Comparative study of the electronic structure of XRu2Si2: probing the Anderson lattice

The k -resolved single particle excitations, as determined by angle-resolved photoemission spectroscopy (ARPES), are compared and contrasted for, LaRu Si , CeRu Si , ThRu Si , and URu Si , isostructural layered compounds with differing 2 nominal f -occupations of f , f , f , and f , respectively. ARPES measurements include 4 d and 5 d -edge resonant photoemission to distinguish f -character and Fermi-energy intensity mapping of Fermi surface contours. Comparison to RLAPW band structure calculations shows very good agreement of the d -band structure away from E . Discrepancies in the F near E region highlight k -dependent effects of f -correlation and f – d hybridization. Approximately equal dimensions of F Fermi contours for X 5 (La, Ce) suggest the exclusion of 4 f electrons from the CeRu Si Fermi surface at temperatures far 2 2 above the Kondo temperature. High-resolution spectra for X 5 (Ce, U) allow comparison of f – d mixing to predictions of the Anderson lattice model. Published by Elsevier Science B.V.


Introduction
band-like s, p or d-states of the solid. For a single material, some properties, e.g. Kondo effects, can be Mixed valent and heavy-fermion f-electron materi-described by the impurity Anderson model, and yet als manifest a challenging interplay of atomic and the f-electrons contribute to the heavy-mass Fermi electron gas physics, generally understood to involve surface (FS) [1][2][3][4]. One theoretical approach to the hybridization between localized f-orbitals and other FS utilizes the band structure calculated in the local density approximation (LDA), including the f-electrons, but renormalizing their scattering phase shifts turbation of the original LDA FS [5]. Alternatively, dimensional materials and also gives access to the results based on theoretical treatments of the Ander-strong 4d → 4f and 5d → 5f resonances that are son lattice Hamiltonian [6][7][8] suggest a model with a commonly used to distinguish f character in anglerenormalized f-level just above E , and renormalized integrated photoemission [9]. This powerful combi-F hybridization to the s-p-d band structure. The two nation of ARPES and resonant photoemission (Rerenormalizations reflect the Kondo effect. Two-band sPES) is additionally greatly enhanced by the use of mixing very near E then shifts the k value the Fermi-energy intensity mapping technique that F F somewhat and enhances the effective mass at k , but provides a visualization of the global k-dependence F the overall FS topology appears to be largely de-of f-weight in multiple Brilloun zones and a detailed termined by the underlying s-p-d band structure in correspondence to the d-band structure. URu Si is 2 2 the absence of hybridization to the f-states.
Although the first f-electron system to receive detailed exthe two approaches must yield the same FS volume perimental treatment with the above combination of to count electrons correctly, it is not a priori obvious photoemission techniques [21]. that they yield the same FS topology.
In testing theoretical models of heavy mass FS Angle integrated electron spectroscopy has been formation it is also very important to compare very successful in revealing single-ion properties similar systems with varying f occupation because [9,10], while quantitative FS information has been LDA band calculations done for varying numbers of obtained only by magneto-oscillatory (MO) tech-f-electrons in the valence band show systematic niques such as the de Haas-van Alphen (dHvA) differences in the Fermi surface topologies. The effect [11,12]. MO techniques do not provide a XRu Si system with X5(La, Ce, Th, U) is a 2 2 global view of the energy and k-dependence of the favorable isostructural series for the comparison of electronic structure, and so are limited for distin-band structure and FS topology with only the 4f or 5f 0 guishing among different theoretical scenarios of occupation being varied. LaRu Si is a 4f rare-earth emission spectroscopy (ARPES) in principle pro-fermion system (g 5350 mJ / mol-K ) with 3 valvides this global view. Momentum-dependent effects ence and is a prime literature example of very good have been reported in ARPES studies of f-electron agreement between renormalized LDA band calculasystems, e.g. high-resolution He I valence band tions and dHvA Fermi surface and effective mass 0 measurements [13,14], amplitude variations of the measurements [22,23]. ThRu Si is a 5f actinide 2 2 1 2 near-E 4f-weight periodic with the Brillouin zone system with 4 valence. URu Si is a nominally 5f F 2 2 [15,16] and claims of ''band-like'' dispersion of system with a moderately large linear specific heat 2 f-states [17,18]. However, because of technical bar-coefficient of g 5180 mJ / mol-K extrapolated from riers, ARPES has never provided enough FS detail in the paramagnetic phase [24,25]. In addition, these systems for its potential to be realized.
URu Si is anti-ferromagnetic below 17.5 K and 2 2 Recent advances in photoemission instrumentation superconducting below 1.2 K. The theoretical interand techniques are beginning to overcome these est in these low temperature phase transitions includbarriers. One direction has been to push the photo-ing the coexistence of magnetism and superconducemission technique close to its ultimate energy tivity has resulted in URu Si being one of the most 2 2 resolution at very low temperatures in order to access heavily studied 5f systems, continuing up to the the small energy scales of the Kondo effect [19].
present [26]. In this paper, the experimental FS Another direction has been to improve the energy topologies and valence band structures of the four resolution at | 1 keV photon energies in order probe XRu Si systems are systematically compared with 2 2 more bulk-sensitive valence structure [20]. The key each other, with LDA band structure calculations, advance exploited in the work described here is the and with expectations from the Anderson lattice recent ability to perform moderately high-resolution model. Only paramagnetic URu Si is studied here. 2 2 ARPES measurements at photon energies greater The paper is organized as follows. The framework than 100 eV. This extended photon energy range is for discussion of the ARPES data is provided by essential for adequate k-space coverage of three Section  pounds. We will use these comparisons to highlight [29] and CeRu Si [30]. The band structures and 2 2 the theoretical issues to be addressed experimentally. Fermi surfaces in this paper are in good agreement The displayed high-symmetry directions of G-Z, with other relativistic LDA calculations for CeRu Si 2 2 Z-(S)-G, and G-X correspond to the k001l, k100l [31] and URu Si [32]. 2 2 and k110l directions of the body-centered tetragonal Common to all four systems is the parabolic (bct) Brillouin zone (BZ). The X-Z direction is dispersion of a cluster of three bands centered along orthogonal to G-X and completes an in-plane tri-Z-(S)-G with a band minimum of¯1.5 eV binding angle. The FS cross-sections are centered at G. The energy. These bands of mostly Ru 4d character energy band calculations for ThRu Si and URu Si (labeled 1-3 in Fig. 1) approach E at the Z-point along G-X.
