Bulk and surface electronic properties of SmB6: a hard x-ray photoelectron spectroscopy study
Y. Utsumi, D. Kasinathan, K-T. Ko, S. Agrestini, M. W. Haverkort, S. Wirth, Y-H. Wu, K-D. Tsuei, D-J. Kim, Z. Fisk, A. Tanaka, P. Thalmeier, L. H. Tjeng
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Bulk and surface electronic properties of SmB : a hard x-ray photoelectronspectroscopy study Y. Utsumi, ∗ D. Kasinathan, K-T. Ko, S. Agrestini, M. W. Haverkort, † S. Wirth, Y-H. Wu, K-D. Tsuei, D-J. Kim, Z. Fisk, A. Tanaka, P. Thalmeier, and L. H. Tjeng Max Planck Institute for Chemical Physics of Solids, N¨othnitzer Straße 40, 01187 Dresden, Germany National Synchrotron Radiation Research Center, 101 Hsin-Ann Road, Hsinchu 30077, Taiwan Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA Department of Quantum Matter, AdSM, Hiroshima University, Higashi-Hiroshima 739-8530, Japan (Dated: June 18, 2018)We have carried out bulk-sensitive hard x-ray photoelectron spectroscopy (HAXPES) measure-ments on in-situ cleaved and ex-situ polished SmB single crystals. Using the multiplet-structurein the Sm 3 d core level spectra, we determined reliably that the valence of Sm in bulk SmB is closeto 2.55 at ∼ J = 0 but also the J = 1 state of the Sm 4 f configuration becomes occupied at elevatedtemperatures. Making use of the polarization dependence, we were able to identify and extract theSm 4 f spectral weight of the bulk material. Finally, we revealed that the oxidized or chemicallydamaged surface region of the ex-situ polished SmB single crystal is surprisingly thin, about 1 nmonly. PACS numbers: 71.20.Eh, 71.27.+a
I. INTRODUCTION
The interplay of strong spin-orbit coupling andelectron-electron correlations in rare earth compoundshas recently been shown theoretically to allow for theemergence of topologically nontrivial surface bands,thereby merging the fields of strongly correlated systemsand Kondo physics with topology. A minimum modelconsisting of localized f -electrons and dispersive conduc-tion electrons with opposite parity provides us a topolog-ical f -electron system that hosts topologically protectedmetallic surface states within a hybridization gap, i.e. atopological Kondo insulator .In this context, it was proposed that the Kondo in-sulator, or intermediate valent system, SmB is a goodcandidate material to qualify as the first strongly corre-lated topological insulator. Indeed, the robust metal-licity which is attributed to a topologically protectedsurface state could be a promising explanation for thelong-standing mysterious low-temperature residual con-ductivity of SmB . SmB has therefore triggered atremendous renaissance in recent years, and many re-search efforts have been made to establish the topologicalnature of the material using a wide range of experimentalmethods, e.g. angle-resolved photoelectron spectroscopy(ARPES) , scanning tunneling spectroscopy , re-sistivity and surface conductance measurements ,and high pressure experiments . A recent special is-sue with foreword provides an excellent overview of thefield .SmB is an intermediate valent compound where thevalence number ( v ) of Sm ion varies between 2+ and3+ as first observed by x-ray absorption experiments .An early magnetic susceptibility study hinted at a va-lence of v ∼ . extracted v ∼ . L x-ray absorption spec-troscopy, the valence numbers v = 2.6-2.65 , 2.53 at T =4.2 K , and 2.52 at T = 2 K were determined. A Sm L γ emission spectroscopy study found v = 2.65 at roomtemperature , and a very recent take-off angle photoe-mission study yielded v = 2.48 at 150 K for the bulk .The Sm valence is an important issue for the theory ofthe proposed topological character of SmB . While an ab-initio based study including the full 4 f -orbital basispredicts the topological insulator phase with v ≈ ,model calculations for materials with cubic symmetryincluding only the Γ quartet states proposed a phasediagram in which SmB is expected to be a band in-sulator for v < < v < to estimate the Sm valence. How-ever, the obtained value varies depending on the experi-mental methods. Here, we performed bulk sensitive hardx-ray photoelectron spectroscopy (HAXPES) to collectthe Sm 3 d core level spectra from which the Sm valencecan be determined . We utilized the intensities of themultiplet structure of the Sm and Sm features, andby doing so, we did not need to model the background,and were therefore able to extract more reliably the ra-tio between the Sm and Sm signals. Since many ofthe reported resistivity and surface conductance experi-ments on SmB have been carried out at ambientconditions or on samples which were prepared at suchconditions, there is also a need to evaluate the effect ofambient conditions on the SmB surface. We thereforeperformed HAXPES on in-situ cleaved SmB and ex-situ polished SmB and compared the results. I n t en s i t y ( a r b . un i t s )
