Electronic structure of correlated electron materials from photoemission in high-quality single crystals

Much of our understanding of heavy fermion systems over the past two decades has been based on the single impurity model and its approximate solutions. We show with numerous examples of photoelectron spectra, especially with YbInCu , 4 that this model is not applicable to stoichiometric heavy fermion compounds. There is overwhelming evidence that the correct description of heavy fermions must include very narrow, hybridized bands which exist already at temperatures far above the thermodynamically determined Kondo temperature, and that these bands are relatively temperature independent. Some form of the periodic Anderson model (PAM) is needed, one which results in very narrow renormalized LDA bands. We compare our data to one form of the PAM. (cid:211) 2001 Elsevier Science B.V.


Introduction
masses [10][11][12].It is also well established that indeed it is the f-electrons that are responsible for the Since their discovery in the mid-seventies [1,2], unusual properties [4].the unusual properties of heavy fermions have Magnetic susceptibility (x) measurements of sparked an avalanche of research over the last two heavy fermion compounds generally yield a Curiedecades.The reader is referred to numerous review Weiss behavior at high temperatures consistent with articles [3][4][5][6][7][8][9].The term heavy fermion refers to a well-developed moment (see, for example, Ref. materials (primarily compounds with elements hav- [8]).Indeed, the f-electrons appear to behave as ing an unfilled 4f or 5f shell) whose electronic non-interacting single impurities at elevated temperaproperties suggest that the conduction electrons have ture, a fact that has promoted an almost religious a very heavy effective mass.deHaas-van Alphen belief in the so-called single impurity model, or SIM measurements have confirmed the existence of heavy [13].Below some characteristic temperature, usually referred to as the Kondo temperature or T , the believed to align anti-parallel to the f-electrons to accept the notion that entirely similar heavy fermion form a singlet state (see, e.g.Ref. [4]).Within the behavior in different materials requires different SIM, the slight hybridization with these ligand models.Towards this end, the PAM offers the electrons pulls some f-DOS to the Fermi energy, E , possibility of extension to more than one f-electron, F and results in a sharp itinerant resonant state called while NCA is already accepted as failing for the case the Kondo resonance, or KR.At still lower tempera-of uranium.tures, a dramatic drop in the electrical resistivity, r, Photoelectron spectroscopy (PES) and the even is interpreted [3] as due to the formation of a more detailed angle resolved PES or ARPES, consticoherent periodic lattice of the KR, called the Kondo tute the most direct measurement of the electronic lattice, where a heavy crystalline mass develops.The structure of a material.Indeed, PES measurements concept of a Kondo or Anderson lattice appears to on heavy fermions have been abundant (see Refs. date back to Lawrence et al. [14], but the reader is [9,25], and references therein) owing to the very referred also to an excellent review of theoretical specific predictions of the GS and NCA regarding approaches by Lee et al. [13].
the width, position, spectral weight, and temperature There is, however, another school of thought that dependence of the f-electron DOS.Much of the early claims that the f-electrons form well-defined Bloch PES work was performed on poly-crystalline samstates and very narrow bands at all temperatures ples, scraped in situ to expose a clean surface.Often, [15][16][17].Conventional band theory (i.e. the local good agreement with the GS approximation was density approximation, or LDA), however, is unable reported [9,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].But while early PES measureto explain the high-temperature properties as well as ments suffered from poor sample quality and somethe very heavy mass.Renormalized band theory may times poor resolution, today's equipment and high yet prove useful.However, the success of the SIM in quality crystals are more than adequate to test NCA.explaining macroscopic bulk phenomena suggests a The bulk of the single crystal work was performed correctness, at least at some level even if it is only by our own Los Alamos group [24, [44][45][46][47][48]. self-consistent.It is our contention that the resolution In order to test the applicability of NCA to heavy of the problem will lie in the combining of some fermions it is important to note that NCA predicts form of the periodic Anderson model (PAM) with complete particle-hole symmetry such that PES LDA.
spectrum for occupied states in Ce (one electron) By far and away the most comprehensive and should bear a resemblance to the spectrum of empty widely accepted model of heavy fermion electronic states in Yb (one hole) and vice versa.This latter structure is the Gunnarsson and Schonhammer ap-prediction is crucial since, unlike in Ce where the proximate solution of SIM [18,19], together with the KR is predicted to peak at k T above E in the B K F non-crossing approximation, or NCA [20][21][22].Sev-empty states, in Yb it is predicted to peak at k T B K eral other treatments are also available, but a univer-below E and is thus fully occupied.The full power F sal behavior for the f-electron DOS that comes out of and high resolution of PES (vs.BIS) can now be all these approximate solutions is the prediction of utilized at high intensity synchrotron beamlines, at scaling of its properties with T .
photon energies which maximize 4f PES cross K While heavy fermion behavior is found in Ce, Yb, sections [49].Thus one may relatively easily mea-U, and other transuranic compounds, NCA is strictly sure the 4f temperature dependence, making Yb applicable only to Ce (one electron) and Yb (one compounds the materials of choice for testing the hole) compounds.PAM in its present form [23,24] is SIM via PES.Indeed, for this test, YbInCu is 4 even more restrictive, being applicable only to the unique, owing to its isostructural phase transition at one f-electron case, but this is primarily a conse-T 540 K whereby T changes from 400 K below V K quence of complexity rather than a fundamental T to 30 K above T .
V V difficulty.Indeed, it is generally accepted that NCA In spite of the appeal of Yb compounds, most fails for open f-shells containing more than one previous investigations have concentrated on Ce f-electron (e.g.uranium).This situation seems highly heavy fermion compounds (Refs.[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]  the presumably intense KR above E as the Fermi hybridized band formation, as we hope to show, we F function broadens with temperature [44].Additional-realize that such a separation is not strictly correct.ly any satellite or surface features are degenerate with bulk features.For these reasons one generally finds that, in order to test the SIM, only parameter 3. Single crystal vs. poly-crystal PES manipulation within NCA is performed [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] until the parametrized Ce compound PES spectrum bears As stated above, much of the early PES work on a resemblance to the measured spectrum.Although heavy fermions was performed on scraped poly-Yb heavy fermion compounds are the obvious choice crystalline samples.Agreement with GS and NCA for an accurate study of NCA applicability, inves-was generally reported [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].With the advent of tigations of Yb compounds are strangely sparse or single crystals, however, this agreement dissipated.It are flawed by use of sintered or poly-crystalline was found that poly-crystals, particularly those specimens.Occasionally single crystal samples are scraped to produce a clean surface, yielded a very utilized but the surfaces are nonetheless prepared by weak intensity at E relative to single crystals.This In this manuscript, then, we primarily report PES (not scraped) in situ at 20 K, and measured at 20 K measurements on stoichiometric single crystal com-(T |35 K).The spectra have been normalized so K pounds, and point out the serious disagreements with GS and NCA.In many materials band formation far above T is evident thus pointing to the need for K periodic models such as PAM.This is especially true in uranium compounds where p-f or d-f hybridized bands are unmistakable.

