Coherent heavy quasiparticles in CePt{}_{5} surface alloy

Coherent heavy quasiparticles in CePt surface alloy

M. Klein Universität Würzburg, Experimentelle Physik VII & Röntgen Research Center for Complex Materials RCCM, Am Hubland, D-97074 Würzburg, Germany    A. Nuber Universität Würzburg, Experimentelle Physik VII & Röntgen Research Center for Complex Materials RCCM, Am Hubland, D-97074 Würzburg, Germany    H. Schwab Universität Würzburg, Experimentelle Physik VII & Röntgen Research Center for Complex Materials RCCM, Am Hubland, D-97074 Würzburg, Germany    N. Tobita Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan    M. Higashiguchi Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan    J. Jiang Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan    S. Fukuda Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan    K. Tanaka Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan    K. Shimada Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739-0046, Japan    M. Mulazzi Universität Würzburg, Experimentelle Physik VII & Röntgen Research Center for Complex Materials RCCM, Am Hubland, D-97074 Würzburg, Germany    F. F. Assaad Universität Würzburg, Institut für Theoretische Physik und Astrophysik, Am Hubland, D-97074 Würzburg, Germany    F. Reinert Universität Würzburg, Experimentelle Physik VII & Röntgen Research Center for Complex Materials RCCM, Am Hubland, D-97074 Würzburg, Germany Karlsruhe Institute of Technology KIT, Gemeinschaftslabor für Nanoanalytik, D-76021 Karlsruhe, Germany
July 19, 2019

We report on the results of a high-resolution angle-resolved photoemission (ARPES) study on the ordered surface alloy CePt. The temperature dependence of the spectra show the formation of the coherent low-energy heavy-fermion band near the Fermi level. This experimental data is supported by a multi-band model calculation in the framework of the dynamical mean field theory (DMFT).

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The physics of -electrons continues to fascinate since the interplay between fundamental interactions gives rise to complex phase diagrams and exotic states of matter lohneysen07rev (). In Kondo systems, the two main energy terms determining the microscopical behavior are the hybridization between localized -states and conduction electrons and the large Coulomb repulsion between -electrons at the same lattice site. At temperatures above the coherence temperature these interactions are purely local and can be explained successfully by the single-impurity Anderson model (SIAM) hewson (); GS83a (); GS83b (); bickers87 (). A very powerful tool which allows to study these local interactions experimentally is photoemission spectroscopy as it directly probes the spectral function of the system. In the past the combination of PES and SIAM lead to a deeper understanding of Kondo systems spectral features like the Kondo resonance (KR) with additional spin-orbit and crystal-field excitations, including their temperature dependence allen05 (); ehm07 (). Nevertheless, at temperatures the localized heavy quasiparticles begin to interact with each other and finally form coherent heavy-fermion bands whose properties cannot be explained by the SIAM any longer hewson (); fulde (). Up to now experimental limitations prevented a closer investigation of this coherent heavy-fermion state by photoemission. In order to observe coherence effects one usually needs temperatures well below the Kondo temperature of the system, has to use momentum-resolving probes and an energy resolution better than . A second problem arises from the surface sensitivity of photoemission techniques, requiring highly-ordered single-crystalline surfaces to observe dispersing features. These surfaces can be produced by in situ cleaving of layered compounds allen05 (); denlinger01 (); wigger07 (); vyalikh08 (); im08 (); koitzsch08 () or by an in situ preparation of thin films of a Ce alloy at the sample surface garnier97a (); danzenbacher05 (); garnier98 (); pillo99 (). The second method has the advantage that the surface quality does not depend on the cleave and the quasi two-dimensional model systems are comparable to theoretical calculations done considering the system structure and dimensionality. It is known that the deposition of 4 ML of Ce and subsequent annealing form a surface alloy that has the same crystal structure as bulk CePt, as found by combined studies of scanning tunneling microscopy, low-energy electron diffraction (LEED) tang93 (); baddeley97 (); berner02 (); vermang06 () and in the reference compound LaPt ramstad99 (). This alloy consists of alternating CePt and Pt-kagome layers, whereas the topmost layer is a Pt layer which makes the alloy less sensitive to surface oxidation. Thus this system is an ideal model system for studying the effects of the periodic Anderson lattice by ARPES. Several earlier investigations on CePt/Pt(111) surface alloys by photoemission revealed the well known signature of the Kondo resonance at the Fermi level and even its spin-orbit partner at  meV andrews95 (); garnier97 (); garnier98 (); pillo99 (). Nevertheless, those experiments were carried out at either too high temperatures or limited by instrumental resolution.
In this Letter we present high-resolution ARPES measurements and Dynamical Mean Field Theory (DMFT) calculations on the CePt/Pt(111) system. We extract the spectral weight as a function of the temperature and show for the first time the transition from a high-temperature phase, in which the system can be described as a set of isolated impurities, to a low-temperature phase where coherent heavy fermion quasiparticles become apparent. The high-resolution ARPES experiments were performed using a Gammadata R4000 analyzer equipped with a monochromatized discharge lamp using the He II emission line ( eV, mainly -polarized). The instrumental resolution was determined by measuring the superconducting gap of a VSi polycrystal  reinert00 (), resulting in  meV at the used spectrometer settings. The resonant photoemission experiments were carried out at BL1 of the HiSOR synchrotron radiation source in Hiroshima, using an SES200 analyzer and linearly polarized light. The total energy resolution (monochromator and analyzer) was  meV at  eV. Following the method of Ref. baddeley97, we prepared ordered surface alloys by depositing  ML of Ce on a Pt(111) surface. The sample was annealed subsequently for  min at  K. The formation of the CePt surface alloy was evidenced by LEED experiments (not shown) giving a -reconstruction, corresponding to a surface alloy with a bulk like CePt stoichiometry and geometry baddeley97 ().

