- Email: [email protected]
A.C. susceptibility of polysulfur nitride (SN)x
Solid State Communications, Vol. 35, pp. 887—890. Pergamon Press Ltd. 1980. Printed in Great Britain. A.C. SUSCEPTIBILITY OF POLYSULFUR NITRIDE (SN)~ Y. 0th, H. Takenaka, H. Nagano and I. Nakada The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan (Received 28January 1980; in revisedfonn 13 May 1980 by W. Sasaki) The complex magnetic susceptibility x’ ix” of superconducting (SN)~ was measured for applied magnetic fields perpendicular and parallel to the fiber axis. Both x’ and x” are found to be very sensitive to the magnitude of the a.c. magnetic field, though not sensitive to that of the d.c. These behaviors can be explained with the model of weakly coupled filamentary superconductors. —
RECENTLY THE MAGNETIC properties of (SN)~in the superconducting region have been reported concerning the static magnetization [1] and the upper critical field [2]. The complete Meissner effect has been observed in the measurement of the a.c. susceptibility [3]. The magnetization measurements suggest that (SN)~ is a weakly coupled filamentary superconductor. If (SN)~consists of the electrically isolated fibers, it is difficult to understand the large diamagnetism measured in the experiments. Turkevich and Klemm [4] have pointed out in the discussion of the upper critical field that the-Josephson éurrent would flow between the fibers. In this communication the study of the imaginary part of the a.c. susceptibility below the transition temperature To is presented. The result together with the behavior of the real part reported in the previous cornmunication [31 can be discussed with a model of weakly coupled filamentary superconductors. The crystals used in this study are prepared by the previously reported method [3]. As remarked, (SN)~has fiber structure [1, 2, 5, 6]. With an X-ray and a transmission electron diffraction, our specimen is a single crystal. However, the dark field electron microscopy shows the existence of a lot of sub-boundaries along the fiber axis similar to those presented by Schultz and Petermann [6]. The mean separation between the boundaries is several hundred angstroms. They are not macroscopic cracks, but regions ofminor mismatching between single crystalline regions in nearly the same orientation. The fact that the macroscopic cracks are not induded in the crystal is also verified by the direct measurement of the density of (SN)~which is made by the heavy liquid method. The value obtained is 2.30 ±0.02g cm~at room temperature which is equal to that deduced from the crystallographic lattice parameters determined by the X-ray method [7]. These mean that the crystal is partitioned into single crystalline fibers by sub-boundaries. The experimental method is the same as that 887
described in the previous paper [3]. The magnetic field it the sample can be represented as H = H~0+ Ha.c. cos ~t + 6, where ~ and Ha.c. cos wt are the d.c. and a.c. magnetic field
respectively, and & is the total residual field (< 5 mOe). The a.c. magnetic susceptibility for the fundamental frequency component, which is selected by a lock-in amplifier, is represented as x = x’ ix”. The susceptibility is anisotropic and signs of II and I indicate the parallel and the perpendicular direction to the molecular chain (fiber axis) respectively. The measurements were made at frequencies of 18, 35, 70 and 280 Hz. The frequency dependence of x” is negligible as far as Ha.c. is sufficiently small, though it appears at the large H~.0.. The temperature dependence of x~at ~ = 0 is shown in Fig. 1 with Ha.c, as a parameter. For Ha.c. <0.034 Oe the dependence of x~ on Ha.c, is quite small. However, a large peak of x~appears at the lower temperature with increasing Ha.c.. The Ha.c, dependence of x~at Hd.C. = 0 is shown in Fig. 2 with temperature as a parameter. As the temperature decreases the peak of x~ increases and shifts towards larger Ha.~,.. The temperature dependence of x~at Hdc = 0 is shown in Fig. 3 with H~.0.as a parameter. For Ha.c. <0.034 Oe the effect of H~.0,is small. With increase of H&.c., x ~ increases rapidly while the clear peak as observed in x~ has not been observed. The Hac dependence of xli at Hd.C. = 0 is shown in Fig. 4 with temperature as a parameter. With decrease of the temperature the peak of x ~increases and shifts towards the larger Ha.c.. The dependence of x~ and x~ on Hd.C. is measured at small constant Ha.c.. In this case the H~0 dependence has not been observed below several oersteds. The notable character of x’ and x” is that they are very sensitive to H~.0.,while not to H~0.This character suggests that the shielding current flows in the loop —
A.C. SUSCEPTIBILITY OF POLYSULFUR NITRIDE (SN)~
888 I
I
I
I
10-
I
—
x
9..