Experimental
Most of the measurements were performed at the Synchrotron Radiation Center of the University of Wisconsin.The latest data (3-dimensional plots of uranium compounds and YbInCu ) were collected 4 using the two dimensional capability of the Scienta analyzer and the PGM beamline.At 60 eV photon energy the instrument resolution was better than 25 meV.The earlier data was obtained using an HA50 VSW analyzer with typically 75 meV resolution.In all cases the background chamber pressure was in the In presenting the spectra, for purposes of brevity, we often refer to the near-E feature as either the F Fig. 1.Comparison of PES spectra for single crystal and poly 4f peak in Ce or the 4f peak in Yb compounds, that the trivalent portion of the spectrum in the 25 quality single crystals one obtains an amazing simito 212 eV range (presumed to be entirely due to the larity in Ce heavy fermion spectra, regardless of T .

K bulk) has equal intensities in both curves when
This can be seen in Fig. 2 (taken from Ref. [24]) measured peak to valley.While the Cu3d features at where spectra for seven Ce heavy fermions (includ-24 eV below E normalize in this way to equal ing two directions for CeBe ) are plotted.One F 13 intensity in both materials (the slight shifts are due to observes the interesting effect that spectral differangle resolved effects), the bulk divalent portion of ences with momentum within the same crystal the Yb-4f spectrum within 2 eV of the Fermi energy (CeBe ) are in fact larger than differences between 13 is dramatically reduced in the poly-crystalline sam-materials whose T values differ by as much as two K ple.The exact nature of this phenomenon is not fully orders of magnitude.All the spectra in Fig. 2 were understood, but it surely resides in the requirement taken at a photon energy of 120 eV which roughly for long range order near the surface to obtain the corresponds to the 4d absorption edge and thus full intensity of the near-E features.An isolated resonantly enhances the 4f emission.The energy F impurity would not suffer from lack of long range order.This would already seem to point toward a narrow band-like nature of these features, and the need for a periodic model such as PAM to model them.
Scraping of surfaces, whether single crystals or poly crystals, has also been shown to have a deleterious effect on the bulk divalent intensity.An experiment by the Los Alamos group on polycrystalline YbAgCu yielded the result [24] that the scraping of 4 the surface completely eliminated the bulk and surface 4f peaks.While this might be interpreted as indicating the existence of a subsurface layer, it is also fully consistent with the notion of loss of long range order and hence coherence of narrow bands.The notion of a subsurface, however, has been negated repeatedly by Joyce et al. [46] who studied a number of Yb compounds at XPS energies where the escape depth of photoelectrons is much longer.This subject will be dealt with in greater detail below in connection with YbInCu .(CeBe ) than between two materials whose T s differ by a factor where the spectrum at anti-resonance (hn 5112 eV) be sufficient to abandon the SIM.In single crystal has been subtracted from the resonance spectrum in PES for all correlated electron systems, any temperaorder to eliminate the very strong Cu3d emission.In ture dependence is completely accounted for by the Fig. 2 one should further note that CeAl and CeSi conventional effects of Fermi function truncation 3 2 are cleaved poly-crystals, with single crystals not (i.e.Fermi statistics) and phonon broadening, withavailable.Further, it should be pointed out that in out any need for NCA effects [46].That this some materials (e.g.CeIn , or CeRh Si , recently broadening is present (to the tune of about 100 meV measured by the Los Alamos group but not pub-at 300 K in nearly all systems) will become clear in lished) no 4f-weight is found at the Fermi energy the discussion of YbInCu , below.Here we first 4 despite a T .10K.This adds further confusion to show that Ce compounds can likewise be explained K the scaling law since a relatively large 4f spectral in this way.as the quintessential trivalent Ce compound [9].We shown with 90 meV resolution at 20 and 300 K (from have the situation that a smaller T yields a larger Ref. [44]).In this figure the 20 K spectrum is first K 4f peak.fitted with a symmetric Lorentzian centered at 220 The point to remember from Fig. 2 is that the meV for the 4f state and a Gaussian peak at 2280 tonically increase with T so that one is forced to the K conclusion that there is no apparent scaling of the 4f spectral weights with T .This lack of scaling for this direction in the Brillouin zone the state is peak shows a positive energy shift (to the right of the fully occupied and not a mere tail of an intense KR. dashed line) while experimentally the peak actually A background was also included.If this entire fitted shifts below the Fermi energy with increasing temlineshape is now convoluted with a Gaussian perature.