- Email: [email protected]
Study of magnetic flux in a Bi2212 single crystal by torsional oscillation
PHYSlCA ELSEVIER
Physica C 263 (1996) 412-415
Study of magnetic flux in a Bi2212 single crystal by torsional oscillation H. Niimi, K. Inoue, S. Kawamata, K. Okuda * Department of Physics and Electronics, Universityof Osaka Prefecture, Sakai, Osaka 593, Japan
Abstract The vortex state of a Bi2Sr2CaCu2Os+~(Bi2212) single crystal was investigated by measuring the free torsional oscillation in magnetic field with special attention to the energy dissipation. The decay time and the oscillation period were measured at temperatures between 4.2 and 100 K under various fields up to 9 kOe. The temperature and field dependences of the energy dissipation due to flux depinning were obtained for the irreversible region. An abrupt increase of the energy dissipation was found around 1 kOe, suggesting the dimensional crossover from the 3D vortex solid to 2D pancakes with increasing field. A large damping anisotropy was also found and explained by a model of two-dimensional vortex pancakes.
1. Introduction The magnetic properties of Bi2212 are characterized by the large anisotropy originating from the layered structure. Various experiments and theoretical works have been done paying attention to the melting of the vortex lattice or the vortex glass, the anomalous depinning and the dimensional crossover of vortex pancakes in the compound. To clarify these problems, we applied torsional oscillation measurements with low frequency below 1 Hz, which is an appropriate method for detecting the energy dissipation accompanied by the change of vortex state, and the results are reported, here.
2. Experimental A free torsional oscillator was made by hanging an inertia disk of a brass cylinder and a quartz rod
* Corresponding author. Fax: 81 722 59 3340; e-mail: [email protected].
from a tungsten suspension wire. Angular oscillation was detected optically. The rotational oscillation axis was perpendicular to the applied field. The oscillation period was about 3 s in zero field. The equation of motion of the torsional oscillator is given as d20
I -7
dO
+r0=0,
77 = "170 -t'- "l/sample,
(1)
K = k 0 + ksample ,
where 1, 0, t, r/0, 'r/sample, k 0 and ksample represent the moment of the inertia of the oscillating system (1 = 5.14 g cmZ), rotational angle, time, the damping constants by the oscillator apparatus, that by the sample itself under magnetic field, the torque coefficient by the restoring force of the suspension wire (k 0 = 0.412 dyn c m / d e g ) and that generated by the sample under magnetic field, respectively. Below Tc and under magnetic fields, the oscillations were damped by energy dissipation proportional to r/sa~pJe. The solution of Eq. (1) becomes 0 = 00 e x p ( - t / r )
0 9 2 1 - 4 5 3 4 / 9 6 / $ 1 5 . 0 0 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 9 2 1 - 4 5 3 4 ( 9 5 ) 0 0 7 8 8 l
cos( tot + tS),
(2)
413
H. Niimi et aL /Physica C 263 (1996) 412-415 10OO
~
~
L
'
¢
.
''~
•
0
•
--1000
tx Z~
±
j
-4000 2OO
~
0
0
0
0
H A_ a b - p l a n e
~. -2000 -3000
declined angle of the crystal axis from the direction of the magnetic field was less than 2 deg. The decay time and the oscillation period were measured at temperatures between 4.2 and 100 K under various fields up to 9 kOe. The Bi2212 single crystals were prepared by the traveling solvent floating zone method. Three sampies with suitable size were used in the measurements. The samples were in the form of thin flat plates of dimensions: (a) 2.5 × 1.3 x 0.02, (b) 1 × 0.5 × 0.02, (c) 0.5 × 0.5 × 0.003 mm 3. These samples were annealed at 618°C for 70 h to homogenize the oxygen distribution in the compound. The superconducting transition temperature and the transition width were Tc = 87.4 K and ATc = 0.8 K.
(a) r
0
i
,
i
n
t~ • 0 @ 0 @
H H H }1 H H
a
I
I
(b)
= = = = =
(ZFC) 3 kO¢ 2 kOe 1 kOe 0.75 kOe 0.5 kOc 0.25 kOc *
I
H ± ab-plane
150
@
H
•
. = ,koo
a~
,~
100
•
= 8 kOe H = 6 kOc
kOc H = 1 kOe H = 0.5 kOe I t = O.25 k O e
0 0 •
50
(FC)
0
A i
i
q
I
I
I
i
I
i
(ZFC)
H//ab-plane
4000
%
3000
O
H = 0.5
kOe
3. Results and discussion
2000 1000
Fig. 1 indicates the temperature dependence of the torque coefficient ksample in several magnetic fields.
