k Dependence of the crystal-field splittings of 4f states in rare-earth systems

Temperature-dependent change of the electronic structure in the Kondo lattice system YbRh2Si2

The heavy-fermion behavior in intermetallic compounds manifests itself in a quenching of local magnetic moments by developing Kondo spin-singlet many-body states combined with a drastic increase of the effective mass of conduction electrons, which occurs below the lattice Kondo temperatureT_K. This behavior is caused by interactions between the strongly localized 4felectrons and itinerant electrons. A controversially discussed question in this context is how the localized electronic states contribute to the Fermi surface upon changing the temperature. One expects that hybridization between the local moments and the itinerant electrons leads to a transition from a small Fermi surface in a non-coherent regime at high temperatures to a large Fermi surface once the coherent Kondo lattice regime is realized belowT_K. We demonstrate, using hard x-ray angle-resolved photoemission spectroscopy that the electronic structure of the prototypical heavy fermion compound YbRh₂Si₂changes with temperature between 100 and 200 K, i.e. far above the Kondo temperature,T_K= 25 K, of this system. Our results suggest a transition from a small to a large Fermi surface with decreasing temperature. This result is inconsistent with the prediction of the dynamical mean-field periodic Anderson model and supports the idea of an independent energy scale governing the change of band dispersion.

Similar temperature scale for valence changes in Kondo lattices with different Kondo temperatures

The Kondo model predicts that both the valence at low temperatures and its temperature dependence scale with the characteristic energy T_K of the Kondo interaction. Here, we study the evolution of the 4f occupancy with temperature in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In agreement with simple theoretical models, we observe a scaling between the valence at low temperature and T_K obtained from thermodynamic measurements. In contrast, the temperature scale T_v at which the valence increases with temperature is almost the same in all investigated materials while the Kondo temperatures differ by almost four orders of magnitude. This observation is in remarkable contradiction to both naive expectation and precise theoretical predictions of the Kondo model, asking for further theoretical work in order to explain our findings. Our data exclude the presence of a quantum critical valence transition in YbRh₂Si₂.

The competition between interactions promoting magnetic order and those suppressing magnetism causes unusual electronic behaviour in Kondo lattice materials. Here, the authors show the energy scale for valence fluctuations is not controlled by the Kondo scale, contrary to expectations from single-site models.

Three-dimensional bulk electronic structure of the Kondo lattice CeIn3 revealed by photoemission

We show the three-dimensional electronic structure of the Kondo lattice CeIn₃ using soft x-ray angle resolved photoemission spectroscopy in the paramagnetic state. For the first time, we have directly observed the three-dimensional topology of the Fermi surface of CeIn₃ by photoemission. The Fermi surface has a complicated hole pocket centred at the Γ-Z line and an elliptical electron pocket centred at the R point of the Brillouin zone. Polarization and photon-energy dependent photoemission results both indicate the nearly localized nature of the 4f electrons in CeIn₃, consistent with the theoretical prediction by means of the combination of density functional theory and single-site dynamical mean-field theory. Those results illustrate that the f electrons of CeIn₃, which is the parent material of CeMIn₅ compounds, are closer to the localized description than the layered CeMIn₅ compounds.

Band structures of 4f and 5f materials studied by angle-resolved photoelectron spectroscopy

Recent remarkable progress in angle-resolved photoelectron spectroscopy (ARPES) has enabled the direct observation of the band structures of 4f and 5f materials. In particular, ARPES with various light sources such as lasers (hν ~ 7 eV) or high-energy synchrotron radiations (hν >/~ 400 eV) has shed light on the bulk band structures of strongly correlated materials with energy scales of a few millielectronvolts to several electronvolts. The purpose of this paper is to summarize the behaviors of 4f and 5f band structures of various rare-earth and actinide materials observed by modern ARPES techniques, and understand how they can be described using various theoretical frameworks. For 4f-electron materials, ARPES studies of CeMIn5(M = Rh, Ir, and Co) and YbRh2Si2 with various incident photon energies are summarized. We demonstrate that their 4f electronic structures are essentially described within the framework of the periodic Anderson model, and that the band-structure calculation based on the local density approximation cannot explain their low-energy electronic structures. Meanwhile, electronic structures of 5f materials exhibit wide varieties ranging from itinerant to localized states. For itinerant U5f compounds such as UFeGa5, their electronic structures can be well-described by the band-structure calculation assuming that all U5f electrons are itinerant. In contrast, the band structures of localized U5f compounds such as UPd3 and UO2 are essentially explained by the localized model that treats U5f electrons as localized core states. In regards to heavy fermion U-based compounds such as the hidden-order compound URu2Si2, their electronic structures exhibit complex behaviors. Their overall band structures are generally well-explained by the band-structure calculation, whereas the states in the vicinity of EF show some deviations due to electron correlation effects. Furthermore, the electronic structures of URu2Si2 in the paramagnetic and hidden-order phases are summarized based on various ARPES studies. The present status of the field as well as possible future directions are also discussed.

