Watching Quantum Critical Transitions
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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 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.
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.]
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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