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Broadened resistive transition under magnetic field and its mechanism in single crystalline (La,Sr)2CuO4
Physica C 162-164 (1989) 1017-1018 North-Holland
Broadened Resistive Transition under Magnetic Field and and Its Mechanism in Single Crystalline(La, Sr)2CuO4 K. Kitazawa*, S. Kamb¢*, M. Naito**, I. Tanaka*** and H. Kojima*** *DepaL~:,ent of Industrial Chemistry, University of Tokyo, 7-3-1 Hongo, Bunkyo-lm, Tokyo 113, Japan **Basic Research Laboratories, NTr, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180, Japan ***Institute of Inorganic Synthesis, Yamanashi University, 7 Miyamae, Kofu 400, Japan A universal scaling (AT-H2/3) is observed in the resistive transition of an LSCO single crystal under magnetic fields. It holds for the whole temperture range of the transition and for any configuration of the magnetic field and the current. We propose a "giant fluctuation" model to explain the experimental results. It has been found that the resistive transition in cuprate superconductors is broadened remarkably when the magnetic field is applied along the caxis. There have been several mechanisms advocated so far in order to explain the fieldinduced broadening phenomenon. It includes superconducting glassy state, 1 giant flux creep or flux flow, 2 Kosterlitz-Thouless transition3 and superconducting fluctuation. 4 The p r e s e n t authors, employing a special single crystal of (La0.93Sr0.07)2CuO4 that has a large c-axis length of ca. 6mm, have shown that the relative orientation of the magnetic field (H) versus the current (I) has little effect on the broadening. Rather the phenomenon only depends on the relative orientation of H versus the c-axis : large for H//c and small for H_Lc.5 This experimental result disproves the first three models, in which the relative H-I orientation is vitally important because all of them essentially assume the net transverse motion of flux lines across the current to give a finite resistance. Hence the superconducting fluctuation seems to be the most promising model at the present stage. This concept, however, has not been fully developed so that it can be c o m p a r e d quantitatively with the experimental results over 0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
the whole range of the transition region. So far only the higher temperature side of the resistivity(p)-T curve in the transition region has been discussed. Therefore here we have made a quantitative analysis on the experimental p-T-H relationship to establish the functional form of the
broadening. We derme the shift in the temperature under the magnetic field as a measure of the broadening : AT(p,H)=T(p,0)-T(p,H). In a typical metallic superconductor, a linear scaling law AT(p,H)-H holds. Tinkhara has recently shown that Iye et ars results6 of the p-T-H relationship on BYCO single crystals for I-I//c and LLc configuration follows the scaling law AT(p,H)-H2/3 and discuss this scaling law based on the flux creep model.7 We have observed that the AT-H2/3 scaling law holds for any configuration: irrespective of I-I//I or H_LI, and H//c or H_Lc. Figure 1 shows the typical example. It is important that a single parameter, AT3/2/I-I, scales the whole region of the transition for any configuration of H and I. It suggests that a single mechanism should explain the whole range of the p-T transition behavior.8 Then the whole range is the manifestation of the fluctuation. In order to stress that this is different but more serious than the conventionally defined
K. Kitazawa et al.
1018 r-I°
Broadened resistive transition under magnetic field I
" "°"~o.%~
O. 08 i
H,c
e.. or,,
,c
%
4 I
0.06~
z!,: 5T
,
A , : 4"[
t
I
0:3T 0 : 2"I"
J
=
-
C
r..
O. 04~!
g
r
I I
]
w~
O. 02~-
L (;.
O0 L
-
.0
-0.5
0.0
LogAT,Z'
0.5
'.0
:,.5
I. ~ H ( ' ' . :
FIGURE 1 Resistive transition as a function of the scaling variable AT3/2/H for H//c and I//c.
