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Temperature dependence of rf and microwave absorption in granular HTSC-determination of Josephson and grain penetration depths
Solid State Communications.Vol. 106. No. 4, pp. 203-206, 1998 0 1998 Publishedby Elscvier Science Ltd Printed in Great Britain 0038-1098l98 $19.00+.00
Pergamon
PII: SOO38-1098(98)00022-2
TEMPERATURE DEPENDENCE OF rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC-DETERMINATION OF JOSEPHSON AND GRAIN PENETRATION DEPTHS P.V. Patanjali,” V. Seshu Bai,b R. Pinto,” M.D. Sastry’ and R. Vijayaraghavand** *Solid State Electronics Group, Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India bSchool of Physics, University of Hyderabad, Hyderabad 500 046, India ‘Radio Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India dSAMEER, IIT Campus Powai, Mumbai 400 076, India (Received 17 November 1997; accepted 24 December 1997 by C.N.R. Rao)
Temperature dependence of power absorption of HTSCs is found to follow the London two fluid model at both radio and microwave frequencies. The two fluid model is shown to account for the Josephson penetration depth at radio frequencies (MHz) and grain penetration depth at microwave frequencies in sintered HTSCs. The Josephson penetration depth determined is of the order of 100 pm. Also, it is discussed that reduced superelectron screening due to short mean free path in HTSC cannot account for the large penetration depth determined from the radio frequency absorption. 0 1998 Published by Elsevier Science Ltd
1. INTRODUCTION Penetration depth has assumed tremendous importance because of its bearing on the mechanism of superconductivity in general and on the nature of pairing states in particular. Various experimental methods have been used to determine the penetration depth in single crystals of HTSCs [l-4]. Steinmeyer et al. [5] have used a pictorquemeter to determine Xt, penetration depth when the screening currents flow in the CuO layers and XI, the inter-plane penetration depth and found XI in BSCCO to be 200 pm. Similar high values XI have been reported by two other groups [6, 71. While there have been many reports on the measurement of intrinsic penetration depth less is known about the Josephson penetration depth in HTSCs and its precise determination. High frequency absorption is one of the sensitive methods used to determine the penetration depth accurately. In our previous report we have determined from the microwave absorption measurements penetration depth of polycrystalline BSCCO to be 0.4 pm [8]. In the present the results of temperature dependent radio (MHz) and microwave (GHz) frequency absorption in polycrystalline
* Author to whom all correspondence addressed.
should be
GdBCO and BSCCO are presented. London two fluid formalism for surface resistance is modified and is used to determine grain penetration depth, X, and intergrain penetration depth, h,. A close observation between the results at MHz and GHz frequencies leads to the conclusion that determination of intergranular penetration depth XJ of granular HTSCs is possible only at radio frequencies and below that. 2. EXPERIMENTAL AND RESULTS Single phase BSCCO (Bi,.~PbO.$rI.$aZCu~Oy) and GdBCO (GdBa2Cu307) are used for the present study. Sample preparation and characterization are given elsewhere [9, lo]. Temperature dependence of radio frequency absorption is carried out using a home made marginal oscillator. Fabrication of the oscillator and the details of the power absorption measurements are given elsewhere [lo]. Sample is placed in the tank coil of the oscillator and as the temperature is varied power output of the oscillator is monitored. Absorption through transition is monitored while warming and cooling the sample at the rate of 0.5 K min-’ and both responses are found to match each other confirming zero temperature gradient between the sample and the sensor and validity of the T, determined. Temperature dependence of microwave absorption is measured using cavity perturbation
203
204
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
technique by monito~ng the microwave power reflected at the cavity ~equency as a function of temperature. For the sake of convenience and comparison between various samples no~alized power abso~tion is de~ned as
where, PN is the absorption above T,. Tmin is chosen such that p(7) is nearly a constant for T < Tmins In Figs. l(a) and (b) variation of power absorption (P(T)) in GdBCO at radio and microwave frequency (9.9 GHz) is shown. Figures 2(a) and (b) show the same in BSCCO.