(FWHM|100 meV) to simulate |100 meV of The large amplitude effect and the positive 4f 5 / 2 phonon broadening, and then convoluted with a 300 peak shift within NCA are a direct consequence of K Fermi function, the resulting lineshape fits the 300 the occupation of only a small tail of a much more K data exactly as shown by the line in the 300 K intense narrow feature above higher binding energy at 300 K (to the left of the feature is very sharp).Thus, the observed shift of the dashed line in Fig. 3).This can only occur if it is peak toward higher binding energies, observed alfully occupied and broadened, most likely by most universally in Ce heavy fermions, favors the phonons (but we cannot rule out other broadening phonon (or other) broadening interpretation.mechanisms).
While we have arbitrarily been calling the It is however fair to ask whether a similar fit can broadening effect as phonon broadening, it must be be obtained with the assumption that the 4f is pointed out that the PAM likewise predicts a 7 / 2 above the Fermi energy and only the tail of this broadening of PES features with temperature, but not feature is occupied, as would be the case for a KR associated with phonons [23,24].Rather, this is due within NCA.It is straightforward to simulate this to a change in the lifetime of the magnetic polarons.case using a Lorentzian centered at 0.04 eV (above Experimentally there is no obvious way to distin-E ) and having a FWHM of 0.06 eV.This new fit is guish between phonons and the magnetic polaron F shown in Fig. 3 as the gray line through the T520 K interactions inherent in the PAM.Suffice it to say spectrum.The parameters for this Lorentzian are that the temperature effects observed in PES measurprisingly close to what one would actually expect surements are not from the outset inconsistent with for a Kondo resonance in a material having a T ¯the PAM predictions.K 400 K so that at first glance it would seem to be consistent with the existence of a KR, and hence the SIM.However, if the temperature is now increased 6. YbInCu : a unique test of the SIM 4 to 300 K, the spectral weight of the Lorentzian representing the KR must be decreased to about half The heavy fermion compound YbInCu has for 4 of its intensity [21,22] and the entire spectrum some time been recognized as possessing perhaps the convoluted with a 300 K Fermi function.The result greatest potential for verification of the applicability is shown as the dark line spectrum superimposed on of the SIM to stoichiometric, crystalline heavy the 300 K data.Immediately we see that far too fermion compounds.It displays an isostructural much temperature dependence is predicted, and it phase transition [51] at T 542 K at which, in high V would take a severe renormalization of the theory to quality single crystals, the volume abruptly increases bring the temperature dependence in line.More by 0.5% below T with no other change in the V importantly, however, the centroid of the simulated crystal structure.Only a very slight change in the s-p-d electronic structure is indicated from PES. transition is observed in the PES spectra.The results The thermodynamically determined Kondo tempera-are illuminating and discussed below.ture, T , changes [51,52] from about 30 K above T Because of the sudden increase in T at T (from to about 400 K below T .Thus the scaling and other 30 K above T to 400 K below T ) as the tempera- depenencies on T are easily tested simply by ture is lowered, the spectral changes predicted from K performing PES measurements above and below T .NCA [21,2] are that: (A) The hole occupancy, n , as Although a recent paper [53] questioned the useful-determined from thermodynamic measurements, ness of YbInCu as a test for the SIM by introducing should decrease from 0.99 to 0.9; (B) divalent 4f single cooldown of the sample) a clear, abrupt phase an order of magnitude; (E) the peak positions of both binding energy (to the left in Fig. 4) by |30 meV T , with serious disagreement above T ).Since at and b, respectively, for several temperatures above shift; see Ref. [46] for a discussion of this effect) and below T (|42 K) at which spectra were taken.