0
J -1000
2
I
'
O
i 40 Temp.
,
L 60 OK)
,
810
1OO
Fig. 1. Temperature dependence of torque coefficient ksample in several magnetic fields. (a) ZFC, H l ab-plane. (b) FC, H ± abplane. (c) ZFC, H II ab-plane.
(a
3 where 00 and 8 are the initial angle and the initial phase, respectively. The decay time ~- and frequency to are given by 21 r= --,
w= ~/(K/I)
- (rl/2I)
z .
(3)
The time dependence of the oscillating angle O(t) at each temperature and field was fitted using a leastsquares program by Eq. (2) to obtain experimental values for ~" and to. r/sampLe was obtained by subtracting 1 / r in zero field from that in magnetic fields. Three kinds of experiment were done: (1) the sample was cooled down in zero field through Tc to 4.2 K (ZFC), then the magnetic field was applied perpendicularly to the ab-plane; (2) the magnetic field was applied perpendicularly to the ab-plane above 100 K and then the sample was cooled down in field through Tc to 4.2 K (FC); (3) the sample was cooled down in zero field, and then the magnetic field was applied parallel to the ab-plane. The initial
3
20
18
16 ~-14
~'2
0
20
40
T(K)
60
8090
Fig, 2. Temperature and field dependences of T / s a m p l e in the case of ZFC and H l ab-plane. (a) 3D plotting. (b) Contour mapping.
H. Niimi et a l . / Physica C 263 (1996) 412-415
414
Fig. l(a) is the case of zero-field cooling (ZFC) and the field direction perpendicular to the ab-plane ( H _Lab-plane). Fig. l(b) is the case of field cooling (FC) and H _Lab-plane. Fig. l(c) is the case of ZFC and the field direction parallel to the ab-plane (H II ab-plane). In the case of ZFC, H_Lab-plane (Fig. l(a)), ksample under field has a negative sign and its magnitude increases abruptly below 20 K with decreasing temperature. The result is consistent with the increase of the magnetic torque coefficient reported previously [1]. On the other hand, in the case of FC, H_l_ab-plane (Fig. l(b)), k~mpLe is positive. This means that the flux pinning makes the field direction perpendicular to the ab-plane stable. In the case of ZFC, H II ab-plane (Fig. l(c)), ksample begins to increase slightly below Tc, increases rapidly at around 40 K, and then remains steady below 20 K. At fields H = 2, t kOe, a hump indicated by an arrow is found, but its origin is not clear at the present time. At 4.2 K, ksample is proportional to H 2.
2 5
(1~) z 1.5
0.5 0
0
20
40
60
80 90
T (K) Fig. 4. Temperature and field dependences of rkarnpje in the case of ZFC and H IIab-plane. (a) 3D plotting. (b) Contour mapping.
40 ,--v.36 32 28 24 20-16 ~-- 12
6
•
2 0
io 0
20
40
T(K)
60
8090
Fig. 3. Temperatureand field dependences of "r/sample in the case of FC and H _Lab-plane. (a) 3D plotting. (b) Contour mapping.
An oscillation damping was observed in the irreversible region, suggesting energy dissipation due to the depinning of the flux lines. The temperature and field dependences of the damping coefficient ~samp~e are obtained as in Figs. 2(a) and (b) for the case of ZFC, H _1_ab-plane, Figs. 3(a) and (b) for the case of FC, H _1_ab-plane, and Figs. 4(a) and (b) for the case of ZFC, H II ab-plane. The solid line in Figs. 2(b) and 3(b) for H _1_ab-plane is the irreversibility line determined by the magnetic torque measurements [2]. In the case of H _Lab-plane, the value of ~sample takes finite positive values below the irreversibility field and shows peaks with some structure inside the irreversibility line in the H-T plane, as shown in Figs. 2 and 3. On the field scale, the damping constant increased abruptly around 1 kOe with increasing field in the range from 4.2 to 30 K. This abrupt increase of the energy dissipation suggests the 3 D - 2 D crossover of vortex pancakes [3].