Vol. 106, No. 4
RSCY’O
(ai 11 9 MHz
i
0.0 -
3. MODEL AND ANALYSIS For stations conditions the electric field does not penetrate the superconductor whereas magnetic field enters the surface layer of thickness X, For non stationary conditions, the magnetic field induces electric field which in turn accelerates the normal electrons. The loss
GdBt’O (a)
I 90
11 9 MHz
’ 00
1 ti:,
Temperature
Fig. 2. Temperature dependence of radio (a) and microwave (b) frequency absorption in BSCCO HTSC. Solid lines are the fits to the model.
Cb)
9.9
GHZ
Fig. 1. Tern~mt~e dependence of radio (a) and microwave (b) frequency abso~tion in GdBCO HTSC. Solid lines are the fits to the model.
in a superconductor is mostly due to these normal electrons which contribute to the power absorption. At low frequencies when the electromagnetic skin depth 6 > A it is the h which limits the penetration of the induced electric field. At sufficiently high frequencies when 6 < h, it is the skin depth which determines the region in which the electrons involve in the conduction process and thereby contribute to the power absorption. Since generally skin depth is always more than the intrinsic penetration depth, XL at least up to about 100 GHz, irrespective of the frequency of operation the ~netratiou depth measurement yields XL. However, in the case of granular HTSCs due to a large number of intergranular Josephson junctions present in the material, one would come across a situation where in 6 < X, at high frequencies and 6 > hi at low frequencies. In such a case only in the latter condition can one be able to determine the precise value of hX7’) and the changes in it with respect to temperature. For granuIar HTSCs with Josephson junctions in between the grains the material can be modeled as shown in Fig. 3. The shielding current flows through the material encompassing Josephson junctions of various strengths. It flows through a depth
Vol. 106, No. 4
205
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
and A/(7’) = @/2e~aX,(T)J&T) with J,J the intergranular Josephson critical current density. Considering J&) = J&0)(1 - (TIT,)) [12] XJ(T) can be written as
/ 6mw
&(I-) =
&i(O)
Jdcmip/rI- (TIT,)I
(4)
The resistivities of GdBCO and BSCCO just above their respective transition temperatures are 10 pa m-l and 15 psllm-’ , respectively. In either case the skin depth at MHz is = 500 pm and at GHz is = 10 pm. Following c & J the model discussed above it is underst~dable that X,(T) Fig. 3. Schematic diagram of the polyc~s~lline HTSC which is of the order of 100 pm can be dete~in~ only with grain (g) and inter~ain regions (4. Field penetrates when the skin depth is more than this value, that is in trough a distance Xgtiin the grain and Ai in the inter-granular region. 6 and Fi”” represent the r-f and MHz frequency range. In GHz range since the am” is 10 ,um, the change in X,(7) alone is monitored. Table 1 microwave skin depths, respectively. shows the skin depths at MHz and GHz for both GdBCO X, in the grain and X, in the intergrain region. The Xi in and BSCCO and the co~esponding X,(O) and X,(O) the Fig. 3 is an average intergranular penetration depth. which are obtained from the fits to the model. It is 8”‘” and 6” are the skin depths of the normal fluid at GHz worth noting that h,(O) values obtained from absorption response at both MHz and GHz match reasonably well and MHz frequency, respectively. A theory of high frequency absorption of super- giving validity to the form of Xeff [equation (2)] and conductors relating it to the penetration depth of a thereby the model. It can be seen from the table that X, of BSCCO is static magnetic field has been given by London [1X]. larger than that of GdBCO. The density of GdBCO is The normalized power absorption p(t) in this formalism 92% and that of BSCCO is 55% [lo]. Therefore, the is given by intergranular junctions in GdBCO are strongly coupled and that in BSCCO are weakly coupled which results in p(T) _ dP _ AX 411 + (fiM&)4]“2 - 1 higher value of XJ in the latter. As a matter of fact PN polycrystalline HTSCs have grains of various sizes