Robust and tunable itinerant ferromagnetism at the silicon surface of the antiferromagnet GdRh2Si2

Spin-polarized two-dimensional electron states (2DESs) at surfaces and interfaces of magnetically active materials attract immense interest because of the idea of exploiting fermion spins rather than charge in next generation electronics. Applying angle-resolved photoelectron spectroscopy, we show that the silicon surface of GdRh₂Si₂ bears two distinct 2DESs, one being a Shockley surface state, and the other a Dirac surface resonance. Both are subject to strong exchange interaction with the ordered 4f-moments lying underneath the Si-Rh-Si trilayer. The spin degeneracy of the Shockley state breaks down below ~90 K, and the splitting of the resulting subbands saturates upon cooling at values as high as ~185 meV. The spin splitting of the Dirac state becomes clearly visible around ~60 K, reaching a maximum of ~70 meV. An abrupt increase of surface magnetization at around the same temperature suggests that the Dirac state contributes significantly to the magnetic properties at the Si surface. We also show the possibility to tune the properties of 2DESs by depositing alkali metal atoms. The unique temperature-dependent ferromagnetic properties of the Si-terminated surface in GdRh₂Si₂ could be exploited when combined with functional adlayers deposited on top for which novel phenomena related to magnetism can be anticipated.

ARPES view on surface and bulk hybridization phenomena in the antiferromagnetic Kondo lattice CeRh2Si2

The hybridization between localized 4f electrons and itinerant electrons in rare-earth-based materials gives rise to their exotic properties like valence fluctuations, Kondo behaviour, heavy-fermions, or unconventional superconductivity. Here we present an angle-resolved photoemission spectroscopy (ARPES) study of the Kondo lattice antiferromagnet CeRh₂Si₂, where the surface and bulk Ce-4f spectral responses were clearly resolved. The pronounced 4f ⁰ peak seen for the Ce terminated surface gets strongly suppressed in the bulk Ce-4f spectra taken from a Si-terminated crystal due to much larger f-d hybridization. Most interestingly, the bulk Ce-4f spectra reveal a fine structure near the Fermi edge reflecting the crystal electric field splitting of the bulk magnetic 4f ¹_5/2 state. This structure presents a clear dispersion upon crossing valence states, providing direct evidence of f-d hybridization. Our findings give precise insight into f-d hybridization penomena and highlight their importance in the antiferromagnetic phases of Kondo lattices.

In rare-earth intermetallics, interaction between localized 4f electrons and itinerant electrons can result in exotic states of matter. Here, the authors use photoemission spectroscopy to reveal and study this interaction in the bulk and at the surface of the Kondo lattice antiferromagnet CeRh₂Si₂.

Strong ferromagnetism at the surface of an antiferromagnet caused by buried magnetic moments

Carrying a large, pure spin magnetic moment of 7 μB per atom in the half-filled 4f shell, divalent europium is an outstanding element for assembling novel magnetic devices in which a two-dimensional electron gas may be polarized due to exchange interaction with an underlying magnetically-active Eu layer. Here we show that the Si-Rh-Si surface trilayer of the antiferromagnet EuRh2Si2 bears a surface state, which exhibits an unexpected and large spin splitting controllable by temperature. The splitting sets in below ~32.5 K, well above the ordering temperature of the Eu 4f moments (~24.5 K) in the bulk, indicating a larger ordering temperature in the topmost Eu layers. The driving force for the itinerant ferromagnetism at the surface is the aforementioned exchange interaction. Such a splitting may also be induced into states of functional surface layers deposited onto the surface of EuRh2Si2 or similarly ordered magnetic materials with metallic or semiconducting properties.