Comparisons involving changing numbers of felectrons are more complex. Comparing La and Ce rise to other sheets of FS, the details of which vary in Fig. 1(a), we see that the hybridization of narrow with the material. Typically, the sheet associated band 4f states above E with broad band states of F with band 4 is a closed hole surface centered at Z, compatible symmetry has the main effect of moving referred to as the ''pillow'' in Ce, and the FS sheet E -crossings already present for LaRu Si and there-F 2 2 associated with band 5 is multiply connected. Also by changing the FS volume to accommodate the notable is the existence of a saddle point in the additional f-electron, without changing the number dispersion of states within 1 eV below E at G. While of E -crossings. The effect on the bands 1, 2 and 3 F F these bands disperse to higher binding energy in the near Z is small enough that the number of small hole k 2 k plane, i.e. along Z-(S)-G and G-X, they pockets near Z is unchanged. The large changes G-point discussed in Section 1.2 and Fig. 4. surface nearly following the BZ contour, and the A key difference among the different theoretical electron sheets associated with band 5 near G band structures is the occurrence and location of the expand. One sheet expands enough to change its 0 narrow 4f and 5f bands. For the f systems, the connectivity similar to ThRu Si . Thus the need to 2 2 unoccupied bands are at least 3 eV above E . For Ce accommodate the additional f electron in going from F the narrow 4f bands are primarily confined to within La to Ce, shared roughly equally between bands 4 1 eV above E , while for U the 5f bandwidth is and 5, makes definite changes in the sizes of the FS F larger (¯2 eV) with greater overlap of the Fermi sheets, and a continuous general variation between level. The larger 5f bandwidth relative to the 4f the two FS topologies is easily seen.
In the hybridization process, the Fermi velocities band structure framework include non-ab initio are decreased, thereby increasing the density of methods of the ''LDA1U'' [33,34] and the restates at E . In particular band 4 has a much normalized-LDA [5]. CeRu Si is regarded as a F 2 2 shallower dispersion at E compared to that in paradigm for the success of the latter method, in F LaRu Si . Indeed, dHvA measurements of FS orbits which the meV Kondo energy scale of the 4f 2 2 in CeRu Si [23] have identified the existence of a electrons is imposed by the empirical modification of 2 2 large FS pocket having a large effective mass that is f-electron scattering phase shifts [5] on the FS. It is primarily responsible for its large specific heat found that the topology of the LDA-FS is hardly 2 coefficient of 350 mJ / mol-K . This FS sheet is changed, but that the resulting masses can be put in consistent with the Z-point pillow FS of band 4, good general agreement with the dHvA masses, providing an example of the origin of heavy mass including the largest mass for the FS sheet of band 4, bands with f-character at E within the LDA frame-F the so-called ''pillow'', mentioned above. There is work. Although the LDA pillow mass is much larger then a good one to one correspondence between for Ce than La, it is nonetheless much smaller than experiment and predictions from theory for the the experimental value in Ce. Indeed, it is well dHvA orbits and masses, and the large T-linear known that the bandwidths of the 4f and 5f electrons specific heat can be accounted for. The invariance of calculated by LDA, are over-estimated by at least an the LDA-FS in the renormalization procedure occurs order-of-magnitude and the calculated effective frequently, but not always, as elucidated by masses are generally too small by factors of 2- 10 Zwicknagl [5]. Although more sophisticated consid- [5]. This large over-estimation of the bandwidth erations are needed, the essential issue is much the occurs because the large electron correlation energies same as in the discussion above for the LDA band (¯6 eV for Ce and¯2 eV for U) are treated in only structures, whether the FS topology is determined an average way in LDA calculations. Enhanced predominantly by the broad band E -crossings. then leads to the quenching of the f magnetic and 5 are pushed even closer to the Z-point and moment and the associated formation of the Suhlbecome heavier in URu Si . However, in contrast to 2 2 Abrikosov or Kondo resonance at the Kondo energy the situation for CeRu Si , the combination of larger 2 2 2 k T above E . Essentially exact solutions have been 5f bandwidth and f occupation results in there B K F given for the ground state and spectral properties of being entirely new bands of f-character dispersing an impurity model valid for Ce [35]. Solutions for downward across E and creating new FS sheets. F the difficult lattice model typically set U to infinity One such new band (6) with a small Fermi velocity and involve other approximations of various sorts for is observed along G-(S)-Z with continuation along simplified situations that lack the real band structure G-X-Z. Also bands 1, 2 and 3 are sufficiently aspects captured by the renormalized LDA. Only a depressed in URu Si that none cross E at the 2 2 F few [6,8] of these solutions yield realistic infor-Z-point. Thus considerable disruption and disconmation about the distribution of f spectral weight on tinuous change of the FS topology from Th to U is both large and small energy scales. Nonetheless the expected within the LDA framework.
Attempts to include electron correlation within the simplest results provide important indications of expected k-space dependence at generic conduction-ty model Kondo resonance, the Kondo energetics of which are captured in the procedure of the renormalband crossings as shown schematically in Fig. 3.