and 6n shapes and intergranular couplings of varying strengths where 6, = [2/~awcr,]“*, 61 = [2/j~uar]“* are the elec- which should give rise a large variation in both X, and X,. tromagnetic skin depths. u, and 01 = Re (a) are the The present two level analysis gives only the average values of these parameters. conductivities in the normal and superconducting The mean free path in HTSC is small. The principal states. X is the penetration depth. In the case of granular HTSCs the X in the equation effect of short mean path is to reduce the superelectron (1) should represent an effective penetration depth, he“, screening so that the imaginary part of conductivity u2, rather than the London penetration depth. Hence for a which is due to the superfluid, becomes u;ff = (Xt/xeff)*a2 = gz/g2 where, g is the reduction factor of granular superconductor one should write screening, while normal fluid conductivity, u,, is unchanged. Effectively the aeff results in a change in (2) penetration depth so the X in equation (1) becomes
JYTZi7
(11
where (3)
“gX”. Previously it was suggested that penetration depth determined from radio frequency absorption is large because of the reduced superelectron screening [ 131 and that the g value determined was 240 which is an order of magnitude larger than that found by Sridhar
Table 1. Various parameters obtained from the model analysis Sample
~~~~m
6:
mw 6,
x:
bow
~~(0)
GdBCO BSCCO
IO 15
460 564
15 19
0.36 0.41
0.39 0.43
81 113
206
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
ef al. [14]. The authors of [13] attributed such an apparent increase in g to its frequency dependence. We, however, feel that the value of g does not have any frequency dependence as the mean free path does not vary with frequency. Further the high value of X”” (72 pm, [13]) can be better understood by considering the contributions from both X, and X, to A& following equations (2) and (1) and our analysis presented here. At this juncture it should be stated that in the h,(O) and AhO) values reported here (see Table 1) no correction has been made to incorporate the effects of reduced superelectron screening. 4. CONCLUSIONS In suck the results of tem~m~re dependent radio and microwave frequency abortion in GdBCO and BSCCO are reported. The London two fluid model is modified to account for the changes in h,(T) and X,(7’)of granular HTSCs aud the results at both MHz and GHz are found to follow the model well. Values of grain and Josephson penetration depths of polycrystalline HTSCs are determined. XJiO) of BSCCO is found to be larger than that of GdBCO. It has also been discussed that reduced superelectron screening due to short mean path in HTSC, though increases h, and XJ, per se cannot account for the large penetration depth determined from radio frequency absorption.
Vol. 106. No. 4
REFERENCES 1. Harshman, D.R., Schneemeyer,
2. 3. 4. 5. 6.
L.F., Waszczak, J.V., Aeppli, G., Cava, R.J., Batlogg, B., Rupp, L.W., Ansaldo, E.J. and Williams, D.L., Phys. Rev., B39, 1989,85 1. Cooper, J.R., Forro, L. and Keszei, B,, Nature, 343, 1990,444. Umezawa, A., Crabtree, G.W., Liu, J.Z., Moran, T.J., Malik, SK., Nunez, L.H., Kwak, W.L. and Sowers, C.H., Phys. Rev., B38, 1988,2843. Mitra, S., Cho, J.H., Lee, W.C., Johnston, D.C. and Kogan, V.G., Phys. Rev., B40, 1989,2674. Steinmeyer, F., Kleiner, R., Muller, P., Muller, H. and Winzer, K., Europhys. I&t., 25, 1994,459. Takahashi, T., Kanoda, K. and Saito, G., Jpn. J.
AppE. Phys., 7,1992,414. Tea, N.H., Physku, C280, 1997,28 1.
:: 9. 10. 11. 12. 13. 14.
Seshu Bai, V., Patanjali, P.V., Bhagat, S.M. and Tyagi, S., J. Supercon., 8, 1995,299. Seshu Bai, V., Ravi, S., Rajasekharan, T. and Gopalair, R., J. Appl. Phys., 70, 1991,4378. Patanjali, P.V., Ph.D. thesis, Univ. of Hyderabad, Hyderabad, 500 046, India, 1997. London, F., Super@&, Vol. 1, p. 86. Dover Publications, 1961. Halbritter, J., Phys. Rev., B46, 1992, 14861. Sen, D., Ghatak, S.K., Chopra, K.L., Markandeyulu, G. and Bhattachatya, D., Solid State Commun., 79, 1991,935. Sridhar, S., Shiffman, C.A. and Hamdeh, H., Phys. Rev., B36,1987,2301.