Interplay of Dirac fermions and heavy quasiparticles in solids

Many-body interactions in crystalline solids can be conveniently described in terms of quasiparticles with strongly renormalized masses as compared with those of non-interacting particles. Examples of extreme mass renormalization are on the one hand graphene, where the charge carriers obey the linear dispersion relation of massless Dirac fermions, and on the other hand heavy-fermion materials where the effective electron mass approaches the mass of a proton. Here we show that both extremes, Dirac fermions, like they are found in graphene and extremely heavy quasiparticles characteristic for Kondo materials, may not only coexist in a solid but can also undergo strong mutual interactions. Using the example of EuRh₂Si₂, we explicitly demonstrate that these interactions can take place at the surface and in the bulk. The presence of the linear dispersion is imposed solely by the crystal symmetry, whereas the existence of heavy quasiparticles is caused by the localized nature of the 4f states.

Structural investigations on YbRh2Si2: from the atomic to the macroscopic length scale

YbRh2Si2 has advanced to a prototype material for investigating physics related to the Kondo effect. An optimization of the synthesis resulted in single crystals of extraordinary crystalline quality. At the atomic scale, we utilize scanning tunneling microscopy to study the topography of cleaved single crystals. A structural and chemical analysis was conducted by highly accurate x-ray diffraction and wavelength dispersive x-ray spectroscopy measurements. The latter indicate a homogeneity range of the YbRh2Si2 phase between approximately 40.0–40.2 at.% Rh. For our high-quality samples the number of defects found on the atomic scale (of the order of 0.3% of the visible lattice sites) is in quantitative agreement with a very small off-stoichiometry within this homogeneity range. Comparing our results for these samples allows an assignment of the structural defects observed at the cleaved surfaces to Rh occupying Si sites and, even less numerous Si in Rh sites. Such an analysis is hampered for samples of lesser quality, but there seem to be numerous empty Si-sites. Based on these observations the results of scanning tunneling spectroscopy can be analyzed in further detail and provide insight into the Kondo physics.

Insight into the f-derived Fermi surface of the heavy-fermion compound YbRh2Si2

Angle-resolved photoelectron spectroscopy (ARPES) was used to study the Fermi surface of the heavy-fermion system YbRh(2)Si(2) at a temperature of about 10 K, i.e., a factor of 2 below the Kondo energy scale. We observed sharp structures with a well-defined topology, which were analyzed by comparing with results of band-structure calculations based on the local-density approximation (LDA). The observed bulk Fermi surface presents strong similarities with that expected for a trivalent Yb state, but is slightly larger, has a strong Yb-4f character, and deviates from the LDA results by a larger region without states around the Γ point. These properties are qualitatively explained in the framework of a simple f-d hybridization model. Our analysis highlights the importance of taking into account surface states and doing an appropriate projection along k(z) when comparing ARPES data with results from theoretical calculations.

From stable divalent to valence-fluctuating behaviour in Eu(Rh(1-x)Ir(x))2Si2 single crystals

We have succeeded in growing high-quality single crystals of the valence-fluctuating system EuIr(2)Si(2), the divalent Eu system EuRh(2)Si(2) and the substitutional alloy Eu(Rh(1-x)Ir(x))(2)Si(2) across the range 0 < x < 1, which we characterized by means of x-ray diffraction, energy-dispersive x-ray spectroscopy, specific heat, magnetization and resistivity measurements. On increasing x, the divalent Eu ground state subsists up to x = 0.25 with a slight increase in Néel temperature, while for 0.3≤x < 0.7 a sharp hysteretic change in susceptibility and resistivity marks the first-order valence transition. For x≳0.7 the broad feature observed in the physical properties is characteristic of the continuous valence evolution beyond the critical end point of the valence transition line, and the resistivity is reminiscent of Kondo-like behaviour while the Sommerfeld coefficient indicates a mass renormalization of at least a factor of 8. The resulting phase diagram is similar to those reported for polycrystalline Eu(Pd(1-x)Au(x))(2)Si(2) and EuNi(2)(Si(1-x)Ge(x))(2), confirming its generic character for Eu systems, and markedly different to those of homologue Ce and Yb systems, which present a continuous suppression of the antiferromagnetism accompanied by a very smooth evolution of the valence. We discuss these differences and suggest them to be related to the large polarization energy of the Eu half-filled 4f shell. We further argue that the changes in the rare earth valence between RRh(2)Si(2) and RIr(2)Si(2) (R = Ce, Eu, Yb) are governed by a purely electronic effect and not by a volume effect.