Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate

Critical magnetic fields of superconducting aluminum-substituted
Ba8Si42Al4 clathrate
Yang Li,1,a)
Jose Garcia,1
Giovanni Franco,2
Junqiang Lu,2
Kejie Lu,1
Bo Rong,3
Basir Shafiq,1
Ning Chen,4
Yang Liu,4
Lihua Liu,5
Bensheng Song,5
Yuping Wei,5
Shardai S. Johnson,6
Zhiping Luo,6
and Zhaosheng Feng7
1
School of Engineering, University of Puerto Rico at Mayaguez, Mayaguez, Puerto Rico 00681-9000,
USA
2
Department of Physics, University of Puerto Rico, Mayaguez, Puerto Rico 00681, USA
3
Communications Research Centre (CRC), Industry Canada, 3701 Carling Avenue, Box 11490, Station H,
Ottawa, Ontario K2H 8S2, Canada
4
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083,
China
5
Department of Physics, University of Science and Technology Beijing, Beijing 100083, China
6
Department of Chemistry and Physics, Fayetteville State University, Fayetteville, North Carolina 28301, USA
7
Department of Mathematics, University of Texas-Pan American, Edinburg, Texas 78541, USA
(Received 2 April 2015; accepted 14 May 2015; published online 3 June 2015)
In recent years, efforts have been made to explore the superconductivity of clathrates containing
crystalline frameworks of group-IV elements. The superconducting silicon clathrate is unusual in
that the structure is dominated by strong sp3
covalent bonds between silicon atoms, rather than the
metallic bonding that is more typical of traditional superconductors. This paper reports on critical
magnetic fields of superconducting Al-substituted silicon clathrates, which were investigated by
transport, ac susceptibility, and dc magnetization measurements in magnetic fields up to 90 kOe.
For the sample Ba8Si42Al4, the critical magnetic fields were measured to be HC1 ¼ 40.2 Oe and
HC2 ¼ 66.4 kOe. The London penetration depth of 4360 A˚ and the coherence length 70 A˚ were
obtained, whereas the estimated Ginzburg–Landau parameter of j ¼ 62 revealed that Ba8Si42Al4 is
a strong type-II superconductor. VC 2015 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4921702]
I. INTRODUCTION
Clathrate materials are extended Si, Ge, and Sn cage-
like solids with sp3
-hybridized networks that encapsulate
guest atoms. A wide variety of electronic and vibrational
properties can be produced in these materials by substitution
upon framework sites or through incorporation of ions in
cage-center positions. The main types of clathrates are
A8(IV)46 such as Ba8Si46 (A—alkali or alkaline-earth metal,
IV—group IV element such as Si, Ge, and Sn). This is the
structural type first synthesized and studied by Cros group.1
However, such clathrates have been overlooked for a long
time due to their complexity in synthesis. The discovery of
relatively high TC superconductivity in alkali-metal-doped
C60 fullerenes has inspired efforts to explore the supercon-
ductivity of group-IV clathrates because of the analogy of
the structure for fullerene and clathrate forming polyhedral
cages.2
In particular, the discovered potential of Ge clath-
rates as thermoelectric materials has stimulated an increased
research in this area.3,4
Superconductivity has been found in several clathrates
containing crystalline frameworks of group-IV elements.5,6
Clathrates are the only known sp3
based superconductors
which are unusual as their structure is dominated by strong
covalent bonds, rather than the more typical metallic bonds
found in traditional superconductors. Therefore, it is crucial
to study clathrate superconductors in order to gain a better
understanding of the origin of the attractive interaction
leading to Cooper pairs and the driving mechanism in sp3
covalent systems. As a precursor research, Caplin group
initially searched for superconductivity in type-I and type-II
Na-Si clathrates; however, these original silicon clathrates
were found not to be superconducting.7
A few years later
the type-I Na-Ba-Si clathrate was prepared and shown to be
superconducting with TC near 4 K.8
Advances in synthesis,
in particular, high-pressure methods, led to the preparation
of Ba8Si46 for which the alkali metals were replaced
completely by Ba.9
This composition achieved a supercon-
ducting TC ¼ 8 K. Ba8Si46 prepared with a slight deficit of
Ba was found to have TC as high as 9.0 K,10
which is a high-
water mark for superconducting transition temperatures
among sp3
-bonded clathrates. Isotope effect measurements
revealed that superconductivity in Ba8Si46 is of the classic
BCS kind, arising from the electron-phonon interaction.11
The enhanced TC in this compound has been shown to arise
predominantly from very sharp features in the electronic
densities of states associated with the extended sp3
-bonded
framework.
