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Magnetization anisotropy of high-Tc superconductors
Physica B 165&166 (1990) 1451-1452 North- Holland
MAGNETIZATION ANISOTROPY OF HIGH-Tc SUPERCONDUCTORS M. TUOMINEN and A. M. GOLDMAN* Center for the Science and Application of Superconductivity and School of Physics and Astronomy University of Minnesota, Minneapolis, Minnesota, 55455, U.S.A. Y. Z. CHANG§ and P. Z. JIANGt Material Science Division, Argonne National Laboratory Argonne, Illinois, 60439, U.S.A. The magnetization anisotropies of Bi2SQCaCU20y and YBa2Cu307-x single crystals have been investigated by simultaneously measuring the longitudinal (ML) and transverse (MT) components of the equilibrium magnetization of crystals oriented at arbitrary angles with respect to the applied field direction using a superconducting susceptometer. In the regime where the simple threedimensional (3D) anisotropic London theory is valid, the measurement of MT/ML yields the anisotropic mass ratio (m3/ml) directly. 1. INTRODUCTION Measurements of the upper critical field, Hc2, parallel and perpendicular to the basal plane of high-Tc superconductors indicate large anisotropy in the value of the Ginzburg-Landau (GL) coherence length in those directions.(l) Measurements of other properties also show anisotropy. The superconductivity of these materials has been speculated to be layer-like in the sense that it nucleates in the copper oxide planes which are in tum coupled by the Josephson effect,(2) Another possible source of anisotropy is unconventional pairing (3) which will not be considered here as it has not been demonstrated experimentally. There is also a possible crossover between the anisotropic 3D regime and the quasi-2D regime of weakly-coupled layers. In the latter regime, the system can exhibit 2D character, and is described by differential-difference equations, resulting in rather different behavior.(4)
2. THEORETICAL BACKGROUND The effective mass formulations of both the GL (5) and London (6) theories predict the existence of a transverse magnetization (perpendicular to B) in addition to the usual longitudinal magnetization (along B) in the mixed state. Kogan has used the London theory to estimate the magnitudes of both the longitudinal and transverse components of magnetization for a uniaxial superconductor (ml = m2 :;:. m3).(7) Torque magnetometry studies of both YBa2Cu307-x and Bi2SQCaCU20y samples have been used to extract an anisotropic mass ratio. (8) The data is very clean but the fit depends not only on m3/ml, but also on other parameters which are not determined independently. However, simultaneous measurements of ML and MT provide a way to determine m3/ml directly without the use of any additional fitting parameters, as the ratio of transverse to longitudinal magnetization *Supported in part by the Air Force Office of Scientific Research under Grant AFOSR 87-0372 and by the Central Administration of the University of Minnesota. §Supported by the National Science Foundation Office of Science and Technology under contract STC8809854. tSupported by the United States Department of Energy Office of Basic Energy Science / Materials Science under contract W-31-109-ENG-38.
0921-4526/90/$03.50
© 1990 -
Elsevier Science Publishers B.V. (North-Holland)
1452
M. Tuominen, A.M. Goldman, Y.Z. Chang, P.Z. Jiang
(1) is a function of only m3/m1 and e, the angle between the c-axis and the field direction. 3. EXPERIMENTAL Reversible magnetization measurements on YBazCu307-x and BizSrzCaCuzOy single crystals were made using a commercial SQUID susceptometer equipped with longitudinal and transverse pick-up coils. We built a sample holder specifically for these measurements, which permitted rotation of the sample about an axis at right angles to the field direction (with an accuracy of ±OJ 0). A best fit of Eq. (1) to the MT!ML(e) data on BizSrzCaCU20y in Fig. 1 gives a value of m3/ml = 280 ± 20. This is to be compared to values of 20 to 3000 reported by others using different methods.(1,8,9) Note that there are systematic uncertainties that plague some experiments, such as the pronounced flux flow resistance in transport measurements and microstructural
misalignment within samples, making it difficult to determine the true thermodynamic values of parameters which describe the superconductivity. Figure 1 also shows the magnetization data for a YBazCu307-x crystal. The mass ratio in this case is found to be 30 ± 5, which is consistent with the measurements of other workers who find values of 25 to 90 (see references in (7». 4. DISCUSSION A close comparison of the fit of Eq. (1) to the the data of Fig. 1 for BizSr2CaCUZOy reveals that Eq. (1) does account for the general trend of the data, but the fit is not within the experimental error of the data points. Simple calculations show that the sample should be in a regime where it shows 20 character, and the effective mass theory may not strictly apply.(4) To our knowledge, explicit calculations which predict the magnitude of the longitudinal and transverse magnetization components for a system of weakly coupled layers have not been made, so we cannot directly determine if such theory would fit the data better than the anisotropic London model. ACKNOWLEDGEMENTS The authors would like to thank Dr. Vladimir Kogan for his many useful suggestions and encouragement.
