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Microwave surface resistance in BSCCO crystal: magnetic field and angular measurement
Physica C 282-287
ELSEVIER
Microwave surface measurement.
resistance
(1997) 1985-1986
in BSCCO
crystal:
magnetic
field and angular
E.Silva a, R.Fastampa b, M.Giura b, R.Marcon a, C.Possanzini b, S.Sarti b, E.L.Wolf c. a Dipartimento di Fisica “E.Amaldi” and INFM, Universid “Roma Tre”, V. Vasca Navale 84,00146 Roma, Italy b Dipartimento di Fisica and INFM, Universita “La Sapienza”, P.le A.Moro 2,00185 Roma, Italy c Physics Department, Polytechnic University, Brooklyn, NY 11201, USA We report on measurement of the microwave surface resistance R,at 48 GHz on a BSCCO (2212 phase) crystal. We describe the procedure developed to perform measurements on crystals by the use of a resonant cavity with end-wall-replacement technique. The measurements are taken as a function of the temperature, magnetic field and angle Q between the field orientation and the (a,b) planes. The measured R, is strongly anisotropic. The overall angular behavior reasonably follows the rind scaling rule, but deviation from this simple behavior appears approaching the parallel orientation. When the field is parallel to the (a,b) planes, a local maximum is observed in R,,instead of a minimum. Finally, we show that the magnetic field dependence of R,cannot be easily reconciled with existing theories for the motion of rigid flux lines. 1. INTRODUCTION B&$2rCaCu208+x (BSCCO) is one of the most anisotropic high- T, superconductors (HTCS), and its properties are often described in terms of twodimensional compound. In particular, physical quantities that depend upon the external magnetic field H and the orientation 6 between the field and the (a,b) planes are thought to scale with ‘the rule [ 11: Q(H, 8) --) Q[H / f(fi>l
(1)
where f(9) is either l/sin9 (pure 2D model) or, in the quasi-2D or 3D models, it is given by:
and it contains the anisotropy ratio as defined by experiments E = H,,(O”)/ H,,(90°).Several confirmed this frame [2]. To apply the scaling rule to transport properties the relative direction of the transport current and the magnetic field should be kept constant. Moreover, it is known that the dissipation in BSCCO presents several peculiarities when H is applied along the (a,b) planes (namely, a dissipation peak instead of a minimum[3,4]), and sometimes this peculiar dissipation is ascribed to c-axis transport [4]. As a consequence of the giant anisotropy of BSCCO (E ranging up to 600), the study of the anisotropic properties requires single crystals or crystalline-quality films to avoid undesirable effects. However, the measurement of microwave surface impedance on small samples (such as single crystals) is a delicate issue: small samples are usually housed in the center of a resonant cavity (position (a) in 0921-4534/97/%17.00 0 Elsevier Science 8.V PII SO921-4534(97)01063-O
All
rightsresewed.
Fig.1). This configuration is strongly favoured, in terms of signal-to-noise ratio, with respect to the endwall position (position (b) in Fig.l), but the microwave field penetrates the sample inducing microwave currents both along the (a,b) planes and along the c axis. This effect can induce peculiar shapes of the dissipation as a function of T and H [5], related to the geometry of the experiment only. The control of the direction of the microwave current density J,- with respect to the crystallographic axes and to the direction of H is then a necessity. 2. EXPERIMENTAL
SETUP
Microwave surface resistance was measured by the end-wall-replacement technique. A resonant cavity mechanically tunable was employed. The field variation AR,(H)=R,(H)-R,(O)is given by:
AR,(H)=G[Q-l(H)-Q-'(O)] where G is a geometrical factor that can be calculated once the frequency (48 GHz), the cavity dimensions and the mode in the cavity (TEol 1) are known. Due to the smallness of the crystal, G is evaluated with a large uncertainty, but it results in a systematic scale factor only. Measurements were taken at fixed temperature, by sweeping the field up to 0.7 T at various angles. The Bi$2rCaCu208+x crystal was grown by directional solidification from the melt [6]. The crystal was repeteadly peeled onto one side in order to obtain a flat, smooth surface, and it was cut in a circular sector shape, of dimensions -2 x 1 mm2.
