Four-Well Tunneling States and Elastic Response of Clathrates

Abstract

We present resonant ultrasound elastic constant measurements of the clathrate compounds Eu8Ga16Ge30 and Sr8Ga16Ge30. The elastic response of the Eu clathrate provides clear evidence for the existence of a new type of four-well tunneling states, described by two nearly degenerate four level systems (FLS). The FLS's are closely linked with the fourfold split positions of Eu known from neutron diffraction density profiles. Using a realistic potential we estimate the tunneling frequencies and show that the energy gap between the two FLS's is of the same order as the Einstein oscillator frequency. This explains why the observed harmonic oscillator type specific heat is not modified by tunneling states. In addition the quadrupolar interaction of FLS's with elastic strains explains the pronounced depression observed in elastic constant measurements. In the case of the Sr clathrate, we show that the shallow dip in the elastic constant c44 is explained using the same type of quadrupolar interaction with a soft Einstein mode instead of a FLS. PACS numbers: 62.30.+d,66.35.+a Clathrate compounds are composed of polyhedral cages with 12-16 faces formed by Si, Ge or Ga atoms [1]. The oversized cages accommodate guest atoms like Ba, Sr, or Eu which exhibit large amplitude anharmonic motion. This leads to a strong scattering of acoustic phonons and a small thermal conductivity. In many cases the electrical conductivity remains high and the resulting large thermoelectric figure of merit has led to sustained interest in this class of compounds. The glass-like low temperature thermal conductivity [2,3] and ultrasound attenuation [4,5] have been interpreted as evidence for the existence of tunneling states. These are commonly discussed within a generic two well potential model leading to two level system (TLS). The thermal conductivity is more glass-like for clathrates with larger atomic displacement parameters (ADP) of the guest atoms. For the clathrates discussed here the ADP's are very large. The nuclear density map for Eu(2) in Eu 8 Ga 16 Ge 30 clearly shows the distinct symmetrically related four maxima, away from the cage center [6,7], leading to the fourfold split site model. Large static ADP for Sr(2), and considerably smaller for Ba(2), in Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 , respectively, point also to the split site model [3,6,8], although the nuclear density maps do not show distinct fourfold maxima.In this letter we present elastic constant measurements on X 8 Ga 16 Ge 30 (X = Eu, Sr) that show anomalies that cannot be naturally explained within a generic TLS model. Instead we propose two new models that we feel are physically appealing because they draw their inspiration from the nuclear density map results.For Eu 8 Ga 16 Ge 30 we introduce a four-well potential model with the proper symmetry of split sites that describes a rotor type tunneling motion. We show that for appropriate potential parameters two partially degenerate FLS's exist. This model explains both the specific heat and elastic anomalies and is co...

Glasslike versus crystalline thermal conductivity in carrier-tunedBa8Ga16X30clathrates(X<

“…First: is the presence of tunnelling states really necessary, or is off-center vibration a sufficient mechanism? The question was raised by Bridges and Downward 13 primarily based on the existing data at the time, where Sr and Eu guests clearly show off-center sites 10,11,12 and glasslike κ(T ), while Ba guests appear to show on-center vibration 10,11,12 (within experimental resolution) and a crystalline peak. Later studies demonstrated glasslike behavior for p-type BGG 15,20 and now for p-type BGS (this work), so this argument by itself is no longer valid, unless a closer look at the Ba vibration in these compounds through microscopic techniques shows that offcenter vibration modes do exist for p-type samples (even if much smaller than for Sr and Eu guests) but not for n-type samples.…”

“…A combination of phonon scattering by TS, resonant scattering on large, Einstein-like localized vibration modes (guest rattling) and Rayleigh scattering was used to adequately reproduce the experimental κ(T ) behavior (henceforth we will refer to this combination as the TRR model). Later investigations amply demonstrated a splitting of the Sr(2) site into four off-center positions, 10,11,12 among which the ions could indeed tunnel.…”

Tunable charge carriers and thermoelectricity of single-crystal Ba8Ga16Sn30

“…In the case of Sr 8 Ga 16 Ge 30 and Eu 8 Ga 16 Ge 30 , the additional presence of a four-fold splitting of an A atom site and the consequent tunnelling of this ion between these four off-center sites is claimed to be the source of truly glass-like behavior in their thermal conductivities at low temperatures [3,4,5,6]. The electron-crystal characteristic of these clathrates is preserved because the charge carriers remain within the cage network and are not significantly affected by the rattling motion of the guest atom.…”

Emergence of Elastic Softening in Sr8Ga16Si30-xGexwith Increasing Ge Concentration

“…As a trial, we estimated the anomalous part of ∆C 44 /C 44 of Sr 8 Ga 16 Ge 30 by assuming that ∆C 44 /C 44 of Sr 8 Ga 16 Si 30 (the sample with x = 0) is the background stiffness, then we tried to fit the anomalous part with the static quadrupolar susceptibility. 5) However, a good fit has not yet been obtained so far. A hint of another possible reason why the softening in C 44 stops is in the Raman scattering experiment.…”

“…However, the softening in C 44 stops at low temperatures, suggesting that the instability tends to disappear. One possible reason why the softening stops is the tunneling motion which, for instance, was discussed by Zerec et al 5) If the tunneling probability enhances at low temperatures, the guest atom does not stop at the minimum position in the anharmonic potential. As a trial, we estimated the anomalous part of ∆C 44 /C 44 of Sr 8 Ga 16 Ge 30 by assuming that ∆C 44 /C 44 of Sr 8 Ga 16 Si 30 (the sample with x = 0) is the background stiffness, then we tried to fit the anomalous part with the static quadrupolar susceptibility.…”