fluctuation, the term "giant fluctuation" may be more appropriate. The S-shaped feature of the resistive transition curve even suggests that there may not be occuring even any phase transition in the rigorous sense. The A T - H 2/3 scaling law is qualitatively understood as follows in the framework of the superconducting fluctuation theory. The energy scale AE relevant to the statistical physics of superconductong fluctuations is given b y Hc2.Vc/Sx where Hc is the thermodynamic critical field and Vc is the coherence volume. The correlation radius of the fluctuation is restricted to the radius of the Landau orbit rL(-(C0/xH)l/2) and hence the fluctuation grows only along the direction of the magnetic field.9 Therefore the coherence volume Vc in the magnetic field is given by rL2~C (H//c) and rL2~a,b (H3_c). Then A~-AT3/2/H is obtained. Because the coherence length is the shortest along the c-axis in the cuprates, we expect the fluctuation to be the most enhanced when the field is applied along the c-axis in accordance with the actual observations. Furthermore comparing different cuprates, the effect of the fluctuation is
then expected to become greater as the c-axis coherence length shortens, which is again in accord with the experimentally o b s e r v e d increasing order of the broadening width in BYCO, LSCO, BSCCO. Since the fluctuation is a pure thermodynamical state, it should not be dependent upon the microstructure in principle. This contrasts with the expectation from the flux creep model. From the practical point of view, this is unfortunate because the zero resistivity Tc should be remarkably lowered under the magnetic field, e.g., by as much as 50K or more for BSCCO (Tc=80K), 20K for LSCO (38.5K) and 10K for BYCO (90K) under the field of 5T in spite of their extremely high He2 values usually reported on the 50%-transition criterion.
REFERENCES 1. K.A.Muller, M.Tak~L~htgeand J.G.Bedonorz, Phys. Rev. Lett. 58 (1987) 1143. 2. Y.Yeshrun and A.P.Malozemoff,Phys. Rev. Lett. 60 (1988) 2202. 3. &Martin, A.T.Fioty, R.M.Fleming, G.P.Epinosa and A.S.Cooper, Phys. Rev. Lettt. 62 (1989) 677. 4. R.Ikeda, T.Ohmi and T.Tsuneto, J. Phys. Soc. Jim. 58 (1989) 1377. 5. K.Kitazawa, S.Kambe, M.Naito, I.Tanakaand H . K o j i m a , J p n . J. Appl. Phys. 26 (1989) L556. . Y.Iye, T.Tamegai, H.Takeya and H.Takei, Jpn. J. Appl. Phys. 26 (1987) L1057. .
M.Tinkham, Phys. Rev. Lett. 61 (1988) 1658.
8. In the resistivity tail region where the supercond-
ucting fluctuation becomes slow enough to be trapped by impurities, the supercondting fluctuation model may be equivalent to that of the flux creep model. 9. P.A.Leeand S.R.Shenoy,Phys.Rev.Lett.28 (1972) 1025.
Broadened Resistive Transition under Magnetic Field and and Its Mechanism in Single Crystalline(La, Sr)2CuO4 K. Kitazawa*, S. Kamb¢*, M. Naito**, I. Tanaka*** and H. Kojima*** *DepaL~:,ent of Industrial Chemistry, University of Tokyo, 7-3-1 Hongo, Bunkyo-lm, Tokyo 113, Japan **Basic Research Laboratories, NTr, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180, Japan ***Institute of Inorganic Synthesis, Yamanashi University, 7 Miyamae, Kofu 400, Japan A universal scaling (AT-H2/3) is observed in the resistive transition of an LSCO single crystal under magnetic fields. It holds for the whole temperture range of the transition and for any configuration of the magnetic field and the current. We propose a "giant fluctuation" model to explain the experimental results. It has been found that the resistive transition in cuprate superconductors is broadened remarkably when the magnetic field is applied along the caxis. There have been several mechanisms advocated so far in order to explain the fieldinduced broadening phenomenon. It includes superconducting glassy state, 1 giant flux creep or flux flow, 2 Kosterlitz-Thouless transition3 and superconducting fluctuation. 4 The p r e s e n t authors, employing a special single crystal of (La0.93Sr0.07)2CuO4 that has a large c-axis length of ca. 6mm, have shown that the relative orientation of the magnetic field (H) versus the current (I) has little effect on the broadening. Rather the phenomenon only depends on the relative orientation of H versus the c-axis : large for H//c and small for H_Lc.5 This experimental result disproves the first three models, in which the relative H-I orientation is vitally important because all of them essentially assume the net transverse motion of flux lines across the current to give a finite resistance. Hence the superconducting fluctuation seems to be the most promising model at the present stage. This concept, however, has not been fully developed so that it can be c o m p a r e d quantitatively with the experimental results over 0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
the whole range of the transition region. So far only the higher temperature side of the resistivity(p)-T curve in the transition region has been discussed. Therefore here we have made a quantitative analysis on the experimental p-T-H relationship to establish the functional form of the
broadening. We derme the shift in the temperature under the magnetic field as a measure of the broadening : AT(p,H)=T(p,0)-T(p,H). In a typical metallic superconductor, a linear scaling law AT(p,H)-H holds. Tinkhara has recently shown that Iye et ars results6 of the p-T-H relationship on BYCO single crystals for I-I//c and LLc configuration follows the scaling law AT(p,H)-H2/3 and discuss this scaling law based on the flux creep model.7 We have observed that the AT-H2/3 scaling law holds for any configuration: irrespective of I-I//I or H_LI, and H//c or H_Lc. Figure 1 shows the typical example. It is important that a single parameter, AT3/2/I-I, scales the whole region of the transition for any configuration of H and I. It suggests that a single mechanism should explain the whole range of the p-T transition behavior.8 Then the whole range is the manifestation of the fluctuation. In order to stress that this is different but more serious than the conventionally defined