300 K250 K200 K150 K100 K050 K020 K005 K
Sm 3 d Sm 3 d Sm 3 dh ν =6.5 keV( in situ cleaved SmB ) Sm Sm Sm Sm FIG. 1. (Color online) Temperature dependence of the Sm 3 d spectra of an in-situ cleaved SmB single crystal. With increasingtemperature, the intensity of the Sm (Sm ) component decreases (increases). II. EXPERIMENTAL
The experiments have been carried out at the Max-Planck-NSRRC HAXPES station at the Taiwan undula-tor beamline BL12XU at SPring-8, Japan. The photonbeam with hν ∼ . ∼
170 meV and the zero of the binding energyof the photoelectrons was determined using the Fermiedge of a gold film. The SmB single crystals used in ourstudy were grown by the aluminium flux method . Onesingle crystal was cleaved in-situ under ultrahigh vac-uum conditions (better than 3 × − mbar). A secondsingle crystal was mirror-polished with an Al O polish-ing pad, cleaned using diluted HCl for 2 minutes, rinsedwith isopropanol, and subsequently transferred into theultrahigh vacuum system. A detailed description of thepolishing procedure can be found in Ref. 25. III. RESULTS AND DISCUSSIONSA. Sm valence
Figure 1 shows the Sm 3 d core level spectra of in-situ cleaved SmB for temperatures ranging from 5 K to 300K. The Sm 3 d spectra are split into a 3 d / and a 3 d / branch due to the spin-orbit interaction. Each of thesebranches is further split into the so-called Sm (4 f )and Sm (4 f ) components which represent the Sm 4 f → c f + e and the Sm 4 f → c f + e transitions,respectively, where c denotes a 3 d core hole and e the out-going photoelectron. With increasing temperature, theintensity of the Sm (Sm ) component gradually de-creases (increases) and consequently, the mean-valence v of Sm moves towards becoming more trivalent. We wouldlike to note that there were no detectable degradation ef-fects of the sample surface after the temperature cycle,see Appendix A.In order to obtain v quantitatively, a simulation analy-sis was performed on the spectra by carrying out atomicfull-multiplet calculations to account for the lineshapeof the Sm 3 d core level spectra . Crystal field effectsare not taken into account since the corresponding energysplittings are minute compared to the lifetime broadeningof the core-hole final states. The hybridization betweenthe Sm and Sm core hole final states is neglectedin view of the fact that their energy separation is muchlarger than the hopping integral between the 4 f J =0and 4 f J =5/2 configurations which is very small due toboth the contracted radial wavefunctions of the Sm 4 f and fractional-parentage matrix element effects . Thecalculated spectra are convoluted with a Lorentzian func-tion for lifetime broadening and a Gaussian to accountfor the instrumental resolution. The experimental spec-tra at a given temperature are then fitted by adjustingthe weights of the calculated Sm and Sm compo-nents such that in the difference spectrum between theexperimental and calculated spectra the fingerprints ofthe Sm and Sm multiplet structures are minimized.The broadening parameters and as well as the values usedfor the Coulomb and exchange multiplet interactions arelisted in Ref. 46.The results for T = 5 K are shown in Fig.2(a). Theexperimental spectrum taken at ∼ (green line) andSm components (brown line) produces a differencespectrum (black line) which shows a gently sloping back- (a) Sm 3 d h ν =6.5 keV( in situ cleaved SmB ) Exp.Sm in 4 f conf.Sm in 4 f conf.Difference I n t en s i t y ( a r b . un i t s ) Sm 3 d Sm 3 d I n t en s i t y ( a r b . un i t s ) (b) Sm 3 d
300 K (Simulation includes J=1 states) h ν =6.5 keV( in situ cleaved SmB ) Exp.Sm in 4 f conf.Sm in 4 f (J=0)Sm in 4 f (J=1)Sm in 4 f conf.Difference (c) Sm 3 d
300 K (Simulation without J=1 states) h ν =6.5 keV( in situ cleaved SmB ) Exp.Sm in 4 f conf.Sm in 4 f conf.Difference I n t en s i t y ( a r b . un i t s ) FIG. 2. (Color online) Multiplet analysis of the Sm 3 d spectra of the in-situ cleaved SmB sample. (a) T = 5 K, (b) T =300 K including the Boltzmann occupation of the J = 1 states of the Sm (4 f ) configuration in the simulation, (c) T =300 K without the J = 1 states of the Sm 4 f . The experimental spectra at 5 K and at 300 K are presented by the purpleand red lines, respectively. The simulations for the Sm and Sm components are displayed by the green and brown lines,and a break down of the J = 0 and J = 1 components of the Sm (4 f ) configuration by the dark green and orange lines,respectively. Black lines represent the inelastic background signal and were obtained by subtracting the simulated multipletstructure from the experimental