xX 8
Vol. 35, No. 11
0
X
-
Ha~ 0.0170e
0.0340e 0.34 Oe X 0.68 Oe D
4
Hac
L.
-
0
~ 5
o 0.0340e 8 0.34 Oe
A
-
X 0.68 Oe
X
-
x
,6-
0.O170e
-
X
~3-
Xt
A A
-
A
2-
1
A
-
A
0
0
8 A
2-
0
A 8A
200 300 I (mK) dependence of xii for different Ha.c.
100
Fig. 3. Temperature
A
at ~/2ir = 70Hz andHdC 0
100
200 I
0.
300
(mK)
-
Fig. 1. Temperature dependence of x~ of (SN)~for different values OfHac at o.,/2ir = 70Hz andHdC = 0.
I
A
10-
0
9
=
I
6 -
-
43 mK
0
c
A
79mK
o
142mP(
~
8
-
8
-
-
.0
82
~ A
A
80
A
o
-
0 A
-
A
~2_8B00D
8A
C7
0
0
a
-
A -
-
-
o
0-
-
-
0
0
0
j 5-0 -
-
3-~ X ~x 2 -~ XX
T A
8
A
x
0
X
34 mK 63 m K 141 m K 205 m K
Fig. 4. The dependence of xli
andHdC=0.
° -
0
X
-
-
30880 A
0
1.0
I 1.5
H~ (Oe) 0
1 ~
I 0.5
-
—1 ____________________________________________ 0 0.5 1.0 1.5 Hoc (Oe)
Fig. 2. The dependence of x~ on Hac at different temperatures at ~/2ir = 70Hz and H~0~ = 0.
OflHa.c.
at w/21r = 70Hz
which includes Josephson junctions, as suggested by Turkevich and Klemm [4]. In the (SN)~crystal each fiber is separated from the neighbors by sub-boundaries which would play a role of the Josephson junctions. For Hdc, after the static magnetic field has penetrated into the Josephson loop, the superconducting loop is reconstructed. However, for the large H~0,the magnetic flux passes the junction for every cycle and there occurs an effective resistance. This is the origin of x”. When the magnetic field is applied, many shielding current loops would appear in the crystal. The shielding current flows
Vol. 00, No.00 a c
A.C. SUSCEPTIBILITY OF POLYSULFUR NITRIDE (SN)~
a
~ ~‘).7 7
)
~
-
77
7
/
cPQd,. , uPQv respectively. J~ ,~ is the maximum Josephson current of the nth junction. According to . .
7
/2’
/ ~s.t
I~ ...
