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On the vortex dynamics in Bi(2212)
imiM Journal of Magnetism and Magnetic Materials 104-107 (1992) 537-538 North-Holland
On the vortex dynamics in Bi(2212) M. Ziese, J. K6tzler, M. Pieper, A. Spirgatis and R. Behr lnstitut fiir Angewandte Physik, Universit&'tHamburg, W-2000Hamburg 36, Germany We report on a comparative study of the vortex dynamics in crystalline and melt processed ceramic Bi2SrzCaCu20 s by ac susceptibility, which is described within the model of Thermally Activated Flux diffusion (TAFF). In the limit of small current densities the resulting activation energy U is independent of J and the temperature and field dependencies of U show evidence for diffusion of two-dimensional vortex lattice defects. Many investigations on the high-Tc superconductors are devoted to the so-called irreversibility line in the H - T plane which has been related to various processes like depinning [1,2], melting [3] or glass formation of vortices [4]. We will show that the irreversibility line of the present materials can be explained by conventional flux creep within an imperfect two-dimensional (2D) vortex lattice [2]. We measured the ac susceptibility of a Bi(2212) ceramic and a Bi(2212) crystal by a well compensated mutual inductance and phase sensitive detection. For driving field amplitudes h < 0 . 1 0 e the susceptibility proved to be independent on h. Following Malozemoff et al. [5] we identify the temperature T i where the absorption exhibits a pronounced maximum, with the onset of irreversibility. As a function of frequency T i obeys Arrhenius' law: u = u o exp
kTi
,
(1)
as shown for the ceramic in fig. 1. As central results, fig. 2 shows the evaluated irreversibility lines Ti(H) at v = 115 Hz of the ceramic and the crystal. We discuss these experimental findings within the model of thermally activated flux creep over free barriers U(T, H, J). The linear behavior of the susceptibility for small h (corresponding to small J ) and the substantial frequency dependence in this regime (fig. 1) suggest that U is independent of the current density for J ~ 0 and that in this limit the vortex motion is diffusive ( T A F F ) [1,2]. This excludes the collective motion of flux bundles characterized by the scaling form U c t J y [6]. The activation energies obtained from Arrhenius' law (eq. (1)) have been fitted to the widely used power laws, T -
n H ]
'
1. In order to illustrate the validity of the power laws in H we displayed the field dependence of U at zero temperature for the crystal and the ceramic in fig. 3. Due to the large anisotropy of the electronic properties of the Bi(2212) material, the vortices may be pictured as 2D vortex discs located in the CuO-planes rather than homogenous lines extending parallel to the c-direction. T h e n the activation energy U(J ~ 0) is related to the pinning of imperfections of the 2D vortex lattice by frozen disorder in the crystal lattice [2,6]. Assuming point defects, one expects for the activation energy the form
where a 0 = ( ~ o / H ) 1/2 denotes the mean distance between the vortices, Uv = ~0/2/-/~(r) ~ (r) ~il(r) the energy of the superconducting correlation volume and ~ ± and ~ II the correlation lengths within and perpendicular to the CuO-planes. On the other hand, for edge dislocation pairs we take following ref. [2]:
Ud(T, H ) = Uv(T ) ( a ° ] 1/2.
Inserting for Bi(2212) H e ( T ) = 6 ( 1 - T / T c) kOe, 2.5
. . . . . . . . . . . . . . . H (k0e)
:
h = 50 m0e
~
45
Tc -- 90.5 K
Z.0
1.5
---~___.
4
(2)
where we normalized the field H rather arbitrarily to H 0 = 1 0 e to define the energy parameter U0 being discussed below. The solid lines in fig. 2 show that the irreversibility lines Ti(H) can be well described by eq. (2). The results for U0, v 0, n and m are listed in table
(3b)
0.8 1.0
.
.
0.Z . .
.
.
.
.
.
.
.
.
.
.
.
/) ( H z ) Fig. 1. Arrhenius plot of the absorption maximum, X"(Ti, H) in different applied fields for the ceramic Bi(2212) sample.
