Nonlinear response of suspended high temperature ... - IEEE Xplore
1753
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTTVITY,VOL. 5, NO. 2,JUNE 1995
Nonlinear Response of Suspended High Temperature Superconducting Thin Film Microwave Resonators Balam A. Willemsena9b,John S. Derovb, Jos6 H. Silvab and S. Sridhar" OPhysics Department, Northeastern Univeristy, Boston, MA 02115 bRome Laboratory, Hanscom AFB., Bedford, MA 01730, USA.
Abstract-The nonlinear microwave surface impedance, Z,(H,r) of Y1Ba2Cu307-6 thin films is measured using suspended patterned resonators. We find that the nonlinear response is well described in terms of a single mechanism, namely the hysteretic ac response of the current-induced critical state.
I. INTRODUCTION A characteristic feature of the high T, superconductors is the very strong power dependence of the microwave response for even moderate microwave powers or surface magnetic fields Hfi[l]. A new explanation of this phenomena has recently become available[2]. In th'is paper we report on results which form part of a comprehensive set of experiments designed to study vortex dynamics and flux penetration using patterned structures resonant at microwave frequencies. The basic parameter measured is the surface impedance 2, = R, iX,.The experiments were specially designed to enable application of dc magnetic fields H d c and to also study the nonlinear response as a function of the microwave magnetic field H,f (or equivalently power). A key feature of the experiments is the high sensitivity over a wide range of Hdc (% 1 Oe to 6 T ) and H d (0 to 1 kOe). This enables precise tests of several issues relating to vortex dynamics and flux penetration in both the field-induced and current-induced critical state. In this paper we will concentrate on the nonlinear rf response. The dc field results will be presented elsewhere[3]. We measure this nonlinear response in terms of 2,(H,f, 7'). We show that the observed nonlinear response is very well described in terms of hysteretic losses due to the ac response of a current-induced critical state. Specifically, the experimental data are in reasonable agreement with a calculation for such hysteretic losses in a rectangular strip. Overall, our data and accompanying analysis provides a new perspective into high frequency response in terms of critical state flux penetration, and a unified picture of a variety of phenomena at fields comparable to H , = J,d, which were not properly explained previously.
11. EXPERIMENTAL The experiments were carried out in suspended thin film resonators, patterned from high quality epitaxial YlBazCu307-6 (YBCO) films. A block diagram of the experimental setup is presented in Fig. 1.
I t
HP8510CANA z
HP 8360C (RF)
H
I
I
-p++
HP 83418 (LO)
-1
+
Manuscript Received October 17, 1994. B. A . Willemsen, e-mail: balamwOneu.edu, fax: (617) 373-2943 SS acknowledges support from Rome Laboratory, Hanscom AFB and the NSF though NSF-DMR-9223850
Fig. 1 . Block diagram of the experimental setup used
Both laser deposited and sputtered films have been studied - in all cases the substrate was LaA103. The resonators were housed in a Cu package in the form of a rectangular cavity with coupling ports through which microwaves were coupled into and out of the resonator using 2 coaxial cables terminated by loops. The position of these loops relative to the sample. and hence the coupling, can be changed even while cold; this enables us to always ensure that we are weakly coupled to the resonator. This enables us to directly measure unloaded Qs. By means of an HP8510C automatic network analyzer, the resonator resonances were easily determined in transmission mode, from which the Q and resonance frequency were determined. The linear response of three types of resonant structures have been studied - meander line, straight line and ring resonators. The resonances are one-dimensional and the resonance frequencies are given by fn = n ( c / L e , ~ )for the line where teff is the effective dielectric constant ( X 10). In the case of a ring such as is dicussed here fn = n(c/2Leefi).At 3 GHz and 5 K Q values for the various resonators usually exceeded 20,000, while at 77 K Q values of 2,000 are typical. The for Z ( H d c ) for the three structures were in very good agreement, thus supporting our methodology for ex-
1051-8223/95$04.00 0 1995 IEEE
1754
tracting the material paramter, Z,, from the inherently geometry dependent quantities Q and f . In what follows, we focus on the nonlinear results obtained from a ring resonator at f = 3.7 GHz, patterned from a d =3800 A thick pulsed laser ablated film on a 0.5 m m thick substrate; to form a ring 1.0 cm in diameter and with a line width of 2a = 100 pm. The film was obtained from Neocera, Inc.