H. Niimi et al./ Physica C 263 (1996) 412-415
(b)
(a)
/
Cu02 HL~ ~
H
y.~
415
displacement of vortex pancakes in the 2D superconducting plane with less energy.
/
4. Summary
~jC u 0 ill
[
]
'i" .i I
z
3
i
/ /"
Fig. 5. A model to explain the anisotropy of %topic as described in the text.
In the case of H II ab-plane (Fig. 4), the damping constant increases below Tc, shows a broad peak and decreases to zero with decreasing temperature, while it remains finite at 4.2 K in the case H _1_ab-plane. The disappearance of 7ilsample at 4.2 K shows that vortices are locked in between the CuO 2 planes. The damping constant T~samp¿e for H II ab-plane is 10 times larger than that for H _1_ab-plane. The anisotropy is explained by assuming the model shown in Fig. 5. In the case of H II ab-plane the damping is caused by the creation and annihilation of vortex pancakes with large energy, while in the case of H _1_ab-plane, the energy dissipation is caused by
The vortex state of a Bi2Sr2CaCu2Os+~(Bi2212) single crystal was investigated by free torsional oscillation in magnetic field. The temperature and field dependences of the torque coefficient ksample and the damping constant '0sample w e r e obtained. An abrupt increase of the energy dissipation T/sample w a s found around 1 kOe in the temperature range from 4.2 to 30 K and it was attributed to the 3D-2D crossover of vortex pancakes. A large anisotropy of the damping constant was observed and the mechanism was discussed by a model which takes into account the energy differences between the excitation and the displacement of vortex pancakes.
References [1] H. Niimi, K. Inoue, S. Kawamata and K. Okuda, Physica C 235-240 (1994) 2637. [2] S. Kawamata, N. Itoh, K. Okuda, T. Mochiku and K. Kadowaki, Physica C 195 (1992) 103. [3] R. Cubitt, E.M. Forgan, G. Yang, S.L. Lee, D. McK. Paul, H.A. Mook, M. Yethiraj, P.H. Kes, T.W. Li, A.A. Menovsky, Z. Tamawski and K. Mortensen, Nature 365 (1993) 407.
Physica C 263 (1996) 412-415
Study of magnetic flux in a Bi2212 single crystal by torsional oscillation H. Niimi, K. Inoue, S. Kawamata, K. Okuda * Department of Physics and Electronics, Universityof Osaka Prefecture, Sakai, Osaka 593, Japan
Abstract The vortex state of a Bi2Sr2CaCu2Os+~(Bi2212) single crystal was investigated by measuring the free torsional oscillation in magnetic field with special attention to the energy dissipation. The decay time and the oscillation period were measured at temperatures between 4.2 and 100 K under various fields up to 9 kOe. The temperature and field dependences of the energy dissipation due to flux depinning were obtained for the irreversible region. An abrupt increase of the energy dissipation was found around 1 kOe, suggesting the dimensional crossover from the 3D vortex solid to 2D pancakes with increasing field. A large damping anisotropy was also found and explained by a model of two-dimensional vortex pancakes.
1. Introduction The magnetic properties of Bi2212 are characterized by the large anisotropy originating from the layered structure. Various experiments and theoretical works have been done paying attention to the melting of the vortex lattice or the vortex glass, the anomalous depinning and the dimensional crossover of vortex pancakes in the compound. To clarify these problems, we applied torsional oscillation measurements with low frequency below 1 Hz, which is an appropriate method for detecting the energy dissipation accompanied by the change of vortex state, and the results are reported, here.
2. Experimental A free torsional oscillator was made by hanging an inertia disk of a brass cylinder and a quartz rod
* Corresponding author. Fax: 81 722 59 3340; e-mail: [email protected].