Pergamon
PII: SOO38-1098(98)00022-2
TEMPERATURE DEPENDENCE OF rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC-DETERMINATION OF JOSEPHSON AND GRAIN PENETRATION DEPTHS P.V. Patanjali,” V. Seshu Bai,b R. Pinto,” M.D. Sastry’ and R. Vijayaraghavand** *Solid State Electronics Group, Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India bSchool of Physics, University of Hyderabad, Hyderabad 500 046, India ‘Radio Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India dSAMEER, IIT Campus Powai, Mumbai 400 076, India (Received 17 November 1997; accepted 24 December 1997 by C.N.R. Rao)
Temperature dependence of power absorption of HTSCs is found to follow the London two fluid model at both radio and microwave frequencies. The two fluid model is shown to account for the Josephson penetration depth at radio frequencies (MHz) and grain penetration depth at microwave frequencies in sintered HTSCs. The Josephson penetration depth determined is of the order of 100 pm. Also, it is discussed that reduced superelectron screening due to short mean free path in HTSC cannot account for the large penetration depth determined from the radio frequency absorption. 0 1998 Published by Elsevier Science Ltd
1. INTRODUCTION Penetration depth has assumed tremendous importance because of its bearing on the mechanism of superconductivity in general and on the nature of pairing states in particular. Various experimental methods have been used to determine the penetration depth in single crystals of HTSCs [l-4]. Steinmeyer et al. [5] have used a pictorquemeter to determine Xt, penetration depth when the screening currents flow in the CuO layers and XI, the inter-plane penetration depth and found XI in BSCCO to be 200 pm. Similar high values XI have been reported by two other groups [6, 71. While there have been many reports on the measurement of intrinsic penetration depth less is known about the Josephson penetration depth in HTSCs and its precise determination. High frequency absorption is one of the sensitive methods used to determine the penetration depth accurately. In our previous report we have determined from the microwave absorption measurements penetration depth of polycrystalline BSCCO to be 0.4 pm [8]. In the present the results of temperature dependent radio (MHz) and microwave (GHz) frequency absorption in polycrystalline
* Author to whom all correspondence addressed.
should be
GdBCO and BSCCO are presented. London two fluid formalism for surface resistance is modified and is used to determine grain penetration depth, X, and intergrain penetration depth, h,. A close observation between the results at MHz and GHz frequencies leads to the conclusion that determination of intergranular penetration depth XJ of granular HTSCs is possible only at radio frequencies and below that. 2. EXPERIMENTAL AND RESULTS Single phase BSCCO (Bi,.~PbO.$rI.$aZCu~Oy) and GdBCO (GdBa2Cu307) are used for the present study. Sample preparation and characterization are given elsewhere [9, lo]. Temperature dependence of radio frequency absorption is carried out using a home made marginal oscillator. Fabrication of the oscillator and the details of the power absorption measurements are given elsewhere [lo]. Sample is placed in the tank coil of the oscillator and as the temperature is varied power output of the oscillator is monitored. Absorption through transition is monitored while warming and cooling the sample at the rate of 0.5 K min-’ and both responses are found to match each other confirming zero temperature gradient between the sample and the sensor and validity of the T, determined. Temperature dependence of microwave absorption is measured using cavity perturbation
203
204
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
technique by monito~ng the microwave power reflected at the cavity ~equency as a function of temperature. For the sake of convenience and comparison between various samples no~alized power abso~tion is de~ned as
where, PN is the absorption above T,. Tmin is chosen such that p(7) is nearly a constant for T < Tmins In Figs. l(a) and (b) variation of power absorption (P(T)) in GdBCO at radio and microwave frequency (9.9 GHz) is shown. Figures 2(a) and (b) show the same in BSCCO.
