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In-plane anisotropy of the resistivity of LSCO single crystal in magnetic fields
Physica B 284}288 (2000) 1011 } 1012
In-plane anisotropy of the resistivity of LSCO single crystal in magnetic "elds H. Iwasaki *, Y. Miyagawa , T. Suzuki , T. Naito , N. Kobayashi School of Materials Science, JAIST Hokuriku, Asahidai 1-1, Tatsunokuchi-machi 923-1292, Ishikawa, Japan Institute for Materials Research, Tohoku University, Aoba-ku 980-8577 Sendai, Japan
Abstract Angular and temperature dependences of the resistivity have been measured in the ab-plane on the sample of La Sr CuO with x"0.18. In the ab-plane a clear anisotropy is observed which is represented as the summation of \V V the twofold and fourfold symmetries. We conclude that the fourfold anisotropy comes from the energy gap by the d-wave pairing with d character. 2000 Elsevier Science B.V. All rights reserved. V \W Keywords: d-wave superconductivity; In-plane anisotropy; La
\V
According to the theory [1], the in-plane anisotropy of the resistivity is related to the superconducting pairing mechanism. However, it is very di$cult to measure it precisely. We have found how to do this. This paper presents the results and the interpretation of the in-plane anisotropy in the LSCO single crystal. Both temperature and angular dependences of the inplane resistivity have been measured in applied magnetic "elds on the sample of La Sr CuO with x"0.18 \V V with the current #owing in the b-axis direction. The magnetic "eld H was applied in the ab-plane. With u being the angle between the ab-plane and H, the position u"03 was found by rotation of the sample when measuring o(u). This process was repeated for each angle h between H and the a-axis for a range from !303 to 1203. After the determination of u"03 the temperature dependence of the resistivity was measured at several magnetic "elds. Out-of-plane anisotropy was conventionally measured by the angular dependence of the resistivity in the ac-plane. c ("m /m ) was estimated to be 10 ?@ A from scaling by the reduced "eld and was found to be quite smaller than that estimated from the resistivity ratio of o /o in the normal state. A ?@ Fig. 1 shows the temperature dependence of the resistivity at some angles h. The resistivity depends clearly on * Corresponding author. Tel.: #81-761-511512; fax: #81761-511149. E-mail address: [email protected] (H. Iwasaki)
Sr CuO V
the angle between the magnetic "eld and the crystal axis, that is, it takes a minimum at about h"903 and a maximum just around h"03. The temperature dependences for all angles h are almost parallel. In Fig. 2, the angular dependences of the resistivity at constant temperatures are plotted for three magnetic "elds, where the temperatures at which the resistivity takes approximately half of the value of the normal state resistivity are selected. The angular dependence around h"03 is quite di!erent from that of around h"903 and a small dip appears just around h"03. Several origins are possible which give an in-plane anisotropy to the resistivity. The "rst is the anisotropy dependent on the angle of the current with the magnetic "eld which was given by Ikeda [2]. The second is the fourfold anisotropy which originates from the e!ective mass or d-wave pairing. The angular dependence of the former depends on the form of the Fermi surface. The latter is determined by the d-wave character such as d symmetry. The third V \W possible origin due to the twin structure in the orthorhombic phase was discarded because it inevitably leads to minima of the resistivity at H "" [1 1 0] and maxima at H "" a- and b-axis. If the "rst and the second mechanisms are assumed, the resistivity is represented by o(h)"o #o #o ! "o #o sin (2h# )#o "sin (2h# )".
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 3 5 8 - 3
1012
H. Iwasaki et al. / Physica B 284}288 (2000) 1011}1012
Fig. 1. Temperature dependences of the resistivity at several angles h. The inset shows the temperature dependences of resistivity in a wide temperature range.
The obtained results are easily explained as the "tting curves given in Fig. 2. A possibility of fourfold anisotropy due to an e!ective mass or an energy gap was pointed out in the LSCO crystal [3]. Here, it should be emphasized in our results that it was necessary to assume the fourfold angular dependence by the energy gap to get a good "t. According to the theory based on the d-wave pairing [1] the di!erence *H between a maximum and a min imum of the upper critical "eld is represented by *H &0.2(1!t)H , where t is the reduced temper ature. If H is de"ned by the midpoint of the resistive transition, the resistivity data could be converted to H . Its angular dependence is qualitatively given by mirroring the resistivity in the h axis in the inset of Fig. 2. In our results *H is given by a(H)(1!t)H , where a(H)
Fig. 2. Angular dependences of the resistivity at three magnetic "elds. The three curves are the "tting ones at H"3.0, 6.0 and 9.0 T. The inset shows the fourfold component of the "tting curve.
depends on the magnetic "eld. a(H) reduces with increasing magnetic "eld. So, our results are not always consistent with the theory though the value of a(H) is close to the theoretical one. This might be due to another contribution to the angular dependence of the resistivity. However, it seems to be simply impossible to explain the present results by "eld-independent a and this is a problem to solve in the future.
References [1] K. Takanaka et al., Phys. Rev. Lett. 75 (1995) 323. [2] R. Ikeda, J. Phys. Sci. Japan 64 (1995) 1683. [3] T. Hanaguri et al., Physica B 165 & 166 (1990) 1449.
