Strongly correlated electron phenomena in filled skutterudite compounds

Physica B 328 (2003) 29–33

Strongly correlated electron phenomena in filled skutterudite compounds M.B. Maple*, E.D. Bauer, N.A. Frederick, P.-C. Ho, W.A. Yuhasz, V.S. Zapf Department of Physics-0319 and Institute for Pure and Applied Physical Sciences, University of California, 9500 Gilman Drive, San Diego, La Jolla, CA 92093-0319, USA

Abstract A rich variety of strongly correlated electron phenomena are found in filled skutterudite compounds. Selected examples of these phenomena and the skutterudite compounds in which they occur are briefly described in this paper. Examples considered include ‘‘hybridization gap’’ semiconductivity (‘‘Kondo insulator’’ behavior), ferromagnetism, valence fluctuation phenomena, heavy fermion behavior, non-Fermi liquid behavior, and heavy fermion superconductivity. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Strongly correlated electron systems; Superconductivity; Magnetism; Filled skutterudite compounds

1. Introduction A rich variety of strongly correlated electron phenomena are found in the filled skutterudite compounds. These phenomena include superconductivity [1], ferromagnetism [2,3], metal–insulator transitions [4], small ‘‘hybridization gap’’ semiconductivity (or ‘‘Kondo insulator’’ behavior) [2,3], valence fluctuation phenomena [2,5–7], heavy fermion behavior [5–8], non-Fermi liquid behavior [9,10], and heavy fermion superconductivity [11,12]. The filled skutterudites have the formula MT4 X12 where M can be an alkaline earth, lanthanide or actinide ion, T is Fe, Ru, or Os, and X is P, As, or Sb and crystallize in the cubic skutterudite LaFe4P12 structure (space group Im3) [13]. The physical properties of the filled skutter*Corresponding author. Tel.: +1-858-534-3968; fax: +1858-534-1241. E-mail address: [email protected] (M.B. Maple).

udites depend sensitively on the M ion and the hybridization between the f-electron states of the M ion and the T and X ligand states. These extraordinary materials have also attracted much interest because of their potential for thermoelectric applications [14]. Selected examples of the strongly correlated electron phenomena found in the filled skutterudites are briefly described in this paper.

2. Hybridization gap semiconductivity: CeFe4P12, UFe4P12, and CeOs4Sb12 Hybridization between localized f-electron and conduction electron states can lead to semiconducting behavior with a small energy gap in the range 10
3–10
1 eV. Rare earth and actinide compounds that exhibit this behavior are referred to as ‘hybridization gap’ semiconductors, or, using more recent terminology, ‘Kondo insulators.’ This

0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 8 0 3 - 3

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behavior was first observed in the compounds SmS in its collapsed ‘gold phase’ and SmB6 (for a review, see Ref. [15]). Two of the earliest examples of small gap semiconductor behavior in f-electron materials based on lanthanide or actinide ions other than Sm were the filled skutterudite compounds CeFe4P12 and UFe4P12 [2]. Plots of electrical resistance R vs. temperature T for CeFe4P12 and UFe4P12 are shown in Fig. 1 [2]. The RðTÞ curves can only be described by a simple activation law of the form R ¼ Ro expðEa =kB TÞ with constant Ea over restricted temperature intervals: Ea ¼ 130 meV (85 KpTp140 K) for CeFe4P12 and Ea ¼ 17 meV (160 KpTp300 K) for UFe4P12. The UFe4P12 compound is noteworthy because it also exhibits ferromagnetic order with a Curie temperature yM ¼ 3:15 K. Recently, semiconducting behavior with a small activation energy Ea E1 meV (25 KpTp50 K) was observed for the compound CeOs4Sb12 [16]. During the past two decades, many compounds of Ce, Sm, Tm,Yb and U have been found to display hybridization gap semiconductivity [17].

3. Valence fluctuation and heavy fermion behavior: CeFe4Sb12 and YbFe4Sb12 Transport, magnetic, and thermal measurements on the compounds CeFe4Sb12 and Yb-

Fig. 1. Electrical resistance R of UFe4P12 and CeFe4P12 normalized to the room temperature resistance. From Ref. [2].

