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Heavy fermion behavior in far infrared optical spectroscopy
Physica B 163 (1990) 224-226 North-Holland
HEAVY FERMION F. MARABELLI Laborarorium
BEHAVIOR
IN FAR INFRARED
OPTICAL
SPECTROSCOPY
and P. WACHTER
fiir Festkijrperphysik,
Swiss Federal Institute of Technology
Ziirich, CH 8093 Ziirich, Switzerland
Since a few years far infrared optical reflectivity measurements have been performed on heavy fermion compounds with high precision and at low temperature (5 K). The results show anomalous structures at low energies, corresponding to excitations of quasiparticles in very narrow bands. Very low values of the plasma frequency are obtained from the analysis of the optical conductivity (-0.2-0.3 eV) which correspond to still smaller values of the unscreened plasma frequency of about 1 meV extracted from the real part of the dielectric constant. The difference is related to the enormous screening due to quasiparticle interaction. Another related feature is an enhanced optical structure at the energy of a few meV which indicates that at least two narrow hybridized f-like quasiparticle bands exist in the vicinity of the Fermi level. Interband which are visible up to 50 K, is not so transitions are thus possible. The temperature dependence of these features, pronounced as expected from Kondo-lattice theories. Several examples can be shown illustrating these characteristics.
In the last few years we applied optical techniques in order to measure the far infrared reflectivity of several intermediate valence and heavy fermion compounds [l, 21. In these compounds the strong interacaction between the f electrons of an actinide or rare earth ion and the conduction electrons with s, p or, generally, d character yield narrow hybridized bands at low temperatures. The metallic systems called ‘heavy fermions’ constitute a limiting case for which the interactions enhance the effective density of states of the narrow bands around the Fermi level up to values hundreds or thousands times larger than in normal metals. This is related to an enhancement of the electronic contribution to the specific heat and to a loss of effects due to localized magnetic moments [3,4]. Then some properties can be described in terms of quasiparticles (where the quasiparticle is an electron “dressed” by all many body interactions) characterized by correspondingly enhanced, renormalized effective masses. The low excitation energies and the high resolution typical of far infrared optical measurements permits to investigate directly the electronic structure and the low energy excitations of the electronic ground state. We performed optical reflectivity measurements in a wide energy range and at low (5 K) as well as at room temperature on some of these compounds: CePd, (which is an intermediate valent metal), UPt, and CeCu, (heavy fermion systems with a linear coefficient of the specific heat rising, respectively, to 450 and 1550 mJ/K*mol [3]) and U,PtC (with a y coefficient of 75 mJ/K*mol [5]). In order to compare the results 0921-4526/90/$03.50 0 Elsevier Science Publishers B.V. (North-Holland)
of CeCu,, reflectivity measureluents on the reference compound LaCu, are also presented. In order to have good quality surfaces and eliminate any oxide layer, all the samples have been freshly polished by using diamond power. The surface damages are then of the order of 1 urn, some orders of magnitude smaller than the wavelength of light in the region of interest. The analysis of the infrared part of the spectrum (down to about 1 meV, -1 mm wavelength) gives us the value of the plasma frequency of the “free” carriers in a narrow quasiparticle band and the energy of a low energy electronic excitation together with the effective mass of the quasiparticles and the contribution to the dielectric function due to the electronelectron screening. The anomalies at energies of the order of some meV observed in the reflectivity spectra of heavy fermion systems (fig. 1) at low temperatures result in a minimum in the optical conductivity. The strong decrease of the conductivity from its static value to this minimum implies a small plasma frequency for the carriers in the band at the Fermi level (fig. 2). Then, a further increase for increasing energy indicates that a gap exists and transitions across this gap can take place. CePd, at low temperature exhibits a relatively small plasma frequency wp* = 0.34 eV. The mass enhancement has been evaluated to be about 40 times the electronic mass [6]. This value is still small compared to m” =250m or m* = 700 m, observed, respectively for UPt 1 and CeCu, [ 1,2]. With a plasma frequency of 0.44 CV one obtains m* = 52 m for UZPtC,.
F. Marabelli and P. Wachter I Heavy fermion
225
behavior in far infrared spectroscopy
95 \
10 Photon
I
15 Energy (meV)
Fig. 1. Optical reflectivity of some intermediate valent and heavy fermion compounds at low temperature and in the low energy range. Notice that no anomalies are observable in the reflectivity of La&,. 15 -
\
’ \\.5_% '0 0.0001
0.001
0.01
0.7 Photon
1 Energy
(eV)
10
Fig. 3. Optical conductivity of CeCu, as obtained from Kramers-Kronig transforms of the reflectivity data measured at different temperatures ranging from 10 to 50 K. At 50 K the enhanced peak at 5 meV has disappeared.
