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Anisotropic ac screening response in the vortex state of superconducting Bi2Sr2CaCu2O8 crystals
Physica C 185-189 (1991) 2227-2228 North-Holland
ANISOTROPIC AC SCREENING RESPONSE IN THE VORTEX STATE OF SUPERCONDUCTING Bi2Sr2CaCu208 CRYSTALS D.G. Steel and J.M. Graybeal
Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S_a_ We r e p o r t m e a s u r e m e n t s of ac screening response in single crystals of superconducting Bi2Sr2CaCu208 as a function of temperature, and applied dc field magnitude and direction. The ac screening response is m e a s u r e d inductively: dc fields are applied with an electromagnet, while a separate ceil provides a small ac drive field. The orientation between the applied dc field and the ac probing field can be varied. For de fields parallel to the crystal c-axis we observe significant anisotropy in the screening response for ac fields parallel to and perpendicular to the c-axis. 1. INTRODUCTION There has been significant interest recently in the vortex properties of the oxide superconductors. Some of the important questions to be addressed by experiment include the predicted existence of additional phase transitions in the mixed state as a consequence of their anisotropy, as well as the implications of disorder (i.e. pinning) on the phase diagram. Consequently we have studied the screening response in single crystals of superconducting Bi2SrsCaCu208 (2212) with Tc = 85I~ The inductive response of these currents probes the vortex response within the crystals as a function of temperature and applied field. Measurements were made using a first-order magnetic gradiometer, designed to allow the study of the anisotropic response of these materials. The magnetometer consists of a solenoid and two pick-up coils. The solenoid is driven with a small ac current (typically 0.1mA, producing a field of 5 mOe) of frequency Vae, the two coils are connected in opposition and the responses null-detected by a lock-in amplifier. Both real and imaginary components of the null signal are monitored. S~.....l~ ..1o~.1 ,,~h;.. one . e ,h~ pick-up ,,,,;l~ This technique allows the screening currents to be probed in a well-defiued and variable direction with respect to both the crystal axes and an external applied dc field. It further allows the ac screening response to be measured over a range of frequencies. 2. RESULTS AND DISCUSSION Only the case where the dc field is parallel to
the crystalline c-axis will be considered in this paper. Measurements have been made both with the ac field parallel to and perpendicular to the caxis. The m e a s u r e m e n t is made at constant dc magnetic field and the temperature is reduced slowly and at a uniform rate. The drive frequency Vac is 40kHz for the traces shown in Figure 1. On cooling, the in-phase component shows an onset of screening response and the out-of-phase component displays a dissipation peak. The origin of such a dissipation peak is consistent with electromagnetic skin depth effects within the crystal.1 Figure 2 shows the peak location as a function of field - the in-phase (x-) component shows similar variation. The peak occurs at a significantly higher temperature for the ease when the ae field is parallel to the c-axis than for the ac field perpendicular to the c-axis. Note that in the former case the screening currents are within the Cu-O layers, while in the latter case they are both within and between the layers. Recent theoretical work2,3 for the case of highly anisotropie superconductors predicts a phase diagram t h a t is qualitatively similar to the e21.[d~lLlX.LIt~llla~l.I $ ~ I ; 7 ~ U J L ~
L£~t ~ - a S u t x ~
•
•
theories the vortex solid is predicted to exhibit twostage melting, with 3D behavior at low fields and a crossover to more 2D behavior above a threshold, estimated to be of order 5kOe for our samples. For the low-field regime, the lowest temperature phase is expected to be the vortex solid (a lattice ha the absence of pinning), the intermediate phase is a vortex line liquid, and the high temperature phase is a liquid of unbound 2D planar vortices.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
2228
D.G Steel, ZM. Graybeal / Anisotropic AC screening response
Although it is tempting to directly compare d a t a with t h e s e theories, it is i m p o r t a n t to recognize t h a t s k i n depth effects add important size- and frequency-dependent factors to the data. Consequently, t h e theory should only be compared to the zero-frequency limit of such experiments. The use of a separate ac drive field readily allows the variation of the frequency with which the vortex structure is probed. Figure 3 shows the variation of tlhe y-component peak as a function of frequency at fixed field. This displays substantial d i s p e r s i o n e v e n at the lowest frequencies (vae=100Hz). This data rules out the existence of a finite t e m p e r a t u r e transition in the temperature and field regime shown in Figure 3. Cautious extrapolation of our present d a t a for the limit Vac-~0 suggests a n upper b o u n d for such a transition of order 25K. In s u m m a r y , t h e s e m e a s u r e m e n t s have shown t h a t in the presence of dc fields applied along the c-axis there is significant anisotropy between the ac screening along the Cu-O planes compared to perpendicular to them. For the case of ac field perpendicular to the planes, we have observed s t r o n g frequency dispersion in the screening response, which brings into question w h e t h e r t h e r e exists a finite t e m p e r a t u r e transition as Vac~0. Amplitude dispersion is seen f~r !vrger ac excitation levels; these measurements were made in the linear response regime.