K. Kitazawa et al.
1018 r-I°
Broadened resistive transition under magnetic field I
" "°"~o.%~
O. 08 i
H,c
e.. or,,
,c
%
4 I
0.06~
z!,: 5T
,
A , : 4"[
t
I
0:3T 0 : 2"I"
J
=
-
C
r..
O. 04~!
g
r
I I
]
w~
O. 02~-
L (;.
O0 L
-
.0
-0.5
0.0
LogAT,Z'
0.5
'.0
:,.5
I. ~ H ( ' ' . :
FIGURE 1 Resistive transition as a function of the scaling variable AT3/2/H for H//c and I//c.
fluctuation, the term "giant fluctuation" may be more appropriate. The S-shaped feature of the resistive transition curve even suggests that there may not be occuring even any phase transition in the rigorous sense. The A T - H 2/3 scaling law is qualitatively understood as follows in the framework of the superconducting fluctuation theory. The energy scale AE relevant to the statistical physics of superconductong fluctuations is given b y Hc2.Vc/Sx where Hc is the thermodynamic critical field and Vc is the coherence volume. The correlation radius of the fluctuation is restricted to the radius of the Landau orbit rL(-(C0/xH)l/2) and hence the fluctuation grows only along the direction of the magnetic field.9 Therefore the coherence volume Vc in the magnetic field is given by rL2~C (H//c) and rL2~a,b (H3_c). Then A~-AT3/2/H is obtained. Because the coherence length is the shortest along the c-axis in the cuprates, we expect the fluctuation to be the most enhanced when the field is applied along the c-axis in accordance with the actual observations. Furthermore comparing different cuprates, the effect of the fluctuation is
then expected to become greater as the c-axis coherence length shortens, which is again in accord with the experimentally o b s e r v e d increasing order of the broadening width in BYCO, LSCO, BSCCO. Since the fluctuation is a pure thermodynamical state, it should not be dependent upon the microstructure in principle. This contrasts with the expectation from the flux creep model. From the practical point of view, this is unfortunate because the zero resistivity Tc should be remarkably lowered under the magnetic field, e.g., by as much as 50K or more for BSCCO (Tc=80K), 20K for LSCO (38.5K) and 10K for BYCO (90K) under the field of 5T in spite of their extremely high He2 values usually reported on the 50%-transition criterion.
REFERENCES 1. K.A.Muller, M.Tak~L~htgeand J.G.Bedonorz, Phys. Rev. Lett. 58 (1987) 1143. 2. Y.Yeshrun and A.P.Malozemoff,Phys. Rev. Lett. 60 (1988) 2202. 3. &Martin, A.T.Fioty, R.M.Fleming, G.P.Epinosa and A.S.Cooper, Phys. Rev. Lettt. 62 (1989) 677. 4. R.Ikeda, T.Ohmi and T.Tsuneto, J. Phys. Soc. Jim. 58 (1989) 1377. 5. K.Kitazawa, S.Kambe, M.Naito, I.Tanakaand H . K o j i m a , J p n . J. Appl. Phys. 26 (1989) L556. . Y.Iye, T.Tamegai, H.Takeya and H.Takei, Jpn. J. Appl. Phys. 26 (1987) L1057. .
M.Tinkham, Phys. Rev. Lett. 61 (1988) 1658.
8. In the resistivity tail region where the supercond-
ucting fluctuation becomes slow enough to be trapped by impurities, the supercondting fluctuation model may be equivalent to that of the flux creep model. 9. P.A.Leeand S.R.Shenoy,Phys.Rev.Lett.28 (1972) 1025.