spectra. ground plus some residual wiggling features which orig-inate mostly from tiny deviations in the peak positionsand peak widths of the multiplet structures. A Sm mean-valence of v = 2.55 is extracted from this spectrum byusing formula v =2+ I /( I + I ). Here, I and I denote the integrated spectral intensities of the Sm and Sm simulated spectra, respectively, optimized tofit the experimental spectrum.In the simulations for the higher temperature spectra,we allow for the Boltzmann occupation of the excitedstates of the Sm. Fig. 2(b) displays the results for the T = 300 K spectrum. Here we can notice that not onlythe J = 0 (dark green line) but also the J = 1 (orangeline) state of the Sm (4 f ) configuration contributes to the spectrum. The energy splitting between the J = 0and J = 1 states was set to 35 meV by fine tuning the4 f spin-orbit and multiplet interactions as to matchthe energy splitting found from inelastic neutron scatter-ing experiments resulting in about 57% occupationfor the J = 0 and 43% for the J = 1 states at roomtemperature. The difference between the experimentalspectrum and the multiplet calculation is a gently slop-ing background curve, similarly smooth like in the 5 Kcase, demonstrating the validity of the analysis proce-dure. We stress that in the simulation we cannot omitthe J = 1 Boltzmann occupation. This is clearly revealedby Fig. 2(c), which shows the poor match between the J = 0 only simulation and the experimental spectrum Temperature (K) 3002502001501005002.662.642.622.602.582.56 S m m ean - v a l en c e Sm mean-valence( in-situ cleaved SmB ) FIG. 3. (Color online) Temperature dependence of the Smmean-valence of the in-situ cleaved SmB sample. for the Sm d / . The deviations can also be observedas strong wiggles in the difference spectrum between theexperimental and the multiplet calculation.We would like to remark that for the Sm part ofthe spectrum, the simulations yield a temperature inde-pendent line shape for the temperatures considered here.The energy splitting between J =5/2 and J =7/2 multi-plets is too large to cause an appreciable Boltzmann oc-cupation of the higher lying J =7/2, so that the spectrumis given primarily by the lower lying J =5/2. Inclusion ofa cubic crystal field will also not produce a temperatureeffect, due to the fact that the Γ and Γ crystal fieldstates originate from the same J quantum number, whileat the same time the crystal field energy scale is abouttwo orders of magnitude smaller than that of the inverselife time of the 3 d core-hole, i.e. any tiny spectral changesdue to the crystal field are washed out by the core-holelife time broadening, see Appendix B.Applying this procedure to spectra taken at other tem-peratures, allowed for a determination of the Sm mean-valence as a function of temperature. The results areplotted in the main panel of Fig.3, revealing a gradualincrease of the Sm valence to a value of v = 2.64 at 300K. In general, our findings for the Sm valence and itstemperature dependence are consistent with the resultsreported in earlier Sm- L , x-ray absorption spectroscopy(XAS) and Sm L γ emission spectroscopy studies .However, our experimental method and analysis are dif-ferent with implications for the reliability of the extractedvalues of the valence. The Sm and Sm componentsin our photoemission core level spectra are well sepa-rated, more so than in the Sm- L , and L γ spectra. Inaddition, the presence of sharp multiplet structures inthe Sm 3 d spectra allows us to unambiguously assign theSm and Sm components, such that their integratedintensities can be determined without having to modelthe background. In this way, we also ensure that the mul-tiplet structures are fitted without violating the atomic 3 d / and 3 d / branching ratio (see the Appendix C). Allthis adds to the reliability of the valence determinationby performing HAXPES on the 3 d level. In comparingour HAXPES results with a recent HAXPES take-off an-gle study carried out at 150 K , we would like to notethat we have found quite a higher value for the valence,namely v = 2.61 at 150 K, while the take-off angle HAX-PES provided a value of only v = 2.48. Perhaps this isrelated to the fact that the take-off angle HAXPES studyhas put more weight in getting a good simulation of thesurface sensitive part of the data and thus less on thebulk properties.One of the interesting findings here is that the low tem-perature valence of v = 2.55 is very close to the borderbetween SmB being a band insulator (for v < < v <
3) as pointedout in Refs. 5 and 6. If we take these numbers seriously,then it is in fact not clear at all that SmB can be ex-pected to be a strongly correlated topological insulator.However, the critical value v c = 2 .
