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Phase breaking effects in magnetoconductivity of YBa2Cu3O7−δ and Bi2Sr2CaCu3O8
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Physica C 235-240 (1994) 1443-1444 North-Holland
.
.
.
.
.
Uill
..
J
PHYSlCA
Phase breaking effects in magnetoconductivity of YBa2Cu3OT_ and Bi2Sr2CaCu208 C. P. Dhard a, S. N. Bhatia a , p. V. P. S. S. Sastry b, j. V. Yakhmi b and A. K. Nigam c a Department of Physics, Indian Institute of Technology, Bombay 400 076, India. b Chemistry Division, Bhabha Atomic Research Centre, Bombay 400 085, India. e Tata Institute of Fundamental Research, Bombay 400 005, India. We have measured the magnetoconductivity of YBazCu3OT'-6 a n d B i 2 S r z C a C u z O s in the magnetic field of 4T and analysed the data in the fluctuation region in the light of Aronov-Hikami-Larkin (AHL) and BieriMaki(BM) theories in their corrected forms and find the BM theory within the clean limit to describe the data more adequetely.
1. I N T R O D U C T I O N
2. R E S U L T S A N D D I S C U S S I O N
Recently Aronov, Hikami and Larkin [1] (AHL) have developed a theory for the magnetoconductivity A n ( H ) taking into account the orbital as well as the Zeeman effects of the magnetic field on the Aslamazov and Larkin (AL) and Maki and Thompson (MT) terms i.e. ALO, MTO and ALZ and MTZ terms. Later Bieri and Maki [2] proposed another theory of A n ( H ) which was valid in the clean limit (l > ~ab(0)) but it gave results identical to those of the AHL theory. Thompson [3] further corrected both these theories by modifying the Zeeman energy which was overestimating the MTZ contribution. The fluctuations in the absence of magnetic field have been extensively studied in high T¢ superconducting systems [4]. Studies have also been attempted in the presence of magnetic field [5], [6] but the data have been interpreted in terms of t h e uncorrec~eo ' ' forms oi" "' t, neore~lca~ "" ' e x p r e s s i o n s consequently yielding divergent results. Semba et al [5] found MTZ contribution to be negligible in YBa2Cu307-6 (YBCO) single crystals whereas Sugawara et al [6] found it to be present in thin films. These studies have been confined only to the YBCO and no attempt has been made to study Bi2Sr=,CaCu2Os (BSCCO) in the same light. Further, studies on the polycrystalline sampies have also not been attempted.
We have measured the magnetoconductivity of polycrystailine YBCO and BSCCO samples in the external magnetic field of 4 Tesla. Field was limited to 4T because for the higher fields the orbital terms show deviations from the H2 behaviour predicted by the above t,heories. The normal state resistivity is found to be metallic above tile temperature ~ 150 K ( ~ 2To) for both tile samples. The drop in resistivity in the transition region is sharp (~ 1 K) in the absence of magn,etic field whereas the resistivity below 7]. onset broadens in the presence of magnetic field. It extends to ~ 18 K for YBCO and 35 K for the BSCCO sample. Total fluctuation conductivity Acr;(H)(= cr(H, T ) - ~ r n ( H , T ) ) contains tne zero field excess conductivity ~ ( 0 ) and tile modifications produced in A~r(0) by the magnetic field. The ex. : . . . . , i data of Acy ( .~',. ~). nf" pe,,,,~e,,~a, . .YBCO . . . w ~ first, fitted to the four ternts of tile A tlL theory with Thompson correction by taking (~(0) , ~ab(0) and re as the adjustable parameters. 7"0 was assumed to vary as re = r~0 /T. Very good agreement could be obtained with ~ ( 0 ) = 1.6J~ ~ab(0) = 9.5~ and v~ = 2.5X10 -13 s (at I00 K). The agreement further improved when BM equations with Thompson correction were used and the mean free path l was allowed to vary with temperature
0921-4534/94/507,00 © 1994- Elsevier Science B.V. All righls rcscrvcd. SSDI 0921-4534(94){)1285-7
C.P Dhard et al./Physica C 235-240 (1994) 1443-1444
1444
;"~1
t
I
i
....