‘uPt, -3OOK
~___5 K IO-
s-
Olo-*
GZ Photon
Fig. 2. Optical Kramers-Kronig
IO_’ Energy
1 (eV)
conductivity of UPt, as obtained transforms of the reflectivity data.
from
These numbers are obtained in the approximation of one narrow (in the order of 1 to 10 meV) parabolic band at the Fermi level. However, the plasma frequencies w p* = 280 meV for UPt, and o,* = 150 meV for CeCu, are consistent with the data of the de Haas-van Alphen experiments [7,8] as well as with the conductivity measurements in the mm wavelength range [9]. A very enhanced structure appears at low temperature in the spectra of the optical conductivity of the two heavy fermion compounds, respectively at 4 and
5 meV (figs. 2 and 3). A corresponding structure can be noticed in the spectrum of U,PtC, at about 10 meV. The oscillator strengths of these optical transitions are relatively small (-0.005-0.02) and correspond to electronic transitions between strongly hybridized f bands. This necessitates the implication that (at least) two narrow, hybridized f bands exist near E,, with E, in one of these bands. The hybridization is necessary in order to enhance the transition probability which would be in the order of 10m6 for bare f levels. The screening effect associated with these excitations is enormous (E, - 20 000) and reduces the decoupled plasma frequencies from about 0.3 eV to values of the order of one meV, proportional to the small values of the renormalized Fermi (or Kondo) temperature T* (T* in CeCu, is about 4K [lo]) according to the theory [ll, 121. This feature is clearly observable in the spectrum of the real part of the dielectric constant (fig. 4). We studied also the temperature dependence of the low frequency spectrum of CeCu, and reveal the existence of the structure at 5 meV up to 50 K (fig. 3). This temperature approximately corresponds to the energy of the gap (5 meV); nevertheless, the intensity of the structure decreases rapidly betwen 20 and 50 K, indicating that a loss of coherence of the quasiparticle
226
F. Marahelli and P. Wachter
I Heavy fermion behavior in far infrared spectroscopy electron-hole) interaction reduces the plasma frequency to a small renormalized plasma frequency.
References
Ill
-
Experiment Bond
-
+ Drude
-Drude
----Bond 0.01
0.02 Photon
Energy
k’.‘)
Fig. 4. Real part of the dielectric constant of C&u, lowest energies. The figure shows the decomposition Drude part and an interband part.
at the into a
bands probably begins at these temperatures. Anyway, these temperatures are one order of magnitude larger than the Kondo temperature; then, the bands are not so temperature dependent as expected from Kondo-lattice theories[l3]. The conclusions are that the electronic structure of heavy fermion compounds at low temperatures is characterized by at least two narrow quasiparticle bands separated by a gap. The weight of the carriers in these bands and the strong electron-electron (or
F. Marabelli. G. Travaglini, P. Wachter and J.J.M. France, Solid State Commun. 59 (1986) 381. PI F. Marabelli, P. Wachter and E. Walker, Phys. Rev. B 39 (1989) 1407. [31 G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755. [41 G.R. Stewart, Z. Fisk and M.S. Wire, Phys. Rev. B 30 (1984) 482. A.L. Giorgi, A.C. Lawson. G.R. PI G.P. Meisner, Stewart, J.O. Willis, MS. Wire and J.L. Smith, Phys. Rev. Lett. 53 (1985) 1829. [61 B.C. Webb, A.J. Sievers and T. Mihalisin, Phys. Rev. Lett. 57 (1986) 1951. [71 L. Taillefer. R. Newbury, G.G. Lonzarich, Z. Fisk and J.L. Smith. J. Magn. Magn. Mat. 63 & 64 (1987) 372. M. Springford. P.T. Coleridge, R. PI P.H.P. Reinders. Baulet and D. Ravot. Phys. Rev. Lett. 57 (1986) 1631. W.P. Beyermann, J.P. Carini and G. Pl A.M. Awasthi, Griiner. Phys. Rev. B 39 (1989) 2377. J. Magn. Magn. Mat. 63 [lOI Y. Onuki and T. Komatsubara, & 64 (1987) 281. [Ill K.W. Becker and P. Fulde, 2. Phys. B 67 (1987) 35. 1121 A.J. Millis, M. Lavagna and P.A. Lee, Phys. Rev. B 36 (1987) 864. [I31 N. Grewe, Solid State Commun. 50 (1984) 19.