56 that separates triv-ial and topological insulator depends on numerous modelparameters and therefore may be subject to fine-tuning.Consequently further investigations, both theoretical andexperimental, are clearly warranted.Another important aspect is the increasing valencewith temperature. This effect even outweighs thermalexpansion, i.e. the increasing presence of Sm (be-ing smaller than Sm ) causes the lattice constant toshrink with temperature (and correspondingly the linearthermal expansion coefficient to have negative values) fortemperatures as high as 150 K . The valence is relatedto the number of 4 f holes (in the degenerate J = 5 / n hf ( T ) = v ( T ) −
2. Without considering hy-bridization it becomes entropically favorable to occupythe more degenerate Sm ( J = 5 /
2) hole states insteadof the Sm ( J = 0) singlet state to decrease the freeenergy. Therefore n hf ( T ) and hence the valence v ( T ) in-crease with temperature. In a more microscopic pictureincluding the hybridization, a part of the hole spectralweight is pushed above the Fermi level, which leads to adecrease in n hf ( T ) when temperature decreases. This isdue to the formation of the bound state of 4 f hole witha conduction electron as in the case of Yb . B. Valence Band
The large inelastic mean-free path of electrons with ki-netic energies of several keV provides an opportunityto collect photoemission spectra that are representativeof the bulk material by carrying out experiments usinghard x-ray photons. The spectra from such HAXPESexperiments can then be used as a reference in a com-parison with spectra taken at lower photon energies inorder to identify features that may originate from thesurface region of the sample. In particular, the contribu-tion of the surface may become significant if ultra-violetphoton energies are used, as in standard angle-resolved (b) LDA+SO SmB with Sm in f configuration (Shifted 1.0 eV to higher binding energies)DifferenceB 2sSm 5p Sm 6sSm 5dSum I n t en s i t y ( a r b . un i t s ) (a) valence band h ν =6.5 keV ( in situ cleaved SmB ) Sm I n t en s i t y ( a r b . un i t s ) (c) Extracted 4f spectral weight horizontal geometryvertical geometry I n t en s i t y ( a r b . un i t s ) Sm Sm H F P I G D F Atomic multiplet structures
FIG. 4. (Color online) (a) Experimental valence band spectraof in-situ cleaved SmB measured in the horizontal (red) andvertical (blue) geometry at T = 50 K. The spectra are nor-malized to the height of the Sm f peaks. (b) Differencebetween the horizontal and vertical geometry spectra togetherwith the B 2 s and Sm 5 p , 5 d , 6 s partial density of states froma non-magnetic band structure calculation with Sm in the f configuration. The densities of states are displayed witha shift of 1 eV towards higher binding energies and weightedwith the photo-ionization cross-section factors as explained inthe text. (c) The experimental valence band spectrum aftera weighted (see text) subtraction of the difference spectrum(b) (black line), together with the assignment of the atomicmultiplet structures (blue sticks and labels) . photoelectron spectroscopy (ARPES) experiments .At the same time, a HAXPES spectrum of SmB can- TABLE I. Subshell photo-ionization cross-section ( σ ) at 6.5keV extrapolated from Ref. 52–54. σ is divided by the numberof electrons in the subshell. β denotes the dipole parameter ofthe angular distribution. The cross-section for horizontal andvertical geometries are obtained by σ [1+ β { θ ) } ].Here θ is the angle between the photo-electron momentum andthe polarization vector E of the light. In the horizontal andvertical geometries, θ =0 and 90 deg., respectively.Atomic σ / e − β Horizontal Verticalsubshell (kb) (kb) (kb)B 2 s p / f / p / p / s d / not be interpreted as representing directly the Sm 4 f spectral weight since the photo-ionization cross-sectionof the Sm 4 f states is not the only one which contributesto the spectrum. Other states, like the B 2 s or Sm5 d , 6 s may also have comparable photo-ionization cross-sections when hard x-rays are used . Table I lists thephoto-ionization cross-sections of the B 2 s , 2 p and Sm4 f , 5 p , 5 d , 6 s orbitals as extracted or interpolated fromthe data provided by Trzhaskovskaya et al. .In order to extract the more relevant Sm 4 f spec-tral weight from HAXPES, we can make use of the pro-nounced dependence of the spectra on the polarization ofthe light as given by the so-called β -asymmetry param-eter of the photo-ionization cross-sections of the variousatomic shells involved . They are also listed in Ta-ble I. In particular, it has been shown experimentally byWeinen et al. , that the s contribution to the spectra canindeed be substantially reduced (albeit not completelysuppressed due to side-scattering effects) if the directionof the collected outgoing photoelectrons is perpendicularto the electric field vector of the light.To make use of this polarization dependence we mea-sured the valence band spectra of the in-situ cleavedSmB crystal using the two photoelectron energy ana-lyzers, one positioned in the horizontal geometry, andthe other mounted in the vertical geometry (see sectionII). The spectra obtained in this manner are displayed inFig. 