As shown in the left inset of Fig. 1, type-I clathrate
Ba8Si46 lattice (space group Pm3n) is an arrangement of two
small pentagonal dodecahedra (Si20) and six big tetrakaideca-
hedra (Si24) offering eight sites per unit cell for guest Ba
atoms. Atomic substitution can tailor these electronic
a)
Author to whom correspondence should be addressed. Electronic mail:
yang.li@upr.edu
0021-8979/2015/117(21)/213912/5/$30.00 VC 2015 AIP Publishing LLC117, 213912-1
JOURNAL OF APPLIED PHYSICS 117, 213912 (2015)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
23.119.216.191 On: Fri, 05 Jun 2015 02:49:12

properties. Substitutions of Si on the framework and Ba in the
center of the cage can profoundly affect superconductivity.
The substitutional effects of Si framework on superconductiv-
ity for Ba8Si46–xLx with L ¼ Ga, Al, Ag, Au, Cu, Ge, and Ni
have been studied by several groups.2
Consistent with the lat-
est research findings, these investigations showed a
progressive decrease of the critical temperature with the
increase in the L content x depending on the substituting
elements. Likewise, the substitutional effects of guest atoms
in the center of cages have also been investigated in the
Ba8–xGxSi46 (G ¼ Sr, Ca, Na, K, and Eu) systems.12–15
In all
these cases, TC was found to decrease with the increase in the
content of substitution atoms, while superconductivity
vanished after a critical substitution level was reached. The
destructive effect on superconductivity generally is attribut-
able to a reduction in density of states at Fermi-level (N(EF)),
and a lowering of the carrier concentration, combined with
the disrupted continuity of the sp3
-hybridized framework.16,17
Based on the calculation of the phonon-dispersion relations
and vibrational density of states for Al-doped silicon clath-
rates,18
the high frequency acoustic branch has a red shift
with the doping of Al. The decreased frequency of bond-
stretching vibration modes is another reason for the suppres-
sion of TC induced by Al substitution. In addition, the
substitution of Eu for Ba results in a strong suppression of
superconductivity; Eu-doping largely decreases the supercon-
ducting volume and the transition temperature TC. Eu atoms
enter the clathrate lattice and their magnetic moment breaks
paired electrons.15
However, one of the more important
aspects, namely, the critical magnetic field of clathrate super-
conductors has not been investigated comprehensively. This
report presents a detailed study of superconducting behavior
in the Al-doped Ba8Si46 clathrate compounds, based on elec-
trical resistivity and magnetic susceptibility measurements in
the low-temperature region. The exceptional attention is
devoted to Ba8Si42Al4 clathrate with robust type-II character-
istics. A careful attempt is made in order to ascertain its basic
superconducting properties. Important superconducting
parameters, such as, the critical fields, coherence length,
penetration depth, and Ginzburg-Landau parameter are also
estimated.
II. EXPERIMENTAL METHODS
The synthesis of Ba8Si46ÀxAlx was performed based on
the multistep melting of Ba, Al, and Si under argon atmos-
phere and subsequent solid-state reaction.19
The samples
were characterized and analyzed by X-ray diffraction and
electron probe microanalyzer (EPMA). Structural refinement
of the powder X-ray diffraction data was carried out using
the GSAS software package.20,21
The samples were analyzed
for resistivity and magnetic susceptibility by a cryogen-free
physical properties measurement system (Cryogenic in
London).
Analysis by powder X-ray diffraction showed character-
istic type-I clathrate reflections for Ba8Si46ÀxAlx samples.
As shown in Fig. 1, the sample of Ba8Si42Al4 with dilute Al-
doping, exhibited the main phase to be type-I clathrate with
small quantities of impure phases such as silicon and BaSi2
(orthorhombic phase). As a result of the refinement, Al was
found to preferentially occupy the 6c framework sites for
dilute doping, however, for heavy substitution, Al inclined
towards a random distribution of the other 16i and 24k sites.