Fe4Sb12 indicate that these materials have a heavy fermion ground state. This observation is particularly interesting since the study of heavy fermion behavior in isostructural compounds of Ce, whose 4f shell contains up to one electron, and its 4f hole counterpart Yb, whose 4f shell contains up to one hole, could shed light on strongly correlated electron phenomena in f-electron materials. The valence of Ce in CeFe4Sb12 is B3+, whereas the valence of Yb in YbFe4Sb12 is intermediate between 2+ and 3+. To our knowledge, YbFe4Sb12 is the first example of a filled skutterudite compound of a lanthanide ion heavier than Eu [5–7]. Electrical resistivity rðTÞ; magnetic susceptibility wðTÞ; and low-temperature specific heat CðTÞ data for YbFe4Sb12 are shown in Fig. 2. The rapid decrease of rðTÞ below B150 K signals the onset of the highly correlated heavy fermion ground state. The wðTÞ data at low temperatures indicated by solid circles have been corrected for small concentrations of magnetic impurities that are responsible for the low temperature tail in the wðTÞ data. The corrected wðTÞ data approach a finite value as T-0; indicating that this compound has a non-magnetic ground state. The CðTÞ=T data for YbFe4Sb12, shown in the inset to Fig. 2, reveal that the electronic specific heat coefficient g ¼ CðTÞ=T as T-0 has a large value B140 mJ/mol K2. The origin of the heavy fermion behavior in CeFe4Sb12 and YbFe4Sb12 is presumably due to the antiferromagnetic interaction

Fig. 2. Electrical resistivity (upper y-axis), magnetic susceptibility (lower y-axis), and specific heat (inset) of YbFe4Sb12. From Ref. [6].

M.B. Maple et al. / Physica B 328 (2003) 29–33

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between the spins of the conduction electrons and the magnetic moments of the Ce and Yb ions that form an ordered sublattice (Kondo lattice). Recently, heavy fermion behavior was observed in several Pr compounds (PrInAg2 [18], PrFe4P12 [19], and PrOs4Sb12 [11,12]) in which the ground state of Pr in the crystalline electric field (CEF) is apparently a non-magnetic G3 doublet that carries an electric quadrupole moment. In these Pr compounds, it is possible that the origin of the heavy fermion behavior is due to the interaction between the Pr electric quadrupole moments and the charges of the conduction electrons. The case of PrOs4Sb12, which also exhibits superconductivity, is discussed later in this article.

Infrared spectroscopy measurements by Dordevic et al. [22] on CeRu4Sb12 and YbFe4Sb12 revealed the formation of a hybridization gap D and an enhanced effective mass m at temperatures below the coherence temperature T  E50 K for both compounds. The experiments yielded the following values: D ¼ 55 meV, m ¼ 80me for CeRu4Sb12; D ¼ 18 meV, m ¼ 25me for YbFe4Sb12. It was also found that these compounds, as well as several other heavy fermion materials with a non-magnetic ground state, obey a universal scaling relationship of the form m =mb EðD=TÞ2 [22].

4. Non-Fermi liquid behavior: CeRu4Sb12

Recently, we observed heavy fermion superconductivity in the filled skutterudite compound PrOs4Sb12 [11,12,23,24]. This is the first heavy fermion superconductor that is a compound of Pr; all of the other B20 known heavy fermion superconductors are compounds of Ce or U. A large value of the effective mass, m  E50me ; was inferred from measurements of: the electronic contribution gT to CðTÞ in the normal state, the superconducting jump in CðTÞ at Tc ; and the slope of the upper critical field curve Hc2 ðTÞ near Tc [11,12]. Analysis of wðTÞ and inelastic neutron scattering measurements on PrOs4Sb12 for a cubic CEF yielded a Pr3+ energy level scheme consisting of a G3 non-magnetic doublet ground state that carries an electric quadrupole moment, a low lying G5 triplet excited state (11 K), a G4 triplet excited state (130 K), and a G1 singlet excited state (313 K) [12]. Such a low lying excited state can also account for the pronounced Schottky anomaly with a peak near 3 K in CðTÞ [12,23,25] and a rolloff in rðTÞ below 10 K, apparently associated with a reduction in charge or spin-dependent scattering from the excited state as it becomes thermally depopulated with decreasing T [11,12]. This Pr3+ energy level scheme suggests that the underlying mechanism of the heavy fermion behavior in PrOs4Sb12 may involve electric quadrupole fluctuations, rather than magnetic dipole fluctuations. It also raises the possibility that electric quadrupole fluctuations play a role in the superconductivity of PrOs4Sb12. On the other