-10
_
r -
_
~ -10.01
W (+lOdBm)
’
0.60in.
YeCO
1’ LaA103
cu
sensitivity, we have chosen to bypass the HP 8517B test set with its built-in directional couplers. 1 W (f30 dBm) of input power was available from an H P 83020A broadband amplifier.
\
a\
YBCO: 100 x 0.38 Km
-zx
-30
-2 5
-I 5
-0 5
05
I 5
25
Frequency (MHz)
Fig. 3. Resonances as a function of rf input power at T = 84 K. Curves are shown for input powers of 0.01 W, 0.1 W and 1 W Fig. 2. Cross sectional view of the resonator.
111. RESULTS A N D DISCUSSION
Typically, discussions of the Bean critical state are restricted to bulk geometries such as cylinders or thick slabs[4], and the critical state is induced by means of externally applied magnetic fields. Recent theoretical advances[5], [6] have renewed interest in applying the a critical state approach to thin films with fields applied perpendicular to the film as well as current driven geometries such as the one we are concerned with here. The existence of a critical state is due to the fact that the current density is limited by J,, and thus saturates when it reaches this value. Thus, for a rectangular current carrying thin strip, a current distribution which minimizes the incursion of flux has a current profile which saturates to J , at the edges and decays as we approach the center of the strip. Another consequence of the critical state is the nonlinear response to ac currents[7]. Since the response of the critical state is inherently history-dependent] the ac response is inherently nonlinear. Such a nonlinear response is best studied at high frequencies] since the effects increase with frequency. We have studied the nonlinear surface impedance as a function of microwave power or microwave magnetic field H,f in the same experimental setup where we have carried out dc field measurements. Here we increase the input power while maintaining a fixed temperature and keep Hdc = 0. In order to take full advantage of the available power and at the same time gain
The strong nonlinear response of the YBCO film is evident from Fig. 3, where the transmitted power near the resonance is shown for different input powers at T = $4 K . There is a dramatic broadening of the resonance, implying increased dissipation and accompanied by a shift of the resonant frequency to lower frequencies, implying a corresponding increase of the reactance. The dependence of surface resistance R, on H,f was obtained from the Q in terms of the 3 dB bandwidth, although we have verified that similar results are obtained if the Q is determined from the insertion loss. The peak surface magnetic field, H,f. was obtained from absolute measurements of the absorbed power as well as the known geometric factors. The results are displayed in Fig. 4. (At lower temperatures, <E 70 K the available power was inadequate to observe any significant deviations from linearity). The plot shows an upward curvature] and close examination shows that the leading behavior is H:f, followed by a faster increase. The nonlinearities increase rapidly with increasing temperature. We do not see any indications of H c l , such as sharp breaks in the R,(H,f) curves (in contrast to Ref. [SI). Recently one of us [a] has proposed that a model based on the ac response of a current-induced critical state in a strip of rectangular cross-section describes the essential features of the microwave nonlinear response. Here the microwave field induces a oscillating current. For an infinite strip, the model yields a nonlinear surface resis/ z 2 , fo(z) = tance & , s t n p ( H r f ) = ( 8 ~ p 0 ~ / ~ ) . f 0 ( z )where (1+z)ln(l+z)+(1-z)ln(l-a)-z2 and z = H ~ / H , .The key result that emerges is that for small H,f. the model yields R , ( H , f ) K H,2,, and increases faster at higher fields.
1755
IV. CONCLUSIONS
n
C
E
w ~
K
8:
0.6
%
4
al 4
0.4 4
4
81 K n80 K +77 K
.r(
v1
2
4
al 0.2 m U-l
5 VI
4
a R
4
+
a
70 E >>$do+ *:+ + e%a 4
0.0
0
0 . 0
0
Microwave Field
0,
H,,
O
O
,
(Oe)
Fig. 4. Nonlinear response represented by R, vs. H,f a t various temperatures (T = 70 K , 77 K , 80 K , 81 K and 83 K , the slopes of the lines increase with increasing T .