8.0
4.0
REFERENCES
(1) J. H. Kang et aI, Appl. Phys. Lett. 53 (1988)
.J
~ 0.0
...
~
(2) -4.0
(3)
-8.0
o
(4) 30
60
90
8
120
150
180
(degrees)
FIGURE 1 The ratio of transverse to longitudinal magnetization plotted vs e for a BizSf2CaCuzOy crystal at 70K and 1.0 Tesla. The solid curve represents the best fit of Eq. 1 to the data, giving m3/ml = 280 ± 20. Also shown is data for a YBa2Cu307-x crystal at 70K and 5.0 Tesla. The dashed line shows the best fit to Eq. 1, giving m3/ml =30 ± 5.
(5) (6) (7) (8) (9)
2560; U. Welp et aI, Phys. Rev. Lett. 62 (1989) 1908 . R. A. Klemm, A. Luther, and M. R. Beasley, Phys. Rev. B 12 (1975) 877. L. 1. Burlachkov, Sov. Phys. JETP 62 (1985) 800; L. P. Gor'kov, JETP Lett. 40 (1984) 1155. L. N. Bulaevskii, V. L. Ginzburg, and A. A. Sobyanin, Sov. Phys. JETP 68 (1988) 1499. V. G. Kogan and J. R. Clem, Phys. Rev. B 24 (1981) 2497. V. G. Kogan, Phys. Rev. B 17 (1981) 1249. V. G. Kogan, M. M. Fang, and S. Mitra, Phys. Rev. B 38 (1988) 11958. D. E. Farrell et aI, Phys. Rev. Lett. 63 (1989) 782. T. T. M. Palstra et aI, Phys. Rev. B 38 (1988) 5102; L. Krusin-Elbaum et aI, Phys. Rev. B 39 (1989) 2936.
MAGNETIZATION ANISOTROPY OF HIGH-Tc SUPERCONDUCTORS M. TUOMINEN and A. M. GOLDMAN* Center for the Science and Application of Superconductivity and School of Physics and Astronomy University of Minnesota, Minneapolis, Minnesota, 55455, U.S.A. Y. Z. CHANG§ and P. Z. JIANGt Material Science Division, Argonne National Laboratory Argonne, Illinois, 60439, U.S.A. The magnetization anisotropies of Bi2SQCaCU20y and YBa2Cu307-x single crystals have been investigated by simultaneously measuring the longitudinal (ML) and transverse (MT) components of the equilibrium magnetization of crystals oriented at arbitrary angles with respect to the applied field direction using a superconducting susceptometer. In the regime where the simple threedimensional (3D) anisotropic London theory is valid, the measurement of MT/ML yields the anisotropic mass ratio (m3/ml) directly. 1. INTRODUCTION Measurements of the upper critical field, Hc2, parallel and perpendicular to the basal plane of high-Tc superconductors indicate large anisotropy in the value of the Ginzburg-Landau (GL) coherence length in those directions.(l) Measurements of other properties also show anisotropy. The superconductivity of these materials has been speculated to be layer-like in the sense that it nucleates in the copper oxide planes which are in tum coupled by the Josephson effect,(2) Another possible source of anisotropy is unconventional pairing (3) which will not be considered here as it has not been demonstrated experimentally. There is also a possible crossover between the anisotropic 3D regime and the quasi-2D regime of weakly-coupled layers. In the latter regime, the system can exhibit 2D character, and is described by differential-difference equations, resulting in rather different behavior.(4)
2. THEORETICAL BACKGROUND The effective mass formulations of both the GL (5) and London (6) theories predict the existence of a transverse magnetization (perpendicular to B) in addition to the usual longitudinal magnetization (along B) in the mixed state. Kogan has used the London theory to estimate the magnitudes of both the longitudinal and transverse components of magnetization for a uniaxial superconductor (ml = m2 :;:. m3).(7) Torque magnetometry studies of both YBa2Cu307-x and Bi2SQCaCU20y samples have been used to extract an anisotropic mass ratio. (8) The data is very clean but the fit depends not only on m3/ml, but also on other parameters which are not determined independently. However, simultaneous measurements of ML and MT provide a way to determine m3/ml directly without the use of any additional fitting parameters, as the ratio of transverse to longitudinal magnetization *Supported in part by the Air Force Office of Scientific Research under Grant AFOSR 87-0372 and by the Central Administration of the University of Minnesota. §Supported by the National Science Foundation Office of Science and Technology under contract STC8809854. tSupported by the United States Department of Energy Office of Basic Energy Science / Materials Science under contract W-31-109-ENG-38.