~
/
Ambegaokar and Baratoff [9], for a symmetrical junc-
tionJ1~,,is represented as
/
7
/
/
/
~
=
(ir/2)r~’A(T)tanh [A(T)/2kBT],
(2)
where r~is the normal resistance of the nth junction and ~(T) is the gap energy, Taking i~(T)to be independent of n, L increases with decreasing temperature in Fig. 5. Schematic diagram of the cross-section of the Josephson loop which appears in (SN)~.aP and ~ ~ proportion to ~(T) tanh (A(T)/2kB T). The effective parallel to the fiber. The a.c. magnetic field is perpenresistance R below T0 appears when the magnetic flux dicular to the paper (H1). The dotted lines are hypopasses the junction. Then it would increase with increasthetical paths to introduce the subloops suchas aPQb, lag HLC, and decrease with decreasing temperature etc. since J~,,,becomes larger at lower temperatures. Above T0, R is assumed to be constant. along each loop passing a number of Josephsonjunctions. Now let us consider the response of the equivalent Just below T0 only a few loops would appear at places~ loop which is put in the mutual inductance coil of the where their maximum Josephson current ~1 are relatively a.c. bridge. The mutual inductance coil consists of the large. As the temperature decreases, .1~at each junction primary and the compensated secondary coil wound increases and each loop expands in dimension. At sufficoaxially. The mutual inductance between the two is ciently low temperatures the shielding current would balanced when the loop is in the normal state. The flow through a three dimensional network resulting mutual inductance changes at the superconducting tranfrom the combination of multiple Josephson junctions. sition. The real and the imaginary part of the change of Let us consider the case ofH1 first. At low tempera- the mutual inductance between the primary and the tures the shielding current would flow in a loop whose secondary are written as M’ and M” respectively. Then b d
t
~
/
889
J:
Q
______
v
cross-section schematically shown in Fig. 5. The current flowsisalong the path parallel and perpendicular to the molecular chain. High supercurrent can flow
along the parallel path as suggested by gap anisotropy measurement [8]. Therefore, the current would pass through a narrow region near the surface of the crystal. On the contrary, in the perpendicular direction the current would flow through the network with randomly distributed junctions. For simplicity, however, we assume as shown in the hatched region in Fig. 5 that the current passes along individual parallel circuit where each has one Josephson Junction and sustains lossless current up to the critical current of the junction. This means that the apparent penetration depth has increased.
The penetration depth increases with increase of H
M’ M”
= =
2/[R2+(wL)2], —AL(wL) ALR(wL)I [R2+ (~L)2],
(3) (4)
= m~m 2, (5) where A is a8IL constant, while m~and m~are mutual inductances between the loop and the primary, and the
A
loop and the secondary coil respectively. The a.c. susceptibility xi and x~ are proportional to the mutual inductance M’ and M” respectively. Therefore, we can discuss the behaviors of the a.c. susceptibility with equations. (3)—(5). When the temperature is low and Hac is small, R ~ 0. Then we obtain M’ ~ —AL andM” ~ 0. Therefore, xi is proportional to
8.~.. In our measurement only the fundamental frequency component of the a.c. susceptibility is selectively observed. The exact analysis of the response of this net-
— L. From equations (1) and (2), xi is proportional to ~.(T) tanh [~(T)/2kBTJ at low temperatures. In the
work is complicated because the Josephsonjunction acts as a non-linear element. In order to simplify the treatment concerning the response of this network to the a.c. magnetic field, the network is replaced by an equivalent loop whose effective self-inductance is L and resistance is R. Then L of the network in Fig. 5 is approximated by
relation assuming the BCS temperature dependence of
L
=
(~
ini~n)ii,
(i
=
1/2
E .i~~
-
With the increase of Hac, R increases monotonously. From equation (3), xi decreases with increase ,fHa.c and T, shifts towards the lower temperature. In the process of decreasing temperature at a constant ~
,
(1)
where I is a total shielding current along the network and 11, 12,. , l~are self-inductances of subloops aPQb, .
experiment, the temperature dependence of x~below about 2lOmK for Hac <0.034 Oe agrees with this
equation(4) means thatM” passes a peak of = c~.,L.WhenR increases with the increase of
AL/2 atR
Ha.c., the peak ofM” shifts towards the lower temperature with increasing height, because L increases at low temperatures. The behaviors agree with the results
shown in Fig. 1.
890
A.C. SUSCEPTIBILITYOF POLYSULFUR NITRIDE (SN)~
The decrease of Xi and the increase of x~ mean that the fraction of the magnetic flux penetration increases. From Fig. 1 and xi reported previously [3] it is deduce that the considerable fraction of the magnetic flux penetrates into (SN)~at Ha.c. 0.34Oe. This is consistent with the result of Dee et al. [1]. According to them their d.c. susceptibility exhibits
hysteresis for the temperature cycle, although no hysteresis is observed in our a.c. susceptibility. This is not a contradiction but is just an evidence that the shielding current flows through the network of the
Vol. 35, No. 11
current loop expands as the temperature decreases. In the discussion above, sub-boundaries between fibers play a role of the Josephson junction. It may be worthwhile to note that, in the theoretical aspect, the same treatment can be applied to the case that the Josephson junction occurs between molecular chains instead of the sub-boundary, as well.