I'
t"
~ "t
I "1 t I'
10000 I ~
--
~Oex
7
}'I°a°° ~"
1001 AGm
I 10
MTO ALO ALZ MTZ
1- l....t I
0.01
... *
•
1
• , l = ~I
D.I
Figure 1. Fluctuation and ,magneto conductivity of YBCO.
as I = lo/T. The values of ~e(0) slightly incree ~d to 2.3A and E,ab(O) decreased to 9.0A. From the values of 6 we obtained 10re0 = 2.5 x 10-12As. To get an estimate of r~ from this product, we note that ! = rvF = rovF/T (i.e. !o = rovr) where r is the transport relaxation time and vr the Fermi velocity of the carriers. The later is estimated as (6-1.¢3) x 106 cm/sec from the relation ~b(O) = livF/TrA with the inplane energy gap parameter given [8] by 2 A / k To= 3.5-8. Now assuming r¢ _"z r this product yields re (100 K) 4.6 X 10-14 s for the lowest estimate of v~, Le. vF = 6 x 106 cm/s. This compares well with the value obtained by Sugawara et al [6]. In the BSCCO the fittings have been found to be equally good with the values of paramete~s ~¢(0), ~b(0) and r~ as 1.93,, 10~ and 1 x 10-~% (100 K) for the AHL theory but the ratio r6/r is >10 which is too large. This ratio reduces to an acceptable value of 2.3 for the corrected BM theory with ~¢(0), ~ab(0) and re as 2.3~, 9.i~ and 1.3 × l0 -13 s and the value of mean free path l :x 55~t. BMT [7] have further assumed ~c(0) and ~b(0) to be temperature dependent. However these functional fo='ms were found to be inappropriate as they lead to the poor quality of
fits and unacceptable values of r#. The magnetoconductivity obtained by subtracting ~aAL(O) and AaMT(O) from A a I ( H , T ) for YBCO is displayed in fig.(1) along with the calculated values of the four field dependent contributions. Similar graphs were obtained for BSCCO also. A f f M T Z has the smallest value over the entire e range, being less than 1% of the total Aam(H, T) for both the systems. The fit does not deteriorate when the term AtrMTZ is dropped altogether. However the rms deviation jumps when the next larger term AtrALZ is dropped. This result is in conformity with the measurements of Semba et al [5] who also find AaMTZ to be negligible in their magnetoconductivity of single crystal YBCO measured at IT. In conclusion it appears that the nature of fluctuations in the presence of magnetic field remains unaffected by the polycrystallinity in both the systems YBCO and BSCCO. Out of the four contributions ALO, ALZ, MTO and MTZ, the MTZ remains negligible in both the systems, Larger value of the mean free paths i ~ 55/~ and smaller correlation lengths ~c(0) "" 2/~ and t:ab(0) = 10/t show both these systenu; to lie within the clean limit despite the polycrystallinity. REFERENCES
1. A.G. Aronov, S. Iq;ikami and A.I. Larkin, Phys. Rev. Letts. 62 (1989) 965; 62, (1989)
2336(E). 2. J.B. Bieri and K. Maki, Phys. Rev. B 42 (1990) 4854. 3. R,S. Th')mpson, Phys. Rev. Letts. 66 (1991) 2280. 4. S. N. Bhatia and C. P. Dhard, Phys. Rev. B 49 (1994) (In press). 5. K. Semba, T. lshii and A. Matsuda, Phys. Rev. Letts. 67, 769 (1991). 6. J. Sugawara, It. [wasaki, N. Kobayashi, H. Yamane and T nirai, Phys. Rev. B 46, 14818 (i992). 7. J.B. Bicri and K. Maki and R.S. Thompson, Phys. Roy. B 44, 4709 (1991). 8. B. Batlogg, in High Temperature Superconductors, edited by K.S. Bedell et al (AddisonWesle Redwood City 1990) p 37.