4(a) in red and blue, respectively. The spectra arenormalized with respect to the peak height of the fea-tures positioned at 0.1 and 1.1 eV binding energy. Thesefeatures are known to originate from the Sm 4 f states.We can clearly observe that there is a very strong polar-ization dependence in a very wide energy region of thespectra, i.e., from 3 eV to 12 eV binding energy. The dif-ference between the two spectra is displayed by the greencurve in Fig. 4(b) and has maxima at about 5 and 10eV. TABLE II. Subshell photo-ionization cross-sections relative tothat of Sm 4 f . The horizontal and vertical cross sections inTable I are divided by those of Sm 4 f . The difference valuesare obtained by subtracting the numbers of the vertical fromthe horizontal.Atomic Horizontal Vertical differencesubshellB 2 s p p s d In order to elucidate the origin of this strong polar-ization dependence, we have listed in Table I the ef-fective photo-ionization cross-sections for the two ge-ometries and performed band structure calculations us-ing the full-potential non-orthogonal local orbital code(FPLO) to extract the B 2 s , 2 p and Sm 4 f , 5 p , 5 d , 6 s partial density of states (PDOS). The local density ap-proximation (LDA) including spin-orbit (SO) couplingwas chosen. We considered a non-magnetic calculationwith the Sm 4 f configuration , and obtained a totalDOS which is quite similar to an earlier calculation forthe same Sm configuration . The PDOSes are multi-plied by the Fermi function and convoluted with a 0.2 eVFWHM Gaussian broadening, and shown in Fig. 4(b).Here we have weighted the relevant PDOSes with thefollowing factors: from Table I we calculate the photo-ionization cross-sections relative to that of the Sm 4 f ,and list them in Table II for each geometry; subsequently,we take the difference of the numbers between the twogeometries and use them as multiplication factors for thePDOSes.Fig. 4(b) compares the experimental horizontal-vs-vertical difference spectrum (green line) with theweighted PDOSes. The sum of these weighted PDOSes(black dashed line) is in reasonable agreement with theexperiment: the two main maxima at 5 and 10 eV energyare reproduced. The fact that the intensity ratio betweenthese two main maxima does not match well can perhapsbe explained by the expected differences in the atomicorbitals used in the photo-ionization cross-section calcu-lations compared to the ones used in the FPLO bandstructure code. We should note that we have artificiallyshifted the results of our calculations by 1 eV towardshigher binding energies in order to better align the po-sitions of the main features. This shift may be viewedas an ad-hoc correction to the band structure calcula-tions which did not take into account the intermediatevalent state of Sm. It is also interesting to note that thephoto-ionization cross-section numbers in Table I and IIare extremely large for the Sm 5 p in comparison to thoseof the other orbitals. Consequently, the inclusion of theSm 5 p becomes important for a quantitative analysis of the valence band HAXPES spectra, although in terms ofelectronic structure, the contribution of the Sm 5 p PDOSto the valence band can be safely neglected.Although the experimental valence band spectrumtaken with the vertical geometry as shown in Fig. 4(a)(blue line) represents already mainly the Sm 4 f spectralweight (see Tables I and II), we nevertheless can make afurther attempt to remove as much as possible the non-4 f contribution by carrying out the following exercise: wesubtract from the vertical spectrum (I v , blue line, Fig.4a) the horizontal-vs-vertical difference spectrum (I h -I v ,green line, Fig. 4b) multiplied by factor A, and we alsosubtract from the horizontal spectrum (I h , red line, Fig.4a) the same horizontal-vs-vertical difference spectrum(I h -I v , green line, Fig. 4b) but now multiplied by factorB, such that the so-obtained spectra are identical: I v -A(I h -I v ) = I h - B(I h -I v ), i.e. B-A =1. We have foundA=0.8 and B=1.8 and we refer to the result as the ex-tracted 4 f spectral weight represented by the black linein Fig. 4(c). If the orbitals that made up the horizontal-vs-vertical difference spectrum were to have the same β asymmetry parameter, then this procedure will removethe non-4 f contributions from the vertical and horizon-tal spectra. Fig. 4(c) displays this extracted 4 f result(black line), together with the assignments of the atomicmultiplet structure (blue sticks and labels) belonging tothe photoemission final states which are reached whenstarting from the Sm and Sm ground states . Wecan clearly see that the extracted 4 f spectral weightspectrum contains most of the sharp multiplet features,not only the high intensity ones at 0.1 and 1.1 eV butalso smaller ones in the energy range between 3 and 12eV. Obviously, there are also some ’left-over’ intensitiesthat do not match the multiplet structure. As explainedabove, the subtraction procedure cannot be perfect sincethe different non-4 f orbitals have different β asymmetryparameters (see Table I).An important result to take from Fig. 4(a) and (c) isthat there are only two main peaks in the energy rangeup to 2 eV, namely at 0.1 