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doi:10.1016/j.ph

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Physica B 359–361 (2005) 1015–1017

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Thermal transport properties of U2Ru2Sn at low temperatures

A. Sancheza,�, S. Paschena, J. Wosnitzab, J.A. Mydosha, A.M. Strydomc,P. de V. du Plessisd, F. Steglicha

aMax-Planck Institute for Chemical Physics of Solids, Nothnitzer Strasse 40, D-01187 Dresden, GermanybInstitute of Solid State Physics, TU Dresden, D-01062 Dresden, Germany

cPhysics Department, Rand Afrikaans University, P. O. Box 524, Johannesburg, South AfricadSchool of Physics, University of the Witwatersrand, P. O. Wits 2050, Johannesburg, South Africa

Abstract

U2Ru2Sn 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 U2Ru2Sn along and perpendicular to the

tetragonal c-axis, in the temperature range between 100mK and 1K, in zero field and in a magnetic field of 6T. Below

400mK, the phonon contribution to kðTÞ shows a T2 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 U2Ru2Sn 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; U2Ru2Sn

U2Ru2Sn has tentatively been classified as aKondo insulator due to features observed in theelectrical resistivity, i.e., a broad maximum around130K and a ‘semiconductor-like’ behaviour below30K [1]. Due to this interesting behaviour, thecompound has subsequently been investigated

e front matter r 2005 Elsevier B.V. All rights reserve

ysb.2005.01.382

ng author. Tel.: +49351 46463219;

463902.

ss: sanchez@cpfs.mpg.de (A. Sanchez).

using different techniques. Specific heat andmagnetic susceptibility [2], as well as NMR [3]provide evidence for the opening of an energygap of approximately 150K. The magnetic sus-ceptibility is anisotropic with the c-axis identi-fied as the easy magnetic axis [2]. The Hallcoefficient reaches large absolute values at lowtemperatures [2].The measurements presented here were per-

formed on phase-pure bars of approximately

d.

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A. Sanchez et al. / Physica B 359– 361 (2005) 1015–10171016

2mm� 1mm� 0:3mm cut from a single-crystalgrown in a four-mirror furnace. The equipmentand the steady-state method used for the measure-ments are standard and have been describedelsewhere [4].Fig. 1 shows the temperature dependence of the

thermal conductivity kðTÞ of U2Ru2Sn along andperpendicular to c in magnetic fields B appliedparallel to the heat current _Q: kðTÞ does notpresent any magnetic-field dependence in thetemperature range investigated. Comparing ourdata with previous results of kðTÞ on polycrystal-line samples [5], the agreement is within experi-mental error. We have estimated the electroniccontribution to the thermal conductivity kWF

e fromthe electrical resistivity measured for the samesamples between 350mK and 10K using theWiedemann–Franz law. For temperatures below350mK, the resistivity was extrapolated fromthe measured values. As seen in Fig. 1, kWF

e is

0.1

0.01

0.1

1 κ phCasimir

κ eWF

.

.

.

.Q || c, B = 0 T

Q, B || c, B = 6 TQ ⊥ c, B = 0 T

Q, B ⊥ c, B = 6 T

U2Ru2Sn

κ (m

W/K

cm)

T (K)

1

Fig. 1. Thermal conductivity of U2Ru2Sn as a function of

temperature with the magnetic field B along and perpendicular

to the c-axis, in fields of 0 and 6T.

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 scatter-ing kCasimirph is estimated from the gas kineticequation using the low-temperature lattice specificheat ðCphð¼ 0:73mJ=molK4

Þ � T3; yD ¼ 240KÞ

[6], and taking the smallest dimensions of bothsamples ð 0:3mmÞ for the mean-free path(cf. dotted line). kCasimir

ph is much larger than thetotal measured kðTÞ: Thus, the phonons appearto be subject to an additional scattering mechan-ism. We may estimate the total phonon contribu-tion askphðTÞ ¼ kðTÞ kWF

e ðTÞ: Below 400mK,kphðTÞ is well approximated by a T2 law forboth crystallographic directions (cf. Fig. 2). Thistemperature dependence can be attributed toscattering of phonons from charge carriers. Theinfluence of the boundary scattering is negligible inthis temperature range. The reduced Lorenznumber L=L0 decreases with decreasing tempera-ture for both crystallographic directions fromabout 30 for _Q k c and 14 for _Q ? c at 1K toabout 9 for _Q k c and 5 for _Q ? c at 0.2K, inagreement with kðTÞ being phonon dominated.Fig. 3 shows the temperature dependence of the

thermopower SðTÞ along and perpendicular to c inzero field and 6T. As for kðTÞ; SðTÞ does notpresent any change under an applied magneticfield of 6 T. For both directions, SðTÞ shows abehaviour linear in T. For _Q k c; SðTÞ is positivewhile for _Q ? c it is negative. This linearbehaviour is attributed to the diffusion thermo-power, since other contributions to SðTÞ such as

0.10.01

0.1

1

.

.Q ||

⊥ c, B = 0 Tc, B = 0 T

Q

~T 2

U2Ru2Sn

κ ph

(mW

/Kcm

)

T (K)

1

Fig. 2. Temperature dependence of the phonon thermal

conductivity of U2Ru2Sn along and perpendicular the c-axis.

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0.0 0.2 0.4 0.6 0.8 1.0-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

.

.

..Q || c, B = 0 T

Q , B ||

⊥ c, B = 6 T

c, B = 6 TQ c, B = 0 TQ , B

U2Ru2Sn

S (µ

V/K

)

T (K)

⊥

Fig. 3. Thermopower of U2Ru2Sn as a function of temperature

with the magnetic field B along and perpendicular the c-axis, in

fields of 0 and 6T.

A. Sanchez et al. / Physica B 359– 361 (2005) 1015–1017 1017

the phonon drag are expected to be negligible inthe temperature range investigated here. Surpris-ing is the different sign of S for both directionssince Hall-effect measurements [6] yield electron-like carriers for both directions. Combining thethermopower results with the charge-carrier con-centration n (n ¼ 4:5� 1020 cm3 at 2K, indepen-dent of direction) estimated from the Hall-effectmeasurements [6] in a one-band model, one may

estimate the effective mass m� of the chargecarriers. For _Q k c; m� is 2m0 while, for _Q ? c weobtain m� ¼ 16m0; where m0 is the free-electronmass. The same trend of a larger residual densityof states for the direction perpendicular to c issuggested from recent Knight–shift experiments[7]. The origin of this remarkable anisotropyremains to be understood.

References

[1] L. Menon, P. de V. du Plessis, A.M. Strydom, Solid State

Commun. 106 (1998) 519.

[2] S. Paschen, V.H. Tran, N. Senthilkumaran, M. Baenitz,

F. Steglich, A.M. Strydom, P. de V. du Plessis,

G. Motoyama, N.K. Sato, Physica B 329–333 (2003) 549.

[3] M. Baenitz, A. Rabis, S. Paschen, N. Senthilkumaran,

F. Steglich, V.H. Tran, P. de V. du Plessis, A.M. Strydom,

Physica B 329–333 (2003) 545.

[4] B. Wand, PhD Thesis TU Darmstadt (1998).

[5] V.H. Tran, S. Paschen, A. Rabis, N. Senthilkumaran,

M. Baenitz, F. Steglich, P. de V. du Plessis, A.M. Strydom,

Phys. Rev. B 67 (2003) 075111.

[6] S. Paschen, et al., unpublished.

[7] A.K. Rajarajan, A. Rabis, M. Baenitz, A.A. Gippius, E.N.

Morozova, J.A. Mydosh, F. Steglich, these Proceedings.