The lattice parameter of Ba8Si42Al4 was calculated as
a ¼ 10.39 A˚ . The lattice parameters of Ba8Si46-xAlx exhibited
an increasing trend with x due to the larger atomic size of Al
than that of Si.17
A JEOL 8530F EPMA was used to determine the stoi-
chiometry and grain size of the samples. The samples were
embedded using Buehler Epoxy Resin and Hardner, which
were placed in a Buehler Cast N’ Vac 1000 Vacuum
Impregnation System to suck out the air bubbles in voids to
fill with the epoxy. These embedded samples were then
mechanically polished to provide a flat surface of the crystals
for the microprobe analysis, and coated with a thin carbon
film for the EPMA analysis. Several spots on each crystal
were analyzed for Ba, Al, and Si using a beam current
density approximately 10 nA. EPMA imaging showed main
phase of clathrate and a small amount of impurity phases
such as Si, BaSi2, and SiO2 at grain boundary. The EPMA
composition analysis on clathrate phase showed the average
composition of crystals (Ba8Si38.83Al3.47) to be consistent
with Zintl concept. As an example shown in the right inset of
Fig. 1, the EPMA mapping obviously showed the homogene-
ity in the distribution of the constituent elements in the clath-
rate phase. A little amount of impurity phase, however,
existed in grain boundaries of sample. To characterize the
grain size, EPMA was used on samples. The microstructures
of the sample are with nubbly grains. There is no texture,
and the grains are randomly oriented with porosity. The av-
erage grain sizes were measured by the linear intercept
method; sample has an average grain size $20 lm.
III. RESULTS AND DISCUSSIONS
The temperature dependence of the AC and DC suscepti-
bility measured on Ba8Si42Al4 is shown in Figs. 2(a) and
2(b), respectively. For both AC and DC magnetic measure-
ments, the superconducting onset temperature TC,onset was
FIG. 1. The refined powder XRD pattern of Ba8Si42Al4 sample can be fully
indexed with the type-I clathrate structure. Red, green, and blue ticks mark
the positions of allowed reflections of type-I clathrate, diamond Si, and
BaSi2, respectively. Right inset: an EPMA image. Left inset: type-I clathrate
structure of Ba8Si46.
213912-2 Li et al. J. Appl. Phys. 117, 213912 (2015)
23.119.216.191 On: Fri, 05 Jun 2015 02:49:12

obtained as 5.7 K. The temperature dependence of the AC
susceptibility was measured in zero static field with ac field
amplitude of 3 Oe at a frequency of 256 Hz. At about 5.7 K,
the sample started to show superconducting characteristics;
the in-phase susceptibility (v0
) suddenly dropped and the out-
of-phase susceptibility (v00
) peaked.
A superconducting transition in Ba8Si42Al4 was also
observed in dc magnetic susceptibility (vdc ¼ M/H) measure-
ments. Figure 2(b) shows the zero-field-cooled (ZFC)
warming data and the field-cooled (FC) data for the applied
magnetic Field at H ¼ 50 Oe. The magnetization observed in
the superconducting state does not saturate at the lowest tem-
perature measured. The enhancement of the diamagnetism
below the superconducting transition temperature TC origi-
nates from the screening supercurrents (ZFC regime) and the
Meissner effect of magnetic flux expulsion (FC regime). Also,
as shown in Fig. 3, the existence of the hysteresis between the
two magnetization curves for the ZFC and the FC modes indi-
cates that the compound is a type-II superconductor. The
superconducting volume fraction was estimated to be 30%
according to the ZFC susceptibility at T ¼ 2 K. On the other
hand, the diamagnetic transition in the FC process is not too
small. This is due to a weak magnetic flux pinning force of
the sample, i.e., the expulsion of the magnetic flux from the
sample by the Meissner effect is large on cooling in the field.
Such a small difference in the magnitude of diamagnetic sus-
ceptibility between ZFC and FC processes is widely observed
for superconductors having weak flux pinning forces.