and 1.1 eV. This is to becontrasted to several photoemission studies using ultra-violet light where the presence of yet another peak at 0.8eV binding energy has been reported . Based onour HAXPES results, we infer that this 0.8 eV peak verylikely originates from the surface region of the SmB ma-terial, supporting the assignment made earlier by Allen et al. . In fact, the extreme sensitivity of this featureto the experimental conditions , e.g. the rapid disap-pearance with time even under ultra-high vacuum condi-tions, suggests strongly that the 0.8 eV peak is caused bySm atoms residing on top of the surface. Given the factthat the (001) surface investigated in the ARPES studiesis polar , a Sm termination must indeed be accompaniedby a substantial electrostatic potential rearrangement forthe Sm atoms at the surface. Yet, STM studies also re-vealed that an unreconstructed Sm-terminated surfaceis rather rare. Instead, complex ordered and disorderedsurface structures are more commonly observed . C. Surface of ex-situ polished SmB One can readily expect that the surface of an ex-situ polished SmB single crystal will be different from theone of an in-situ cleaved sample. Not only will any Smpresent on the surface be oxidized, but also the oxida-tion process may in principle continue further into thebulk material, thereby creating a thicker surface region inwhich the Sm may have a valence different from the bulkvalue. In order to investigate the consequences of an ex-situ preparation of the samples, we also carried out Sm3 d core-level photoemission studies on ex-situ polishedSmB samples.In Fig. 5(a) the Sm 3 d / spectrum of an ex-situ pol-ished SmB and its temperature dependence is presented.It exhibits the same Sm and Sm components withthe same temperature tendency as the in-situ cleavedSmB . However, the Sm mean-valences are shifted tohigher values over the entire temperature range as com-pared to those of the in-situ cleaved sample: For the ex-situ polished SmB we obtained v = 2.61 at 20 K and v =2.68 at 250 K, see Fig. 5(b). This is to be compared to2.55 and 2.64, respectively, for the in-situ cleaved SmB .Clearly, an analysis of the spectra obtained for the ex-situ polished SmB sample has now to take into accountthe possibility of a non-uniform value of v at the surfaceand in the bulk. To accomplish this, we adopt a mini-mal model (even simpler than the one used in Ref. 39)in which we assume that the sample can be divided intotwo regions, namely the surface region which has the Smin its fully oxidized 3+ state, v surf = 3, and the bulkregion which has its pristine intermediate-valence prop-erties v bulk , see the inset of Fig. 5(b). This allows us toset up an equation for the measured average valence v av of the ex-situ polished SmB taking also into account theprobing depth of the photoemission measurement: v av Z ∞ e − z/λ dz = v surf Z d e − z/λ dz + v bulk Z ∞ d e − z/λ dz. (1)Here, λ is the inelastic mean-free path of the photoelec-trons, z the distance from the surface, and d the thicknessof the surface region. After integration, one can obtain d from dλ = ln (cid:20) v surf − v bulk v surf − v av (cid:21) . (2)Using the experimental values of v bulk (Fig. 3) and v av (Fig. 5(b)) as well as an estimated inelastic mean-free path of about ∼
72 ˚A for 5.5 keV photoelectrons ,we arrive at a thickness d ≈ d ≈ ex-situ polished SmB is rather small, about 1 nm. It appears that SmB has a surface which is relatively’leak-tight’ against exposure to ambient atmosphere.One then might conjecture that this could explain whymany of the conductivity measurements carried outunder ambient conditions exhibit a surprisingly highreproducibility . IV. SUMMARY
We have performed bulk sensitive hard x-ray photo-electron spectroscopy measurements on in-situ cleavedSmB to elucidate the Sm valence and the Sm 4 f spec-tral weight of the bulk material. The multiplet structurein the Sm 3 d core level spectra provides a reliable base foran analysis of the valence. This analysis results in a valueof v = 2.55 at ∼ . The strong increase ofthe valence with temperature suggests that this is drivenby the entropic gain in free energy due to the higher de-generacy of the magnetic Sm f state compared tothe non-magnetic 4 f singlet state of the Sm . At ele-vated temperatures we can clearly observe in our spectrathe presence of the Boltzmann occupation of the J = 1state of the Sm 4 f configuration. The strong polariza-tion dependence in the valence band spectra allowed usto extract the Sm 4 f spectral weight, thereby disentan-gling surface from bulk contributions to the valence bandspectra collected by ARPES. The measurements on ex-situ polished SmB single crystals revealed an oxidized orchemically damaged surface region which is surprisinglythin, of order 1 nm only. ACKNOWLEDGMENTS
We would like to thank Thomas Mende and ChristophBecker for their skillful technical assistance and SahanaR¨oßler for helpful discussions. D. K. acknowledges fund-ing from the Deutsche Forschungsgemeinschaft throughSPP 1666. K-T. K. acknowledges support from the MaxPlanck-POSTECH Center for Complex Phase Materi-als and the NRF (Grant. No. 2016K1A4A4A01922028)funded by MSIP of Korea.
