4f magnetic moment to hold. 2 to a relatively narrow energy window of ∆ = 1.1±0.2 In the case of Fig. 3a), the Ce 4f polarization amounts 2 meV.ThedeterminationoftheotherCFparameter(∆1) toapprox.0.13µB/atom. Thecorrespondingasymmetry on the basis of NI XAS data alone is less obvious. Sce- intheXAspectraislargestattheM4 edgeandamounts narios with −1 meV <∼ ∆2 <∼ 5 meV can be made to to about 3.7% of the TEY signal. satisfactorily match the sequence of experimental spec- Thetemperaturedependenceofthemagneticresponse tra. This is largely owed to the smallness of the linear atnormalandobliqueincidence,respectively,isshownin dichroism associated with the |3/2(cid:105) fraction of the ini- Fig. 3b) and c). Each dichroic spectrum is multiplied by tial state. The choice of parameters ∆ and ∆ for the the value of the temperature at which it was obtained. 1 2 simulationsinFig.2d)thereforealreadyaccountsforthe In this way, perfect Curie behavior would be reflected information gained from considering the XMCD signal by a constant XMCD magnitude in the plots. At low which we shall discuss next. temperature in particular, the occurrence of single ion The paramagnetic Ce 4f response was probed in an magnetic anisotropy is obvious. Its sign and magnitude appliedmagneticfieldofµ H =1.5T.Whilesufficiently are directly related to the crystal field splitting scheme. 0 smalltowarrantlinearresponse,itcausesanXMCDsig- XMCD data therefore provide an independent probe of nal which can reliably be measured over a considerable the CF scheme within the same set of experiments. temperature range. Fig. 3a) displays the dichroic spec- Amorequantitativeevaluationcanbeperformedafter trum for the case of largest magnetic polarization ob- extractingthetemperaturedependentCe4f susceptibil- tained in the present work, alongside with the simulated itiesfromtheXMCDdata[21]. Tosecondordertheyare XMCD spectrum. We notice that the spectral appear- given [32, 33] by the following expressions for the mag- ance of the XMCD is well accounted for by the atomic netic field applied along (χ||) and perpendicular (χ⊥) to calculations, which were solely optimized to match the the hexagonal axis, respectively: isotropic spectrum. A notable exception is once again g2µ2 the spectral feature at 903 eV, which produces a small χ = B (1+9p +25p ) (2) || 4k TZ 1 2 butdistinctcontributiontomagneticdichroismintheex- B g2µ2 (cid:18) 16k T periment,butisburiedinthedichroismproducedbythe χ = B · 9+ B + mainM4peakinthecalculation. Asinourpreviouswork ⊥ 4kBTZ ∆1 (cid:18) (cid:19) (cid:19) [21],wedeterminetheCe4f polarizationbyapplyingthe 10k T 16k T 10k T + B − B p − B p (3) orbital moment XMCD sum rule [31] and assuming the ∆ −∆ ∆ 1 ∆ −∆ 2 2 1 1 2 1 4 unlikely, though, considering the small 4f hybridization found in the XA spectra and the photoemission results by Schwab et al. [22]. It is most likely, therefore, that the discrepancy is mostly due to an underestimation of the Ce 4f orbital moment in the sum rule evaluation. In conclusion, we have presented a soft x-ray absorp- tion study of an ultrathin, ordered intermetallic phase induced by alloying a sub-monolayer quantity of Ce into the surface of Ag(111). Exploring the temperature de- pendencesofboth,linearandcircularx-raydichroism,we showthatitispossibletoexploretheenergyscaleswhich characterizethismaterial. Inadditiontothesmallnessof T [22],wefindthatbothCFsplittingsandmagneticex- K change coupling occur on energy scales of about 1 meV and below. Our findings highlight both the enormous