In addition, FC magnetization values were carried out as
a function of temperature in applied fields from 50 to 5 kOe,
as shown in Fig. 3. Flux expulsion (Meissner effect)
decreases with increasing external field; the magnetic field
easily suppresses the magnitude of superconducting response.
We observed that with applied field increasing, there occurs a
strong reduction in superconducting volume. As shown in the
inset of Fig. 3, the superconducting volume Vsup decreases
with increasing field in a log linear behavior, log Vsup ¼ a þ b
log H, with a ¼ 1.9 and b ¼ À1.4.
Fig. 4 shows the initial magnetization at low fields. The
magnetization gradually deviates from the perfect diamagne-
tization line. The lower critical field HC1(T) of this supercon-
ductor from the first deviation from linearity in the low-field
regions in the M(H) scans was estimated to be of the order
of HC1(0) ¼ 40.2 Oe, as shown in the inset of Fig. 5,
assuming a simple parabolic T dependence in the form of
HC1(T) ¼ HC1(0)(1 À t2
) where t ¼ T/TC.
The large changes at T ¼ 5.7 K in the AC and DC sus-
ceptibility were accompanied by a distinct drop in electrical
resistivity of the Ba8Si42Al4 sample. The four-probe trans-
port measurements also confirmed that Ba8Si42Al4 enters
into a superconducting state at 5.7 K. The sample showed a
metallic behavior in the normal state. The agreement of the
transition temperatures measured by both ac and dc suscepti-
bility as well as resistivity is a clear evidence of bulk super-
conductivity in Ba8Si42Al4.
Temperature dependence of the upper critical field HC2
of Ba8Si42Al4 is shown in Fig. 5. HC2 is estimated based on
the electrical resistivity R(T) and R(H) measurement, respec-
tively. As shown in the right inset of Fig. 5, the R-H
measurements were carried out at various fixed temperatures
which were set near and below TC from 2 to 6 K. The sample
FIG. 2. Magnetic susceptibility of Ba8Si42Al4 vs. temperature. (a)
Temperature dependence of the in-phase (v0
) and out-of-phase (v00
) AC sus-
ceptibility, measured in the zero field, (b) DC magnetization measurement
under the ZFC/FC protocol is shown for an external field of 50 Oe.
FIG. 3. The ZFC magnetization under different fields for Ba8Si42Al4. Inset:
Superconducting volume (Vsup) decreasing with external field according to a
linear log behavior, with the fitted curve log Vsup ¼ a þ b log H.
FIG. 4. The magnetization curves at various temperatures from 2 to 5.5 K
for Ba8Si42Al4. The inset shows T dependence of the lower critical field
HC1(T). The dashed line is a fit assuming a parabolic T dependence, giving
HC1 (0) ¼ 40.2 Oe.
23.119.216.191 On: Fri, 05 Jun 2015 02:49:12

was warmed up to 20 K before the R-H measurement at each
temperature was taken. Above superconducting transition
temperature, the normal resistance of sample was about 55
mX. The upper critical field HC2 at different temperatures
was obtained from the R-H measurements at the field where
the resistance reached half of the normal-state resistance RN.
The arrow points to the defined upper critical field HC2 at
2 K. The resistance approaches RN gradually because of the
magnetoresistance effect. A broadening of the transition
curves was observed at low temperature, which is caused at
least partially by flux-flow effects at high magnetic fields.
The transition widths gradually broaden from 14.2 kOe at 5 K
to 26.1 kOe at 2 K. The solid square symbols (᭿) in Fig. 5
show HC2 vs temperature for the Ba8Si42Al4, which were
determined from R(H) curve collected at various fixed tem-
peratures. This HC2 curve shows a perfect linear dependence
on T near TC, which is a typical property of a superconductor
with a high value of the Ginzburg-Landau parameter j.