HEAVY FERMION F. MARABELLI Laborarorium
BEHAVIOR
IN FAR INFRARED
OPTICAL
SPECTROSCOPY
and P. WACHTER
fiir Festkijrperphysik,
Swiss Federal Institute of Technology
Ziirich, CH 8093 Ziirich, Switzerland
Since a few years far infrared optical reflectivity measurements have been performed on heavy fermion compounds with high precision and at low temperature (5 K). The results show anomalous structures at low energies, corresponding to excitations of quasiparticles in very narrow bands. Very low values of the plasma frequency are obtained from the analysis of the optical conductivity (-0.2-0.3 eV) which correspond to still smaller values of the unscreened plasma frequency of about 1 meV extracted from the real part of the dielectric constant. The difference is related to the enormous screening due to quasiparticle interaction. Another related feature is an enhanced optical structure at the energy of a few meV which indicates that at least two narrow hybridized f-like quasiparticle bands exist in the vicinity of the Fermi level. Interband which are visible up to 50 K, is not so transitions are thus possible. The temperature dependence of these features, pronounced as expected from Kondo-lattice theories. Several examples can be shown illustrating these characteristics.
In the last few years we applied optical techniques in order to measure the far infrared reflectivity of several intermediate valence and heavy fermion compounds [l, 21. In these compounds the strong interacaction between the f electrons of an actinide or rare earth ion and the conduction electrons with s, p or, generally, d character yield narrow hybridized bands at low temperatures. The metallic systems called ‘heavy fermions’ constitute a limiting case for which the interactions enhance the effective density of states of the narrow bands around the Fermi level up to values hundreds or thousands times larger than in normal metals. This is related to an enhancement of the electronic contribution to the specific heat and to a loss of effects due to localized magnetic moments [3,4]. Then some properties can be described in terms of quasiparticles (where the quasiparticle is an electron “dressed” by all many body interactions) characterized by correspondingly enhanced, renormalized effective masses. The low excitation energies and the high resolution typical of far infrared optical measurements permits to investigate directly the electronic structure and the low energy excitations of the electronic ground state. We performed optical reflectivity measurements in a wide energy range and at low (5 K) as well as at room temperature on some of these compounds: CePd, (which is an intermediate valent metal), UPt, and CeCu, (heavy fermion systems with a linear coefficient of the specific heat rising, respectively, to 450 and 1550 mJ/K*mol [3]) and U,PtC (with a y coefficient of 75 mJ/K*mol [5]). In order to compare the results 0921-4526/90/$03.50 0 Elsevier Science Publishers B.V. (North-Holland)
of CeCu,, reflectivity measureluents on the reference compound LaCu, are also presented. In order to have good quality surfaces and eliminate any oxide layer, all the samples have been freshly polished by using diamond power. The surface damages are then of the order of 1 urn, some orders of magnitude smaller than the wavelength of light in the region of interest. The analysis of the infrared part of the spectrum (down to about 1 meV, -1 mm wavelength) gives us the value of the plasma frequency of the “free” carriers in a narrow quasiparticle band and the energy of a low energy electronic excitation together with the effective mass of the quasiparticles and the contribution to the dielectric function due to the electronelectron screening. The anomalies at energies of the order of some meV observed in the reflectivity spectra of heavy fermion systems (fig. 1) at low temperatures result in a minimum in the optical conductivity. The strong decrease of the conductivity from its static value to this minimum implies a small plasma frequency for the carriers in the band at the Fermi level (fig. 2). Then, a further increase for increasing energy indicates that a gap exists and transitions across this gap can take place. CePd, at low temperature exhibits a relatively small plasma frequency wp* = 0.34 eV. The mass enhancement has been evaluated to be about 40 times the electronic mass [6]. This value is still small compared to m” =250m or m* = 700 m, observed, respectively for UPt 1 and CeCu, [ 1,2]. With a plasma frequency of 0.44 CV one obtains m* = 52 m for UZPtC,.
F. Marabelli and P. Wachter I Heavy fermion
225
behavior in far infrared spectroscopy
95 \
10 Photon
I
15 Energy (meV)
Fig. 1. Optical reflectivity of some intermediate valent and heavy fermion compounds at low temperature and in the low energy range. Notice that no anomalies are observable in the reflectivity of La&,. 15 -
\
’ \\.5_% '0 0.0001
0.001
0.01
0.7 Photon
1 Energy
(eV)
10
Fig. 3. Optical conductivity of CeCu, as obtained from Kramers-Kronig transforms of the reflectivity data measured at different temperatures ranging from 10 to 50 K. At 50 K the enhanced peak at 5 meV has disappeared.