FIG.4. InversemagneticCe4f susceptibilitiesofCeAg ,de- x terminedfromXMCDmeasurements,alongwithsimulations sensitivity of soft x-ray absorption and the usefulness of accordingtoeq.4. CFparametersarethesameasinFig.2d). scheduling XMCD experiments when characterizing rare earth systems with soft x-rays. This extension comes at little cost, since many soft x-ray end stations provide At an intermediate angle θ the susceptibility reads the means to perform both linear and circular dichroism measurements. cos2θ sin2θ χ = + , (4) θ χ−1−λ χ−1−λ WewishtothankH.SchwabandF.Reinertforhelpful || ⊥ discussions as well as H. Kießling and B. Mu¨nzing for wherewehaveadditionallyallowedformagneticcoupling assistance with experiments. This work was funded by between Ce sites at the mean field level (λ). theDeutscheForschungsgemeinschaftthroughFOR1162. In Fig. 4 we show the temperature dependence of the Accesstosynchrotronradiationwaspartiallygrantedby inverse Ce 4f susceptibilities. The crystal field splitting HZB. We also gratefully acknowledge HZB stafffor their induced anisotropy leads to an offset between χ−1 and support during beam time. || χ−1 which is nearly constant in the temperature range ⊥ spanned by our experiments. It is notably well percepti- ble up to high temperatures, where the precise determi- nationoflineardichroisminourexperimentisquitechal- ∗ [email protected] lenging. Themagnitudeofthisoffsetsensitivelydepends [1] P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 on the CF excitation energies ∆ and ∆ . Nevertheless, (2008). 1 2 the magnetic response in this temperature range is not [2] P. Gegenwart, F. Steglich, C. Geibel, and M. Brando, sufficienttopinpointthenumericalvaluesof∆ ,∆ and Eur. Phys. J. Special Topics 224, 975 (2015). 1 2 [3] N. Grewe and F. Steglich, in Handbook on the Physics λ. Inconjunctionwiththerestrictionson∆ fromabove, 2 and Chemistry of Rare Earths, Vol. 14, edited by K. A. however, we can determine the combination of param- Gschneider, Jr. and L. Eyring (Elsevier, Amsterdam, eters which produces the best simultaneous agreement 1991) p. 343. with both linear and circular dichroism. [4] H. von Lo¨hneysen, A. Rosch, M. Vojta, and P. Wo¨lfle, The outcome of the parameter optimization is dis- Rev. Mod. Phys. 79, 1015 (2007). played in both Fig. 2d) and Fig. 4 for the thermal evo- [5] Y. Yang, Z. Fisk, H.-O. Lee, J. D. Thompson, and lution of the NI XAS and the inverse susceptibilities, re- D. Pines, Nature 454, 611 (2008). [6] M.Sacchi,F.Sirotti, andG.Rossi,SolidStateCommun. spectively. Weobtain∆ =0±0.4meV,∆ =1.25±0.05 1 2 81, 977 (1992). meV and an insignificantly small mean field coupling λ. [7] P.Hansmann,A.Severing,Z.Hu,M.W.Haverkort,C.F. These are the parameter values used for the simulations Chang,S.Klein,A.Tanaka,H.H.Hsieh,H.J.Lin,C.T. displayed in Figs. 2d) and 4. Chen,B.Fak,P.Lejay, andL.H.Tjeng,Phys.Rev.Lett. Thecorrectslopesinχ−1(T)inFig.4areonlyobtained 100, 066405 (2008). by allowing for an overall reduction of the Ce magnetic [8] T. Willers, B. Fak, N. Hollmann, P. O. Ko¨rner, Z. Hu, moment by about 13% compared to the value expected A. Tanaka, D. Schmitz, M. Enderle, G. Lapertot, L. H. for free Ce3+ ions, however. From numerical simulations Tjeng, andA.Severing,Phys.Rev.B80,115106(2009). [9] T.Willers,Z.Hu,N.Hollmann,P.O.Ko¨rner,J.Gegner, withinthesimplifiedNCAschemeproposedbyZwicknagl T. Burnus, H. Fujiwara, A. Tanaka, D. Schmitz, H. H. etal.[34]weestimatethataKondotemperatureofTK >∼ Hsieh, H.