Appendix A: Reproducibility of the Sm 3 d spectra In order to verify the absence of surface degradationeffects, we compare in Fig. 6 the Sm 3 d / spectrum mea-sured at 50 K at the beginning of the experiment with theone measured at the very end of the temperature cycle(50 K →
20 K → →
100 K →
200 K →
250 K →
300 K →
250 K200 K150 K100 K050 K020 K I n t en s i t y ( a r b . un i t s ) Sm Sm (a) Sm 3 d h ν =6.5 keV( ex-situ polished SmB ) SmB bulksurface z d λ vacuum2.702.682.662.642.622.60 S m m ean - v a l en c e (b) Sm mean-valence( ex-situ polished SmB ) Temperature (K) 300250200150100500
FIG. 5. (Color online) (a) Temperature dependence of the Sm 3 d / spectra of the ex-situ polished SmB single crystal. (b)The temperature dependence of the Sm mean-valence as extracted from the Sm spectra in (a). The inset shows a schematicmodel of the bulk and surface regions as used in the fits, see text. Here, d is the thickness of the surface region, λ the inelasticmean-free path of the photoelectrons and z the distance from the sample surface. that the observed temperature evolution of Sm 3 d spec-trum is real. The total measurement time for the cyclewas 33 hours. Sm 3 d
50 K in-situ cleaved SmB (after background subtraction) Sm Sm I n t en s i t y ( a r b . un i t s ) FIG. 6. (Color online) Sm 3 d / spectra measured at 50 K atthe beginning of the experiment (red line) and the end of thetemperature cycle (blue line). Appendix B: Crystal electric field effect on the Sm d spectrum In the case of Sm f (Sm ), the lowest 4 f multipletstates are given by the J =5/2 and J =7/2, with the latterabout 130 meV higher in energy. A cubic crystal electricfield splits the J =5/2 further into the quartet Γ and thedoublet Γ states. Although the precise value of the crys-tal field for SmB is still not known, if we adopt the valueof the crystal field for NbB determined from inelastic neutron scattering experiments , the energy differencebetween the Γ and Γ states is about 13 meV, which isabout one tenth of that between the J =5/2 and J =7/2levels.Assuming the same crystal field, we have calculated theSm 3 d core-level spectrum for T =1 K and T =300 K. Theresults are shown in Fig. 7. In contrast with the Sm spectra, where we found the large temperature effects,we here clearly observe that the spectra are practicallyidentical. One reason is that the energy splitting between J =5/2 and J =7/2 is too large to cause an appreciableBoltzmann occupation of the J =7/2 for the temperaturesconsidered here, i.e. only the J =5/2 contribute to thespectrum. Another reason is that the inclusion of thecubic crystal electric field does not add any noticeablenew spectral features due to the fact that the Γ and Γ states originate from the same J quantum number, whileat the same time the crystal field energy scale is abouttwo orders of magnitude smaller than that of the inverselife time of the 3 d core-hole. Appendix C: Background correction for the Sm 3 d spectra The standard procedure in the literature in evaluat-ing the valence of mixed valent strongly correlated sys-tems from core level spectra is to first make a correctionfor the background signal due to inelastic electron scat-tering processes, and then to evaluate the intensities ofthe relevant configurations, in our case, the Sm andSm . The problem is that for this procedure to workaccurately one needs to know the loss-function (in pho-toemission) in order to know what line shape the back-ground should have. However, the loss-function is usu-ally not known and it is a major effort to determine it
300 K001 K I n t en s i t y ( a r b . un i t s ) Sm 3 d in 4 f conf. (Simulation includes J=5/2 and 7/2 states) FIG. 7. (Color online) Calculated Sm 3 d core-level spectrumfor a Sm ion at T =1 K (blue dashed line) and T =300 K(red line) with the cubic crystal field for NdB in Ref. 61.The J =5/2 Γ ground state, the J =5/2 Γ excited stateat ∼