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
M. Ziese et al. / On the rortex dynamics in Bi(2212)
538 100
,
i
%
,
,
,
,
,
1 O0
~.~
Ceramic
~
V = lls H~
: N
"~ -~ ~
Crystal
:
~
To= 80 K *
Crystal I IC : \ I,/= I15 Hz
0.01
b=
\" l0
I
I
I
I
50 T (K)
30
I
70
~ ~ It
0.45
~ -0.18
i
I
90 102
Fig. 2. lrreversibility fines for ceramic and crystalline Bi(2212); solid curves represent fits to eq. (2) as described in the text. ~,± = 40(1 - T / T c) I / 2 ,~ and ~ , = 2 . 1 ( 1 A [7] we obtain with H 0 = 1 0 e :
(4a)
__
T
]3/4
103
104 tt [ O e ] t°s
Fig. 3. Field dependence of the activation energy at T = 0 determined from eqs. (l) and (2) for ceramic and crystal.
T / T c) I/2
T
eV.
(4b)
]
C o m p a r i n g the e x p e r i m e n t a l results on the ceramic (table 1) to the prediction of pinning of vortex point defects eq. (4a), we find substantial a g r e e m e n t in the m a g n i t u d e of the energy p a r a m e t e r U 0 as well as in the exponents m and n describing the field and t e m p e r a ture effects on U. In the crystal, the w e a k e r irreversibility characterized by U 0 = 0.34 eV and the field e x p o n e n t m are close to the predictions for the dislocation m e d i a t e d irreversibility (eq. 4b)) b u t not so the t e m p e r a t u r e e x p o n e n t n. A t p r e s e n t we have no explanation for this discrepancy, however, we emphasizc that the e x p o n e n t s n and m were strongly correlated in our fit, so that a slight variation in m causes large changes in n and additional investigations taking also into account the shape of the absorption a b o u t T~(H) are indicated. Moreover, at the low t e m p e r a t u r e s of interest for the crystal, one may p e r h a p s also question the validity of the t e m p e r a t u r e b e h a v i o r supposed in eq. (4b). W e presently d e t e r m i n e the irreversibility on Table 1 Experimental parameters of the Arrhenius' law (eq. (1)) and the activation energy U(T, H) (eq. (2)) for ceramic and crystal
Ceramic Crystal IIc
~
0.I Oe I
i0
•
To= 9O.5 K
m
n
UU(eV)
vl) (Hz)
0.45 + 0.05 0.18_+0.05
1.0 + 0.2 0.2_+0.2
8.65 0.20
7.4 × 106 1.2×10 l°
the crystal with H • c to chcck the p r o p o s e d dislocation m e c h a n i s m in more detail. Figures 2 a n d 3 also illustrate that a b o u t T = 40 K, c o r r e s p o n d i n g to H = 0.5 kOe, the irrcversibility line of the crystal exhibits a crossover to some diffcrent behavior. W c tentatively ascribe this effect to a dimensional crossover from vortex discs to vortex lines, which was estimated by Kes for Bi(2212) to occur n e a r 3 kOc [2] and will be also subject of futurc work. In conclusion, we have shown that the vortcx dynamics in Bi(2212) can be explained by considering diffusive motion of vortex defects in the 2D lattice. In the case of the ceramic, our results reveal r a t h e r strong evidence for pinning of point defects in the vortex lattice, while in the crystal the p r e s e n c e of edge dislocation pairs appears to be the most p r o b a b l e m e c h a nism. Obviously, the different vortex defects arisc from the different p r e p a r a t i o n techniques for the ccramic [8] and the crystal [9]. W e are i n d e b t e d to K. Kowaleswki and W. Al3mus ( F r a n k f u r t a.M.) and J. Bock (Hiirth) providing the crystal a n d the melt processed ceramic, respectively.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
P.H. Kes et al., Supercond. Sci. Technol. 1 (1989) 242. C.3. van der Beek and P.H. Kes, preprint. D.R. Nelson et al., Phys. Rev. B 39 (1989) 9174. M.P.A. Fisher, Phys. Rev. Lett. 62 (1989) 1415. A.P. Malozemoff, Phys. Rev. B 38 (1988) 7203. M.V. Feigel'man et al., Physica C 167 (1990) 177. S. Hayashi et al., Physica C 174 (1991) 329. J. Bock and B. Preisler, ICMC 90, 9-11 May 199(/. W. Assmus and J. Kowalewski, Eur. J. Solid State and Inorg. Chem. in press (1990).