Acknowledgement The authors thank Prof. S. Kobayashi and Prof. H. Fukuyama for helpful discussions. also thank Mr. K. Suzuki and Mr. M. Ichihara for They performing measurements by electron —
Josephsonjunctions. The Ha.c, dependence of xi in Fig. 2 can be also explained with this model. When Ha.c. is large, R does not vanish. Then M’
microscope.
andM” depend on ~. AtR ~ i.e. at sufficiently low temperatures, M” must decrease with increase of ~. This is confirmed at Ha.c. = 0.68 Oe experimentally. Next, let us consider the case ofH11. Iii ~
1.
the shielding current must flow always perpendicular to the molecular chain. There is no parallel path like aP and bQ shown in Fig. 5. Thus the shielding current must flow through junctions of low J. Therefore, the effect for shielding the magnetic field decreases as shown experimentally. This consideration can explain the behaviors of x~ and xii~ In conclusion, the dependence of the complex susceptibility of(SN)~on temperature and magnetic field can be explainedwith the model of the weakly coupled filamentary superconductors. In this model the shielding current passes Josephson junctions and the
3.
REFERENCES
2.
RH. Dee, D.H. Dollard, B.G. Turrell &J.F. Carolan, Solid W.G. State Clark, Commun. 24,469 (1977). LI. Azevedo, G. Deutscher, R.L. Greene, G.B. Street & L.J. Suter, Solid State Commun. 19, 197 (1976).
4. 5. 6. 7. 8. 9.
Y. 0th, H. Takenaka, H. Nagano & I. Nakada, Solid State Commun. 32, 659 (1979). L.A. Turkevich & R.A. Klemm, Phyx Rev. B19, 2520 (1979).C. Elbaum, L.F. Nichols, H.I. Kao & R.I. Civiak, M.M. Labes,Phys. Rev. B14, 5413 (1976). J.M. Schultz & J. Petermann, Phil. Mug. 40, 27 (1979). R.H. Baughman & R.R. Chance,!. Chem. Phys. 64, 1869 (1976). G. Binnig & H.E. Hoenig, Z Physik B32, 23 (1978). V. Ambegaokar & A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); 11, 104 (1963).
RECENTLY THE MAGNETIC properties of (SN)~in the superconducting region have been reported concerning the static magnetization [1] and the upper critical field [2]. The complete Meissner effect has been observed in the measurement of the a.c. susceptibility [3]. The magnetization measurements suggest that (SN)~ is a weakly coupled filamentary superconductor. If (SN)~consists of the electrically isolated fibers, it is difficult to understand the large diamagnetism measured in the experiments. Turkevich and Klemm [4] have pointed out in the discussion of the upper critical field that the-Josephson éurrent would flow between the fibers. In this communication the study of the imaginary part of the a.c. susceptibility below the transition temperature To is presented. The result together with the behavior of the real part reported in the previous cornmunication [31 can be discussed with a model of weakly coupled filamentary superconductors. The crystals used in this study are prepared by the previously reported method [3]. As remarked, (SN)~has fiber structure [1, 2, 5, 6]. With an X-ray and a transmission electron diffraction, our specimen is a single crystal. However, the dark field electron microscopy shows the existence of a lot of sub-boundaries along the fiber axis similar to those presented by Schultz and Petermann [6]. The mean separation between the boundaries is several hundred angstroms. They are not macroscopic cracks, but regions ofminor mismatching between single crystalline