Vol. 106, No. 4
RSCY’O
(ai 11 9 MHz
i
0.0 -
3. MODEL AND ANALYSIS For stations conditions the electric field does not penetrate the superconductor whereas magnetic field enters the surface layer of thickness X, For non stationary conditions, the magnetic field induces electric field which in turn accelerates the normal electrons. The loss
GdBt’O (a)
I 90
11 9 MHz
’ 00
1 ti:,
Temperature
Fig. 2. Temperature dependence of radio (a) and microwave (b) frequency absorption in BSCCO HTSC. Solid lines are the fits to the model.
Cb)
9.9
GHZ
Fig. 1. Tern~mt~e dependence of radio (a) and microwave (b) frequency abso~tion in GdBCO HTSC. Solid lines are the fits to the model.
in a superconductor is mostly due to these normal electrons which contribute to the power absorption. At low frequencies when the electromagnetic skin depth 6 > A it is the h which limits the penetration of the induced electric field. At sufficiently high frequencies when 6 < h, it is the skin depth which determines the region in which the electrons involve in the conduction process and thereby contribute to the power absorption. Since generally skin depth is always more than the intrinsic penetration depth, XL at least up to about 100 GHz, irrespective of the frequency of operation the ~netratiou depth measurement yields XL. However, in the case of granular HTSCs due to a large number of intergranular Josephson junctions present in the material, one would come across a situation where in 6 < X, at high frequencies and 6 > hi at low frequencies. In such a case only in the latter condition can one be able to determine the precise value of hX7’) and the changes in it with respect to temperature. For granuIar HTSCs with Josephson junctions in between the grains the material can be modeled as shown in Fig. 3. The shielding current flows through the material encompassing Josephson junctions of various strengths. It flows through a depth
Vol. 106, No. 4
205
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
and A/(7’) = @/2e~aX,(T)J&T) with J,J the intergranular Josephson critical current density. Considering J&) = J&0)(1 - (TIT,)) [12] XJ(T) can be written as
/ 6mw
&(I-) =
&i(O)
Jdcmip/rI- (TIT,)I
(4)
The resistivities of GdBCO and BSCCO just above their respective transition temperatures are 10 pa m-l and 15 psllm-’ , respectively. In either case the skin depth at MHz is = 500 pm and at GHz is = 10 pm. Following c & J the model discussed above it is underst~dable that X,(T) Fig. 3. Schematic diagram of the polyc~s~lline HTSC which is of the order of 100 pm can be dete~in~ only with grain (g) and inter~ain regions (4. Field penetrates when the skin depth is more than this value, that is in trough a distance Xgtiin the grain and Ai in the inter-granular region. 6 and Fi”” represent the r-f and MHz frequency range. In GHz range since the am” is 10 ,um, the change in X,(7) alone is monitored. Table 1 microwave skin depths, respectively. shows the skin depths at MHz and GHz for both GdBCO X, in the grain and X, in the intergrain region. The Xi in and BSCCO and the co~esponding X,(O) and X,(O) the Fig. 3 is an average intergranular penetration depth. which are obtained from the fits to the model. It is 8”‘” and 6” are the skin depths of the normal fluid at GHz worth noting that h,(O) values obtained from absorption response at both MHz and GHz match reasonably well and MHz frequency, respectively. A theory of high frequency absorption of super- giving validity to the form of Xeff [equation (2)] and conductors relating it to the penetration depth of a thereby the model. It can be seen from the table that X, of BSCCO is static magnetic field has been given by London [1X]. larger than that of GdBCO. The density of GdBCO is The normalized power absorption p(t) in this formalism 92% and that of BSCCO is 55% [lo]. Therefore, the is given by intergranular junctions in GdBCO are strongly coupled and that in BSCCO are weakly coupled which results in p(T) _ dP _ AX 411 + (fiM&)4]“2 - 1 higher value of XJ in the latter. As a matter of fact PN polycrystalline HTSCs have grains of various