In addition, the left inset of Figure 5 shows the R(T)
curves of the sample Ba8Si42Al4 at different applied fields. In
the normal state, the sample resistance change is flat from 60
mX at 300K to 55 mX just above the transition temperature,
which still showed weak metallic temperature dependence
with residual resistivity ratios (RRR) of 1.1 only. Here, the
upper critical field HC2 in R(T) measurement was defined as
the zero resistance temperature limit. The temperature
dependence of HC2 labelled with the solid circle symbol (•) is
plotted in Fig. 5. Using the values of HC2 for zero resistance
TC0, the upper critical field was evaluated to be HC2 ¼ 66.4
kOe and TC ¼ 5.32 K by fitting the data to the generalized
Ginzburg-Landau model: HC2(T) ¼ HC2(0)(1 À t2
)/(1 þ t2
),
where t ¼ T/TC. This fitted HC2(0) is below the BCS Pauli
paramagnetic limit (HC2,Pauli ¼ 1.83 TC ¼ 97.4 kOe). From
the estimates of HC1 and HC2, the penetration depth, k,
and the coherence length, n, were determined using
the Ginzburg–Landau equations:22
l0HC2 ¼ U0
2pn2 and
l0HC1 ¼ U0
4pk2 lnðk=nÞ þ C1Þð , where j ¼ k/n is the
Ginzburg–Landau parameter, U0 ¼ phc=e is the flux quan-
tum, and C1 ¼ 0.497.23
From HC1 ¼ 40.2 Oe and HC2 ¼ 66.4
kOe, k ¼ 4360 A˚ and n ¼ 70 A˚ were obtained. Hence, j % 62
was found indicating this material is a strongly type-II super-
conductor. These values can be compared to those obtained
for Ba8Si46 (k % 4000 A˚ , n % 72 A˚ , and j % 56).24
We found
that both materials have the same order of magnitude for k
and n. It is evident that in the type IX chiral-structure clath-
rate Ba24Ge100, k % 6500 A˚ and n % 310A˚ (Ref. 25) are
bigger than the values for Ba8Si40Al4 reported here.
The existence of the superconducting mixed state char-
acterizes Ba8Si42Al4 as a type-II superconductor. Evidence
for a type II superconducting state can be seen as well in Fig.
6 where M-H loop has been plotted for T ¼ 2, 3, and 4 K.
Figure 6 shows that the magnetic field dependence of the
magnetization M below TC is irreversible. At these tempera-
tures, the magnetic hysteresis (the width of the M-H loops)
decreases with the applied field, but remains nonzero at 50
kOe below T ¼ 4 K.
Because our superconducting Ba8Si42Al4 sample is a
polycrystalline compound, which contains a large array of
grains and grain boundaries through which the current can
flow. Application of a magnetic field to the polycrystalline
sample sets up screening currents both within grains and on
a macroscopic scale. Consequently, the irreversible magnetic
moment Dm is a direct measure of these screening currents,
and can be written as a sum of inter- and intra-granular
contributions
Dm5ð2=3ÞV½KJinter 1 a0JintraŠ; (1)
where V is the volume of the superconductor, a0 is the typi-
cal grain size, and K the length scale of coherent current
flow (current carrying length scale).26
Analysis of Dm
requires knowledge of K, which is complicated by the
presence of weak links in polycrystalline superconductors.
With increasing magnetic field and temperature, the weak
FIG. 5. Temperature dependence of the upper critical field HC2 of
Ba8Si42Al4. The solid circle symbols (•) were determined from zero resist-
ance temperature TC0 in the R(T) data, and the dashed line is a fit to the data
using a GL model, giving HC2(0) ¼ 66.4 kOe. The solid square symbols (᭿)
were determined from R(H) curve collected at fixed temperature. Right
inset: R(H) curve at fixed temperature. The black arrow indicates the deter-
mined upper critical field at 2 K. Left inset: the resistance versus temperature
at various fields H from 0 to 90 kOe with an interval 5 kOe. The black arrow
indicates the zero resistance temperature corresponding to the upper critical
field at H ¼ 0.
FIG. 6. M-H hysteresis of Ba8Si42Al4 at 2, 3, and 4 K, respectively. Upper
inset: JC-H dependences at 2, 3, and 4 K, respectively. Lower inset: The pin-
ning force FP( ¼ jJC Â Hj) against magnetic field H.