regions in nearly the same orientation. The fact that the macroscopic cracks are not induded in the crystal is also verified by the direct measurement of the density of (SN)~which is made by the heavy liquid method. The value obtained is 2.30 ±0.02g cm~at room temperature which is equal to that deduced from the crystallographic lattice parameters determined by the X-ray method [7]. These mean that the crystal is partitioned into single crystalline fibers by sub-boundaries. The experimental method is the same as that 887
described in the previous paper [3]. The magnetic field it the sample can be represented as H = H~0+ Ha.c. cos ~t + 6, where ~ and Ha.c. cos wt are the d.c. and a.c. magnetic field
respectively, and & is the total residual field (< 5 mOe). The a.c. magnetic susceptibility for the fundamental frequency component, which is selected by a lock-in amplifier, is represented as x = x’ ix”. The susceptibility is anisotropic and signs of II and I indicate the parallel and the perpendicular direction to the molecular chain (fiber axis) respectively. The measurements were made at frequencies of 18, 35, 70 and 280 Hz. The frequency dependence of x” is negligible as far as Ha.c. is sufficiently small, though it appears at the large H~.0.. The temperature dependence of x~at ~ = 0 is shown in Fig. 1 with Ha.c, as a parameter. For Ha.c. <0.034 Oe the dependence of x~ on Ha.c, is quite small. However, a large peak of x~appears at the lower temperature with increasing Ha.c.. The Ha.c, dependence of x~at Hd.C. = 0 is shown in Fig. 2 with temperature as a parameter. As the temperature decreases the peak of x~ increases and shifts towards larger Ha.~,.. The temperature dependence of x~at Hdc = 0 is shown in Fig. 3 with H~.0.as a parameter. For Ha.c. <0.034 Oe the effect of H~.0,is small. With increase of H&.c., x ~ increases rapidly while the clear peak as observed in x~ has not been observed. The Hac dependence of xli at Hd.C. = 0 is shown in Fig. 4 with temperature as a parameter. With decrease of the temperature the peak of x ~increases and shifts towards the larger Ha.c.. The dependence of x~ and x~ on Hd.C. is measured at small constant Ha.c.. In this case the H~0 dependence has not been observed below several oersteds. The notable character of x’ and x” is that they are very sensitive to H~.0.,while not to H~0.This character suggests that the shielding current flows in the loop —
A.C. SUSCEPTIBILITY OF POLYSULFUR NITRIDE (SN)~
888 I
I
I
I
10-
I
—
x
9..
xX 8
Vol. 35, No. 11
0
X
-
Ha~ 0.0170e
0.0340e 0.34 Oe X 0.68 Oe D
4
Hac
L.
-
0
~ 5
o 0.0340e 8 0.34 Oe
A
-
X 0.68 Oe
X
-
x
,6-
0.O170e
-
X
~3-
Xt
A A
-
A
2-
1
A
-
A
0
0
8 A
2-
0
A 8A
200 300 I (mK) dependence of xii for different Ha.c.
100
Fig. 3. Temperature
A
at ~/2ir = 70Hz andHdC 0
100
200 I
0.
300
(mK)
-
Fig. 1. Temperature dependence of x~ of (SN)~for different values OfHac at o.,/2ir = 70Hz andHdC = 0.
I
A
10-
0
9
=
I
6 -
-
43 mK
0
c
A
79mK
o
142mP(
~
8
-
8
-
-
.0
82
~ A
A
80
A
o
-
0 A
-
A
~2_8B00D
8A
C7
0
0
a
-
A -
-
-
o
0-
-
-
0
0
0
j 5-0 -
-
3-~ X ~x 2 -~ XX
T A
8
A
x
0
X
34 mK 63 m K 141 m K 205 m K
Fig. 4. The dependence of xli
andHdC=0.
° -
0
X
-
-
30880 A
0
1.0
I 1.5
H~ (Oe) 0
1 ~
I 0.5
-
—1 ____________________________________________ 0 0.5 1.0 1.5 Hoc (Oe)
Fig. 2. The dependence of x~ on Hac at different temperatures at ~/2ir = 70Hz and H~0~ = 0.