ized LDA. One sees again in this view of heavy mass The key features in Fig. 3 for a dispersing formation the tendency that the basic FS topology is conduction band include: (i) the renormalization of determined by the conduction band E -crossings in 9 the bare f-level binding energy (´) to a position (´) the absence of f-state hybridization, which we take in just above the Fermi level, (ii) avoided crossings that 0 2 this paper to be that of the f compounds. form a hybridization gap and two branches (E and 1 For CeRu Si there is a general similarity between E ) with continuous variation of f -d character 2 2 the Anderson lattice schematic of Fig. 3 and the mixing from the flat to the dispersing states, and (iii) comparison within the LDA to LaRu Si in Fig. 1, a potentially great reduction of the new Fermi f-''bands'' by ARPES, and has been used in arguadjustable parameters, but in a full microscopic ments for the (complete) failure of the single impuritreatment they are linked to the original Hamiltonian ty model [17,18]. We see here that the success of the parameters through Kondo-like relations. The re-LDA for the FS of a Ce material can be viewed as normalized f-level above E is essentially the impuri-F perhaps somewhat fortuitous in that mixing with the 0 4f bands mainly changes the f FS by pushing its E F crossings to accommodate the f-electron. But for URu Si , where the LDA FS is very different from 2 2 that of ThRu Si , as seen in Fig. 2, it is unclear that 2 2 the expectations for the various pictures will be the same. Although dHvA data seem to be explained by LDA calculations for some heavy fermion uranium materials, e.g. UPt [36,37], this is not the case for 3 URu Si [38,39]. The antiferromagnetic phase tran- 2 2 sition at 17.5 K in URu Si , and a possible associ- 2 2 ated change in the Fermi surface, complicates the comparison of LDA, dHvA and ARPES. Nevertheless, one can hypothesize that the difficulty for URu Si reflects the kind of gross difference from 2 2 0 the f situation seen in the band structure comparison of Fig. 2. The experimental studies of paramagnetic URu Si described here offer the 2 2 possibility to test this hypothesis. One other very important aspect of the correlated picture may be testable by ARPES experiments. If the low energy scale effects of hybridization can somehow be turned off, then the f-electrons are atomic-like with local magnetic moments. Friedel should no longer count the f-electrons and should 0 revert to that of the f compound. One way to meV and Du 50.368. Samples were typically meaaccomplish this is by the full restoration of the sured at the ALS within a 12 h period after cleavage, f-magnetic moment, e.g. through magnetic ordering while multi-day experiments were performed at the or very high magnetic fields. Indeed for CeRu Si SRC. 2 2 dHvA frequencies above a metamagnetic transition ARPES experiments at a fixed photon energy at¯8 T change abruptly to values in closer measure along spherical arcs in k-space. Fig. 4  T where the magnetic moment is unquenched, the and kinetic energy of the photoelectron [42]. Perpen-K FS should exclude the f-electrons. dicular to the surface, the relation between the photoelectron and photohole momenta (k ) also z 1.2. Experiment involves the surface potential which is parametrized by an ''inner potential step'' V whose value is 0 The ARPES experiments were performed at two empirically adjusted to be consistent with ARPES synchrotrons with three different end stations. Low spectral signatures. For example, Fig. 5 shows photon energy (14-35 eV) experiments were per-normal emission spectra of URu Si , acquired from 2 2 formed at the Ames / Montana beamline at the SRC both synchrotrons, spanning a broad photon energy synchrotron with a fixed sample / moveable detector range from 14 eV to 230 eV and traversing -G-Z-Ggeometry and with energy and angular resolutions of multiple times. While these spectra tend always to DE550-100 meV and Du 528. Photons from an show a resolution-limited peak very close to E , the F ERG monochromator with energies greater than 40 eV but lower resolution were also available at the SRC beamline. Samples were pre-aligned with Laue diffraction, cooled via a He refrigerator and then cleaved and measured in ultra-high vacuum ( , 4 3 211 10 Torr) at a sample temperature of T¯25 K. Rare-earth samples were cleaved and measured at # 150 K, while radioactive actinide samples were cleaved at room temperature before being immediately transferred to a LN-cooled sample manipulator 210 and measured, all in a vacuum typically , 1 3 10 Torr. Refined sample alignment was determined in situ by the symmetry of the Fermi-energy emission intensity maps. In addition, high resolution experi- . For such direct comparisons to bulk band theory, suitable choices of higher photon energies, as in Fig. 4, correspond to measurement arcs that are close approximations to the high-symmetry directions of G-(S)-Z and G-X-G (or Z-X-Z). However, the theoretical band structure of the XRu Si systems, 2 2 consisting of small hole pockets at the G and Z points, can be very sensitive to the precise measurement arc, e.g. an arc not cutting through the center of a small ellipsoidal pocket can affect the size of the measured ellipsoidal contour or even miss the pocket and show a band maximum below E (no Fermi F crossing). This sensitivity to k and the curvature of z the measurement is partially alleviated by kz broadening [43] that arises from the finite mean free path of the electrons, resulting in some blurring of the three-dimensionality of the FS topologies. Nevertheless, when a measurement does not pass close to a the well-known resonant enhancement in the valence a constant kinetic energy window as a function of band near E for URu Si at the U 5d → 5f absorp-sample or detector angle and / or photon energy. tion maxima of 98 and 108 eV. Intensity modulations highlight the passing (or close Since resonant valence band photoemission mea-approach) of bands through this energy window surements around 100 eV photon energy are very which when set at the Fermi-level, identifies the near the minimum of the electron escape depth, k-space location of the approach or crossing of indicating extreme surface sensitivity, it is important dispersing bands that form the Fermi-surface. Paralto call attention to any bulk signatures that might be lel detection or automated motions allow a much present in our ARPES data. The identification of higher sampling density and larger range of k-space G-point signatures over five Brillouin zones along emission directions to be sampled than normally normal emission and k -dependent FS maps is strong achievable with acquisition of individual spectra. z evidence for bulk character in the states being probed Acquisition of these global ''FS maps'', which also with ARPES. Additional evidence of bulk character provide information on sample alignment, matrixis the favorable agreement between experimental element and polarization effects, is very useful in instructing where to focus attention with more detailed high-resolution spectra. SRC experimental maps were acquired with semi-automation of two orthogonal angles of the detector in a fixed sample geometry. ALS Beamline 7.0 maps were acquired via automated spherical-coordinate sample rotations. While differencing of on-and off-resonance angleintegrated valence spectra is a common procedure to isolate the f partial density of states, the separate onand off-resonance FS maps for X5(Ce, U) provide separate and complementary information. On-resonance FS maps are important to understand the k-space distribution of f-states, and off-resonance FS maps are important both for the comparison of FS 0 contours to the f system as well as for the correlation of on-resonance f-weight to the d-FS contours. In addition, the assumption for such subtraction procedures, that the non-f cross-section variation with photon energy is minimal, is less valid for angle-resolved photoemission and for large differences in photon energy. Thus, in this paper, the onand off-resonance FS maps are presented separately without attempts at differencing.