from a tungsten suspension wire. Angular oscillation was detected optically. The rotational oscillation axis was perpendicular to the applied field. The oscillation period was about 3 s in zero field. The equation of motion of the torsional oscillator is given as d20
I -7
dO
+r0=0,
77 = "170 -t'- "l/sample,
(1)
K = k 0 + ksample ,
where 1, 0, t, r/0, 'r/sample, k 0 and ksample represent the moment of the inertia of the oscillating system (1 = 5.14 g cmZ), rotational angle, time, the damping constants by the oscillator apparatus, that by the sample itself under magnetic field, the torque coefficient by the restoring force of the suspension wire (k 0 = 0.412 dyn c m / d e g ) and that generated by the sample under magnetic field, respectively. Below Tc and under magnetic fields, the oscillations were damped by energy dissipation proportional to r/sa~pJe. The solution of Eq. (1) becomes 0 = 00 e x p ( - t / r )
0 9 2 1 - 4 5 3 4 / 9 6 / $ 1 5 . 0 0 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 9 2 1 - 4 5 3 4 ( 9 5 ) 0 0 7 8 8 l
cos( tot + tS),
(2)
413
H. Niimi et aL /Physica C 263 (1996) 412-415 10OO
~
~
L
'
¢
.
''~
•
0
•
--1000
tx Z~
±
j
-4000 2OO
~
0
0
0
0
H A_ a b - p l a n e
~. -2000 -3000
declined angle of the crystal axis from the direction of the magnetic field was less than 2 deg. The decay time and the oscillation period were measured at temperatures between 4.2 and 100 K under various fields up to 9 kOe. The Bi2212 single crystals were prepared by the traveling solvent floating zone method. Three sampies with suitable size were used in the measurements. The samples were in the form of thin flat plates of dimensions: (a) 2.5 × 1.3 x 0.02, (b) 1 × 0.5 × 0.02, (c) 0.5 × 0.5 × 0.003 mm 3. These samples were annealed at 618°C for 70 h to homogenize the oxygen distribution in the compound. The superconducting transition temperature and the transition width were Tc = 87.4 K and ATc = 0.8 K.
(a) r
0
i
,
i
n
t~ • 0 @ 0 @
H H H }1 H H
a
I
I
(b)
= = = = =
(ZFC) 3 kO¢ 2 kOe 1 kOe 0.75 kOe 0.5 kOc 0.25 kOc *
I
H ± ab-plane
150
@
H
•
. = ,koo
a~
,~
100
•
= 8 kOe H = 6 kOc
kOc H = 1 kOe H = 0.5 kOe I t = O.25 k O e
0 0 •
50
(FC)
0
A i
i
q
I
I
I
i
I
i
(ZFC)
H//ab-plane
4000
%
3000
O
H = 0.5
kOe
3. Results and discussion
2000 1000
Fig. 1 indicates the temperature dependence of the torque coefficient ksample in several magnetic fields.
0
J -1000
2
I
'
O
i 40 Temp.
,
L 60 OK)
,
810
1OO
Fig. 1. Temperature dependence of torque coefficient ksample in several magnetic fields. (a) ZFC, H l ab-plane. (b) FC, H ± abplane. (c) ZFC, H II ab-plane.
(a
3 where 00 and 8 are the initial angle and the initial phase, respectively. The decay time ~- and frequency to are given by 21 r= --,
w= ~/(K/I)
- (rl/2I)
z .
(3)
The time dependence of the oscillating angle O(t) at each temperature and field was fitted using a leastsquares program by Eq. (2) to obtain experimental values for ~" and to. r/sampLe was obtained by subtracting 1 / r in zero field from that in magnetic fields. Three kinds of experiment were done: (1) the sample was cooled down in zero field through Tc to 4.2 K (ZFC), then the magnetic field was applied perpendicularly to the ab-plane; (2) the magnetic field was applied perpendicularly to the ab-plane above 100 K and then the sample was cooled down in field through Tc to 4.2 K (FC); (3) the sample was cooled down in zero field, and then the magnetic field was applied parallel to the ab-plane. The initial
3
20
18
16 ~-14
~'2
0
20
40
T(K)
60
8090
Fig, 2. Temperature and field dependences of T / s a m p l e in the case of ZFC and H l ab-plane. (a) 3D plotting. (b) Contour mapping.