Non-Fermi liquid (NFL) behavior in f-electron materials is manifested as weak power law and logarithmic divergences in temperature in the physical properties at low temperatures. Experiments on a variety of f-electron systems suggest that there are two routes to NFL behavior in these materials, a single ion route involving an unconventional Kondo effect and an inter-ionic interaction route associated with order parameter fluctuations in the vicinity of a second-order magnetic (or, possibly, quadrupolar) phase transition that has been suppressed to zero temperature (quantum critical point). For many of the felectron systems, rðTÞ; CðTÞ; and wðTÞ have the following NFL temperature dependences for T5T0 : (i) rðTÞB1
aðT=T0 Þn where jajE1; ao0 or >0, and nE121:5; (ii) CðTÞ=TBð
1=T0 Þln ðT=T0 Þ or BT 1þl ; and (iii) wðTÞB1
ðT=T0 Þ1=2 ; Bð
1=T0 ÞlnðT=T0 Þ or BT 1þl [20,21]. Takeda and Ishikawa [9] reported that CeRu4Sb12 exhibits strongly correlated electron behavior with NFL temperature dependences at low temperatures. The electrical resistivity r varies as T 1:6 ; and C=T diverges with decreasing T as
ln T between B0.3 and B1 K and more rapidly below B0.3 K down to the low-temperature limit (B0.15 K) of the measurement. In subsequent studies on CeRu4Sb12, Bauer et al. [10] found that the low-temperature upturn in wðTÞ varies as T
0:35 between B2 and 20 K.

5. Heavy fermion superconductivity: PrOs4Sb12

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hand, we cannot completely exclude the possibility that the ground state is a G1 singlet, in which case the heavy fermion state could then be associated with low lying CEF excitations. From magnetoresistance and magnetization measurements [23,24,26], we have also found evidence for a region in the H2T plane for H > 4:5 T and To1:5 K in which there may be magnetic or quadrupolar order. This suggests that the superconducting phase may occur in the vicinity of a magnetic or quadrupolar quantum critical point (QCP). The H2T phase diagram, derived from magnetoresistance and magnetization measurements, showing the superconducting region and the high field ordered phase is shown in Fig. 3. The line that intersects the high field ordered state represents the inflection point of the roll-off in rðTÞ at low temperatures and is a measure of the splitting between the Pr3+ ground and the first excited states, which decreases with field. The high field ordered phase has also been observed by means of large peaks in the specific heat [25,27] and thermal expansion [28] in magnetic fields >4.5 T and temperatures below 1.5 K.

Two features in CðTÞ of PrOs4Sb12 suggest that the superconductivity of this compound is unconventional in nature: the power law T-dependence in the superconducting state, Cs ðTÞET 2:5 (after the Schottky anomaly and bT 3 lattice contributions have been subtracted from the CðTÞ data), and a ‘double-step’ structure in the jump in CðTÞ associated with superconductivity that suggests that there are two distinct superconducting phases with different Tc ’s: Tc1 E1:8 K and Tc2 E1:7 K [12,25]. Recent transverse field mSR [29] and Sb-NQR measurements on PrOs4Sb12 [31] are consistent with an isotropic energy gap. These measurements, along with specific heat measurements [25], indicate strong coupling superconductivity. These findings suggest an s-wave, or, perhaps, a Balian–Werthamer pwave order parameter. Recently, the superconducting energy gap structure of PrOs4Sb12 was investigated by means of thermal conductivity measurements in magnetic fields rotated relative to the crystallographic axes by Izawa et al. [30]. These measurements reveal two regions in the H2T plane, a low field region in which the superconducting energy gap DðkÞ has two point nodes, and a high field region where DðkÞ has six point nodes. It is possible that the line lying between the low and high field superconducting phases is associated with the transition at Tc2 ; whereas the line between the high field phase and the normal phase, Hc2 ðTÞ; is associated with Tc1 : Clearly, PrOs4Sb12 will constitute a significant challenge for theoretical description, and more research will be required to further elucidate the nature of the superconducting state [32,33]. Acknowledgements This research was supported by US DOE Grant No. DE-FG03-86ER-45230, US NSF Grant No. DMR-00-72125, and the NEDO International Joint Research Program.

Fig. 3. Magnetic field–temperature (H2T) phase diagram of PrOs4Sb12 showing the regions containing the superconducting (SC) and high field ordered phase (HFOP). The dashed line is a measure of the splitting between the Pr3+ G3 ground state and G5 excited state (see text for further details).

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