The atomic stacking (-X-Si-Ru-Si-X-) of the body-centered tetragonal (bct) crystal structure of the XRu Si system makes the material very amenable 2 2 to cleavage in vacuum to expose clean (001)  (URu Si ) having the largest (smallest) unit cell. 2 2 Crystals were formed by a rapidly cooled arc-melt technique that produces mm-sized crystalline flakes of varying domain purity, i.e. high quality large rare-earth flakes and smaller mixed domain actinide URu Si measurements. Low energy electron diftopologies. 2 2 fraction was performed on selected samples after ARPES measurements and relatively sharp (unreconstructed) 1 3 1 patterns were exhibited in each case. spond to the Z and G points, respectively, at normal emission. The maps were acquired over a 1208 azimuth and a 308 polar angle range, and have been 2. Results: X5La, Ce corrected for misorientation of the sample surface to the sample goniometer rotation axes, two-fold 2.1. LaRu Si symmetrized, and plotted as a projection onto the 2 2 k 2 k plane. BCT Brillouin zone borders are over- Three main pieces of FS are observed to repeat in multiple Brillouin zones in the experimental maps of Fig. 6(a,b): (i, ii) small circular closed sheets centered at G and Z and (iii) a large sheet centered at Z that extends into the second BZ. The two maps in Fig. 6 do not distinguish the disconnectedness along k of the small FS pockets at G and Z. In fact, since   theory predicts (i) three concentric hole pockets centered on Z, (ii) very small electron pockets offset from and surrounding G and (iii) a large hole surface originates from bands that disperse symmetrically centered on Z whose diameter extends into the next along Z-(S)-G. BZ's. The qualitative agreement between the ex-Band theory shows a complicated region near G perimental maps and the theory is very good, al-arising from band hybridizations. A key feature, though the experimental FS maps do not resolve the though, is the existence of a mostly unoccupied band small Z point contour into three concentric pockets, (5) just above E at G that dips below E forming eV with 0.58 polar angle steps along two azimuth pocket corresponds to the outer-edge of the large angles separated by 458 that correspond to the Gcontour in the FS maps of Fig. 6, i.e. the contour that (S)-Z and G-X-G high symmetry directions. For has the connectivity of the large hole-surface of band comparison, the theoretical band structure along the 4. A possible reconciliation of this discrepancy is same two directions is shown in Fig. 7 agrees better with the valence band image in Fig.  stages of making an interpretation of the data and we 7(a), which shows that bands (1-3) disperse very proceed with qualitative observations, looking for close to E at G, possibly even forming a small hole signatures of the theoretical models discussed in F surface. Next to the small electron pocket, roughly Section 1.1. We find some very interesting surprises. halfway between G and Z, there is a fuzzy region of Fig. 8(a) shows reverse grayscale images of near-E weight that correlates with the ''football-CeRu Si valence band spectra at 154 eV, corre- shaped'' E intensities on the interior boundary of sponding to the G-point at normal emission. Com-F the large Z-point hole surfaces seen in Fig. 6 and parison of this data to that of LaRu Si in Fig. 7(a) 2 2 discussed earlier in terms of k -broadening.
shows that the two band structures below¯0.5 eV z Along G-X-G we observe a dominant band binding energy are virtually identical including reladispersion that is symmetric about the X point also tive intensities of spectral weight. Similarly the with a band minimum of¯1.6 eV and a second agreement of the band structure below 0.5 eV is also band dispersing downwards from the X-point at very good in comparison to the LDA calculation 0.5 eV binding energy. Both of these features are shown in Fig. 8(b). The different relative weights at present in the band theory, albeit with a greater G at normal emission and G in the second BZ can splitting of the bands. The band theory also predicts result from the curvature of the k-space measuresmall electron pockets (above and below) the X-point ments arcs, i.e. the measurements cut below G in the (visible only with 3D FS figures) originating from second BZ. The major difference between the two fairly flat dispersions that are probably very sensitive systems is the presence of weight at E over large F in size to band dispersions and location of the regions of the FS. This intensity originates from Ce chemical potential. Some experimental weight at E F near the X-point has the wrong dispersion compared to the theoretical bands, but may be related to the hypothesis concerning bands 4 and 5 in the preceding paragraph.
So far we have established the ability of ARPES to identify the basic band structure and FS topology of LaRu Si , and have demonstrated the basic 2 2 validity of the LDA band structure calculations. Good agreement between experiment and theory is observed not only below 0.5 eV binding energy, but also in the FS region including large hole surfaces centered on Z in LaRu Si and small electron 2 2 pockets around G. The large hole surface centered on Z is the important ''pillow'' FS which is predicted to become very heavy in CeRu Si , as described in This section presents ARPES information on the FS and on the global variation of the 4f-weight of has not been achieved previously in ARPES studies CeRu Si . 2 Fig. 9(a) acquired at 91 eV, which is below the 122 eV resonance so that the 4f states are weaker, and which is in a region of large d-cross section. This map was acquired over a 2208 azimuth range out to 308 polar angle and has been 4-fold symmetrized. We begin by calling attention to a weaker feature of great importance for our discussion below. Glancing back and forth between Fig. 6(b) and Fig. 9(a), initially with attention to the central BZ, reveals in 9(a) the dim pattern of a large surface centered on the second BZ Z-points and extending into the central BZ, very similar to the one in LaRu Si . The pairs of straight 2 2 segments of intensity on either side of the X-points are parts of such large pieces of FS. One also sees some of the additional intensity ascribed in Fig. 6(b) to k -broadening of this large FS piece. Other clearly z observable features include (i) a bright intensity at the normal emission G-point, (ii) an intense closed contour in the second BZ's that correspond to near G-points, (iii) weak intensity and possibly small closed topologies around the Z-points. Fig. 9(c) shows calculated 2D FS contours for CeRu Si . The existence of small closed contours at 2 2 the G and Z-points is in qualitative agreement with the image of Fig. 9(a). At first glance their similar sizes and shapes tempt one to associate the large Z-point contour in experiment with the large Z-point electron contour in theory. Apparently absent in this association is the pillow hole FS contour that closely follows the square BZ boundary centered on Z, of the data suggests the reverse interpretation, that the theoretical electron surface is not observed and that the band 4 hole FS does appear in the data, but Ce compound. Strong support for this conclusion is with the larger surface appropriate to the La com-provided by the great overall similarity of the pound (Fig. 6(c)) rather than the smaller one of the experimental data for La and Ce, and by the spectra of Fig. 9(d) showing the dispersions that define the plane of the linearly-polarized photon electric-field large surface near the X-point along the Z-X-Z vector. Further studies are warranted to investigate direction. The spectra clearly show a single hole the true origin of this behavior. In general, the band (relative to Z) on each side of the X-point, as is 4f-character ellipses have a size and shape that appropriate for the single larger hole surface of the closely match the strongest d-character contours in La compound, whereas one would observe two Fig. 9(a). This gives an overall impression of fbands and two FS crossings for the adjacent hole and weight having a very close correspondence to the electron surfaces predicted for the Ce compound (see locations of the off-resonance d-band FS, except for also Fig. 1(a)). Equivalent spectra for the La com-the large hole pocket of band 4. pound are very similar in showing the single band.