‘uPt, -3OOK
~___5 K IO-
s-
Olo-*
GZ Photon
Fig. 2. Optical Kramers-Kronig
IO_’ Energy
1 (eV)
conductivity of UPt, as obtained transforms of the reflectivity data.
from
These numbers are obtained in the approximation of one narrow (in the order of 1 to 10 meV) parabolic band at the Fermi level. However, the plasma frequencies w p* = 280 meV for UPt, and o,* = 150 meV for CeCu, are consistent with the data of the de Haas-van Alphen experiments [7,8] as well as with the conductivity measurements in the mm wavelength range [9]. A very enhanced structure appears at low temperature in the spectra of the optical conductivity of the two heavy fermion compounds, respectively at 4 and
5 meV (figs. 2 and 3). A corresponding structure can be noticed in the spectrum of U,PtC, at about 10 meV. The oscillator strengths of these optical transitions are relatively small (-0.005-0.02) and correspond to electronic transitions between strongly hybridized f bands. This necessitates the implication that (at least) two narrow, hybridized f bands exist near E,, with E, in one of these bands. The hybridization is necessary in order to enhance the transition probability which would be in the order of 10m6 for bare f levels. The screening effect associated with these excitations is enormous (E, - 20 000) and reduces the decoupled plasma frequencies from about 0.3 eV to values of the order of one meV, proportional to the small values of the renormalized Fermi (or Kondo) temperature T* (T* in CeCu, is about 4K [lo]) according to the theory [ll, 121. This feature is clearly observable in the spectrum of the real part of the dielectric constant (fig. 4). We studied also the temperature dependence of the low frequency spectrum of CeCu, and reveal the existence of the structure at 5 meV up to 50 K (fig. 3). This temperature approximately corresponds to the energy of the gap (5 meV); nevertheless, the intensity of the structure decreases rapidly betwen 20 and 50 K, indicating that a loss of coherence of the quasiparticle
226
F. Marahelli and P. Wachter
I Heavy fermion behavior in far infrared spectroscopy electron-hole) interaction reduces the plasma frequency to a small renormalized plasma frequency.
References
Ill
-
Experiment Bond
-
+ Drude
-Drude
----Bond 0.01
0.02 Photon
Energy
k’.‘)
Fig. 4. Real part of the dielectric constant of C&u, lowest energies. The figure shows the decomposition Drude part and an interband part.
at the into a
bands probably begins at these temperatures. Anyway, these temperatures are one order of magnitude larger than the Kondo temperature; then, the bands are not so temperature dependent as expected from Kondo-lattice theories[l3]. The conclusions are that the electronic structure of heavy fermion compounds at low temperatures is characterized by at least two narrow quasiparticle bands separated by a gap. The weight of the carriers in these bands and the strong electron-electron (or
F. Marabelli. G. Travaglini, P. Wachter and J.J.M. France, Solid State Commun. 59 (1986) 381. PI F. Marabelli, P. Wachter and E. Walker, Phys. Rev. B 39 (1989) 1407. [31 G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755. [41 G.R. Stewart, Z. Fisk and M.S. Wire, Phys. Rev. B 30 (1984) 482. A.L. Giorgi, A.C. Lawson. G.R. PI G.P. Meisner, Stewart, J.O. Willis, MS. Wire and J.L. Smith, Phys. Rev. Lett. 53 (1985) 1829. [61 B.C. Webb, A.J. Sievers and T. Mihalisin, Phys. Rev. Lett. 57 (1986) 1951. [71 L. Taillefer. R. Newbury, G.G. Lonzarich, Z. Fisk and J.L. Smith. J. Magn. Magn. Mat. 63 & 64 (1987) 372. M. Springford. P.T. Coleridge, R. PI P.H.P. Reinders. Baulet and D. Ravot. Phys. Rev. Lett. 57 (1986) 1631. W.P. Beyermann, J.P. Carini and G. Pl A.M. Awasthi, Griiner. Phys. Rev. B 39 (1989) 2377. J. Magn. Magn. Mat. 63 [lOI Y. Onuki and T. Komatsubara, & 64 (1987) 281. [Ill K.W. Becker and P. Fulde, 2. Phys. B 67 (1987) 35. 1121 A.J. Millis, M. Lavagna and P.A. Lee, Phys. Rev. B 36 (1987) 864. [I31 N. Grewe, Solid State Commun. 50 (1984) 19.