Figure 1: (color online) Top left: ARPES data set ( meV,  K) around the -point (second Brillouin zone) at the resonance ( eV=). Top right: Energy distribution curves (EDC) taken from top left panel, bottom left: Respective momentum distribution curves (MDC) ( point indicated by thicker line). The data taken at the Fermi level are indicated by a thick dashed line. Bottom right: Comparison between the EDC at the point measured on- (solid yellow line) and off-resonance (dashed blue line). KR, SO and IS indicate the Kondo resonance, the spin-orbit partner, and the ionization structure.

To clarify the electronic structure of the CePt surface alloy, Fig. 1 displays measurements at the resonant excitation energy ( eV) at  K, measured in the second Brillouin zone around . The bottom right panel gives the comparison of the spectrum at the point with the off-resonance data ( eV). It shows clearly the main features, namely the KR near the Fermi level , the spin-orbit partner (SO) around 0.25 eV, and the ionization peak (IS) at even higher binding energies. The KR, with its maximum a few meV above , reflects the low-energy excitations of the system and shows a distinct temperature dependence bickers87 (). ARPES data at the resonance energy (other panels) show again these two structures, without being able to resolve a band dispersion (see energy distribution curves (EDC, top right panel)), superimposed by the steep conduction band dispersion, which can be found equivalently in the reference compound LaPt (not shown). The conduction band appears more clearly in the momentum distribution curves (MDC, bottom left), that represent horizontal cuts through the color-scaled data set at the top. In the following we analyse the high-resolution ARPES data in more detail. Applying a well established method to restore the thermally occupied part of the spectrum up to an energy of above the Fermi level greber97 (); ehm01b () we divide the ARPES spectra recorded along the -direction by the Fermi-Dirac function calculated at the experimental temperature.

Figure 2: (color online) Temperature dependence of the ARPES data normalized by the Fermi distribution. The data were acquired as a function of temperature from the lowest to the highest (top to bottom:  K,  K and  K). The spectra show a conduction band (hatched area) and a narrow structure above (indicated by the blue horizontal arrow), the Kondo resonance. With rising temperature, the Kondo resonance broadens and shifts away from . The two insets schematically show the transition from the coherent low-temperature regime to the local regime at high temperatures.

Fig. 2 shows the resulting data for  K,  K and  K. The irregular black/white pattern above the Fermi level is due to the amplified scatter in the experimental background. At the lowest temperature ( K) the intensity maximum is situated right at or slightly above the Fermi level. A few meV below the conduction band sharply bends towards the -point. Additionally another very narrow horizontal band, pinned at the , appears at larger -values. This structure seems to be separated from the conduction band around , as a gapping of the intensity at  Å suggests. The results are consistent with the generic mean-field heavy-fermion picture of a flat f-character band hybridizing with the conduction band of the system. This scenario is sketched in inset to the low temperature data. To estimate the hybridization gap we plot in Fig. 3 the integrated intensities taken from two momentum regions:  Å and  Å respectively (as indicated by the non-hatched area in Fig. 2). The region, where the intense conduction band lies, is not taken into account by the integration. The result of the integration is given in Fig. 3: It shows that the binding energies of the intensity maxima differ by  meV. This shift in energy represents a measure for the size of the hybridization gap due to the hybridization between the conduction band and the Ce  states.