OflHa.c.
at w/21r = 70Hz
which includes Josephson junctions, as suggested by Turkevich and Klemm [4]. In the (SN)~crystal each fiber is separated from the neighbors by sub-boundaries which would play a role of the Josephson junctions. For Hdc, after the static magnetic field has penetrated into the Josephson loop, the superconducting loop is reconstructed. However, for the large H~0,the magnetic flux passes the junction for every cycle and there occurs an effective resistance. This is the origin of x”. When the magnetic field is applied, many shielding current loops would appear in the crystal. The shielding current flows
Vol. 00, No.00 a c
A.C. SUSCEPTIBILITY OF POLYSULFUR NITRIDE (SN)~
a
~ ~‘).7 7
)
~
-
77
7
/
cPQd,. , uPQv respectively. J~ ,~ is the maximum Josephson current of the nth junction. According to . .
7
/2’
/ ~s.t
I~ ...
~
/
Ambegaokar and Baratoff [9], for a symmetrical junc-
tionJ1~,,is represented as
/
7
/
/
/
~
=
(ir/2)r~’A(T)tanh [A(T)/2kBT],
(2)
where r~is the normal resistance of the nth junction and ~(T) is the gap energy, Taking i~(T)to be independent of n, L increases with decreasing temperature in Fig. 5. Schematic diagram of the cross-section of the Josephson loop which appears in (SN)~.aP and ~ ~ proportion to ~(T) tanh (A(T)/2kB T). The effective parallel to the fiber. The a.c. magnetic field is perpenresistance R below T0 appears when the magnetic flux dicular to the paper (H1). The dotted lines are hypopasses the junction. Then it would increase with increasthetical paths to introduce the subloops suchas aPQb, lag HLC, and decrease with decreasing temperature etc. since J~,,,becomes larger at lower temperatures. Above T0, R is assumed to be constant. along each loop passing a number of Josephsonjunctions. Now let us consider the response of the equivalent Just below T0 only a few loops would appear at places~ loop which is put in the mutual inductance coil of the where their maximum Josephson current ~1 are relatively a.c. bridge. The mutual inductance coil consists of the large. As the temperature decreases, .1~at each junction primary and the compensated secondary coil wound increases and each loop expands in dimension. At sufficoaxially. The mutual inductance between the two is ciently low temperatures the shielding current would balanced when the loop is in the normal state. The flow through a three dimensional network resulting mutual inductance changes at the superconducting tranfrom the combination of multiple Josephson junctions. sition. The real and the imaginary part of the change of Let us consider the case ofH1 first. At low tempera- the mutual inductance between the primary and the tures the shielding current would flow in a loop whose secondary are written as M’ and M” respectively. Then b d
t
~
/
889
J:
Q
______
v
cross-section schematically shown in Fig. 5. The current flowsisalong the path parallel and perpendicular to the molecular chain. High supercurrent can flow
along the parallel path as suggested by gap anisotropy measurement [8]. Therefore, the current would pass through a narrow region near the surface of the crystal. On the contrary, in the perpendicular direction the current would flow through the network with randomly distributed junctions. For simplicity, however, we assume as shown in the hatched region in Fig. 5 that the current passes along individual parallel circuit where each has one Josephson Junction and sustains lossless current up to the critical current of the junction. This means that the apparent penetration depth has increased.
The penetration depth increases with increase of H
M’ M”
= =
2/[R2+(wL)2], —AL(wL) ALR(wL)I [R2+ (~L)2],
(3) (4)
= m~m 2, (5) where A is a8IL constant, while m~and m~are mutual inductances between the loop and the primary, and the
A
loop and the secondary coil respectively. The a.c. susceptibility xi and x~ are proportional to the mutual inductance M’ and M” respectively. Therefore, we can discuss the behaviors of the a.c. susceptibility with equations. (3)—(5). When the temperature is low and Hac is small, R ~ 0. Then we obtain M’ ~ —AL andM” ~ 0. Therefore, xi is proportional to
8.~.. In our measurement only the fundamental frequency component of the a.c. susceptibility is selectively observed. The exact analysis of the response of this net-
— L. From equations (1) and (2), xi is proportional to ~.(T) tanh [~(T)/2kBTJ at low temperatures. In the
work is complicated because the Josephsonjunction acts as a non-linear element. In order to simplify the treatment concerning the response of this network to the a.c. magnetic field, the network is replaced by an equivalent loop whose effective self-inductance is L and resistance is R. Then L of the network in Fig. 5 is approximated by
relation assuming the BCS temperature dependence of
L
=
(~
ini~n)ii,
(i
=
1/2
E .i~~
-
With the increase of Hac, R increases monotonously. From equation (3), xi decreases with increase ,fHa.c and T, shifts towards the lower temperature. In the process of decreasing temperature at a constant ~
,
(1)
where I is a total shielding current along the network and 11, 12,. , l~are self-inductances of subloops aPQb, .
