For decades, intermetallic compounds of rare-earth metals have been favorite systems of the research community studying strong electron correlations in solids. Nowadays rare-earth intermetallics are often treated as model systems for studies of zero-temperature quantum critical phase transitions, since heavy-fermion rare-earth compounds (in which the electron effective mass is orders of magnitude larger than the bare electron mass) have provided the clearest evidence for these continuous phase transitions, which are controlled by such parameters as chemical composition, magnetic field, and pressure, rather than temperature. A new study of a europium-based compound by an international team led by researchers from the Technische Universität Dresden in Germany hints that this compound could join well-known compounds of cerium, ytterbium, and uranium as a new material suitable for research on quantum critical transitions. This finding is exciting, since physicists hope that the use of a new material will give an additional degree of freedom for researching quantum critical behavior.

Thirty years ago, the discovery of superconductivity in the paramagnetic rare-earth intermetallic compound CeCu₂Si₂ followed in 1986 by the first observation of high-temperature superconductivity in the complex oxide materials ushered in the era of strong electron correlations in solids. In the case of the rare-earth intermetallics, the complex physics of heavy-fermion metals is governed by the delicate interaction between electrons in the partially filled 4f shells and itinerant (delocalized) electrons in the valence band. These interactions underlie phenomena like magnetism, mixed-valence behavior, and the Kondo effect. Thus far, research on the quantum critical transitions has been restricted to compounds of cerium (which has one electron in the f shell) and ytterbium (with one hole in the f shell).

Europium-based intermetallics are of special interest not only because the magnetic trivalent europium state can switch to a non-magnetic divalent state, giving rise to a mixed-valence behavior, but because seven electrons in the half-filled 4f shell in the europium ground state can interact with the delocalized valence electrons, possibly resulting in hybridization between these states, a feature associated with heavy-fermion behavior. To investigate this aspect, the researchers used angle-resolved photoemission (ARPES) at BESSY Beamline UE112_PGM-2b and ALS Beamline 12.0.1, accompanied by computational studies based on a periodic Anderson model, of the europium 4f⁶ final state in EuNi₂P₂.

The angle-resolved photoemission spectroscopy (ARPES) data for the localized europium 4f⁶ final states in the rare-earth intermetallic compound EuNi₂P₂ might suggest to some the strings of a musical instrument, as in the harp and its player shown at the right. The red "bumps" do not correspond to badly plucked strings but instead indicate hybridization between an f state and a delocalized nickel-derived valence band state and an associated energy splitting, a key finding in the experiment. [Figure courtesy of S. Molodtsov.]

The electron structure derived from the ARPES spectra reveal several important features: the individual components of the characteristic line-shape due to the emission from the 4f states, splittings and dispersion of a valence band whose origin is mainly nickel 3d states, the crossing points (energy and momentum) of the europium 4f lines with the nickel 3d-based band, and additional splittings and shifts at around 0.6 eV below the Fermi level. Band-structure calculations that treat europium 4f as core states confirm the presence of a nickel 3d-derived band but with a finite f character at the europium site, so that it is able to hybridize with the europium 4f states. The splitting of the multiplet component at 0.6 eV is also properly reproduced and explained. These findings demonstrate the importance of momentum-dependent interactions for the understanding of the properties of the 4f mixed-valence systems.

Heavy-fermion properties would be expected if the hybridized states were much closer to the Fermi level. For this to occur, the d band as well as the 4f multiplet would have to be shifted towards the Fermi energy. In principle, this shift could be achieved by redesigning the unit cell of the 4f compound. Such a possibility offers an intriguing opportunity for creating novel intermetallic systems with an ensemble of 4f states at the Fermi level providing a foundation for Kondo and heavy-fermion behavior.

Energy bands in crystalline EuNi₂P₂ as a function of momentum in reciprocal space. Left: Experimental ARPES spectra (brightness corresponds to intensity) obtained for energies and momenta (here represented by the "azimuthal angle") near the crossing of the europium 4f⁶ final states and the 3d band of nickel in the mixed-valence compound EuNi₂P₂. The bumps indicative of hybridization are again visible here. Center: Theoretically derived (LDA) band structure projected on the (001) surface Brillouin zone along the direction from the zone center to a zone edge x̅. Hybridization of the europium states with states from the valence band marked by the dark balls is possible near point "a", owing to their matching symmetry. Size of the balls represents strength of hybridization. Right: Numerical simulation (PAM) of the hybridization between the 3d band of nickel and the components of the europium 4f state well reproduces the experimental data.

Research conducted by S. Danzenbächer, D.V. Vyalikh, A. Kade, C. Laubschat, and S.L. Molodtsov (Technische Universität Dresden, Germany); Yu. Kucherenko (Technische Universität Dresden, and National Academy of Sciences of Ukraine); N. Caroca-Canales, C. Krellner, and C. Geibel (Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden); A.V. Fedorov (ALS); and D.S. Dessau (University of Colorado, Boulder); and R. Follath and W. Eberhardt (BESSY, Germany).

Research funding: Deutsche Forschungsgemeinschaft; the Science and Technology Center in Ukraine; the U.S. Department of Energy, Office of Basic Energy Sciences (BES); and the U.S. National Science Foundation. Operation of the ALS is supported by BES.

Publication about this research: S. Danzenbächer, D. V. Vyalikh, Yu. Kucherenko, A. Kade, C. Laubschat, N. Caroca-Canales, C. Krellner, C. Geibel, A. V. Fedorov, D. S. Dessau, R. Follath, W. Eberhardt, and S. L. Molodtsov, “Hybridization phenomena in nearly half-filled f-shell electron systems: Photoemission study of EuNi₂P₂,” Phys. Rev. Lett. 102, 026403 (2009).

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