Figure 3: (color online) Left: Integration of the intensity for  Å (solid line) and for  Å (dashed) at three different temperatures. The figure shows that at  K the binding energy of the intensity maxima of the outer- and inner- hybridized bands differ by  meV. With rising temperature the difference vanishes. Right: Similar quantity as obtained from the modeling of the experiment (see text). In the inset the spectral function integrated over the whole Brillouin zone is shown. The units of the inset x-scale are electronvolts.

It might be noticed that the experimental data shift towards the unoccupied states with increasing temperature while the maxima in the theoretical spectra stay constantly at . This finding is due to scattering effects in the photoemission process (both from imperfections and from final state effects). Those lead to contributions from other regions in -space, resembling the integrated density of states which shows the observed temperature dependent shift ehm01 (). When our calculated spectral function is integrated over the whole Brillouin zone, the maximum shifts towards the unoccupied states as anticipated bickers87 () (inset of Fig. 3). Since this additional contribution is not angle dependent, it does not significantly alter the analysis of the band dispersion.

The hallmark of the heavy-fermion state lies in its temperature dependence. As the temperature is raised, the hybridized band structure gives way to the bare conduction band thus signaling the crossover from the heavy Fermion state with large Luttinger volume to the high temperature phase where the -electrons are localized and drop out of the Luttinger volume. The two extreme situations are shown in the insets of Fig. 2. The temperature dependence of the experimental results is consistent with this interpretation. The flat band at  Å broadens and shifts away from . As mentioned above, this temperature dependence is similar to the evolution of the Kondo resonance of systems in which the Ce atoms behave as isolated impurities bickers87 (); ehm07 (). At the same time the structure around the -point ( Å) acquires spectral weight and evolves towards the emergence of a light band crossing the Fermi energy. This growth in spectral weight is consistent with the closing of the hybridization gap. In the high temperature limit, i.e. clearly above , and as sketched in the inset, only the conduction band disperses (as sketched in the inset). We note that the temperature dependence is consistent with DMFT calculations for the two-dimensional Kondo lattice beach08 (); suppl (). The starting point for the theoretical modeling of the experiment presented in Fig. 4 is a tight binding fit of the low energy features of the bulk reference compound LaPt. The step to CePt is taken at the model level by including an -multiplet. The center position of the -multiplet can be read from Fig. 1 and is set to  eV. We have included a spin orbit splitting of  meV and set the Coulomb repulsion to infinity such as to allow solely for and configurations. Assuming a -independent constant hybridization matrix element leaves us with a single free parameter which we set by fitting at best the temperature dependence of the experimental data (see Fig. 3). We solve this multi-band Anderson model within the DMFT approximation using an non-crossing approximation (NCA) solver. The details of the approach will be presented elsewhere Werner_Assaad_unpublished (). Fig. 4(a) shows the total spectral function at low temperature,  K. The sharp intense features correspond to the LaPt bands. At this low temperature and on this large energy scale we observe distinct rather dispersionless features which stem from the -electrons: i) the bare -level at  eV ii) the weak spin-orbit partner of the KR at  eV and iii) the KR at . The temperature evolution of the spectral function, as given in Figs. 4(c–f) vs. energy and momentum, describes nicely the experimental findings (see Fig. 2). In the considered temperature range, the emergence of a hybridized band structure, that shows the change of the heavy quasiparticle dispersion and - consequently - the change of the Fermi surface topology, is apparent in this multi-band periodic Anderson model.

Figure 4: (color online) a) Theoretical total spectral function plotted at  K vs. energy and momentum in a wide energy scale. Zoom near the Fermi level with b)  K, c)  K, d)  K, e)  K. In all the panels the intensities are plotted in a logarithmic scale indicated in the bars on the right side of each image. As indicated, the x-axis spans -vectors in the first Brillouin zone from the high symmetry point over to .

In conclusion we demonstrated that on high quality CePt films grown on Pt(111), high-resolution ARPES experiments allow to extract the temperature dependence of the spectral weight. At high temperatures we observe the well known Kondo resonance with a less intense spin-orbit feature, superimposed by the conduction bands. At low temperatures a remarkable change in the band dispersion appears: in the vicinity of the Fermi level the Kondo resonance evolves into hybridized heavy quasiparticle bands thus signaling, at the single-particle level, the onset of the coherent heavy-fermion Fermi-liquid state. A comparison with DMFT+NCA calculations of a multi-band Anderson model which takes into account the band structure of the reference compound, LaPt, supports these conclusions and allows a detailed analysis of the microscopic interactions.

This work was supported by the JSPS and the Deutsche Forschungsgemeinschaft within the Forschergruppe 1162. We’d like to thank Hans Kroha for helpful discussions. The synchrotron-radiation experiments were done under the approval of HSRC Proposal No. 07-A-42. We acknowledge the FOR1162 DFG project for financial support.



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