On the vortex dynamics in Bi(2212) M. Ziese, J. K6tzler, M. Pieper, A. Spirgatis and R. Behr lnstitut fiir Angewandte Physik, Universit&'tHamburg, W-2000Hamburg 36, Germany We report on a comparative study of the vortex dynamics in crystalline and melt processed ceramic Bi2SrzCaCu20 s by ac susceptibility, which is described within the model of Thermally Activated Flux diffusion (TAFF). In the limit of small current densities the resulting activation energy U is independent of J and the temperature and field dependencies of U show evidence for diffusion of two-dimensional vortex lattice defects. Many investigations on the high-Tc superconductors are devoted to the so-called irreversibility line in the H - T plane which has been related to various processes like depinning [1,2], melting [3] or glass formation of vortices [4]. We will show that the irreversibility line of the present materials can be explained by conventional flux creep within an imperfect two-dimensional (2D) vortex lattice [2]. We measured the ac susceptibility of a Bi(2212) ceramic and a Bi(2212) crystal by a well compensated mutual inductance and phase sensitive detection. For driving field amplitudes h < 0 . 1 0 e the susceptibility proved to be independent on h. Following Malozemoff et al. [5] we identify the temperature T i where the absorption exhibits a pronounced maximum, with the onset of irreversibility. As a function of frequency T i obeys Arrhenius' law: u = u o exp
kTi
,
(1)
as shown for the ceramic in fig. 1. As central results, fig. 2 shows the evaluated irreversibility lines Ti(H) at v = 115 Hz of the ceramic and the crystal. We discuss these experimental findings within the model of thermally activated flux creep over free barriers U(T, H, J). The linear behavior of the susceptibility for small h (corresponding to small J ) and the substantial frequency dependence in this regime (fig. 1) suggest that U is independent of the current density for J ~ 0 and that in this limit the vortex motion is diffusive ( T A F F ) [1,2]. This excludes the collective motion of flux bundles characterized by the scaling form U c t J y [6]. The activation energies obtained from Arrhenius' law (eq. (1)) have been fitted to the widely used power laws, T -
n H ]
'
1. In order to illustrate the validity of the power laws in H we displayed the field dependence of U at zero temperature for the crystal and the ceramic in fig. 3. Due to the large anisotropy of the electronic properties of the Bi(2212) material, the vortices may be pictured as 2D vortex discs located in the CuO-planes rather than homogenous lines extending parallel to the c-direction. T h e n the activation energy U(J ~ 0) is related to the pinning of imperfections of the 2D vortex lattice by frozen disorder in the crystal lattice [2,6]. Assuming point defects, one expects for the activation energy the form
where a 0 = ( ~ o / H ) 1/2 denotes the mean distance between the vortices, Uv = ~0/2/-/~(r) ~ (r) ~il(r) the energy of the superconducting correlation volume and ~ ± and ~ II the correlation lengths within and perpendicular to the CuO-planes. On the other hand, for edge dislocation pairs we take following ref. [2]:
Ud(T, H ) = Uv(T ) ( a ° ] 1/2.
Inserting for Bi(2212) H e ( T ) = 6 ( 1 - T / T c) kOe, 2.5
. . . . . . . . . . . . . . . H (k0e)
:
h = 50 m0e
~
45
Tc -- 90.5 K
Z.0
1.5
---~___.
4
(2)
where we normalized the field H rather arbitrarily to H 0 = 1 0 e to define the energy parameter U0 being discussed below. The solid lines in fig. 2 show that the irreversibility lines Ti(H) can be well described by eq. (2). The results for U0, v 0, n and m are listed in table
(3b)
0.8 1.0
.
.
0.Z . .
.
.
.
.
.
.
.
.
.
.
.
/) ( H z ) Fig. 1. Arrhenius plot of the absorption maximum, X"(Ti, H) in different applied fields for the ceramic Bi(2212) sample.