Another important view of the 4f-weight variation The surprising finding is that, in contrast to dHvA near E in CeRu Si is given by the valence band results, we observe a FS that is essentially the same spectra for off-and on-resonance photon energies. as that of the La compound, i.e. that excludes the Ce Fig. 10 shows a polar angle variation of valence 4f electrons. As a hypothesis for understanding this spectra along the k110l azimuth corresponding to the result we recall from Section 1.1 the conjecture [22] G-X-G at 154 eV and Z-X-Z at 122 eV. The that such may be the case for T 4 T and we take above-resonance VB map of Fig. 8(a) along k110l is K note that the temperature of these measurements is a subset of the spectra in Fig. 10(a) and a 458 six to seven times that of T¯20 K, whereas the diagonal in the on-resonance FS map image of Fig.   K dHvA data are taken for low T ( , 3 K) in the Fermi 9(b) corresponds to the spectra in Fig. 10(b). The liquid regime. It is then very interesting to tune the spectra are acquired with 0.58 angular steps (Dk2 1 photon energy to the 4d → 4f resonance and observe 0.05 A ) and high-symmetry spectra are labeled the k-space locations of the 4f weight. Fig. 9(b) and indicated by bold lines. An incremental energy shows an on-resonance FS map of mostly 4f-charac-shift has been applied to provide a better visual ter for CeRu Si acquired at 122 eV (corresponding perspective of the large weight variation at E . What 2 2 F to the Z-point at normal emission). Essentially no 4f weight is observed for the large Z-point 4f hole surface. This finding is certainly consistent with our hypothesis. However we should also recall that in the Anderson impurity model the portion of the 4f weight below E that is directly associated with the F low energy scale of the Kondo resonance is in any case very small. The 4f-weight occurs at the elliptical contours centered on the G and Z points. The dHvA and renormalized LDA masses of the FS at these points are not greatly enhanced and the FS volume does not have a large contribution for the 4f electrons. Thus the finding of 4f weight may not be inconsistent with the high temperature of the measurements. We note the peculiarity that, while the major-axes of the Z-point elliptical contours are radial at normal emission, the contours centered on G have a 458 rotation of the major elliptical axis that breaks mirror symmetry about the k100l plane. For this reason the map in Fig. 9(b) has only been 2-fold symmetrized. This symmetry breaking is possibly due to a polari-  Fig. 10(a), where the Ce 4f cross photoemission allows measurement of a single dosection is still relatively strong, is a persistence of a main in the perpendicular direction, the lateral peak impinging on E throughout most of the spectra domain size was too small to obtain high quality F with the exception of the X-point. On-resonance Ce ARPES data on ThRu Si in the rotating sample / 2 2 4f weight in Fig. 10(b) becomes especially enhanced fixed detector geometry at the ALS where the beam at points near the normal emission Z-point with a spot inherently moves on the sample surface. In clear correspondence to the locations of the E addition, sample alignment for the fixed sample / F crossings of a hole-like d-band. In addition, a moveable detector geometry at the SRC was further gigantic enhancement of the Ce 4f weight is ob-complicated by differences in orientation of the Laue served at one side of the Z-point in the second BZ.
patterns before and after cleavage, indicating domain The amplitude of this f-weight makes it difficult to inhomogeneity as a function of depth. The result was discern a similar connection to a weaker amplitude that FS maps at the SRC were a necessary ingredient d-band E -crossing. However, the correspondence of to determine the sample orientation and hence to F this strong peak to a distinct elliptical FS contour know where to acquire spectra. The results in this feature in the FS map of Fig. 9(b) is evidence that section are shown only for low photon energies there does exist a d-band crossing associated with ( # 35 eV). 0 this f-weight.
Since ThRu Si is an f metal similar to 2 2 We note further that while the E peak in Fig. 10 LaRu Si , we expect a very similar band structure F 2 2 exhibits dramatic intensity variations as a function of and FS topology with differences related primarily to 41 31 angle, there is no distinct dispersion of spectral the different Th and La valences as discussed in weight away from E with one notable exception of Section 1.1. Fig. 11(a, b) shows a FS map of mixing region at the Z-point is discussed in more Z points. The more severe curvature of the hemisdetail in Section 3.1 with comparison to observations pherical measurement surface at low photon energy, for URu Si that are presented in the next section.