13 meV and higher lying J =7/2 excited states around130 meV are included for the initial state (see text). Thespectra were convoluted with a Lorentzian function withFWHM=0.45 eV and a Gaussian function with FWHM=0.22eV. experimentally. It is obvious that different assumptionsfor the line shape of the background will lead to differ-ent background-corrected spectra and thus likely to dif-ferent values for the valence. To illustrate the ambigui-ties that enter when using a background correction pro-cedure, we now apply the generally used integral back-ground correction to our 5 K spectrum, see panel (a)of Fig. 8. It is interesting to note that this integralbackground shows discrepancies to the background thatwe have obtained using the multiplet line shape analy-sis as displayed in Fig. 2 (a), see panel (b) of Fig. 8and compare the black dashed line with the black line,respectively. Consequently, there are also discrepanciesbetween the integral-background-corrected spectrum andthe optimal simulation from Fig. 2 (a), i.e. comparethe red line with the blue line, respectively, in panel (c)of Fig. 8. The integral-background-corrected spectrumhas in fact intensities over a wide energy range that can-not be accounted for by the multiplet structures. Alsothe intensity of the 3 d / relative to the 3 d / has in-creased in the integral-background corrected spectrumin comparison with the multiplet theory, meaning thatthe integral-background corrected spectrum violates theatomic branching ratio between 3 d / and 3 d / compo-nents. This indicates that our multiplet line shape anal-ysis can give a more reliable Sm valence value than theone using integral background. ∗ [email protected] † Present Address: Institute for theoretical physics, Heidel-berg University, 69120 Heidelberg, Germany M. Dzero, K. Sun, V. Galitski, and P. Coleman, Phys. Rev.Lett. , 106408 (2010). T. Takimoto, J. Phys. Soc. Jpn. , 123710 (2011). M. Dzero, K. Sun, P. Coleman, and V. Galitski, Phys. Rev.B , 045130 (2012). F. Lu, J. Z. Zhao, H. Weng, Z. Fang, and X. Dai, Phys.Rev. Lett. , 096401 (2013). M. Dzero, and V. Galitski, J. Exp. Theor. Phys. , 449(2013). V. Alexandrov, M. Dzero, and P. Coleman, Phys. Rev.Lett. , 226403 (2013). J. W. Allen, B. Batlogg, and P. Wachter, Phys. Rev. B ,4807 (1979). B. Gorshunov, N. Sluchanko, A. Volkov, M. Dressel, G.Knebel, A. Loidl, and S. Kunii, Phys. Rev. B , 1808(1999). K. Flachbart, K. Gloos, E. Konovalova, Y. Paderno, M.Reiffers, P. Samuely, and P. ˇSvec, Phys. Rev. B, , 085104(2001). N. Xu, P. K. Biswas, C. E. Matt, R. S. Dhaka, Y. Huang,N. C. Plumb, M. Rodovi´c, J. H. Dil, E. Pomjakushina, K.Conder, A. Amato, Z. Salman, D. Mck. Paul, J. Mesot, H.Ding, and M. Shi, Phys. Rev. B , 121102(R) (2013). Z. -H. Zhu, A. Nicolaou, G. Levy, N. P. Butch, P. Syers, X.F. Wang, J. Paglione, G. A. Sawatzky, I. S. Elfimov, andA. Damasceli, Phys. Rev. Lett. , 216402 (2013). M. Neupane, N. Alidoust, S. -Y. Xu, T. Kondo, Y. Ishida,D. -J. Kim, C. Liu, I. Belopolski, Y. J. Jo, T. -R. Chang,H. -T. Jeng, T. Durakiewicz, L. Balicas, H. Lin, A. Bansil,S. Shin, Z. Fisk, and M. Z. Hasan, Nat. Commun. , 2991(2013). J. Jiang, S. Li, T. Zhang, Z. Sun, F. Chen, Z. R. Ye, M.Xu, Q. Q. Ge, S. Y. Tan, X. H. Niu, M. Xia, B. P. Xie,Y. F. Li, X. H. Chen, H. H. Wen, and D. L. Feng, Nat.Commun. , 3010 (2013). J. D. Denlinger, J. W. Allen, J. S. Kang, K. Sun, B. I. Min,D. J. Kim, and Z. Fisk, JPS Conf. Proc. , 017038 (2014). N. Xu, C. E. Matt, E. Pomjakushina, X. Shi, R. S. Dhaka,N. C. Plumb, M. Radovi´c, P. K. Biswas, D. Evtushinsky,V. Zabolotnyy, J. H. Dil, K. Conder, J. Mesot, H. Ding,and M. Shi, Phys. Rev. B , 085148 (2014). M. M. Yee, Y. He, A. Soumyanarayanan, D. -J. Kim, Z.Fisk, and J. E. Hoffman, arXiv:1380.1085 (2013). S. R¨oßler, T. -H. Jang, D. -J.Kim , L. H. Tjeng, Z. Fisk, F.Steglich, and S. Wirth, Proc. Natl. Acad. Sci. USA ,4798 (2014). W. Ruan, C. Ye, M. Guo , F. Chen, X. Chen, G. M. Zhang,and Y. Wang, Phys. Rev. Lett. , 136401 (2014). S. R¨oßler, L. Jiao, D. -J. Kim, S. Seiro, K. Rasim, F.Steglich, L. H. Tjeng, Z. Fisk and S. Wirth, Phil. Mag. , 3262 (2016). L. Jiao, S. R¨oßler, D. -J. Kim, L. H. Tjeng, Z. Fisk, F.Steglich, and S. Wirth, Nat. Commun. , 13762 (2016). M. Ciomaga Hatnean, M. R. Lees, D. McK. Paul, and G.Balakrishnan, Scientific Rep. , 3403 (2013). Sm 3 d Sm 3 d I n t en s i t y ( a r b . un i t s ) (a) Sm 3 d ExperimentIntegral background
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