1986
E. Silua et al. /Physica
coupling iris hole
glass platelet
C 282-287 (1997) 19X-1986
Ag layer
Tuning s
2 0.2
Fig.1: Sketch of the cavity, crystal position (not to scale) and microwave currents direction (dotted line). The crystal was attached to a thin glass platelet with GE703 1 varnish. Subsequently, the “rear” of the crystal and all the glass platelet was covered with an Ag evaporation. The so-obtained sandwich was mounted as an end wall of the cavity (depicted in Fig.l), and backed by an indium foil and a massive copper block. In this way we obtained (a) good conductivity of the end-wall, without interruptions of the (circular) microwave currents; (b) TEM mode suppression by the glass spacing; (c) almost straight microwave current path on the crystal, with .!$I H; (d) Jr-// (a,b) planes only. The glass platelet was mounted to place the crystal at the maximum microwave electric field location. H could be tilted with respect to the (a,b) planes. R,(T) and ac susceptibility gave T, = 80.0 zk 0.5 K. 3. RESULTS
AND DISCUSSION
In Fig.2 we report AR,(H) for 6=6.5”+90” at 70 K. The constant orientation of H with respect to Jrf allows us to apply the scaling rule, Eq.(l). Successful scaling is obtained. The experimental f(s) (plotted in the insert), coincides with Usin6, or with f(s) = (sin26 + ~-~cos~fi)-~‘~ (3D anisotropic function) with E = 50 as a lower bound. Due to the anomaly described below, we cannot identify the scaling function, but we just demonstrate that a scaling exists, with anisotropy not less than 50.
0.1
0
0 0.5 I-I U) Fig.3: Peaked AR, for 6 = 0” and flat dissipation for Q = 3.5’, at T = 70 K. Below 6.5” the dissipation suddenly drops, and at 6 = 3.5” it is flat: the magnetic field has almost no effect. At 6 = O”, the dissipation raises to a small (compare the vertical scales in Figs. 2 and 3) peak at Hpeak = 0.2 T, and slowly decreases (Fig.3). A very similar behavior was reported previously [4]: the flattening was ascribed to a lock-in transition, and the peak to c-axis dissipation. However, while the lock-in transition could explain the flattening of our data at 6 = 3.5”, our geometry rules out the explanation of the peak in terms of c-axis transport. Further measurements are underway to study in depth the dissipation close to the parallel orientation. In summary, we have presented measurements of the anisotropic, field-dependent surface resistance at 48 GHz taken on a BSCCO single crystal with Jr.// (a,b) and Jr.J_ H (constant Lorentz-force configuration). The scaling rule, Eq.( l), is obeyed up to -5” from the (a,b) planes. We give a lower bound for e. When H // (a,b) we find a peak in the magnetic response, whose origin is not yet clear but it does not lie on c-axis properties, as ruled out by the fact that J,.f// (a,b) planes. REFERENCES
0
0.5
H / f@) V)
Fig.2: Scaled AR, for 192 6.5” (T = 70 K). Inset: scaling function I and comparison with theory.
1 Z.Hao, J.R.Clem, Phys. Rev. B 46 (1992) 5853 2 H.Raffy et al., Phys. Rev. Leti. 66 (1991) 2515; R.Fastampa et al., Phys. Rev. B 49 (1994) 15959; R.Marcon et al., Phys. Rev. B 50 (1994) 13684 3 Y.Iye et al., Physicu C 174 (1991) 227; R.Fastampa et al., Europhys. Lett. 18 (1992) 75 4 H.Enriquez et al., Phys. Rev. B 53 (1996) R14757 5 N.Exon et al., IEEE Trans. Appl. Supercond. 3 (1993) 1442; C.E.Gough et al., Phys. Rev. B 50 (1994) 488 6 H.J.Tao et al., Phys. Rev. B 45 (1992) 10622
ELSEVIER
Microwave surface measurement.