23.119.216.191 On: Fri, 05 Jun 2015 02:49:12

links tend to fragment the pattern of screening currents, so
that K cannot be equated simply to the sample physical
dimension. However, previous analysis has shown that at
given T and H, the initial “reverse-leg” magnetic susceptibil-
ity is proportional to K, which allows the latter to be
estimated27
ðdDM=dBÞ/ðK=tÞ; (2)
where t is the thickness of the superconductor. A series of
magnetization loops of Ba8Si42Al4 sample at 2 K were also
measured. According to the initial “reverse-leg” magnetic
susceptibility, the current carrying length scale K was
estimated under different applied magnetic fields. The length
scale of coherent current flow rapidly decreased with the
field. When the applied field increases, the dominant mag-
netic screening currents circulate only on a scale correspond-
ing to a grain size ($20 lm). This implies that at high fields
the intergranular current is rather small, and the intragranular
current is dominant. Thus, at high fields Dm becomes
increasingly dominated by the intra-granular term in Eq. (1).
Therefore, only the contribution of intragranular current
needs to be considered, so that the critical current density
JC 5 3Dm/2Va0, where Dm and a0 are the irreversible mag-
netic moment and the average size of grains, respectively,
and V is the sample volume. The JC-H dependence at 2, 3,
and 4 K, respectively, for Ba8Si42Al4 sample is shown in the
upper right inset of Fig. 6. The flux pinning behavior of
Ba8Si42Al4 compound can be inferred from lower right inset
of Fig. 6, which plots the pinning force FP( 5 jJC 3 Hj)
against magnetic field. The irreversible magnetic moment
would be caused by defects and finely dispersed impurities
in the grain boundary of the sample; they trap magnetic flux
through the sample, however, such precipitate phases may
not be responsible for the JC increase in intragranular. We
note that at a given temperature, the JC decreases rapidly
with the increasing applied field, especially at higher
temperature, which indicating that the flux pinning is still
rather weak in Ba8Si42Al4. For instance, at 2 K, the JC
decreases from a maximum of 1.7 Â 106
A/cm2
at H ¼ 0 to
4.8 Â 105
A/cm2
at H ¼ 4 kOe. For Ba8Si42Al4 sample, the
field-dependent JC(H) showed that the pinning behavior is
similar to neither high-TC cuprate superconductors nor MgB2
compound. As shown in Fig. 6, there is no JC(H) second
peak and fishtail, which appeared in the Eu1–xYxBa2Cu3Oy.28
On the other hand, the JC(H) of Ba8Si42Al4 does not have a
good field-dependent behavior such as in the MgB2,
especially in the high field regions.29
Clearly, in Ba8Si42Al4
compound, there are no structural deficiencies acting as
effective pinning centers, although structural defects induced
by Al-doping into the Si framework result in some flux
pinning.
In conclusion, detailed investigations of the properties
of a superconductor Ba8Si42Al4 clathrate are reported.
Magnetization and transport measurements have been
performed, which showed the Ba8Si42Al4 clathrate is a bulk
superconductor. The upper and lower critical fields are
estimated to be HC1(0) ¼ 40.2 Oe and HC2 ¼ 66.4 kOe,
respectively. The London penetration depth k ¼ 4360 A˚ and
the coherence length n ¼ 70 A˚ are obtained, while the
Ginzburg–Landau parameter j ¼ 62 indicates this material is
a strong type-II superconductor.
ACKNOWLEDGMENTS
This work was supported in part by the National Science
Foundation (DMR-0821284), NASA (NNX10AM80H and
NNX07AO30A). The EPMA work at FSU was supported by
NSF (HRD-1436120) and DoD (W911NF-09-1-0011 and
W911NF-14-1-0060).
1
J. S. Kasper, P. Hagenmuller, M. Pouchard, and C. Cros, Science 150,
1713 (1965).
2
J. H. Ross, Jr. and Y. Li, in Nanoscale Magnetic Materials and
Applications, edited by J. P. Liu, E. Fullerton, O. Gutfleisch, and D.
Sellmyer (Springer-Verlag, New York, 2009), p. 105.
3
J. S. Tse, K. Uehara, R. Rousseau, A. Ker, C. I. Ratcliffe, M. A. White,
and G. MacKay, Phys. Rev. Lett. 85, 114 (2000).