delineated by the dashed lines in Fig. 4a and b. V The data were normalized to equal total integrated Interestingly (but not surprisingly for a conventional intensities (including the entire valence band region, effect), the slow shift with increasing temperature is not shown), with secondary electron features sub-opposite to the direction one would expect [21,22] tracted.The thick-lined spectrum in each frame from NCA.The hole occupancy, n (i.e.essentially h represents data at 150 K, the highest temperature at the percentage of the total 4f signal that is found in which data were taken and at which the sample was the trivalent configuration of this mixed valent cleaved in situ.The grouping of the peaks according system), was determined in a separate measurement to the high-temperature or low-temperature phase is [55] and found to decrease from 0.72 above T to V rather striking, and demonstrates a bulk phase transi-0.6below T .These latter values are not in keeping V tion.No significant temperature effect is observed in with the thermodynamically determined values as to the intensities below T , with the peaks overlaying bring into question the validity of the SIM (recall the V each other quite well.Some slight intensity change is paraphrased statement from Ref.
[39]).seen in the 4f peak above T , but this can for the With confidence that the features in Fig. 4 repre-5 / 2 V most part be accounted for on the basis of phonon sent bulk divalent 4f intensity, the subsurface having broadening discussed above [46,55].The 150 K been dismissed, let us see how Fig. 4 compares with spectrum displays a full width at half maximum respect to the NCA predictions delineated above.We (FWHM) which is about 10% larger than that consider them point by point in the following: observed for the 50 K spectrum (105 vs. 95 meV; i.e.
(A) The hole occupancy, n , was measured h about 50 meV of broadening is evident at 150 vs. 50 separately from the data presented in Fig. 4, and is K).The 25-meV instrument resolution yields a not shown here.It was done at a photon energy of negligible effect here.By contrast, the 4f peak 500 eV where surface features and Cu3d states are 7 / 2 exhibits a clearly discernible increase in intensity substantially diminished so that errors due to non-f above T as the temperature is lowered.This, background are minimized.It is found that n V h however, is a consequence of the effect of the Fermi changes suddenly from 0.72 above T to 0.6 below V function truncation, combined with a convolution of T .Thus, while the Dn is consistent with thermo-V h the same 50 meV phonon broadening.The FWHM of dynamic findings [51,52] at the transition, the absothe 4f increases from about 55 meV at T , to lute values are so out of line that we should not T there is no change in the FWHM of either the even higher (see the theory section in Ref. [24]).We  rower than that below T .This is not immediately toward 150 K, a gradual shift of both the 4f and V 5 / 2 evident from the calculated spectra in Fig. 5b, where 4f occurs in a direction opposite to NCA expecta-7 / 2 spectra were broadened by 70 meV, thus masking the tions.By 150 K this shift has reached as much as 10 change in width.Even more damaging to NCA and meV and is shown by the dashed lines in Fig. 4. By contrast, such a shift is entirely consistent with related to each other and to the SIM, but they are not conventional effects discussed in Ref. [46].simply an extension of the SIM.They yield new Clearly YbInCu does not conform with the SIM physics.The PAM calculations for model systems 4 and NCA, nor do most stoichiometric heavy fermion have been carried out to a sufficient degree that a compounds.We conclude that the SIM is inapplic-number of trends can be gleaned from them.For this able to such materials.At the same time we cannot reason we elaborate below on the origins and deny that the SIM successfully explains much of predictions of PAM.thermodynamic data, and is, at least, internally self- The formation of narrow f-bands within the PAM consistent.However, a recent attempt [57] to use is based on the Nozieres exhaustion principle [60].parameters obtained from thermodynamic and X-ray Nozieres argued that since the screening cloud of a (L edge) data [58]  were at least an order of magnitude too small.Thus r (0) is the conduction electron density at E , may d F while the SIM is internally self-consistent for param-be screened by the conventional Kondo effect.The eters obtainable via thermodynamic measurements, it f-moment together with its conduction-band screenfails to provide correct values not measurable by ing cloud forms a spin polaron.Nozieres then thermodynamic techniques.
proposed that the spin polaron and unscreened sites may be mapped onto particles and holes of a singleband Hubbard model with local Coulomb repulsion 7. Models beyond the SIM U .The polarons hop from site to site and effectiveff ly screen all the moments in a dynamical fashion.

