Off-center rattling modes and glasslike thermal conductivity in the type-I clathrate Ba
8
Ga
16
Sn
30
K. Suekuni,
1
Y. Takasu,
2
T. Hasegawa,
3
N. Ogita,
3
M. Udagawa,
3,4
M. A. Avila,
1,
* and T. Takabatake
1,4
1
Department of Quantum Matter, ADSM, Hiroshima University, Higashi-Hiroshima 739-8530, Japan
2
St. Marianna University School of Medicine, Kawasaki, Kanagawa 216-8511, Japan
3
Graduate School of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
4
Institute for Advanced Materials Research, Hiroshima University, Higashi-Hiroshima 739-8530, Japan
Received 29 November 2009; revised manuscript received 24 February 2010; published 19 May 2010
Type-I clathrate Ba
8
Ga
16
Sn
30
is unique for showing glasslike behavior in the lattice thermal conductivity
L
irrespective of the charge carrier type. For better understanding the relation between this behavior and guest
rattling, polarized Raman-scattering measurements have been performed on carrier-tuned single crystals. The
appearance of a symmetry-forbidden mode in the E
g
symmetry spectrum indicates that the Ba atoms are
rotating among the off-center positions in the tetrakaidecahedron. On cooling from 300 to 4 K, the energies of
E
g
and T
2g
guest modes decrease by 15% and 25%, respectively. This drastic decrease originates from the
strongly anharmonic potential with a quartic term of the atomic displacement. The energy of 14 cm
-1
for the
T
2g
mode at 4 K is the lowest among intermetallic clathrates. These results for Ba
8
Ga
16
Sn
30
are compared with
those for type-I Eu
8
Ga
16
Ge
30
and Sr
8
Ga
16
Ge
30
whose
L
T show similar glasslike behavior with a plateau.
The comparison between three systems indicates that the guest rattling energy is proportional to the tempera-
ture range of the plateau in
L
T.
DOI: 10.1103/PhysRevB.81.205207 PACS numbers: 82.75.-z, 63.20.Ry, 65.40.-b, 78.30.-j
I. INTRODUCTION
Anharmonic vibrations of guest atoms encapsulated in an
oversize cage are referred to as “rattling” which often occurs
in intermetallic clathrates as well as filled skutterudites and
-pyrochlore oxides.
1–3
The rattling is thought to give rise to
various interesting phenomena, such as suppression of ther-
mal conductivity in type-I clathrates Sr
8
Ga
16
Ge
30
SGG and
-Eu
8
Ga
16
Ge
30
-EGG,
1,4–8
heavy-fermion behavior in the
filled skutterudite SmOs
4
Sb
12
,
9
and strong coupling super-
conductivity in -pyrochlore KOs
2
O
6
.
10
Type-I clathrates
have a cubic primitive structure which is composed of two
kinds of cages, dodecahedron and tetrakaidecahedron. The
guest in the tetrakaidecahedron is loosely bound to the cage
and therefore vibrates with larger amplitude and lower en-
ergy than the cage atoms.
The lattice part of thermal conductivity,
L
T, for
X
8
Ga
16
Ge
30
with X = Sr and Eu shows glasslike behavior as
presented in Fig. 1. The
L
is approximately proportional to
T
2
below 1 K, unlike the typical T
3
dependence in crystalline
materials.
7,8
By association with glassy systems, the T
2
be-
havior has been attributed to phonon scattering by tunneling
of two-level systems, whereas the plateau at around 10 K is
attributed to resonant phonon scattering by the guest
rattling.
1,4,7,8
At room temperature, the magnitude of
L
for
X
8
Ga
16
Ge
30
X =Sr and Eu is in the range
0.6–1.3 W / K m,
1
being lower than that of the vitreous SiO
2
1–2 W / K m.
11
The important role of umklapp process in
the acoustic-phonon scattering was pointed out based on in-
elastic neutron-scattering study of the filled skutterudite.
12
An umklapp process can occur even for low-energy acoustic
phonons by means of weakly dispersive rattling phonons
with a low-energy level of approximately 50 K. This idea has
been applied to explain the low value of
L
in the clathrate
Ba
8
Ga
16
Ge
30
BGG.
13
Raman-scattering spectroscopy has been proved to be a
powerful method to investigate dynamical properties of guest
rattling in various clathrates,
14–16
in spite of the fact that not
all vibrational modes can be detected by this technique. In
type-I clathrates, the vibrational modes of the guests in the
dodecahedron X1 are Raman inactive, while those in the
tetrakaidecahedron X2 are Raman active. Taking advantage
of this site selection, we have determined the symmetry and
energy of the rattling for X2 in X
8
Ga
16
Ge
30
X =Eu, Sr, and
Ba and X
8
Ga
16
Si
30-x
Ge
x
X =Sr and Ba.
15,16
In -EGG and
SGG the Eu2 and Sr2 rattling modes are described as a ro-
tation mode among the off-center sites. On the other hand,
for BGG the Ba2 mode is described as nearly on-center vi-
bration. The energies for X2=Ba, Sr, and Eu in X
8
Ga
16
Ge
30
are 46 K, 42 K, and 26 K, respectively, at 2 K.
15
This energy
sequence is in agreement with those derived from inelastic
neutron scattering and nuclear inelastic scattering.
17
Further-
more, this sequence directly correlates with the lowering of
L
. Thus, the rattling is thought to give rise to the glasslike
behavior of
L
T in the systems with X2=Eu and Sr.
Recently, single-crystal x-ray diffraction studies of type-I
Ba
8
Ga
16
Sn
30
-BGS revealed that the Ba2 guests have
large off-center displacements of 0.4 Å irrespective of the
charge carrier type.
18
Both n- and p-type crystals show glass-
like behavior in
L
T as is shown in Fig. 1. Analysis of the
specific heat has given a characteristic energy of 20 K for the
Ba2 rattling, which is lower than 26 K for Eu2 in
-EGG.
15,16,18,19
In this work, we have performed Raman-
scattering experiments in the temperature range from 4 to
300 K to investigate the symmetry and energy of Ba2 rattling
in off-center and glassy system -BGS in detail. The prelimi-
nary analysis of the spectra at 5 K has been reported in a
previous paper.
20
We demonstrate here a correlation between
the guest rattling energy and the temperature range of the
plateau in
L
T by comparing the data with those for
-EGG and SGG.
15,16
PHYSICAL REVIEW B 81, 205207 2010
1098-0121/2010/8120/2052075 ©2010 The American Physical Society 205207-1