0921-4526/90/$03.50
© 1990 -
Elsevier Science Publishers B.V. (North-Holland)
1452
M. Tuominen, A.M. Goldman, Y.Z. Chang, P.Z. Jiang
(1) is a function of only m3/m1 and e, the angle between the c-axis and the field direction. 3. EXPERIMENTAL Reversible magnetization measurements on YBazCu307-x and BizSrzCaCuzOy single crystals were made using a commercial SQUID susceptometer equipped with longitudinal and transverse pick-up coils. We built a sample holder specifically for these measurements, which permitted rotation of the sample about an axis at right angles to the field direction (with an accuracy of ±OJ 0). A best fit of Eq. (1) to the MT!ML(e) data on BizSrzCaCU20y in Fig. 1 gives a value of m3/ml = 280 ± 20. This is to be compared to values of 20 to 3000 reported by others using different methods.(1,8,9) Note that there are systematic uncertainties that plague some experiments, such as the pronounced flux flow resistance in transport measurements and microstructural
misalignment within samples, making it difficult to determine the true thermodynamic values of parameters which describe the superconductivity. Figure 1 also shows the magnetization data for a YBazCu307-x crystal. The mass ratio in this case is found to be 30 ± 5, which is consistent with the measurements of other workers who find values of 25 to 90 (see references in (7». 4. DISCUSSION A close comparison of the fit of Eq. (1) to the the data of Fig. 1 for BizSr2CaCUZOy reveals that Eq. (1) does account for the general trend of the data, but the fit is not within the experimental error of the data points. Simple calculations show that the sample should be in a regime where it shows 20 character, and the effective mass theory may not strictly apply.(4) To our knowledge, explicit calculations which predict the magnitude of the longitudinal and transverse magnetization components for a system of weakly coupled layers have not been made, so we cannot directly determine if such theory would fit the data better than the anisotropic London model. ACKNOWLEDGEMENTS The authors would like to thank Dr. Vladimir Kogan for his many useful suggestions and encouragement.
8.0
4.0
REFERENCES
(1) J. H. Kang et aI, Appl. Phys. Lett. 53 (1988)
.J
~ 0.0
...
~
(2) -4.0
(3)
-8.0
o
(4) 30
60
90
8
120
150
180
(degrees)
FIGURE 1 The ratio of transverse to longitudinal magnetization plotted vs e for a BizSf2CaCuzOy crystal at 70K and 1.0 Tesla. The solid curve represents the best fit of Eq. 1 to the data, giving m3/ml = 280 ± 20. Also shown is data for a YBa2Cu307-x crystal at 70K and 5.0 Tesla. The dashed line shows the best fit to Eq. 1, giving m3/ml =30 ± 5.
(5) (6) (7) (8) (9)
2560; U. Welp et aI, Phys. Rev. Lett. 62 (1989) 1908 . R. A. Klemm, A. Luther, and M. R. Beasley, Phys. Rev. B 12 (1975) 877. L. 1. Burlachkov, Sov. Phys. JETP 62 (1985) 800; L. P. Gor'kov, JETP Lett. 40 (1984) 1155. L. N. Bulaevskii, V. L. Ginzburg, and A. A. Sobyanin, Sov. Phys. JETP 68 (1988) 1499. V. G. Kogan and J. R. Clem, Phys. Rev. B 24 (1981) 2497. V. G. Kogan, Phys. Rev. B 17 (1981) 1249. V. G. Kogan, M. M. Fang, and S. Mitra, Phys. Rev. B 38 (1988) 11958. D. E. Farrell et aI, Phys. Rev. Lett. 63 (1989) 782. T. T. M. Palstra et aI, Phys. Rev. B 38 (1988) 5102; L. Krusin-Elbaum et aI, Phys. Rev. B 39 (1989) 2936.