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Physica B 359–361 (2005) 1015–1017 www.elsevier.com/locate/physb
Thermal transport properties of U2 Ru2Sn at low temperatures A. Sancheza,, S. Paschena, J. Wosnitzab, J.A. Mydosha, A.M. Strydomc, P. de V. du Plessisd, F. Steglicha a
Max-Planck Institute for Chemical Physics of Solids, No¨thnitzer Strasse 40, D-01187 Dresden, Germany b Institute of Solid State Physics, TU Dresden, D-01062 Dresden, Germany c Physics Department, Rand Afrikaans University, P. O. Box 524, Johannesburg, South Africa d School of Physics, University of the Witwatersrand, P. O. Wits 2050, Johannesburg, South Africa
Abstract U2 Ru2 Sn has been classiﬁed as the ﬁrst tetragonal U-based Kondo insulator. Here, we present measurements of the thermal conductivity k and thermopower S of high-quality single-crystalline U2 Ru2 Sn along and perpendicular to the tetragonal c-axis, in the temperature range between 100 mK and 1 K, in zero ﬁeld and in a magnetic ﬁeld of 6 T. Below 400 mK, the phonon contribution to kðTÞ shows a T 2 behaviour for both directions that can be attributed to phonons scattered by electrons. SðTÞ presents a linear behaviour in the whole temperature range. S is positive along the c-axis and negative perpendicular to the c-axis. Using a one-band model the effective mass m is estimated to be 2m0 along and 16m0 perpendicular to the c-axis, where m0 is the free-electron mass. This indicates that U2 Ru2 Sn has a highly anisotropic residual density of states within the pseudogap. r 2005 Elsevier B.V. All rights reserved. PACS: 72.15.Eb; 72.20.Pa; 71.27.þa Keywords: Thermal transport; Kondo insulator; U2 Ru2 Sn
U2 Ru2 Sn has tentatively been classiﬁed as a Kondo insulator due to features observed in the electrical resistivity, i.e., a broad maximum around 130 K and a ‘semiconductor-like’ behaviour below 30 K . Due to this interesting behaviour, the compound has subsequently been investigated Corresponding author. Tel.: +49 351 46463219;
fax: +49 351 46463902. E-mail address: [email protected]
using different techniques. Speciﬁc heat and magnetic susceptibility , as well as NMR  provide evidence for the opening of an energy gap of approximately 150 K. The magnetic susceptibility is anisotropic with the c-axis identiﬁed as the easy magnetic axis . The Hall coefﬁcient reaches large absolute values at low temperatures . The measurements presented here were performed on phase-pure bars of approximately
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.382
ARTICLE IN PRESS A. Sanchez et al. / Physica B 359– 361 (2005) 1015–1017
2 mm 1 mm 0:3 mm cut from a single-crystal grown in a four-mirror furnace. The equipment and the steady-state method used for the measurements are standard and have been described elsewhere . Fig. 1 shows the temperature dependence of the thermal conductivity kðTÞ of U2 Ru2 Sn along and perpendicular to c in magnetic ﬁelds B applied _ kðTÞ does not parallel to the heat current Q: present any magnetic-ﬁeld dependence in the temperature range investigated. Comparing our data with previous results of kðTÞ on polycrystalline samples , the agreement is within experimental error. We have estimated the electronic contribution to the thermal conductivity kWF from e the electrical resistivity measured for the same samples between 350 mK and 10 K using the Wiedemann–Franz law. For temperatures below 350 mK, the resistivity was extrapolated from the measured values. As seen in Fig. 1, kWF is e
U2Ru2Sn κ Casimir ph
distinctly smaller than the measured total kðTÞ (cf. solid line for Q_ k c and dashed line for Q_ ? c). The phonon contribution due to boundary scatteris estimated from the gas kinetic ing kCasimir ph equation using the low-temperature lattice speciﬁc heat ðC ph ð¼ 0:73 mJ=molK4 Þ T 3 ; yD ¼ 240 KÞ , and taking the smallest dimensions of both samples ð 0:3 mmÞ for the mean-free path (cf. dotted line). kCasimir is much larger than the ph total measured kðTÞ: Thus, the phonons appear to be subject to an additional scattering mechanism. We may estimate the total phonon contribution askph ðTÞ ¼ kðTÞ kWF e ðTÞ: Below 400 mK, kph ðTÞ is well approximated by a T 2 law for both crystallographic directions (cf. Fig. 2). This temperature dependence can be attributed to scattering of phonons from charge carriers. The inﬂuence of the boundary scattering is negligible in this temperature range. The reduced Lorenz number L=L0 decreases with decreasing temperature for both crystallographic directions from about 30 for Q_ k c and 14 for Q_ ? c at 1 K to about 9 for Q_ k c and 5 for Q_ ? c at 0.2 K, in agreement with kðTÞ being phonon dominated. Fig. 3 shows the temperature dependence of the thermopower SðTÞ along and perpendicular to c in zero ﬁeld and 6 T. As for kðTÞ; SðTÞ does not present any change under an applied magnetic ﬁeld of 6 T. For both directions, SðTÞ shows a behaviour linear in T. For Q_ k c; SðTÞ is positive while for Q_ ? c it is negative. This linear behaviour is attributed to the diffusion thermopower, since other contributions to SðTÞ such as
. Q || c, . Q, B || . Q ⊥ c, . Q, B ⊥
B =0 T c, B = 6 T B =0 T c, B = 6 T 1
Q. || c, B = 0 T Q ⊥ c, B = 0 T
1 T (K)
Fig. 1. Thermal conductivity of U2 Ru2 Sn as a function of temperature with the magnetic ﬁeld B along and perpendicular to the c-axis, in ﬁelds of 0 and 6 T.
Fig. 2. Temperature dependence of the phonon thermal conductivity of U2 Ru2 Sn along and perpendicular the c-axis.
ARTICLE IN PRESS A. Sanchez et al. / Physica B 359– 361 (2005) 1015–1017
estimate the effective mass m of the charge carriers. For Q_ k c; m is 2m0 while, for Q_ ? c we obtain m ¼ 16m0 ; where m0 is the free-electron mass. The same trend of a larger residual density of states for the direction perpendicular to c is suggested from recent Knight–shift experiments . The origin of this remarkable anisotropy remains to be understood.
0.0 -0.4 -0.8 -1.2 -1.6 -2.0 0.0
Q. || c, B = 0 T Q. , B || c, B = 6 T Q. ⊥ c, B = 0 T Q , B ⊥ c, B = 6 T
T (K) Fig. 3. Thermopower of U2 Ru2 Sn as a function of temperature with the magnetic ﬁeld B along and perpendicular the c-axis, in ﬁelds of 0 and 6 T.
the phonon drag are expected to be negligible in the temperature range investigated here. Surprising is the different sign of S for both directions since Hall-effect measurements  yield electronlike carriers for both directions. Combining the thermopower results with the charge-carrier concentration n (n ¼ 4:5 1020 cm 3 at 2 K, independent of direction) estimated from the Hall-effect measurements  in a one-band model, one may
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