4
B. B. Iversen, A. E. C. Palmqvist, D. E. Cox, G. S. Nolas, G. D. Stucky, N.
P. Blake, and H. Metiu, J. Solid State Chem. 149, 455 (2000).
5
F. M. Grosche, H. Q. Yuan, W. Carrillo-Cabrera, S. Paschen, C.
Langhammer, F. Kromer, G. Sparn, M. Baenitz, Yu. Grin, and F. Steglich,
Phys Rev Lett 87, 247003 (2001).
6
F. M. Grosche, H. Q. Yuan, W. Carrillo-Cabrera, S. Paschen, C.
Langhammer, F. Kromer, G. Sparn, M. Baenitz, Y. Grin, and F. Steglich,
Phys. Rev. Lett. 87, 247003 (2001).
7
B. Roy, K. E. Sim, and A. D. Caplin, Philos. Mag. B 65, 1445 (1992).
8
H. Kawaji, H. Horie, S. Yamanaka, and M. Ishikawa, Phys. Rev. Lett. 74,
1427 (1995).
9
M. Imai, T. Hirano, T. Kikegawa, and O. Shimomura, Phys. Rev. B 58,
11922 (1998).
10
H. Fukuoka, J. Kiyoto, and S. Yamanaka, Inorg. Chem. 42, 2933 (2003).
11
K. Tanigaki, T. Shimizu, K. M. Itoh, J. Teraoka, Y. Moritomo, and S.
Yamanaka, Nature Mater. 2, 653 (2003).
12
P. Toulemonde, Ch. Adessi, X. Blase, and A. San Miguel, Phys. Rev. B
71, 094504 (2005).
13
P. Toulemonde, A. San Miguel, A. Merlen, R. Viennois, S. Le Floch, Ch.
Adessi, X. Blase, and J. L. Tholence, J. Phys. Chem. Solids 67, 1117
(2006).
14
H. Fukuoka, J. Kiyoto, and S. Yamanaka, J. Phys. Chem. Solids 65, 333
(2004).
15
L. Liu, S. Bi, B. Peng, and Y. Li, J. Appl. Phys. 117, 17E117 (2015).
16
Y. Li, R. H. Zhang, Y. Liu, N. Chen, Z. P. Luo, X. Q. Ma, G. H. Cao, Z. S.
Feng, C.-R. Hu, and J. H. Ross, Jr., Phys. Rev. B 75, 054513 (2007).
17
Y. Li, J. Garcia, N. Chen, L. H. Liu, F. Li, Y. Wei, S. Bi, G. H. Cao, and
Z. S. Feng, J. Appl. Phys. 113, 203908 (2013).
18
L. Liu, S. Bi, N. Chen, F. Li, Y. Liu, G. Cao, and Y. Li, Physica C 506, 94
(2014).
19
Y. Li and J. H. Ross, Jr., Appl. Phys. Lett. 83, 2868 (2003).
20
A. C. Larson and R. B. von Dreele, Los Alamos National Laboratory
Report No. LAUR 86-748, 2000.
21
B. H. Toby, J. Appl. Crystallogr. 34, 210 (2001).
22
V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950).
23
C.-R. Hu, Phys. Rev. B 6, 1756 (1972).
24
I. M. Gat, Y. Fudamoto, and A. Kinkhabwala, Physica B 289-290, 385
(2000).
25
R. Viennois, P. Toulemonde, C. Paulsen, and A. San-Miguel, J. Phys.:
Condens. Matter 17, L311 (2005).
26
A. D. Caplin, IEEE Trans. Appl. Supercond. 5, 1864 (1995).
27
M. A. Angadi, A. D. Caplin, J. R. Laverty, and Z. X. Shen, Physica C 177,
479 (1991).
28
Y. Li, G. Perkins, A. D. Caplin, Q. Z. Ma, and G. H. Cao, Supercond. Sci.
Technol. 13, 1029 (2000).
29
P. Kovac, I. Husek, T. Melisek, L. Kopera, and J. Kovac, Supercond. Sci.
Technol. 27, 065003 (2014).
23.119.216.191 On: Fri, 05 Jun 2015 02:49:12

Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (9)

Similar to Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate

Similar to Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate (20)

Recently uploaded

Recently uploaded (20)

Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate