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Thermal conductivity of F-electron systems ErO4Ho0.6Rh4B4 and URu2Si2
PhysicaC 162-164 (1989) 1653-1654 NoRh-Hogand
THERMAL CONDUCTIVITY OF F-ELECTRON SYSTEMS Er0 4Hoo.6Rh4B4 AND URu2Si2 M.A. LOPEZDE LA TORRE, R. VILLAR, S. VIEIRA, M.B. MAPLE(*) and M.S. TORIKACHVILI(*) Dpto. de Fisica de la Materia Condensada,C - l l l , Universidad Aut6noma de Madrid, Cantoblanco, 28049-Madrid, Spain and (*) Dpt. of Physics, University of California, San Diego, La Jolla, California-92093, USA. We h a v e measured the thermal conductivity of the reentrant ferromagnetic superconductor Ero.4Hoo.6Rh4B4 and the heavy fermion superconductor URu2Si2. For these two materials thermal conduction behaves in a very different form. We can explain the thermal conductivity of Ero.4Hoo.6Rh4B4 in terms of BCS theory, but in URu2SI2 we find a behavlour that clearly suggest unconventional superconductivity. A comparisonwith results in UPt3 allows us to speculate with the p o s s i b i l i t y of p-wave or d-wave superconductivity. f i e l d and between4.2 K and 16 K in an applied
i . INTRODUCTION In
this
work we discuss our
results of
f i e l d of 1T. In the temperature region 4.2 K < T < 16 K
thermal conductivity measurementsperformed on polycrystalline Ero.4Hoo.6Rh4B 4 We compare these results
with the theoretical
BCS curve in order to obtain the
superconducting state
information about
also
K(1T) shows a dependence linear in T.
support
results
t i v i t y is negligible. Then: K(1T) = Kn ~ Ken, Results
in UPt3
unconventional
in
zero
K(OT) = Ks ~ Kes field
f o r T > T c (T c ~ 7.3 K). we can
superconductivity.
Then we
can considerate that the l a t t i c e thermal conduc-
in both materials.
For URu2Si2, we compare with that
and URu2Si2.
compare w i t h
o v e r l a p w i t h K (1T) I f we c a l c u l a t e Ks/K n
the p r e d i c t i o n of Bardeen
et al [1]. 2. EXPERIMENTALDETAILS Thermal performed
measurements were
Kes
pumped He3 cryostat for both
Ken
conductivity in
a
materials, and in a pumped He4 the
Y = A/KBT ,
FI(-y) = !zdz/(l+eZ+Y)
two thermometer
procedure. For measurements in applied magnetic
Our r e s u l t s are
displayed
in
f i e l d we used carbon thermometers instead of
curve (1) f o r 2A(O)/KBT c = 3.52.
the
where we can be
usual germanium resistence thermometers.
Our samples were a rod diameter ~ 3.1
(1)
2F1(0)
cryostat with a
superconducting solenoid for Ero.4Hoo.6Rh4B4. The method used was
2F1 (-y) + 2yln (l+e"y) + yZ/(1+eY)
(length
~
30 mm,
mm) of polycrystalline URu2Si2
e f f e c t s do for
sure
Kes/Ken,
this ratio
than the
of 10 mm2 of polycrystalllne Ero.4Hoo.6Rh4B4.
3.52 < 2A(O)/KBTc < 4.
BCS
prediction.
Measurements of URu2Si2
We have measured the thermal conductivity of Ero.4Hoo.6Rh4B4 between 1K and 16 K in
zero
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
us
lattice
conduction
in
zero
is
slightly
We can
lower
estimate
thermal conductivity of field
between 0.6 K and 25 K. for
1 with
not d i s t u r b our approximate r e s u l t s
and a 9.5 mm long sample with irregular section
3. RESULTS
that
Fig.
In the region
to carry out
have been performed I t has been impossible
measurementsin
applied
M.A. Lopez de la Torre et aL ~f-electron systems Ero.~loo.e,Rh~B~ and URuzSi2
1654 magnetic f i e l d
below4.2
K.
Thenwe analyse
our results in the following form:
URu2Si2.
In the temperature region from Tc ~ 1.6 K to ? K,
K(T) is
well f i t t e d to the
K = aT + bT2,
with
expression
a = .1083 Wm"1
K-2,
linear
state,
contribution
and the
suppose that to
the
represents of
the
the normal
quadratic term is the l a t t i c e ThenKen = aT, Kin
= bT2.
We
Kin = bT2 is also the upper l i m i t
lattice
thermal
conduction in
the
superconducting state, because for T < I K 2~z KB4 1
In this
case, results
prediction
of
T3 = cT3
We
These results agree f a i r l y well Monien et al.
[3] and Hirschfeld et al. [4] for p-wave and dwave superconducting states. the parity
The problemof
of URu2Si2 superconducting state is
an open question.
Results
in
specific heat
support an even-parity state, characterized by quadratic terms in the thermal properties for T < Tc [5,6]. Ks/Kn
We have to note that below T < 1.2 show an almost linear
according with
15~3 v2s
do not agree
BCS theory.
represent results in UPt3 that show a similar
K,
Kl ~
the
with theoretical calculations of
electronic thermal conductivity contribution.
with
behaviour [2].
b = 3.071 x 10-2 Wm-1K -3. The
Ks = K(T) - bT2. In Fig. 1 we display Ks/Kn for
the
existence
dependence
of a quadratic
term in Ks(T). with c
= 2.1
x 10-2 Wm-1 K-4 and l = 15 pm (l ACKNOWLEDGEMENTS
is the mean grain size).
We thank Dr. F. Mesegu~ for lending us the He4 cryostat with the superconducting solenoid. Financial support from Comite Conjunto Hispano-
I.Q
Americano is also acknowledged. 0.!
REFERENCES t.
•
1.
/ /
C0.6
P
/
2.
/ / / /
~'~ OA /
3.
t /
0.2
/
4.
f
O.C'
0.0
~
~ l
0.2
t
I
t
0.4
0.6
0.8
19
TIT c
FIGURE 1 Measured r a t i o of the superconducting to normal thermal conductivity for URu2Si2 ( • ), Ero.4Hoo.6Rh4B4 ([]) and UPt3 (A). Dashedline is the BCS theoretical curve with a value of 2A(O)/kBTc = 3.52. We can estimate
the
electronic thermal
conductivity of the superconducting state to be
5. 6.
J. Bardeen, G. Rickayzen and L. Tewordt, Phys. Rev. 113 (1959) 982. A. Sulpice, P. Gundit, J. Chaussy, J. Flouquet, D. Jaccard, P. Lejay and J.L. Tholence, J. Low Temp. Physics. 62 (1986) 39. M. Monien, K. Scharnberg, L. Tewordt and D. Walker, Solid State Comm. vol. 61, n° 9 (1987)581-585. P.J. Hirschfeld, P. Wolfle and D. Einzel, Phys. Rev. B, 37 (1988) 83. M. Kato and K. Machida, Phys. Rev. B, 3? (1988) 1510. G . P . Volovik and L.P. Gor'kov, Zh. Exp. Teor. Fiz. 88 (1985) 1412.
THERMAL CONDUCTIVITY OF F-ELECTRON SYSTEMS Er0 4Hoo.6Rh4B4 AND URu2Si2 M.A. LOPEZDE LA TORRE, R. VILLAR, S. VIEIRA, M.B. MAPLE(*) and M.S. TORIKACHVILI(*) Dpto. de Fisica de la Materia Condensada,C - l l l , Universidad Aut6noma de Madrid, Cantoblanco, 28049-Madrid, Spain and (*) Dpt. of Physics, University of California, San Diego, La Jolla, California-92093, USA. We h a v e measured the thermal conductivity of the reentrant ferromagnetic superconductor Ero.4Hoo.6Rh4B4 and the heavy fermion superconductor URu2Si2. For these two materials thermal conduction behaves in a very different form. We can explain the thermal conductivity of Ero.4Hoo.6Rh4B4 in terms of BCS theory, but in URu2SI2 we find a behavlour that clearly suggest unconventional superconductivity. A comparisonwith results in UPt3 allows us to speculate with the p o s s i b i l i t y of p-wave or d-wave superconductivity. f i e l d and between4.2 K and 16 K in an applied
i . INTRODUCTION In
this
work we discuss our
results of
f i e l d of 1T. In the temperature region 4.2 K < T < 16 K
thermal conductivity measurementsperformed on polycrystalline Ero.4Hoo.6Rh4B 4 We compare these results
with the theoretical
BCS curve in order to obtain the
superconducting state
information about
also
K(1T) shows a dependence linear in T.
support
results
t i v i t y is negligible. Then: K(1T) = Kn ~ Ken, Results
in UPt3
unconventional
in
zero
K(OT) = Ks ~ Kes field
f o r T > T c (T c ~ 7.3 K). we can
superconductivity.
Then we
can considerate that the l a t t i c e thermal conduc-
in both materials.
For URu2Si2, we compare with that
and URu2Si2.
compare w i t h
o v e r l a p w i t h K (1T) I f we c a l c u l a t e Ks/K n
the p r e d i c t i o n of Bardeen
et al [1]. 2. EXPERIMENTALDETAILS Thermal performed
measurements were
Kes
pumped He3 cryostat for both
Ken
conductivity in
a
materials, and in a pumped He4 the
Y = A/KBT ,
FI(-y) = !zdz/(l+eZ+Y)
two thermometer
procedure. For measurements in applied magnetic
Our r e s u l t s are
displayed
in
f i e l d we used carbon thermometers instead of
curve (1) f o r 2A(O)/KBT c = 3.52.
the
where we can be
usual germanium resistence thermometers.
Our samples were a rod diameter ~ 3.1
(1)
2F1(0)
cryostat with a
superconducting solenoid for Ero.4Hoo.6Rh4B4. The method used was
2F1 (-y) + 2yln (l+e"y) + yZ/(1+eY)
(length
~
30 mm,
mm) of polycrystalline URu2Si2
e f f e c t s do for
sure
Kes/Ken,
this ratio
than the
of 10 mm2 of polycrystalllne Ero.4Hoo.6Rh4B4.
3.52 < 2A(O)/KBTc < 4.
BCS
prediction.
Measurements of URu2Si2
We have measured the thermal conductivity of Ero.4Hoo.6Rh4B4 between 1K and 16 K in
zero
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
us
lattice
conduction
in
zero
is
slightly
We can
lower
estimate
thermal conductivity of field
between 0.6 K and 25 K. for
1 with
not d i s t u r b our approximate r e s u l t s
and a 9.5 mm long sample with irregular section
3. RESULTS
that
Fig.
In the region
to carry out
have been performed I t has been impossible
measurementsin
applied
M.A. Lopez de la Torre et aL ~f-electron systems Ero.~loo.e,Rh~B~ and URuzSi2
1654 magnetic f i e l d
below4.2
K.
Thenwe analyse
our results in the following form:
URu2Si2.
In the temperature region from Tc ~ 1.6 K to ? K,
K(T) is
well f i t t e d to the
K = aT + bT2,
with
expression
a = .1083 Wm"1
K-2,
linear
state,
contribution
and the
suppose that to
the
represents of
the
the normal
quadratic term is the l a t t i c e ThenKen = aT, Kin
= bT2.
We
Kin = bT2 is also the upper l i m i t
lattice
thermal
conduction in
the
superconducting state, because for T < I K 2~z KB4 1
In this
case, results
prediction
of
T3 = cT3
We
These results agree f a i r l y well Monien et al.
[3] and Hirschfeld et al. [4] for p-wave and dwave superconducting states. the parity
The problemof
of URu2Si2 superconducting state is
an open question.
Results
in
specific heat
support an even-parity state, characterized by quadratic terms in the thermal properties for T < Tc [5,6]. Ks/Kn
We have to note that below T < 1.2 show an almost linear
according with
15~3 v2s
do not agree
BCS theory.
represent results in UPt3 that show a similar
K,
Kl ~
the
with theoretical calculations of
electronic thermal conductivity contribution.
with
behaviour [2].
b = 3.071 x 10-2 Wm-1K -3. The
Ks = K(T) - bT2. In Fig. 1 we display Ks/Kn for
the
existence
dependence
of a quadratic
term in Ks(T). with c
= 2.1
x 10-2 Wm-1 K-4 and l = 15 pm (l ACKNOWLEDGEMENTS
is the mean grain size).
We thank Dr. F. Mesegu~ for lending us the He4 cryostat with the superconducting solenoid. Financial support from Comite Conjunto Hispano-
I.Q
Americano is also acknowledged. 0.!
REFERENCES t.
•
1.
/ /
C0.6
P
/
2.
/ / / /
~'~ OA /
3.
t /
0.2
/
4.
f
O.C'
0.0
~
~ l
0.2
t
I
t
0.4
0.6
0.8
19
TIT c
FIGURE 1 Measured r a t i o of the superconducting to normal thermal conductivity for URu2Si2 ( • ), Ero.4Hoo.6Rh4B4 ([]) and UPt3 (A). Dashedline is the BCS theoretical curve with a value of 2A(O)/kBTc = 3.52. We can estimate
the
electronic thermal
conductivity of the superconducting state to be
5. 6.
J. Bardeen, G. Rickayzen and L. Tewordt, Phys. Rev. 113 (1959) 982. A. Sulpice, P. Gundit, J. Chaussy, J. Flouquet, D. Jaccard, P. Lejay and J.L. Tholence, J. Low Temp. Physics. 62 (1986) 39. M. Monien, K. Scharnberg, L. Tewordt and D. Walker, Solid State Comm. vol. 61, n° 9 (1987)581-585. P.J. Hirschfeld, P. Wolfle and D. Einzel, Phys. Rev. B, 37 (1988) 83. M. Kato and K. Machida, Phys. Rev. B, 3? (1988) 1510. G . P . Volovik and L.P. Gor'kov, Zh. Exp. Teor. Fiz. 88 (1985) 1412.