It is our contention that the crux of the problem
The hopping constant of this effective single-band lies in the failure of the SIM to account for the model is strongly suppressed by the overlap of the periodic nature of the f-electrons.These f-electrons screened and unscreened states.Hence the Kondo are not impurities imbedded in a matrix, as in an scale of the effective model, T , becomes much PAM alloy, but rather they form into Bloch states by way less than T .There are then two temperature SIM of hybridization with the ligand p or d conduction scales.This has the effect that for a given thermoelectrons even at high temperatures.This, of course, dynamically measured T one has much more hy-K is not a new idea, but it has been ignored by much of bridization than previously assumed within the SIM the correlated electron community owing to the (just as we find in our PES data), and one must go to complexities involved in introducing the Anderson temperatures far above T in order for T to be the Hamiltonian as a perturbation on a band calculation.dominant temperature scale (again, as per our PES Moreover, until our high-resolution PES measure-data).The PAM is believed to more correctly dements on high-quality single crystals, the existence scribe the strong correlation of electrons in Kondo of narrow f-bands could not be verified.We will lattice systems.While for more than a decade the show below that the existence of these f-bands can SIM has been the paradigm for comparison with no longer be denied.But we first digress somewhat PES, it cannot account for the coherent nature of into possible models that can yield robust narrow electrons (i.e.periodic Bloch states) now observed bands at temperatures far above the Kondo tempera-both above and below T , nor the increased hybridi-K ture.zation.The PAM, in principle, accounts for these There are a number of models which may eventu-effects.ally prove successful, such as renormalized bands Some of the PAM results are consistent with a [15,17] 6, where the model calculations are a Kondo peak which has a weaker temperature for the metallic state with n ,0.8.The excitation dependence and thus persists up to much higher localized to only a small portion of the zone, and that 4f .The first incontrovertible evidence for disper- .ic with the Brillouin zone, were first reported [61] It has been suggested that the strong amplitude for the compound CePt (where 0,x,1).These variations observed in the Ce4f peak are nothing 21x 5 / 2 were observed at a temperature (120 K) which more than photoelectron diffraction in single crysexceeded T by a factor of more than 10.Actual tals.This however ignores the fact that the amplitude K dispersion of the 4f , while likely present, was not effect is periodic with the inverse lattice and often 5 / 2 clearly observed using older electron spectrometers.associated with a slight dispersion away from the The same experiment was later repeated by Garnier Fermi energy and a broadening of the quasiparticle et al. [62] and, while they did not report dispersion peaks.Most importantly, however, the amplitude of the 4f , a careful examination of their data variations are very different for the 4f versus the the KR broadens and loses intensity away from E .F 0 effect) despite the mere 200 meV separation between center.Clearly this is neither the so-called f peak of them.This argues against photoelectron diffraction Ce compounds nor the spin-orbit split sideband, the in Ce compounds since the two features have the 4f , which is normally observed at about 20.25 eV 7 / 2 0 same origin and orbital character and thus would be below E .The f peak, to the extent that it is not F expected to display identical diffraction effects.associated with the surface, is clearly present at With the development of the Scienta electron 22.5 eV.Photon energy dependence tests show that energy analyzers it is now possible to collect ARPES the PES cross section of the new 20.4 eV feature spectra with unprecedented energy and angular res-scales precisely with other 4f-electron features, thus olution.This has been utilized in the mapping of the making it a third 4f-band in the spectrum and having CeSb electronic structure (ferromagnetic below 10 about 20 meV of dispersion.At this point there is no 2 K, measured at 20 K; T ,10 K) which is displayed explanation for this band within any model, although K in the 3D plot in Fig. 8. Color coding (in this and all preliminary LDA calculations suggest a peaking of color figures to follow) is simply a measure of some f-intensity in this part of the Brillouin zone.In relative intensity, although the highest intensity all likelihood, then, this is an LDA-derived feature peaks, red in color, are often associated coincidental-which probably plays no role in the correlation ly with f-intensity.The longer scans in Fig. 8b effects due to being far removed from E .Nonethe-F 0 capture the f peak at about 22.5 eV, while in Fig.