sizes and 6n shapes and intergranular couplings of varying strengths where 6, = [2/~awcr,]“*, 61 = [2/j~uar]“* are the elec- which should give rise a large variation in both X, and X,. tromagnetic skin depths. u, and 01 = Re (a) are the The present two level analysis gives only the average values of these parameters. conductivities in the normal and superconducting The mean free path in HTSC is small. The principal states. X is the penetration depth. In the case of granular HTSCs the X in the equation effect of short mean path is to reduce the superelectron (1) should represent an effective penetration depth, he“, screening so that the imaginary part of conductivity u2, rather than the London penetration depth. Hence for a which is due to the superfluid, becomes u;ff = (Xt/xeff)*a2 = gz/g2 where, g is the reduction factor of granular superconductor one should write screening, while normal fluid conductivity, u,, is unchanged. Effectively the aeff results in a change in (2) penetration depth so the X in equation (1) becomes
JYTZi7
(11
where (3)
“gX”. Previously it was suggested that penetration depth determined from radio frequency absorption is large because of the reduced superelectron screening [ 131 and that the g value determined was 240 which is an order of magnitude larger than that found by Sridhar
Table 1. Various parameters obtained from the model analysis Sample
~~~~m
6:
mw 6,
x:
bow
~~(0)
GdBCO BSCCO
IO 15
460 564
15 19
0.36 0.41
0.39 0.43
81 113
206
rf AND MICROWAVE ABSORPTION IN GRANULAR HTSC
ef al. [14]. The authors of [13] attributed such an apparent increase in g to its frequency dependence. We, however, feel that the value of g does not have any frequency dependence as the mean free path does not vary with frequency. Further the high value of X”” (72 pm, [13]) can be better understood by considering the contributions from both X, and X, to A& following equations (2) and (1) and our analysis presented here. At this juncture it should be stated that in the h,(O) and AhO) values reported here (see Table 1) no correction has been made to incorporate the effects of reduced superelectron screening. 4. CONCLUSIONS In suck the results of tem~m~re dependent radio and microwave frequency abortion in GdBCO and BSCCO are reported. The London two fluid model is modified to account for the changes in h,(T) and X,(7’)of granular HTSCs aud the results at both MHz and GHz are found to follow the model well. Values of grain and Josephson penetration depths of polycrystalline HTSCs are determined. XJiO) of BSCCO is found to be larger than that of GdBCO. It has also been discussed that reduced superelectron screening due to short mean path in HTSC, though increases h, and XJ, per se cannot account for the large penetration depth determined from radio frequency absorption.
Vol. 106. No. 4
REFERENCES 1. Harshman, D.R., Schneemeyer,
2. 3. 4. 5. 6.
L.F., Waszczak, J.V., Aeppli, G., Cava, R.J., Batlogg, B., Rupp, L.W., Ansaldo, E.J. and Williams, D.L., Phys. Rev., B39, 1989,85 1. Cooper, J.R., Forro, L. and Keszei, B,, Nature, 343, 1990,444. Umezawa, A., Crabtree, G.W., Liu, J.Z., Moran, T.J., Malik, SK., Nunez, L.H., Kwak, W.L. and Sowers, C.H., Phys. Rev., B38, 1988,2843. Mitra, S., Cho, J.H., Lee, W.C., Johnston, D.C. and Kogan, V.G., Phys. Rev., B40, 1989,2674. Steinmeyer, F., Kleiner, R., Muller, P., Muller, H. and Winzer, K., Europhys. I&t., 25, 1994,459. Takahashi, T., Kanoda, K. and Saito, G., Jpn. J.
AppE. Phys., 7,1992,414. Tea, N.H., Physku, C280, 1997,28 1.
:: 9. 10. 11. 12. 13. 14.
Seshu Bai, V., Patanjali, P.V., Bhagat, S.M. and Tyagi, S., J. Supercon., 8, 1995,299. Seshu Bai, V., Ravi, S., Rajasekharan, T. and Gopalair, R., J. Appl. Phys., 70, 1991,4378. Patanjali, P.V., Ph.D. thesis, Univ. of Hyderabad, Hyderabad, 500 046, India, 1997. London, F., Super@&, Vol. 1, p. 86. Dover Publications, 1961. Halbritter, J., Phys. Rev., B46, 1992, 14861. Sen, D., Ghatak, S.K., Chopra, K.L., Markandeyulu, G. and Bhattachatya, D., Solid State Commun., 79, 1991,935. Sridhar, S., Shiffman, C.A. and Hamdeh, H., Phys. Rev., B36,1987,2301.