I
t~O
I
9.o
I
I
[~Increasing dc FieldI-
~ 1.5 o
~ 1.0 ¢= 0.5 I
0.(
0
40
60 80 Temperature, K
100
FIG. 1: Real component of screening response for dc field parallel to and ac field perpendicular to caxis. Traces correspond to different dc fields. I
I
hl
I
I
I
_
"o
5-
I-
A a¢ field II c-axis [] a c f i e l d l c-axisl_
O
4o
A
3-0
A A
2o
A
1-
%
P Din I 3o 4 0 - 5 0
I
~1
60
70-80
Peak Temperature, K 3. ACKNOWLEDGEMENTS We would like to thank J.R. Clem and A.E. Koshelev for helpful discussions. We also thank L.G. Rubin a n d the Francis B i t t e r National Magnet Laboratory. This work was supported by the US Office of Naval Research via contract N00014-88-K-0479. DGS acknowledges support from the SERC (UK), and JMG acknowledges a Sloan Research Fellowship.
FIG. 2: Temperature of dissipation peak as a function of applied dc field (dc field parallel to c-axis). I
100
:~ 80
I
I
400 Oe field I 0 1600Oe fieldI O 3715Oe field[ ac field II c-axisI |
I~
O
N
~6040
o
o
REFERENCES 1. V.B. G e s h k e n b e i m , V.M. V i n o k u r and R. Fehrenbacher, Phys. Rev. B 43, 3748 (1991). 2. D.S. Fisher, M.P.A. Fisher and D.A. Huse, Phys. Rev. B 43, 130 (1991) 3. L.I. Glazman and A.E. Koshelev, Phys. Rev. B 43, 2835 (1991)
I
0
o o
o
~o ~ ~
ib~i
50 "~'" 60
i
70
Peak Temperature, K FIG. 3: T e m p e r a t u r e of dissipation p e a k as a function of ac field frequency (dc field and ac field parallel to c-axis).
ANISOTROPIC AC SCREENING RESPONSE IN THE VORTEX STATE OF SUPERCONDUCTING Bi2Sr2CaCu208 CRYSTALS D.G. Steel and J.M. Graybeal
Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S_a_ We r e p o r t m e a s u r e m e n t s of ac screening response in single crystals of superconducting Bi2Sr2CaCu208 as a function of temperature, and applied dc field magnitude and direction. The ac screening response is m e a s u r e d inductively: dc fields are applied with an electromagnet, while a separate ceil provides a small ac drive field. The orientation between the applied dc field and the ac probing field can be varied. For de fields parallel to the crystal c-axis we observe significant anisotropy in the screening response for ac fields parallel to and perpendicular to the c-axis. 1. INTRODUCTION There has been significant interest recently in the vortex properties of the oxide superconductors. Some of the important questions to be addressed by experiment include the predicted existence of additional phase transitions in the mixed state as a consequence of their anisotropy, as well as the implications of disorder (i.e. pinning) on the phase diagram. Consequently we have studied the screening response in single crystals of superconducting Bi2SrsCaCu208 (2212) with Tc = 85I~ The inductive response of these currents probes the vortex response within the crystals as a function of temperature and applied field. Measurements were made using a first-order magnetic gradiometer, designed to allow the study of the anisotropic response of these materials. The magnetometer consists of a solenoid and two pick-up coils. The solenoid is driven with a small ac current (typically 0.1mA, producing a field of 5 mOe) of frequency Vae, the two coils are connected in opposition and the responses null-detected by a lock-in amplifier. Both real and imaginary components of the null signal are monitored. S~.....l~ ..1o~.1 ,,~h;.. one . e ,h~ pick-up ,,,,;l~ This technique allows the screening currents to be probed in a well-defiued and variable direction with respect to both the crystal axes and an external applied dc field. It further allows the ac screening response to be measured over a range of frequencies. 2. RESULTS AND DISCUSSION Only the case where the dc field is parallel to