-J. Lin, C. T. Chen, E. D. Bauer, J. L. Sarrao, 20 K would be required to produce this reduction by E.Goremychkin,M.Koza,L.H.Tjeng, andA.Severing, Kondoscreening. SuchahighvalueforT appearsquite Phys. Rev. B 81, 195114 (2010). K 5 [10] T.Willers,J.C.Cezar,N.B.Brookes,Z.Hu,F.Strigari, Phenom. 86, 93 (1997). P.Ko¨rner,N.Hollmann,D.Schmitz,A.Bianchi,Z.Fisk, [20] G. van der Laan, E. Arenholz, A. Schmehl, and D. G. A. Tanaka, L. H. Tjeng, and A. Severing, Phys. Rev. Schlom, Phys. Rev. Lett. 100, 067403 (2008). Lett. 107, 236402 (2011). [21] C.Praetorius,M.Zinner,A.Ko¨hl,H.Kießling,S.Bru¨ck, [11] T.Willers,D.T.Adroja,B.D.Rainford,Z.Hu,N.Holl- B. Muenzing, M. Kamp, T. Kachel, F. Choueikani, mann, P. O. Ko¨rner, Y.-Y. Chin, D. Schmitz, H. H. P. Ohresser, F. Wilhelm, A. Rogalev, and K. Fauth, Hsieh, H.-J. Lin, C. T. Chen, E. D. Bauer, J. L. Sar- Phys. Rev. B 92, 045116 (2015). rao, K. J. McClellan, D. Byler, C. Geibel, F. Steglich, [22] H.Schwab,M.Mulazzi,J.Jiang,H.Hayashi,T.Habuchi, H. Aoki, P. Lejay, A. Tanaka, L. H. Tjeng, and A. Sev- D. Hirayama, H. Iwasawa, K. Shimada, and F. Reinert, ering, Phys. Rev. B 85, 035117 (2012). Phys. Rev. B 85, 125130 (2012). [12] T. Willers, F. Strigari, N. Hiraoka, Y. Q. Cai, M. W. [23] J. Kemmer, C. Praetorius, A. Kro¨nlein, P.-J. Hsu, Haverkort, K.-D. Tsuei, Y. F. Liao, S. Seiro, C. Geibel, K.Fauth, andM.Bode,Phys.Rev.B90,195401(2014). F. Steglich, L. H. Tjeng, and A. Severing, Phys. Rev. [24] M. Zinner et al., Unpublished results. Lett. 109, 046401 (2012). [25] T. Kachel, F. Eggenstein, and R. Follath, Journal of [13] F. Strigari, T. Willers, Y. Muro, K. Yutani, T. Taka- Synchrotron Radiation 22, 1301 (2015). batake,Z.Hu,Y.-Y.Chin,S.Agrestini,H.-J.Lin,C.T. [26] M. W. Haverkort, M. Zwierzycki, and O. K. Andersen, Chen, A. Tanaka, M. W. Haverkort, L. H. Tjeng, and Phys. Rev. B 85, 165113 (2012). A. Severing, Phys. Rev. B 86, 081105 (2012). [27] M. W. Haverkort et al., http://www.quanty.org. [14] T. Willers, F. Strigari, Z. Hu, V. Sessi, N. B. Brookes, [28] F. Strigari, T. Willers, Y. Muro, K. Yutani, T. Taka- E. D. Bauer, J. L. Sarrao, J. D. Thompson, A. Tanaka, batake, Z. Hu, S. Agrestini, C.-Y. Kuo, Y.-Y. Chin, H.- S. Wirth, L. H. Tjeng, and A. Severing, Proceedings J. Lin, T. W. Pi, C. T. Chen, E. Weschke, E. Schierle, of the National Academy of Sciences 112, 2384 (2015), A. Tanaka, M. W. Haverkort, L. H. Tjeng, and A. Sev- http://www.pnas.org/content/112/8/2384.full.pdf. ering, Phys. Rev. B 87, 125119 (2013). [15] G.Schu¨tz,W.Wagner,W.Wilhelm,P.Kienle,R.Zeller, [29] B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. R. Frahm, and G. Materlik, Phys. Rev. Lett. 58, 737 Sawatzky,R.C.Karnatak, andJ.M.Esteva,Phys.Rev. (1987). B 32, 5107 (1985). [16] G. van der Laan, B. T. Thole, G. A. Sawatzky, J. B. [30] S. Schippers, Int. Rev. At. Mol. Phys. 2, 151 (2011). Goedkoop,J.C.Fuggle,J.-M.Esteva,R.Karnatak,J.P. [31] B. T. Thole, P. Carra, F. Sette, and G. van der Laan, Remeika, and H. A. Dabkowska, Phys. Rev. B 34, 6529 Phys. Rev. Lett. 68, 1943 (1992). (1986). [32] K.H.MaderandM.W.Swift,J.Phys.Chem.Solids29, [17] C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, 1759 (1968). G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and [33] H. Lueken, M. Meier, G. Klessen, W. Bronger, and F. Sette, Phys. Rev. Lett. 75, 152 (1995). J. Fleischhauer, J. Less-Comm. Met. 63, P35 (1979). [18] J. Sto¨hr, Journal of Magnetism and Magnetic Materials [34] G. Zwicknagl, V. Zevin, and P. Fulde, Z. Phys. B 79, 200, 470 (1999). 365 (1990). [19] J. van Elp and B. Searle, J. Electron Spectrosc. Relat.