less it underscores the band formation and indicates 8a we show an expanded view (1 eV wide scans) that any successful model will probably have to near the Fermi energy.Although any dispersion of incorporate LDA bands.The PAM, in principle, will the 4f is less than 10 meV, the amplitudes of both do that.ing.)Such a localization of the 4f intensity in the which in Yb compounds is associated with the KR.zone is possible within the PAM but cannot be Nonetheless, the amplitudes of both the 4f (at 5 / 2 0 explained within the SIM.The f peak at 22.5 eV about 21.3 eV) as well as the 4f can be strongly below E , that is to say, the feature which in the SIM momentum dependent.This is most certainly the F is identified with the purely localized trivalent 4f case in YbCu Si , a heavy fermion compound with 2 2 state, actually disperses by as much as 100 meV.The T |35 K.In Fig. 9 we show 3D plots of ARPES K failure to see clear dispersion of the 4f in Fig. 8, spectra obtained for YbCu Si , taken within 3 eV of on the other hand, is understood, assuming p-f E and using hn 540 eV (Fig. 9a) and hn 560 eV F hybridized bands, from the following scenario: at (Fig. 9b).The instrument resolution is about 25 meV hn 560 eV, the p-cross section is vanishingly small in both plots, even at 60 eV where the 4f-PES cross and we are measuring only the f-portion of the section dominates.It had previously been demonbands.Dispersion, on the other hand, is present only strated [46] that bulk 4f features are nearly temperain the region of p-character of the bands.All this is ture independent.In Fig. 9b bulk derived 4f intensity again entirely consistent with the PAM description of dramatically peaks at the zone center where it is correlated behavior in stoichiometric compounds (see much stronger than the surface features, while at conclusion (i) above).
u 52128, the intensity drops by a factor of 3 to Perhaps the most intriguing feature in Fig. 8 is the where it is much smaller than the surface states.We band at 20.4 eV, situated just off from the zone assume that these are p-f rather than d-f hybridized of f-intensity near the zone corner (268).An unexplained 4f feature at 20.4 eV has never been heretofore observed in any heavy fermion system.We associate it with LDA-derived bands.bands (there are no d-electrons available), and the dispersive p-portion of the bands, if it exists, is not seen due to a vanishingly small cross section.In any case, most of the 4f intensity is concentrated in only a small portion of the zone, amazingly similar to PAM predictions.In Fig. 9a we show the same data but now taken at hn 540 eV.The concentration of f-character at the center of the zone is no longer observable.We interpret this as meaning that the orbital character of the features observed at hn 540 eV is different from that observed at 60 eV (owing to a smaller f-cross section) and that indeed the feature at E is strongly p-f hybridized.At 40 eV we more F easily observe the p-electron portion of the near-E F band, which, surprisingly, is still dispersionless.ruled out in Refs.[46,54]).The fact that they are much less intense than the presumably p-f hybridized bulk features at 40 eV is entirely consistent with their lower PES cross section.It is also an argument occupancy is no longer valid.Such a decrease occurs against photoelectron diffraction (PD) being the in nearly every mixed valent Yb compound that we source of the amplitude effect since preliminary investigated.Together with this decrease, one usually calculations suggest that the decrease in photon also observes that the linewidth of the divalent energy (from 60 to 40 eV) is insufficient to cause features has narrowed and that the 4f gains in 7 / 2 such dramatic PD effects.It is not possible at this intensity relative to the 4f (this is also evident in 5 / 2 time to completely rule out PD as the source of the Fig. 9a).amplitude effect in YbCu Si , pending a complete One might at first glance be tempted to ascribe the 2 2 band calculation which is presently in progress.change in the 4f intensity at 40 eV to surface However, based on the similarity to Ce and U sensitivity, and hence revive the subsurface scenario.compounds, where PD effects are more easily ruled While the arguments for YbInCu above have al-4 out, we submit that the PAM more effectively ready emphatically ruled out this effect, we point out explains the momentum dependence in Yb heavy in addition to the above arguments that the escape fermions.
depth scenario requires a very gradual change from The p-f hybridization appears to be pervasive in bulk to subsurface as the kinetic energy of the Yb heavy fermions.In YbInCu the dramatic locali-photoelectrons decreases, unlike the nearly exponen-4 zation of the 4f intensity was not observed, but we tial change observed between 40 and 60 eV.If a nonetheless invoke p-f hybridization in order to subsurface were to exist, such that its T were much K explain the photon energy dependence of the 4f larger than that of the bulk, then for some range of energies.The interesting fact is that the ratio of the the subsurface.This is never observed.A more likely divalent to trivalent signal, while it is more or less interpretation for the rapid decrease in the trivalent constant for all photon energies above 60 eV (up to intensity relative to the divalent at 40 eV is that the XPS energies), shows a dramatic change in the 40 eV divalent portion of the spectrum consists of ultraspectrum.In particular, the trivalent portion of the 4f narrow p-f hybridized bands (again, we assume that signal decreases dramatically relative to the bulk d-f is unlikely), while the trivalent, or localized divalent signal, so that a determination of the 4f hole portion of the signal, consists of pure 4f states.At hn 560 eV and above (i.e.where the 4f PES cross section is large relative to the p-cross section) one then obtains the same ratio between the divalent and trivalent features.Below 60 eV, on the other hand, the 4f cross section drops exponentially while the p-cross section increases.This results in a quenching of the trivalent signal, while the p-electron portion of the divalent signal gains in intensity.This may explain the observation [66] of Yb4f signal at 7 / 2 photon energies as low as 21.2 eV where the 4f cross section should be vanishingly small.Interestingly enough, this non-f intensity is even narrower than the f-intensity.Were it a pure 4f signal due to a higher-T subsurface, it would in fact have to be broader.K Such a p-f admixture is inconsistent with the predictions of the SIM, but is obtained through the application of the PAM.