experiment, the temperature dependence of x~below about 2lOmK for Hac <0.034 Oe agrees with this
equation(4) means thatM” passes a peak of = c~.,L.WhenR increases with the increase of
AL/2 atR
Ha.c., the peak ofM” shifts towards the lower temperature with increasing height, because L increases at low temperatures. The behaviors agree with the results
shown in Fig. 1.
890
A.C. SUSCEPTIBILITYOF POLYSULFUR NITRIDE (SN)~
The decrease of Xi and the increase of x~ mean that the fraction of the magnetic flux penetration increases. From Fig. 1 and xi reported previously [3] it is deduce that the considerable fraction of the magnetic flux penetrates into (SN)~at Ha.c. 0.34Oe. This is consistent with the result of Dee et al. [1]. According to them their d.c. susceptibility exhibits
hysteresis for the temperature cycle, although no hysteresis is observed in our a.c. susceptibility. This is not a contradiction but is just an evidence that the shielding current flows through the network of the
Vol. 35, No. 11
current loop expands as the temperature decreases. In the discussion above, sub-boundaries between fibers play a role of the Josephson junction. It may be worthwhile to note that, in the theoretical aspect, the same treatment can be applied to the case that the Josephson junction occurs between molecular chains instead of the sub-boundary, as well.
Acknowledgement The authors thank Prof. S. Kobayashi and Prof. H. Fukuyama for helpful discussions. also thank Mr. K. Suzuki and Mr. M. Ichihara for They performing measurements by electron —
Josephsonjunctions. The Ha.c, dependence of xi in Fig. 2 can be also explained with this model. When Ha.c. is large, R does not vanish. Then M’
microscope.
andM” depend on ~. AtR ~ i.e. at sufficiently low temperatures, M” must decrease with increase of ~. This is confirmed at Ha.c. = 0.68 Oe experimentally. Next, let us consider the case ofH11. Iii ~
1.
the shielding current must flow always perpendicular to the molecular chain. There is no parallel path like aP and bQ shown in Fig. 5. Thus the shielding current must flow through junctions of low J. Therefore, the effect for shielding the magnetic field decreases as shown experimentally. This consideration can explain the behaviors of x~ and xii~ In conclusion, the dependence of the complex susceptibility of(SN)~on temperature and magnetic field can be explainedwith the model of the weakly coupled filamentary superconductors. In this model the shielding current passes Josephson junctions and the
3.
REFERENCES
2.
RH. Dee, D.H. Dollard, B.G. Turrell &J.F. Carolan, Solid W.G. State Clark, Commun. 24,469 (1977). LI. Azevedo, G. Deutscher, R.L. Greene, G.B. Street & L.J. Suter, Solid State Commun. 19, 197 (1976).
4. 5. 6. 7. 8. 9.
Y. 0th, H. Takenaka, H. Nagano & I. Nakada, Solid State Commun. 32, 659 (1979). L.A. Turkevich & R.A. Klemm, Phyx Rev. B19, 2520 (1979).C. Elbaum, L.F. Nichols, H.I. Kao & R.I. Civiak, M.M. Labes,Phys. Rev. B14, 5413 (1976). J.M. Schultz & J. Petermann, Phil. Mug. 40, 27 (1979). R.H. Baughman & R.R. Chance,!. Chem. Phys. 64, 1869 (1976). G. Binnig & H.E. Hoenig, Z Physik B32, 23 (1978). V. Ambegaokar & A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); 11, 104 (1963).