causes the 17 eV FS map to cut through G at normal 2 2 emission, but then pass intermediate between G and Z in the second BZ (see Fig. 4). Similarly at 30 eV, 3. Results: X5Th, U normal emission cuts intermediate between G and Z while larger angles pass directly through the second In this section we present a comparison of the data BZ Z-point. The relative intensities at the points 0 for the actinide systems containing 5f thorium and labeled G and Z in Fig. 11(a,b)  orientation of ThRu Si samples currently available (Fig. 5) could be due to the more restricted k-space 2 2 is considerably less than for LaRu Si . In particular, range or to photon energy differences. Fig. 11(c) 2 2 Laue diffraction patterns of the ThRu Si samples shows the theoretical FS contours of ThRu Si .  binding energy. In addition, on both sides of the X-point we observe weight near E that is ex-F perimentally determined (data not shown) to be small electron pockets unresolved in Fig. 12(a). The gener-  Fig. 12, much better agreement is will produce a large deviation in comparison of FS observed. In Fig. 12(a) we observe a parabolic contours, but the EDC's show better general agreedispersion along G-(S)-Z similar to the one in ment for this band. Overall we conclude for LaRu Si that forms a hole-pocket at Z. Different, ThRu Si that agreement with band theory is rela- though, from LaRu Si , is that one band approaching tively good. 2 2 Z does not reach E and has a band maximum at F 0.4 eV binding energy. This observation is con-3.2. URu Si 2 2 1 sistent with Th having a valence of 4 and the chemical potential being higher relative to LaRu Si . Fig. 13(a) presents reverse grayscale images of 2 2 Also in Fig. 12, along G-X-G we observe general URu Si valence band spectra along two high-sym- 2 2 qualitative agreement in the bands from 0.5 to 2.0 eV metry azimuths at two different off-resonance photon down to below 1 eV have no correspondence to theory. At 156 eV, the G-(S)-Z data show a strong electron-like dispersion centered on G that crosses E F close to the midpoint between G and Z. This band dispersion can be traced all the way to¯1.5 eV binding energy at the G-point. Its presence is also evident at lower photon energies with weaker relative intensity and it serves as an additional signature that distinguishes the G and Z points. Along G-X-G, a data set from 85 eV is chosen to highlight a second anomaly relative to the LDA calculation, i.e. the presence of a distinct hole pocket centered on the ''X''-point. This band dispersion can be traced to below 0.5 eV and has no clear theoretical counterpart in the URu Si band calculations that predict the 2 2 possible presence of a small electron-like pocket arising from a shallow dispersing band of f-character that dips below E . F Another view of this ''X''-point discrepancy is in the comparison of an experimental E intensity map F at 85 eV in Fig. 14(a), with the theoretical FS contours in Fig. 14(c). The off-resonance FS map was acquired over a 808 azimuth range and 358 polar  midway between Z and G along normal emission, a bct BZ centered on Z is overplotted on the FS map to energies. The residual f-weight far above-resonance reflect the fact that the measurement surface cuts at 156 eV is evident near E in contrast to the near close to G along k100l and close to Z along k110l in F complete suppression of f-weight and strong d-cross the second BZ's. At k corresponding to the Xi section below 1.5 eV observed for the 85 eV data. points, a squarish closed contour is nicely observed Comparison to the other XRu Si band structures to additionally repeat near the outer edge of the FS 2 2 and to the LDA calculations in Fig. 13(b) show again map at the boundary between the second and third the common features of a parabolic-like band disper-radial BZ's. All three of these relatively small FS sions with band minima at¯1.6 eV binding energy contours at G, Z, and X originate from hole-like and symmetry around the X-point and midway dispersions as shown in Fig. 13. In contrast, the between G and Z. Also at the Z-point, band maxima theoretical FS contours, Fig. 14(c), show signifi-at¯0.5 eV and¯0 eV are observed in agreement cantly larger hole pockets at the G-point and small with bands (1,2) and 3, respectively, in the LDA electron pockets at the X-point. calculation. Spectral intensity near E just adjacent The reason for these large discrepancies with LDA F to the Z-point along Z-(S)-G has a possible corre-theory has already been speculated in Section 1.1 as spondence to bands 4 and / or 5.
due to the over-estimation of the 5f band width However, in contrast to the other XRu Si sys-which produces f-bands that disperse too strongly 2 2 tems, the experimental bands in Fig. 13(a) also reveal and cause unrealistic disruptions of the d-band FS. quite strong disagreements with the LDA calculation With this concept in mind we try to deduce the in the near-E region where experimental dispersions origin of the URu Si X-point hole-pocket by look-F 2 2 more like the very narrow states of the Anderson lattice schematic of Fig. 3 than like the LDA 5f bands. We then speculate that for URu Si , the 2 2 presence of such U 5f states, in addition to creating a very narrow band of states just above E , pushes the F U-d electron-like band to lower energy (perhaps completely below E with correspondence to the F arrow in Fig. 13(a)). The result is that the U-d and Ru-d crossing point is also moved to lower energy, thereby allowing the X-point Ru-d hole-pocket to remain as the unhybridized continuation of band 4 above E . Similarly, and perhaps more simply, a F possible correspondence can be made between the anomalous electron-like dispersion centered at G in URu Si , which is particularly strong at 156 eV 2 2 0 along G-(S)-Z, and bands 4 and / or 5 in the 5f LDA band structure of ThRu Si . 2 2 Next we compare the d-character off-resonance FS map of URu Si to an on-resonance FS map in Fig. 2 2 14(b) acquired at 112 eV where U 5f character is enhanced. The data was acquired over 1208 azimuth and 358 polar angle ranges and has also been 4-fold symmetrized. Similar to Fig. 14(a), normal emission of this map probes midway between G and Z and the overplotted BZ boundary centered on G reflects the k measurement points in the second BZs. Despite i this measurement surface complication, we can immediately make the qualitative observation of the lack of appearance of closed FS contours. Rather, the FS map gives the impression of points of U 5f weight mostly at high symmetry points. Additional intensity midway from ''Z'' to ''G'' corresponds to 13. Its contour is suggestive of a larger closed hole (bold) and electron (fine) Fermi surface topologies.
surface but is not conclusive. Apart from this FS f-weight, the dominant on-resonance f-weight can be 0 ing at the 5f ThRu Si band structure (Fig. 12), described as being confined to the interior of the 2 2 where small electron pockets on either side of the off-resonance d-character hole-pockets. X-point were found experimentally and could be A spectral function view of this off / on-resonance consistent with a slightly modified LDA band 5. The behavior is shown in Fig. 15 measured along the dispersions of bands 4 and 5 near X appear to diagonal k110l direction at the same photon energies originate from the crossing-point hybridization be-as the FS maps. Similar to Fig. 10 for CeRu Si , the . At 112 eV, the spectra near normal (as just discussed) and that very little dispersion emission reveal the presence of a second distinct occurs along the P-X-P direction. Indeed, because hole-like dispersion that appears to cross E just the k periodicity along P-X-P is half of that along F z outside of the strongly resonating weight at normal G-Z-G (see Fig. 4), much less dispersion is calcuemission. At low photon energy, normal emission lated along P-X-P for all four compounds. Exspectra of URu Si at G at 18 eV reveal a finite perimentally, the ''X''-point pocket is as robust a 2 2 binding energy peak with¯50 meV gap relative to spectral feature to sample surface ''aging'' as other E , consistent with He I ARPES measurements [14].
parts of the BZ, thus suggesting that it is not a F At the diagonal BZ edge, labeled ''X / P'', a hole-surface state. pocket band dispersion is observed to significantly This observed two-dimensionality of the ''X''decrease in amplitude from 85 to 112 eV, while a point FS works in our favor in attempts to make weak E peak at the center of the pocket is observed direct comparison of off-and on-resonance spectra in F to increase in amplitude. The reduction in amplitude simple terms of changing f and d cross-sections. of the dispersing band arises from the decreasing However, it is still a valid concern that different d-cross section with increasing photon energy. Also, parts of the BZ are being probed at 85 eV and 112 eV the amplitude of the f-character resonance at the in Fig. 15. The k-space guide in Fig. 4 tells us that interior of the hole-pocket is approximately 1 / 3 the these two photon energies actually arc through height of the resonance at normal emission. Also similar parts of the BZ (closer to ''P''-points) below significant is that the on-resonance spectra reveal the and above an X-point at¯102 eV. In Fig. 16, offnear-complete absence of any f-weight resonance and on-resonance spectra at the ''X''-point are between the ''G'' and ''X'' points. We focus closer presented for a smaller difference in photon energy attention in Section 4.1 on this ''X''-point hole (102 and 108 eV), higher resolution (DE¯40 meV, pocket in URu Si to further elucidate and discuss Du¯0.28) and a sample temperature of 100 K. 2 2 of f-weight on the unoccupied side of the d-band dispersion, e.g. at the interior of a hole-pocket.
The relative enhancement of f-weight between the interior and exterior of a hole-pocket is sensitive to 9 the values of´and V 9. To illustrate this we f compare in Fig. 17 on-resonance valence spectra from the ''X''-point crossing in URu Si to a similar 2 2 idealized crossing point at the normal emission Zpoint hole-pocket at 122 eV in CeRu Si . While the 2 2 URu Si spectra in Fig. 17 URu Si can be qualitatively understood to result coefficient twice as large as that of URu Si , is 2 2 Similar to Fig. 15, the confinement of U 5f weight to the interior of the d-band hole pocket is quite striking in appearance, and at this resolution shows no dispersion away from the d-band crossings. This k-space distribution of f-weight is a key signature of the Anderson lattice model, i.e. that ''f-dispersion'' occurs only through hybridization to dispersing s-p-d states. In the vicinity of a d-band E -crossing, the lattice model, with suitable mathe-F matical transformation [6,7], is formally equivalent to the two-band mixing model of a dispersionless effective f level hybridizing with a free-electron band dispersion with renormalized hybridization (V 9). As illustrated in Fig. 3, this hybridization at the f and d crossing point above E creates a small   sistence of Ce 4f weight throughout most of the BZ f-enhancement at normal emission compared to the 9 in Fig. 10(b) and Fig. 17 An important aspect of the Anderson single im-17. Such lineshape analysis will be presented else-purity and lattice models is the temperature depenwhere.
dence of the Kondo peak as the system is cooled As discussed in Section 1.1, the reduction of below the Kondo temperature. Predictions for lattice Fermi-velocities and formation of heavy bands with-models exist [8], but thus far the models are not in the Anderson lattice model is also evident in the realistic as to degeneracy or conduction electron renormalized two-band approximation. Lineshape number for Ce, Yb or U [48]. For the impurity model analysis of low temperature high-resolution spectra below T a sharpening or increase of the k-inte-K has the potential to identify and quantify such grated photoemission f-spectral weight is expected effective mass increase near E even if not visible by for Ce and Yb, with differences originating from the F direct inspection The spectra in Fig. 17 for both one f-electron and one f-hole character, respectively CeRu Si and URu Si show small hints of such [35]. Such temperature dependence has been re-2 2 2 2 slope-reduction near E . We should also note that ported for Ce [19] and Yb [49] compounds, but also F these two idealized k-space locations are expected to disputed [18,50]. Experimentally no significant temonly exhibit modest mass enhancements (m* / m , perature variation in photoemission has yet been 10). It is other sheets of FS, such as the CeRu Si reported for any U compound [18]. URu Si , with an 2 2 2 2 ''pillow'' that have been identified by dHvA and intermediate Kondo temperature of¯70 K [51], is renormalized LDA to possess the very large effective favorable for such a temperature-dependent study of mass of greater than 100. the f-weight at different locations in k-space. The Also we should point out that the two idealized X-point was chosen for its idealized electronic f -d crossing points shown in Fig. 17 do not repre-structure of an isolated d-band hole pocket hybridizsent the regions in k-space of strongest f-spectral ing with U 5f states, and for the relative absence of weight. Figs. 9(b) and 14(b) show much stronger d-states below E at the center of the hole pocket. f-weight at the second BZ 122 eV ''Z''-point in Fig. 18 shows such angular-resolved spectra from CeRu Si and at normal emission at 112 eV in the center of the X-point measured at resonance (108 2 2 URu Si . These large variations in f-weight ARPES eV) for temperatures in the experimental sequence of 2 2 intensity can result from different topologies (FS 100 K, 50 K and 25 K. A striking temperature surface sizes and bare E velocities) of the underly-dependent enhancement of the E peak is observed F F ing d-band as well as from matrix element effects. for lower temperatures. The increase from 100 K to surface universally result in an enhancement of the 2 eV peak and a reduction of the E peak relative to the F spin-orbit sideband. It has been demonstrated that quantitative separation of surface and bulk contributions to the f-spectral weight in angle-integrated valence band photoemission can be achieved by exploiting the variable electron escape depths at multiple photon energies [56], and that this surface and bulk decomposition is essential for an understanding of the spectra in relation to bulk thermodynamic properties [55]. Recent advances in energy resolution of valence photoemission at high photon energies ( | 1 keV) [20] where bulk sensitivity is enhanced, show promise for refinement of quantitative modeling of angle-integrated f-spectral weight. edges ( | 100 eV), we have accumulated various observations bearing on surface effects aided by the 25 K is almost a factor of two in the raw data k-dependence of the spectra from different cleaves. without consideration of a temperature-invariant To illustrate, Fig. 19 shows intensity images of inelastic background (and greater than 400% with on-resonance valence band spectra along Z-X-''Z'' subtraction of this background). This large tempera-for two different ''good'' and ''bad'' cleaved surture variation is consistent with observations by faces of CeRu Si . The ''good'' data in panel (a), an 2 2 point-contact spectroscopy of a resonance at E intensity representation of the same data as shown in F appearing below 60 K [52] and is interpreted as Fig. 17(b), exhibit strongly dispersing d-band states possible evidence for the Kondo singlet condensation. Previously no significant temperature variation of angle-integrated valence spectra from scraped single crystals of URu Si [53] was observed. A 2 2 more complete analysis of this Kondo-like temperature dependence in URu Si will be presented 2 2 elsewhere.