Qualititatively this is indeed the case in the present experiments, since the leading behavior at low fields in Fig. 4 is Hi. Note that the theory naturally implies a scaled response in terms of the scaled field 2 , as shown in Fig. 5 the experimental data can also be represented in such a fashion. For a quantitative comparison, the above expression is shown in Fig. 5 as a solid line. Evidently the theory coincides almost exactly with the experiment. However it should be noted that the data continue to increase even beyond saturation field which is the same as H , ( T ) , and that we have introduced a temperature dependent scaling factor R O ,0: ~ H , which is not predicted by the theory. This may be due to the failure of the assumption that the critical state “follows” the microwave field even at 3.7 GHz. Further work is currently under way to understand the dynamics. However it is evident that the essential physics is captured by the description in terms of the ac response of the critical state. Also, it must be noted that the field scales required for the scaling correspond to critical currents Jc(77 K) x 2 x lo6 A/cm2, comparable with independent dc measurements on similar films. n
b
2
1.0
P?
E
0.8
0.6
LI
5
rn a
0.4 0.2
0
rn
n -.-n 0.00
0.25
0.50
0.75
1.00
1.25
S c a l e d Field Hr,/HS,=*(T) Fig. 5. Scaled plot of the R,(H,f) data from Fig. 4. The solid line represents the theory.
Our work implies that a single mechanism is responsible for the nonlinear response, namely ac hysteretic losses related to penetration of magnetic flux. This is in contrast to other analyses which require two distinct mechanisms above and below H,1[8]. The ac response of the critical state induced by a current thus provides an excellent description of the nonlznear response measured at high frequencies, although further work is needed to understand the dynamics of penetration. In separate work we have shown that the dc field dependence at fields comparable to J,d is also well described in terms a critical state model[9]. This work shows that high frequency experiments can provide a unique probe of electrodynamic phenomena in superconductors. In turn the analysis presented in this work provides a unified understanding of a variety of apparently complex phenomena at high frequencies in superconducting films.
REFERENCES “Raising the power[l] Zhi-Yuan Shen and Charles Wilker, handling capacity of hts circuits”, Microwaves 8 RF, pp. 129138, April 1994. [2] S. Sridhar, “Nonlinear microwave impedance of superconductors and ac response of the critical state”, A p p l . Phys. Lett., vol. 65, no. 8, pp. 1054-1056, August 1994. [3] Balam A. Willemsen, John S. Derov, JosC H. Silva, and S. Sridhar, “Vortex dynamics in patternedYBazCu307-& thin films”, A p p l . Phys. Lett., submitted, 1994. [4] C. P. Bean, “Magnetization of hard superconductors”, Phys. Rev. Lett., vol. 8 , pp. 250-253, 1962. [5] Ernst Helmut Brandt, “Dynamics of flat superconductors in a perpendicular magnetic field”, Phys. Rev. Lett., vol. 71, pp. 2821-2824,1993. [SI E. Zeldov, John R. Clem, M. M. McElfresh, and M. Darwin, “Magnetization and transport currents in thin superconducing films.”, Phys. Rev. B, vol. 49, pp. 9802, 1994. [7] W. T. Norris, “Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets”, J. Phys. D,vol. 3 , pp. 489, 1970. [8] P. P. Nguyen, D. E. Oates, G. Dresselhaus, and M. S. Dresselhaus, “Nonlinear surface impedance for Y B a z C ~ 3 0 7 - thin ~ films: Measurements and a coupled-grain model”, Phys. Rev. B , vol. 48, pp. 6400, 1993. [9] Balam A. Willemsen, John S. Derov, JosC H. Silva, and S. Sridhar, “Critical state flux penetration and linear microwave response in YBa~Cu307-6 thin films”, in preparation, 1995.