the crystalline c-axis will be considered in this paper. Measurements have been made both with the ac field parallel to and perpendicular to the caxis. The m e a s u r e m e n t is made at constant dc magnetic field and the temperature is reduced slowly and at a uniform rate. The drive frequency Vac is 40kHz for the traces shown in Figure 1. On cooling, the in-phase component shows an onset of screening response and the out-of-phase component displays a dissipation peak. The origin of such a dissipation peak is consistent with electromagnetic skin depth effects within the crystal.1 Figure 2 shows the peak location as a function of field - the in-phase (x-) component shows similar variation. The peak occurs at a significantly higher temperature for the ease when the ae field is parallel to the c-axis than for the ac field perpendicular to the c-axis. Note that in the former case the screening currents are within the Cu-O layers, while in the latter case they are both within and between the layers. Recent theoretical work2,3 for the case of highly anisotropie superconductors predicts a phase diagram t h a t is qualitatively similar to the e21.[d~lLlX.LIt~llla~l.I $ ~ I ; 7 ~ U J L ~
L£~t ~ - a S u t x ~
•
•
theories the vortex solid is predicted to exhibit twostage melting, with 3D behavior at low fields and a crossover to more 2D behavior above a threshold, estimated to be of order 5kOe for our samples. For the low-field regime, the lowest temperature phase is expected to be the vortex solid (a lattice ha the absence of pinning), the intermediate phase is a vortex line liquid, and the high temperature phase is a liquid of unbound 2D planar vortices.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
2228
D.G Steel, ZM. Graybeal / Anisotropic AC screening response
Although it is tempting to directly compare d a t a with t h e s e theories, it is i m p o r t a n t to recognize t h a t s k i n depth effects add important size- and frequency-dependent factors to the data. Consequently, t h e theory should only be compared to the zero-frequency limit of such experiments. The use of a separate ac drive field readily allows the variation of the frequency with which the vortex structure is probed. Figure 3 shows the variation of tlhe y-component peak as a function of frequency at fixed field. This displays substantial d i s p e r s i o n e v e n at the lowest frequencies (vae=100Hz). This data rules out the existence of a finite t e m p e r a t u r e transition in the temperature and field regime shown in Figure 3. Cautious extrapolation of our present d a t a for the limit Vac-~0 suggests a n upper b o u n d for such a transition of order 25K. In s u m m a r y , t h e s e m e a s u r e m e n t s have shown t h a t in the presence of dc fields applied along the c-axis there is significant anisotropy between the ac screening along the Cu-O planes compared to perpendicular to them. For the case of ac field perpendicular to the planes, we have observed s t r o n g frequency dispersion in the screening response, which brings into question w h e t h e r t h e r e exists a finite t e m p e r a t u r e transition as Vac~0. Amplitude dispersion is seen f~r !vrger ac excitation levels; these measurements were made in the linear response regime.
I
t~O
I
9.o
I
I
[~Increasing dc FieldI-
~ 1.5 o
~ 1.0 ¢= 0.5 I
0.(
0
40
60 80 Temperature, K
100
FIG. 1: Real component of screening response for dc field parallel to and ac field perpendicular to caxis. Traces correspond to different dc fields. I
I
hl
I
I
I
_
"o
5-
I-
A a¢ field II c-axis [] a c f i e l d l c-axisl_
O
4o
A
3-0
A A
2o
A
1-
%
P Din I 3o 4 0 - 5 0
I
~1
60
70-80
Peak Temperature, K 3. ACKNOWLEDGEMENTS We would like to thank J.R. Clem and A.E. Koshelev for helpful discussions. We also thank L.G. Rubin a n d the Francis B i t t e r National Magnet Laboratory. This work was supported by the US Office of Naval Research via contract N00014-88-K-0479. DGS acknowledges support from the SERC (UK), and JMG acknowledges a Sloan Research Fellowship.
FIG. 2: Temperature of dissipation peak as a function of applied dc field (dc field parallel to c-axis). I
100
:~ 80
I
I
400 Oe field I 0 1600Oe fieldI O 3715Oe field[ ac field II c-axisI |
I~
O
N
~6040
o
o
REFERENCES 1. V.B. G e s h k e n b e i m , V.M. V i n o k u r and R. Fehrenbacher, Phys. Rev. B 43, 3748 (1991). 2. D.S. Fisher, M.P.A. Fisher and D.A. Huse, Phys. Rev. B 43, 130 (1991) 3. L.I. Glazman and A.E. Koshelev, Phys. Rev. B 43, 2835 (1991)
I
0
o o
o
~o ~ ~
ib~i
50 "~'" 60
i
70
Peak Temperature, K FIG. 3: T e m p e r a t u r e of dissipation p e a k as a function of ac field frequency (dc field and ac field parallel to c-axis).