In-plane anisotropy of the resistivity of LSCO single crystal in magnetic "elds H. Iwasaki *, Y. Miyagawa , T. Suzuki , T. Naito , N. Kobayashi School of Materials Science, JAIST Hokuriku, Asahidai 1-1, Tatsunokuchi-machi 923-1292, Ishikawa, Japan Institute for Materials Research, Tohoku University, Aoba-ku 980-8577 Sendai, Japan
Abstract Angular and temperature dependences of the resistivity have been measured in the ab-plane on the sample of La Sr CuO with x"0.18. In the ab-plane a clear anisotropy is observed which is represented as the summation of \V V the twofold and fourfold symmetries. We conclude that the fourfold anisotropy comes from the energy gap by the d-wave pairing with d character. 2000 Elsevier Science B.V. All rights reserved. V \W Keywords: d-wave superconductivity; In-plane anisotropy; La
\V
According to the theory [1], the in-plane anisotropy of the resistivity is related to the superconducting pairing mechanism. However, it is very di$cult to measure it precisely. We have found how to do this. This paper presents the results and the interpretation of the in-plane anisotropy in the LSCO single crystal. Both temperature and angular dependences of the inplane resistivity have been measured in applied magnetic "elds on the sample of La Sr CuO with x"0.18 \V V with the current #owing in the b-axis direction. The magnetic "eld H was applied in the ab-plane. With u being the angle between the ab-plane and H, the position u"03 was found by rotation of the sample when measuring o(u). This process was repeated for each angle h between H and the a-axis for a range from !303 to 1203. After the determination of u"03 the temperature dependence of the resistivity was measured at several magnetic "elds. Out-of-plane anisotropy was conventionally measured by the angular dependence of the resistivity in the ac-plane. c ("m /m ) was estimated to be 10 ?@ A from scaling by the reduced "eld and was found to be quite smaller than that estimated from the resistivity ratio of o /o in the normal state. A ?@ Fig. 1 shows the temperature dependence of the resistivity at some angles h. The resistivity depends clearly on * Corresponding author. Tel.: #81-761-511512; fax: #81761-511149. E-mail address: [email protected] (H. Iwasaki)
Sr CuO V
the angle between the magnetic "eld and the crystal axis, that is, it takes a minimum at about h"903 and a maximum just around h"03. The temperature dependences for all angles h are almost parallel. In Fig. 2, the angular dependences of the resistivity at constant temperatures are plotted for three magnetic "elds, where the temperatures at which the resistivity takes approximately half of the value of the normal state resistivity are selected. The angular dependence around h"03 is quite di!erent from that of around h"903 and a small dip appears just around h"03. Several origins are possible which give an in-plane anisotropy to the resistivity. The "rst is the anisotropy dependent on the angle of the current with the magnetic "eld which was given by Ikeda [2]. The second is the fourfold anisotropy which originates from the e!ective mass or d-wave pairing. The angular dependence of the former depends on the form of the Fermi surface. The latter is determined by the d-wave character such as d symmetry. The third V \W possible origin due to the twin structure in the orthorhombic phase was discarded because it inevitably leads to minima of the resistivity at H "" [1 1 0] and maxima at H "" a- and b-axis. If the "rst and the second mechanisms are assumed, the resistivity is represented by o(h)"o #o #o ! "o #o sin (2h# )#o "sin (2h# )".
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 3 5 8 - 3
1012
H. Iwasaki et al. / Physica B 284}288 (2000) 1011}1012
Fig. 1. Temperature dependences of the resistivity at several angles h. The inset shows the temperature dependences of resistivity in a wide temperature range.
The obtained results are easily explained as the "tting curves given in Fig. 2. A possibility of fourfold anisotropy due to an e!ective mass or an energy gap was pointed out in the LSCO crystal [3]. Here, it should be emphasized in our results that it was necessary to assume the fourfold angular dependence by the energy gap to get a good "t. According to the theory based on the d-wave pairing [1] the di!erence *H between a maximum and a min imum of the upper critical "eld is represented by *H &0.2(1!t)H , where t is the reduced temper ature. If H is de"ned by the midpoint of the resistive transition, the resistivity data could be converted to H . Its angular dependence is qualitatively given by mirroring the resistivity in the h axis in the inset of Fig. 2. In our results *H is given by a(H)(1!t)H , where a(H)
Fig. 2. Angular dependences of the resistivity at three magnetic "elds. The three curves are the "tting ones at H"3.0, 6.0 and 9.0 T. The inset shows the fourfold component of the "tting curve.
depends on the magnetic "eld. a(H) reduces with increasing magnetic "eld. So, our results are not always consistent with the theory though the value of a(H) is close to the theoretical one. This might be due to another contribution to the angular dependence of the resistivity. However, it seems to be simply impossible to explain the present results by "eld-independent a and this is a problem to solve in the future.
References [1] K. Takanaka et al., Phys. Rev. Lett. 75 (1995) 323. [2] R. Ikeda, J. Phys. Sci. Japan 64 (1995) 1683. [3] T. Hanaguri et al., Physica B 165 & 166 (1990) 1449.