resistance
(1997) 1985-1986
in BSCCO
crystal:
magnetic
field and angular
E.Silva a, R.Fastampa b, M.Giura b, R.Marcon a, C.Possanzini b, S.Sarti b, E.L.Wolf c. a Dipartimento di Fisica “E.Amaldi” and INFM, Universid “Roma Tre”, V. Vasca Navale 84,00146 Roma, Italy b Dipartimento di Fisica and INFM, Universita “La Sapienza”, P.le A.Moro 2,00185 Roma, Italy c Physics Department, Polytechnic University, Brooklyn, NY 11201, USA We report on measurement of the microwave surface resistance R,at 48 GHz on a BSCCO (2212 phase) crystal. We describe the procedure developed to perform measurements on crystals by the use of a resonant cavity with end-wall-replacement technique. The measurements are taken as a function of the temperature, magnetic field and angle Q between the field orientation and the (a,b) planes. The measured R, is strongly anisotropic. The overall angular behavior reasonably follows the rind scaling rule, but deviation from this simple behavior appears approaching the parallel orientation. When the field is parallel to the (a,b) planes, a local maximum is observed in R,,instead of a minimum. Finally, we show that the magnetic field dependence of R,cannot be easily reconciled with existing theories for the motion of rigid flux lines. 1. INTRODUCTION B&$2rCaCu208+x (BSCCO) is one of the most anisotropic high- T, superconductors (HTCS), and its properties are often described in terms of twodimensional compound. In particular, physical quantities that depend upon the external magnetic field H and the orientation 6 between the field and the (a,b) planes are thought to scale with ‘the rule [ 11: Q(H, 8) --) Q[H / f(fi>l
(1)
where f(9) is either l/sin9 (pure 2D model) or, in the quasi-2D or 3D models, it is given by:
and it contains the anisotropy ratio as defined by experiments E = H,,(O”)/ H,,(90°).Several confirmed this frame [2]. To apply the scaling rule to transport properties the relative direction of the transport current and the magnetic field should be kept constant. Moreover, it is known that the dissipation in BSCCO presents several peculiarities when H is applied along the (a,b) planes (namely, a dissipation peak instead of a minimum[3,4]), and sometimes this peculiar dissipation is ascribed to c-axis transport [4]. As a consequence of the giant anisotropy of BSCCO (E ranging up to 600), the study of the anisotropic properties requires single crystals or crystalline-quality films to avoid undesirable effects. However, the measurement of microwave surface impedance on small samples (such as single crystals) is a delicate issue: small samples are usually housed in the center of a resonant cavity (position (a) in 0921-4534/97/%17.00 0 Elsevier Science 8.V PII SO921-4534(97)01063-O
All
rightsresewed.
Fig.1). This configuration is strongly favoured, in terms of signal-to-noise ratio, with respect to the endwall position (position (b) in Fig.l), but the microwave field penetrates the sample inducing microwave currents both along the (a,b) planes and along the c axis. This effect can induce peculiar shapes of the dissipation as a function of T and H [5], related to the geometry of the experiment only. The control of the direction of the microwave current density J,- with respect to the crystallographic axes and to the direction of H is then a necessity. 2. EXPERIMENTAL
SETUP
Microwave surface resistance was measured by the end-wall-replacement technique. A resonant cavity mechanically tunable was employed. The field variation AR,(H)=R,(H)-R,(O)is given by:
AR,(H)=G[Q-l(H)-Q-'(O)] where G is a geometrical factor that can be calculated once the frequency (48 GHz), the cavity dimensions and the mode in the cavity (TEol 1) are known. Due to the smallness of the crystal, G is evaluated with a large uncertainty, but it results in a systematic scale factor only. Measurements were taken at fixed temperature, by sweeping the field up to 0.7 T at various angles. The Bi$2rCaCu208+x crystal was grown by directional solidification from the melt [6]. The crystal was repeteadly peeled onto one side in order to obtain a flat, smooth surface, and it was cut in a circular sector shape, of dimensions -2 x 1 mm2.