Physica C 235-240 (1994) 1443-1444 North-Holland
.
.
.
.
.
Uill
..
J
PHYSlCA
Phase breaking effects in magnetoconductivity of YBa2Cu3OT_ and Bi2Sr2CaCu208 C. P. Dhard a, S. N. Bhatia a , p. V. P. S. S. Sastry b, j. V. Yakhmi b and A. K. Nigam c a Department of Physics, Indian Institute of Technology, Bombay 400 076, India. b Chemistry Division, Bhabha Atomic Research Centre, Bombay 400 085, India. e Tata Institute of Fundamental Research, Bombay 400 005, India. We have measured the magnetoconductivity of YBazCu3OT'-6 a n d B i 2 S r z C a C u z O s in the magnetic field of 4T and analysed the data in the fluctuation region in the light of Aronov-Hikami-Larkin (AHL) and BieriMaki(BM) theories in their corrected forms and find the BM theory within the clean limit to describe the data more adequetely.
1. I N T R O D U C T I O N
2. R E S U L T S A N D D I S C U S S I O N
Recently Aronov, Hikami and Larkin [1] (AHL) have developed a theory for the magnetoconductivity A n ( H ) taking into account the orbital as well as the Zeeman effects of the magnetic field on the Aslamazov and Larkin (AL) and Maki and Thompson (MT) terms i.e. ALO, MTO and ALZ and MTZ terms. Later Bieri and Maki [2] proposed another theory of A n ( H ) which was valid in the clean limit (l > ~ab(0)) but it gave results identical to those of the AHL theory. Thompson [3] further corrected both these theories by modifying the Zeeman energy which was overestimating the MTZ contribution. The fluctuations in the absence of magnetic field have been extensively studied in high T¢ superconducting systems [4]. Studies have also been attempted in the presence of magnetic field [5], [6] but the data have been interpreted in terms of t h e uncorrec~eo ' ' forms oi" "' t, neore~lca~ "" ' e x p r e s s i o n s consequently yielding divergent results. Semba et al [5] found MTZ contribution to be negligible in YBa2Cu307-6 (YBCO) single crystals whereas Sugawara et al [6] found it to be present in thin films. These studies have been confined only to the YBCO and no attempt has been made to study Bi2Sr=,CaCu2Os (BSCCO) in the same light. Further, studies on the polycrystalline sampies have also not been attempted.
We have measured the magnetoconductivity of polycrystailine YBCO and BSCCO samples in the external magnetic field of 4 Tesla. Field was limited to 4T because for the higher fields the orbital terms show deviations from the H2 behaviour predicted by the above t,heories. The normal state resistivity is found to be metallic above tile temperature ~ 150 K ( ~ 2To) for both tile samples. The drop in resistivity in the transition region is sharp (~ 1 K) in the absence of magn,etic field whereas the resistivity below 7]. onset broadens in the presence of magnetic field. It extends to ~ 18 K for YBCO and 35 K for the BSCCO sample. Total fluctuation conductivity Acr;(H)(= cr(H, T ) - ~ r n ( H , T ) ) contains tne zero field excess conductivity ~ ( 0 ) and tile modifications produced in A~r(0) by the magnetic field. The ex. : . . . . , i data of Acy ( .~',. ~). nf" pe,,,,~e,,~a, . .YBCO . . . w ~ first, fitted to the four ternts of tile A tlL theory with Thompson correction by taking (~(0) , ~ab(0) and re as the adjustable parameters. 7"0 was assumed to vary as re = r~0 /T. Very good agreement could be obtained with ~ ( 0 ) = 1.6J~ ~ab(0) = 9.5~ and v~ = 2.5X10 -13 s (at I00 K). The agreement further improved when BM equations with Thompson correction were used and the mean free path l was allowed to vary with temperature
0921-4534/94/507,00 © 1994- Elsevier Science B.V. All righls rcscrvcd. SSDI 0921-4534(94){)1285-7
C.P Dhard et al./Physica C 235-240 (1994) 1443-1444
1444
;"~1
t
I
i
....