Surface effects
Surface effects in photoemission of f-electron systems need to be taken seriously. For Ce compounds there is a sizable body of literature with discussion of surface effects in terms of increased 4f binding energy and reduced f-hybridization resulting from smaller near-neighbor coordination at the surface [54,55]. Angle-integrated Ce valence spectra 1 0 exhibit three main features: (i) a broad f → f electron removal peak at¯2 eV, (ii) a Kondo resonance spin-orbit sideband at¯0.3 eV and (iii) a Fig. 19. Comparison of on-resonance valence spectra for narrow peak impinging on E corresponding to the F CeRu Si for two different cleave surfaces. The image in (a) is an 2 2 occupied tail of the Kondo resonance. The reduced intensity representation of the data in Fig. 17(b). Angle-averaged hybridization and increased binding energy at the spectra for each data set are also shown. and large f-weight intensity variation near E . The the averaged spectrum in Fig. 19(a) is similar to that F ''bad'' data in panel (b), in contrast, show streaks of reported in a bulk-sensitive angle-integrated resonant k-independent spectral weight at 0.3, 0.8 and 1.6 eV photoemission study [20] at the Ce 3d edge, and the binding energy, and a relatively smaller amplitude of spectrum reported in Ref.
[20] as being typical of dispersing d-bands and near-E f-states. The 0.3 eV resonant photoemission at the Ce 4d edge is similar F peak corresponds to the Kondo sideband energy to that of the poorer surface in Fig. 19(b). Thus, it while the precise origin of the other two peaks is may be that for CeRu Si at least, spectra mostly 2 2 currently unknown. Also, since the reverse grayscale characteristic of the bulk can be obtained at lower of each image has been separately adjusted to photon energy if the surface is sufficiently free of optimally enhance the intensity contrast, the k -aver-steps, edges, etc., or if the analysis area is very i aged spectrum of each data set has additionally been small. More complete angle-averaging efforts, complotted in Fig. 19 for a more direct comparison of the parison between Ce 3d and 4d edges, and correlation different amplitude variations of the two cleaves.
to Si 2p core-level shifts will be presented elsewhere. Also measured are multiple Si 2p core-level surfaceshifted peaks with varying intensities from cleave to cleave. Such variations in Si 2p spectra and ARPES 5. Summary quality as illustrated in Fig. 19 occur not only between different cleaves, but also for different The general picture that emerges from the expoints on the same cleaved surface, probed using a perimental band structure measurements and FS 100 mm synchrotron beam spot, and with sample maps of the XRu Si intermetallic compounds with 2 2 ''aging'' and / or poor vacuum. comparison to LDA calculations, is similar to that We cannot make a unified picture yet, but there speculated in the discussion in Section 1.1. Namely, are two main considerations of: (i) different possible (i) good agreement with the d-band structure away cleavage planes of XRu Si (001) which contains an from E is found for all compounds, (ii) relatively 2 2 F alternating atomic layering of -X-Si-Ru-Si-X-, good agreement in the d-band derived FS contours is 0 and (ii) the different number of steps and edges found for the f compounds, especially for La, (iii) contributing k-independent surface spectral weight. for X5Ce measured above its Kondo temperature, While the surface structure of the XRu Si systems the FS appears to be essentially like that for La, and 2 2 has not been experimentally determined yet, all (iv) the near-E region for URu Si is substantially indicating a lack of multi-zone reconstruction. and CeRu Si Fermi surfaces suggests the exclusion 2 2 Macroscopically rough regions on the cleaved sur-of f-electrons from the FS in the high temperature face will contain a significant enhancement of the state. The anomalous FS features in URu Si can be 2 2 surface area in general, especially of the edge-type of traced to theoretical bands in the ThRu Si elec- 2 2 Ce atoms which lack long range order and which tronic structure and suggest unrealistic disruptions of 2 have smaller near-neighbor coordination leading to the d-band Fermi surface in LDA of f systems. the spectral changes consistent with what is observed Resonant ARPES of the Ce and U systems show in Fig. 19(b). The correlation of Si 2p surface core-extremely large variations in 4f and 5f spectral level shifts to valence spectra and to surface topog-weights throughout the BZ. The FS mapping techraphy is a promising approach to further understand-nique provides the global k-space view of the fing of the surface structure. spectral weight that gives the relation to the underly-Another important objective, which also involves ing d-band structure and Fermi surface. Results the surface contribution, is to make connection back include spectral signatures of Anderson lattice to angle-integrated resonant photoemission, a rather physics, e.g. the k-space confinement of f-spectral difficult task for single-crystal surfaces requiring the weight at the Fermi level to the interior of d-band summing of spectra from many different angles. The hole Fermi surfaces signifies mixing of d and averaged spectra in Fig. 19 show an initial step in renormalized f-states. Detailed comparison of onthis effort. It is very interesting to note that the ratio resonance spectra at isolated d-band crossings in of the Kondo sideband to the main Kondo peak in CeRu Si and URu Si reveal differences in the f -d