1986
E. Silua et al. /Physica
coupling iris hole
glass platelet
C 282-287 (1997) 19X-1986
Ag layer
Tuning s
2 0.2
Fig.1: Sketch of the cavity, crystal position (not to scale) and microwave currents direction (dotted line). The crystal was attached to a thin glass platelet with GE703 1 varnish. Subsequently, the “rear” of the crystal and all the glass platelet was covered with an Ag evaporation. The so-obtained sandwich was mounted as an end wall of the cavity (depicted in Fig.l), and backed by an indium foil and a massive copper block. In this way we obtained (a) good conductivity of the end-wall, without interruptions of the (circular) microwave currents; (b) TEM mode suppression by the glass spacing; (c) almost straight microwave current path on the crystal, with .!$I H; (d) Jr-// (a,b) planes only. The glass platelet was mounted to place the crystal at the maximum microwave electric field location. H could be tilted with respect to the (a,b) planes. R,(T) and ac susceptibility gave T, = 80.0 zk 0.5 K. 3. RESULTS
AND DISCUSSION
In Fig.2 we report AR,(H) for 6=6.5”+90” at 70 K. The constant orientation of H with respect to Jrf allows us to apply the scaling rule, Eq.(l). Successful scaling is obtained. The experimental f(s) (plotted in the insert), coincides with Usin6, or with f(s) = (sin26 + ~-~cos~fi)-~‘~ (3D anisotropic function) with E = 50 as a lower bound. Due to the anomaly described below, we cannot identify the scaling function, but we just demonstrate that a scaling exists, with anisotropy not less than 50.
0.1
0
0 0.5 I-I U) Fig.3: Peaked AR, for 6 = 0” and flat dissipation for Q = 3.5’, at T = 70 K. Below 6.5” the dissipation suddenly drops, and at 6 = 3.5” it is flat: the magnetic field has almost no effect. At 6 = O”, the dissipation raises to a small (compare the vertical scales in Figs. 2 and 3) peak at Hpeak = 0.2 T, and slowly decreases (Fig.3). A very similar behavior was reported previously [4]: the flattening was ascribed to a lock-in transition, and the peak to c-axis dissipation. However, while the lock-in transition could explain the flattening of our data at 6 = 3.5”, our geometry rules out the explanation of the peak in terms of c-axis transport. Further measurements are underway to study in depth the dissipation close to the parallel orientation. In summary, we have presented measurements of the anisotropic, field-dependent surface resistance at 48 GHz taken on a BSCCO single crystal with Jr.// (a,b) and Jr.J_ H (constant Lorentz-force configuration). The scaling rule, Eq.( l), is obeyed up to -5” from the (a,b) planes. We give a lower bound for e. When H // (a,b) we find a peak in the magnetic response, whose origin is not yet clear but it does not lie on c-axis properties, as ruled out by the fact that J,.f// (a,b) planes. REFERENCES
0
0.5
H / f@) V)
Fig.2: Scaled AR, for 192 6.5” (T = 70 K). Inset: scaling function I and comparison with theory.
1 Z.Hao, J.R.Clem, Phys. Rev. B 46 (1992) 5853 2 H.Raffy et al., Phys. Rev. Leti. 66 (1991) 2515; R.Fastampa et al., Phys. Rev. B 49 (1994) 15959; R.Marcon et al., Phys. Rev. B 50 (1994) 13684 3 Y.Iye et al., Physicu C 174 (1991) 227; R.Fastampa et al., Europhys. Lett. 18 (1992) 75 4 H.Enriquez et al., Phys. Rev. B 53 (1996) R14757 5 N.Exon et al., IEEE Trans. Appl. Supercond. 3 (1993) 1442; C.E.Gough et al., Phys. Rev. B 50 (1994) 488 6 H.J.Tao et al., Phys. Rev. B 45 (1992) 10622