I'
t"
~ "t
I "1 t I'
10000 I ~
--
~Oex
7
}'I°a°° ~"
1001 AGm
I 10
MTO ALO ALZ MTZ
1- l....t I
0.01
... *
•
1
• , l = ~I
D.I
Figure 1. Fluctuation and ,magneto conductivity of YBCO.
as I = lo/T. The values of ~e(0) slightly incree ~d to 2.3A and E,ab(O) decreased to 9.0A. From the values of 6 we obtained 10re0 = 2.5 x 10-12As. To get an estimate of r~ from this product, we note that ! = rvF = rovF/T (i.e. !o = rovr) where r is the transport relaxation time and vr the Fermi velocity of the carriers. The later is estimated as (6-1.¢3) x 106 cm/sec from the relation ~b(O) = livF/TrA with the inplane energy gap parameter given [8] by 2 A / k To= 3.5-8. Now assuming r¢ _"z r this product yields re (100 K) 4.6 X 10-14 s for the lowest estimate of v~, Le. vF = 6 x 106 cm/s. This compares well with the value obtained by Sugawara et al [6]. In the BSCCO the fittings have been found to be equally good with the values of paramete~s ~¢(0), ~b(0) and r~ as 1.93,, 10~ and 1 x 10-~% (100 K) for the AHL theory but the ratio r6/r is >10 which is too large. This ratio reduces to an acceptable value of 2.3 for the corrected BM theory with ~¢(0), ~ab(0) and re as 2.3~, 9.i~ and 1.3 × l0 -13 s and the value of mean free path l :x 55~t. BMT [7] have further assumed ~c(0) and ~b(0) to be temperature dependent. However these functional fo='ms were found to be inappropriate as they lead to the poor quality of
fits and unacceptable values of r#. The magnetoconductivity obtained by subtracting ~aAL(O) and AaMT(O) from A a I ( H , T ) for YBCO is displayed in fig.(1) along with the calculated values of the four field dependent contributions. Similar graphs were obtained for BSCCO also. A f f M T Z has the smallest value over the entire e range, being less than 1% of the total Aam(H, T) for both the systems. The fit does not deteriorate when the term AtrMTZ is dropped altogether. However the rms deviation jumps when the next larger term AtrALZ is dropped. This result is in conformity with the measurements of Semba et al [5] who also find AaMTZ to be negligible in their magnetoconductivity of single crystal YBCO measured at IT. In conclusion it appears that the nature of fluctuations in the presence of magnetic field remains unaffected by the polycrystallinity in both the systems YBCO and BSCCO. Out of the four contributions ALO, ALZ, MTO and MTZ, the MTZ remains negligible in both the systems, Larger value of the mean free paths i ~ 55/~ and smaller correlation lengths ~c(0) "" 2/~ and t:ab(0) = 10/t show both these systenu; to lie within the clean limit despite the polycrystallinity. REFERENCES
1. A.G. Aronov, S. Iq;ikami and A.I. Larkin, Phys. Rev. Letts. 62 (1989) 965; 62, (1989)
2336(E). 2. J.B. Bieri and K. Maki, Phys. Rev. B 42 (1990) 4854. 3. R,S. Th')mpson, Phys. Rev. Letts. 66 (1991) 2280. 4. S. N. Bhatia and C. P. Dhard, Phys. Rev. B 49 (1994) (In press). 5. K. Semba, T. lshii and A. Matsuda, Phys. Rev. Letts. 67, 769 (1991). 6. J. Sugawara, It. [wasaki, N. Kobayashi, H. Yamane and T nirai, Phys. Rev. B 46, 14818 (i992). 7. J.B. Bicri and K. Maki and R.S. Thompson, Phys. Roy. B 44, 4709 (1991). 8. B. Batlogg, in High Temperature Superconductors, edited by K.S. Bedell et al (AddisonWesle Redwood City 1990) p 37.