U compounds
Both dispersion and restriction of the f-intensity to only a small portion of the zone are unmistakable in uranium compounds.Indeed, here we observe not only p-or d-electron dispersion, but actual f-electron dispersion.In the case of uranium compounds f-d  [67] shows that the most intense peak, which exists again a dramatic difference between the two frames.for only the first 38 around the zone center, agrees Indeed, the strong f-intensity in Fig. 12b (again quite well with the calculated bands.Quite obviously localized to only a small portion of the zone; near the these data will have to be repeated using a Scienta zone corner along the G-X direction) appears preanalyzer, but they nevertheless show the essential cisely in the location where in Fig. 12a the dfeatures of narrow bands and similarity to LDA intensity (we assume we are dealing here with bands.They will have to be repeated as well due to uranium 6d electrons) has a deep minimum.Here the the fact that the data in Fig. 11 are taken at hn 530 5f portion of the band actually shows dispersion to eV which argues for a substantial p-or d-admixture.
the tune of about 50 meV, rather than just intensity modulation.This is a classic example of d-f hybridi-f-electrons.Again, then, we are dealing with band zation.The measured bands agree almost exactly antiferromagnetism which is somewhat reflected in with the calculated bands of Oppeneer et al. [68], its ordered moment of about 1.89 m .Once again, B with the exception that they appear to be strongly too, the f-intensity is confined to the center of the renormalized (much narrower) at the Fermi energy Brillouin zone, making once again reasonable convs.calculations.This again would seem consistent tact with the PAM. with the expectations from the PAM, although calcu-Realizing that it is difficult to observe 5f disperlations for real systems are not yet forthcoming.The sion in Figs. 12 and 13, we show in Fig. 14 a blowup excellent agreement with band calculations as to the of the first 100 meV of the ARPES spectra taken at location of the 5f states would also argue strongly hn 560 eV for both UAsSe and USb .Here it is 2 against PD as the source of the large intensity trivial to see the 5f dispersion and the decrease of variation of the 5f signal.It would be indeed intensity as the bands change character to d-like pathological that PD would fortuitously yield an away from the Fermi energy.amplitude diminution precisely at those momenta It might be useful to point out that most of the where band calculations predict the change in orbital results shown here can serve as a warning to those character from f to d.
performing measurements on f-electron systems The magnetic moment almost surely must be using only HeI or HeII radiation.The above results carried by the strongly hybridized f-band at the show that they may be measuring only the p-or Fermi energy and we are clearly dealing with band d-portion of the hybridized f-bands, which could magnetism.The ordered moment is measured to be easily mislead interpretation.At the very least, the 2.5 m which is only slightly below the purely determination of n values in Yb compounds, where B h localized case.What is surprising is that the f-band correct f-spectral weights are crucial, should only be occupies such a small part of the zone.Based on attempted at photon energies above 60 eV.band calculations, the f-band actually crosses E .structure of stoichiometric heavy fermion com-13, for data taken at hn 533 eV (Fig. 13a), 40 eV pounds; namely, there exist at E very narrow, F (Fig. 13b), and 60 eV (Fig. 13c), so that we empha-possibly renormalized, p-f or d-f hybridized bands.size p-electrons, d-electrons, and f-electrons, respec-These are clearly observable in uranium compounds tively.Quite obviously in Fig. 13a the sharp peak via f-electron band dispersion, while in Ce and Yb (most likely of p-electron origin) is at the Fermi compounds the momentum dependence of the amenergy, but appears to dissipate at u 50; i.e. near the plitude constitutes the main evidence.Spectroscopic center of the Brillouin zone where it begins to data on YbInCu demonstrate that the SIM predic-4 hybridize with the f-states.By contrast, in Fig. 13c, tions fail, and most likely some version of the PAM the f-intensity at the Fermi energy begins to build is needed.As pointed out by Jarrell, the PAM is not precisely where the p-intensity is waning.Thus we merely an extension of the SIM, but rather introconclude that we have again a classic case, this time duces new physics which is in better agreement with of p-f hybridization, with the f-portion of the band PES data.The successful model will have to inshowing unmistakable dispersion.
corporate LDA bands which in UAsSe are in agree-Interestingly enough, the d-like portion of the ment with ARPES results -except at E , where F spectrum, which should be emphasized at 40 eV in they are flatter.The existence of f-spectral weight in Fig. 13b, is actually a separate band, slightly re-only a small portion of the Brillouin zone would moved (by about 100 meV) from the Fermi energy, seem to agree with the predictions of the PAM as and in this case does not seem to hybridize with the discussed in [24].In all cases it appears that as the