H. Niimi et a l . / Physica C 263 (1996) 412-415
414
Fig. l(a) is the case of zero-field cooling (ZFC) and the field direction perpendicular to the ab-plane ( H _Lab-plane). Fig. l(b) is the case of field cooling (FC) and H _Lab-plane. Fig. l(c) is the case of ZFC and the field direction parallel to the ab-plane (H II ab-plane). In the case of ZFC, H_Lab-plane (Fig. l(a)), ksample under field has a negative sign and its magnitude increases abruptly below 20 K with decreasing temperature. The result is consistent with the increase of the magnetic torque coefficient reported previously [1]. On the other hand, in the case of FC, H_l_ab-plane (Fig. l(b)), k~mpLe is positive. This means that the flux pinning makes the field direction perpendicular to the ab-plane stable. In the case of ZFC, H II ab-plane (Fig. l(c)), ksample begins to increase slightly below Tc, increases rapidly at around 40 K, and then remains steady below 20 K. At fields H = 2, t kOe, a hump indicated by an arrow is found, but its origin is not clear at the present time. At 4.2 K, ksample is proportional to H 2.
2 5
(1~) z 1.5
0.5 0
0
20
40
60
80 90
T (K) Fig. 4. Temperature and field dependences of rkarnpje in the case of ZFC and H IIab-plane. (a) 3D plotting. (b) Contour mapping.
40 ,--v.36 32 28 24 20-16 ~-- 12
6
•
2 0
io 0
20
40
T(K)
60
8090
Fig. 3. Temperatureand field dependences of "r/sample in the case of FC and H _Lab-plane. (a) 3D plotting. (b) Contour mapping.
An oscillation damping was observed in the irreversible region, suggesting energy dissipation due to the depinning of the flux lines. The temperature and field dependences of the damping coefficient ~samp~e are obtained as in Figs. 2(a) and (b) for the case of ZFC, H _1_ab-plane, Figs. 3(a) and (b) for the case of FC, H _1_ab-plane, and Figs. 4(a) and (b) for the case of ZFC, H II ab-plane. The solid line in Figs. 2(b) and 3(b) for H _1_ab-plane is the irreversibility line determined by the magnetic torque measurements [2]. In the case of H _Lab-plane, the value of ~sample takes finite positive values below the irreversibility field and shows peaks with some structure inside the irreversibility line in the H-T plane, as shown in Figs. 2 and 3. On the field scale, the damping constant increased abruptly around 1 kOe with increasing field in the range from 4.2 to 30 K. This abrupt increase of the energy dissipation suggests the 3 D - 2 D crossover of vortex pancakes [3].
H. Niimi et al./ Physica C 263 (1996) 412-415
(b)
(a)
/
Cu02 HL~ ~
H
y.~
415
displacement of vortex pancakes in the 2D superconducting plane with less energy.
/
4. Summary
~jC u 0 ill
[
]
'i" .i I
z
3
i
/ /"
Fig. 5. A model to explain the anisotropy of %topic as described in the text.
In the case of H II ab-plane (Fig. 4), the damping constant increases below Tc, shows a broad peak and decreases to zero with decreasing temperature, while it remains finite at 4.2 K in the case H _1_ab-plane. The disappearance of 7ilsample at 4.2 K shows that vortices are locked in between the CuO 2 planes. The damping constant T~samp¿e for H II ab-plane is 10 times larger than that for H _1_ab-plane. The anisotropy is explained by assuming the model shown in Fig. 5. In the case of H II ab-plane the damping is caused by the creation and annihilation of vortex pancakes with large energy, while in the case of H _1_ab-plane, the energy dissipation is caused by
The vortex state of a Bi2Sr2CaCu2Os+~(Bi2212) single crystal was investigated by free torsional oscillation in magnetic field. The temperature and field dependences of the torque coefficient ksample and the damping constant '0sample w e r e obtained. An abrupt increase of the energy dissipation T/sample w a s found around 1 kOe in the temperature range from 4.2 to 30 K and it was attributed to the 3D-2D crossover of vortex pancakes. A large anisotropy of the damping constant was observed and the mechanism was discussed by a model which takes into account the energy differences between the excitation and the displacement of vortex pancakes.
References [1] H. Niimi, K. Inoue, S. Kawamata and K. Okuda, Physica C 235-240 (1994) 2637. [2] S. Kawamata, N. Itoh, K. Okuda, T. Mochiku and K. Kadowaki, Physica C 195 (1992) 103. [3] R. Cubitt, E.M. Forgan, G. Yang, S.L. Lee, D. McK. Paul, H.A. Mook, M. Yethiraj, P.H. Kes, T.W. Li, A.A. Menovsky, Z. Tamawski and K. Mortensen, Nature 365 (1993) 407.