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Electron-State Hybridization in Heavy-Fermion Systems Print

Heavy-fermion systems are characterized by electrons with extremely large effective masses. The corresponding heavy-electron "quasiparticle" states are close to the Fermi energy and govern the thermodynamic, transport, and, in part, magnetic properties of these materials. In the case of rare-earth compounds, the quasiparticle states arise from the interactions (hybridization) of valence states with strongly localized 4f states. The question as to whether it is sufficient to treat the f states as localized impurities (single-impurity Anderson model) or whether the periodic crystal symmetry must be considered (periodic Anderson model) has been the subject of extensive debate. An international team of researchers from Germany, Ukraine, India, and the U.S. has performed angle-resolved photoemission spectroscopy (ARPES) studies of the heavy-fermion system YbIr2Si2. The results show a strong momentum (directional) dependence of the hybridization that clearly rules out the single-impurity model in favor of the lattice model.

Exploiting Anisotropy

Anisotropy is a fancy word for a simple concept: dependence on direction. For example, you can get lost in a forest of isotropic trees (they look the same in every direction), but not if you know that moss grows on them anisotropically (only on the north side). An even better method for getting your bearings is to measure the directionality (anistropy) of the Earth's magnetic field (using a compass). Modern technology is replete with examples of anistropy at work. Polarized lenses in sunglasses filter light waves that oscillate in a certain direction. Flat-screen televisions utilize liquid crystals whose molecules line up under the influence of electric fields. High-performance read-write drives exploit the directionality of properties such as electrical conductivity and resistance. In this work, Molodtsov et al. examine the momentum dependence (i.e., the anisotropy) of electron state hybridization in a heavy-fermion compound containing the rare-earth element, ytterbium (Yb). Their findings are of high importance for both the understanding and the tailoring of the anisotropic electronic, transport, and magnetic properties of heavy-fermion superconducting, thermoelectric, and ultrafast optomagnetic devices.

Representation of the crystal structure of YbIr2Si2 (the letter T represents a transition metal, in this case, Ir) and the shapes of the Yb 4f and Ir 5d orbitals involved in hybridization.

The 14 "rare-earth" elements following lanthanum in the periodic table are characterized by the successive filling of inner 4f states with electrons while the number of valence electrons remains almost constant. Since the 4f shell lies relatively close to the atomic core, the f orbitals do not contribute to chemical bonding and tend to retain their atomic-like properties in solids. This holds particularly for their high magnetic moments. As a consequence, a number of rare-earth compounds belong to the strongest hard magnetic species frequently used as permanent magnets and magnetic storage materials. However, at temperatures below a critical temperature (the Kondo temperature, TK), the 4f magnetic moments can be fully screened by the spins of itinerant electrons. This interaction retards the itinerant electrons and greatly increases their effective mass. Within the Anderson model, the phenomenon may be described by electron hopping between the states.

Most direct experimental insight into this problem may be expected from ARPES, which reflects the momentum-resolved response of the electronic system (i.e., electron energy dispersion). Expected features in the spectrum of a heavy-fermion system include a sharp virtual bound state (below TK, called the Kondo resonance) and narrow, 4f-derived quasiparticle bands near the Fermi level (EF). ARPES studies of heavy-fermion narrow-band compounds are only possible, however, under superior conditions with high-photon-flux experimental equipment providing ultrahigh energy (serveral meV) and angle resolution (a few tenths of a degree).

At ALS Beamline 10.0.1, ARPES spectra of YbIr2Si2 were taken at 20 K (below TK ~ 40 K) and 55-eV photon energy for different emission angles (Θ). The results demonstrate for the first time the strong angle (i.e., momentum) dependence of the hopping interactions in a heavy-fermion system. Two valence bands are visible, one of which intersects with the Yb 4f surface emission at 0.6-eV binding energy. In the region of the interaction, the 4f state splits into two components separated by up to 0.25 eV. At the same emission angles, further peaks appear at lower binding energy, including a signal in the region of the Kondo resonance immediately at EF.

ARPES spectra of the heavy-fermion system YbIr2Si2 showing two parabola-shaped valence bands on the left, one of which intersects the 4f surface emission of the rare-earth element Yb. Signal in the region of EF reveals strongly anisotropic behavior.

Since a proper description of rare-earth systems by means of conventional approximations used in band structure theory is not possible because of strong Coulomb repulsions between the electrons in the relatively compact 4f shells, the data were analyzed within the framework of a simplified periodic Anderson model: starting from valence bands obtained from the calculation of an isostructural La/Ba compound and two Yb 4f states close to EF and at 0.6-eV binding energy, the 4f emission spectra were obtained within the periodic Anderson model assuming momentum conservation upon electron hopping. The calculated 4f ARPES spectra nicely reproduce all 4f characteristic features of the experiment. The results, obtained for the compound YbIr2Si2, can readily be used to understand the properties of other heavy-fermion systems in which momentum-dependent anisotropies may be of primary importance in future electronic and magnetic applications.

ARPES spectra calculated on the basis of the periodic Anderson model nicely reproduce all 4f characteristic features of the experiment.


Research conducted by S. Danzenbächer, C. Laubschat, D.V. Vyalikh, and S.L. Molodtsov (Dresden University of Technology); Y. Kucherenko (Dresden University of Technology and National Academy of Sciences of Ukraine); Z. Hossain (Max Planck Institute for Chemical Physics of Solids and Indian Institute of Technology); C. Geibel (Max Planck Institute for Chemical Physics of Solids); X.J. Zhou, W.L. Yang, and N. Mannella (Stanford University and ALS); Z. Hussain (ALS); and Z.-X. Shen (Stanford University).

Research funding: German Research Foundation; German Ministry for Education and Research; U.S. Department of Energy, Office of Basic Energy Sciences (BES); National Science Foundation; and Office of Naval Research. Operation of the ALS is supported by BES.

Publication about this research: S. Danzenbächer, Y. Kucherenko, C. Laubschat, D.V. Vyalikh, Z. Hossain, C. Geibel, X.J. Zhou, W. Yang, N. Mannella, Z. Hussain, Z.-X. Shen, and S.L. Molodtsov, "Energy dispersion of 4f-derived emissions in photoelectron spectra of the heavy-fermion compound YbIr2Si2," Phys. Rev. Lett. 96, 106402 (2006).