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
M. Ziese et al. / On the rortex dynamics in Bi(2212)
538 100
,
i
%
,
,
,
,
,
1 O0
~.~
Ceramic
~
V = lls H~
: N
"~ -~ ~
Crystal
:
~
To= 80 K *
Crystal I IC : \ I,/= I15 Hz
0.01
b=
\" l0
I
I
I
I
50 T (K)
30
I
70
~ ~ It
0.45
~ -0.18
i
I
90 102
Fig. 2. lrreversibility fines for ceramic and crystalline Bi(2212); solid curves represent fits to eq. (2) as described in the text. ~,± = 40(1 - T / T c) I / 2 ,~ and ~ , = 2 . 1 ( 1 A [7] we obtain with H 0 = 1 0 e :
(4a)
__
T
]3/4
103
104 tt [ O e ] t°s
Fig. 3. Field dependence of the activation energy at T = 0 determined from eqs. (l) and (2) for ceramic and crystal.
T / T c) I/2
T
eV.
(4b)
]
C o m p a r i n g the e x p e r i m e n t a l results on the ceramic (table 1) to the prediction of pinning of vortex point defects eq. (4a), we find substantial a g r e e m e n t in the m a g n i t u d e of the energy p a r a m e t e r U 0 as well as in the exponents m and n describing the field and t e m p e r a ture effects on U. In the crystal, the w e a k e r irreversibility characterized by U 0 = 0.34 eV and the field e x p o n e n t m are close to the predictions for the dislocation m e d i a t e d irreversibility (eq. 4b)) b u t not so the t e m p e r a t u r e e x p o n e n t n. A t p r e s e n t we have no explanation for this discrepancy, however, we emphasizc that the e x p o n e n t s n and m were strongly correlated in our fit, so that a slight variation in m causes large changes in n and additional investigations taking also into account the shape of the absorption a b o u t T~(H) are indicated. Moreover, at the low t e m p e r a t u r e s of interest for the crystal, one may p e r h a p s also question the validity of the t e m p e r a t u r e b e h a v i o r supposed in eq. (4b). W e presently d e t e r m i n e the irreversibility on Table 1 Experimental parameters of the Arrhenius' law (eq. (1)) and the activation energy U(T, H) (eq. (2)) for ceramic and crystal
Ceramic Crystal IIc
~
0.I Oe I
i0
•
To= 9O.5 K
m
n
UU(eV)
vl) (Hz)
0.45 + 0.05 0.18_+0.05
1.0 + 0.2 0.2_+0.2
8.65 0.20
7.4 × 106 1.2×10 l°
the crystal with H • c to chcck the p r o p o s e d dislocation m e c h a n i s m in more detail. Figures 2 a n d 3 also illustrate that a b o u t T = 40 K, c o r r e s p o n d i n g to H = 0.5 kOe, the irrcversibility line of the crystal exhibits a crossover to some diffcrent behavior. W c tentatively ascribe this effect to a dimensional crossover from vortex discs to vortex lines, which was estimated by Kes for Bi(2212) to occur n e a r 3 kOc [2] and will be also subject of futurc work. In conclusion, we have shown that the vortcx dynamics in Bi(2212) can be explained by considering diffusive motion of vortex defects in the 2D lattice. In the case of the ceramic, our results reveal r a t h e r strong evidence for pinning of point defects in the vortex lattice, while in the crystal the p r e s e n c e of edge dislocation pairs appears to be the most p r o b a b l e m e c h a nism. Obviously, the different vortex defects arisc from the different p r e p a r a t i o n techniques for the ccramic [8] and the crystal [9]. W e are i n d e b t e d to K. Kowaleswki and W. Al3mus ( F r a n k f u r t a.M.) and J. Bock (Hiirth) providing the crystal a n d the melt processed ceramic, respectively.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
P.H. Kes et al., Supercond. Sci. Technol. 1 (1989) 242. C.3. van der Beek and P.H. Kes, preprint. D.R. Nelson et al., Phys. Rev. B 39 (1989) 9174. M.P.A. Fisher, Phys. Rev. Lett. 62 (1989) 1415. A.P. Malozemoff, Phys. Rev. B 38 (1988) 7203. M.V. Feigel'man et al., Physica C 167 (1990) 177. S. Hayashi et al., Physica C 174 (1991) 329. J. Bock and B. Preisler, ICMC 90, 9-11 May 199(/. W. Assmus and J. Kowalewski, Eur. J. Solid State and Inorg. Chem. in press (1990).