F
scraping.Measurement of cleaved single crystal occurs both in Yb and Ce heavy fermions.In Fig.1, surfaces of Yb compounds has been primarily uti-a comparison is made [24] between single-and lized by the Los Alamos group [24,[44][45][46][47][48].poly-crystalline YbCu Si , both specimens cleaved 2 2 Single crystal samples were cleaved in situ at typically 20 K and measured at 20 K (unless otherwise indicated).

4 4 . 2 Fig. 2 .
Fig. 2. PES spectra for a number of Ce heavy fermions with T s

Fig. 4 .
Fig. 4. The bulk divalent 4f and 4f peaks in the PES spectra of YbInCu , taken at the indicated temperatures.Note the spectacular

d 1 .Fig. 6 .
Fig. 6.Excitation spectra for two temperatures calculated from the PAM for various vectors in a cubic zone.Both f and d features are sharp at E .But as the band pulls down below E it becomes primarily d-like and broad, as found experimentally.At higher temperatures only a F F broadening effect is predicted.

Fig. 7 .
Fig. 7. ARPES spectra at two angles for CeBe taken at 20 K and hn 540 eV.Both the KR and the 4f disperse significantly.Note how 13 7 / 2

2 268
not track with each other.The bulk of 8.2.Yb compounds the 4f intensity is found near the zone corner (near 5 / in Fig.8), indicating, perhaps that n .1 (we In general, Yb compounds display almost undep assume that only p-electrons are available for screen-tectable dispersion (10 meV or less) in the 4f peak 7 / 2

Fig. 9 .
Fig. 9. Three dimensional ARPES spectra for YbCu Si taken at 20 K and (a) hn 540 eV, (b) hn 560 eV.The 4f PES cross section 2 2dominates at 60 eV where most of the 4f spectral weight is concentrated near the zone center.By contrast, at 40 eV no such concentration is evident probably because the orbital character of the features is more p-or d-like.Note that the surface state intensity is strongly diminished relative to the 4f .

/ 2 grated
Fig. 10 are shown angle inte-photon energies we should observe two closely 7 YbInCu spectra taken at various photon spaced divalent features representing the bulk and 4

Fig. 12 .
Fig. 12.Three dimensional ARPES spectra within 200 meV of E for ferromagnetic UAsSe at: (a) hn 540 eV, emphasizing d-emission, and F (b) hn 560 eV, emphasizing f-emission.The strong f-electron feature in (b) fits precisely in the notch of the d-bands in (a) -a classic example of f-d hybridization.The pure f-electron band in (b) disperses by |50 meV.

F
Finally we consider the the antiferromagnet USb , 2 whose ARPES spectra, taken with a Scienta and 9. Conclusions shown in color 3D, are depicted in Fig.13.The Neel temperature for this material is 200 K while ourWe have shown with numerous examples that measurements were done at 20 K to avoid Fermi there is a common theme regarding the electronic function smearing.Three frames are shown in Fig.

Fig. 13 .
Fig. 13.ARPES spectra within 200 meV of E for antiferromagnetic USb at three photon energies: (a) 33 eV, emphasizing p-emission (b) F 2 40 eV, emphasizing d-emission, and (c) 60 eV emphasizing f-emission.The dispersive pure f-band in (c) smoothly diminishes and becomes the p-band in (a).The d-band in (b) is a separate band and is not hybridized with the f-states.

Fig. 14 .
Fig. 14.ARPES spectra for UAsSe and USb within the first 100 meV of the Fermi energy in order to more clearly display the dispersion of 2 the 5f bands.The photon energy is 60 eV where the photoemission cross section for 5f states is near its maximum while the p-and d-electron cross sections are suppressed.The loss of intensity as the 5f bands disperse away from the Fermi energy is indicative of hybridization with por d-electrons.
Convolution with a understand this behavior if the KR (or any sharp Fermi function only without broadening is found to feature above E ) is positioned within k T of the 300 F B be insufficient to fit the 300 K spectrum exactly.K Fermi energy (i.e.within about 20 meV of E ) and F By contrast, 100 meV of broadening (whether due it's width is no more than about 50 meV.At 300 K, to phonons or other effects -see below) combined the Fermi function samples only about the first 50 with Fermi function convolution are entirely suffi-meV above E .Any DOS beyond that is irrelevant.The experimental shift away from the Fermi provided that the peak of the narrow DOS feature is energy, by contrast, is a direct consequence of the below the Fermi energy and fully occupied as broadening of the 4f feature.A peak shift can not E .It is easy to F spectrum, called the photon fit.F cient to explain all temperature effects in Fig.3, 5 / 2 assumed in the fits.That this is the case is evidenced be obtained if only the Fermi function convolution is by the fact that the peak of the 4f shifts toward used with no phonon broadening (assuming the 7 / 2