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTTVITY,VOL. 5, NO. 2,JUNE 1995
Nonlinear Response of Suspended High Temperature Superconducting Thin Film Microwave Resonators Balam A. Willemsena9b,John S. Derovb, Jos6 H. Silvab and S. Sridhar" OPhysics Department, Northeastern Univeristy, Boston, MA 02115 bRome Laboratory, Hanscom AFB., Bedford, MA 01730, USA.
Abstract-The nonlinear microwave surface impedance, Z,(H,r) of Y1Ba2Cu307-6 thin films is measured using suspended patterned resonators. We find that the nonlinear response is well described in terms of a single mechanism, namely the hysteretic ac response of the current-induced critical state.
I. INTRODUCTION A characteristic feature of the high T, superconductors is the very strong power dependence of the microwave response for even moderate microwave powers or surface magnetic fields Hfi[l]. A new explanation of this phenomena has recently become available[2]. In th'is paper we report on results which form part of a comprehensive set of experiments designed to study vortex dynamics and flux penetration using patterned structures resonant at microwave frequencies. The basic parameter measured is the surface impedance 2, = R, iX,.The experiments were specially designed to enable application of dc magnetic fields H d c and to also study the nonlinear response as a function of the microwave magnetic field H,f (or equivalently power). A key feature of the experiments is the high sensitivity over a wide range of Hdc (% 1 Oe to 6 T ) and H d (0 to 1 kOe). This enables precise tests of several issues relating to vortex dynamics and flux penetration in both the field-induced and current-induced critical state. In this paper we will concentrate on the nonlinear rf response. The dc field results will be presented elsewhere[3]. We measure this nonlinear response in terms of 2,(H,f, 7'). We show that the observed nonlinear response is very well described in terms of hysteretic losses due to the ac response of a current-induced critical state. Specifically, the experimental data are in reasonable agreement with a calculation for such hysteretic losses in a rectangular strip. Overall, our data and accompanying analysis provides a new perspective into high frequency response in terms of critical state flux penetration, and a unified picture of a variety of phenomena at fields comparable to H , = J,d, which were not properly explained previously.
11. EXPERIMENTAL The experiments were carried out in suspended thin film resonators, patterned from high quality epitaxial YlBazCu307-6 (YBCO) films. A block diagram of the experimental setup is presented in Fig. 1.
I t
HP8510CANA z
HP 8360C (RF)
H
I
I
-p++
HP 83418 (LO)
-1
+
Manuscript Received October 17, 1994. B. A . Willemsen, e-mail: balamwOneu.edu, fax: (617) 373-2943 SS acknowledges support from Rome Laboratory, Hanscom AFB and the NSF though NSF-DMR-9223850
Fig. 1 . Block diagram of the experimental setup used
Both laser deposited and sputtered films have been studied - in all cases the substrate was LaA103. The resonators were housed in a Cu package in the form of a rectangular cavity with coupling ports through which microwaves were coupled into and out of the resonator using 2 coaxial cables terminated by loops. The position of these loops relative to the sample. and hence the coupling, can be changed even while cold; this enables us to always ensure that we are weakly coupled to the resonator. This enables us to directly measure unloaded Qs. By means of an HP8510C automatic network analyzer, the resonator resonances were easily determined in transmission mode, from which the Q and resonance frequency were determined. The linear response of three types of resonant structures have been studied - meander line, straight line and ring resonators. The resonances are one-dimensional and the resonance frequencies are given by fn = n ( c / L e , ~ )for the line where teff is the effective dielectric constant ( X 10). In the case of a ring such as is dicussed here fn = n(c/2Leefi).At 3 GHz and 5 K Q values for the various resonators usually exceeded 20,000, while at 77 K Q values of 2,000 are typical. The for Z ( H d c ) for the three structures were in very good agreement, thus supporting our methodology for ex-
1051-8223/95$04.00 0 1995 IEEE
1754
tracting the material paramter, Z,, from the inherently geometry dependent quantities Q and f . In what follows, we focus on the nonlinear results obtained from a ring resonator at f = 3.7 GHz, patterned from a d =3800 A thick pulsed laser ablated film on a 0.5 m m thick substrate; to form a ring 1.0 cm in diameter and with a line width of 2a = 100 pm. The film was obtained from Neocera, Inc.
-10
_
r -
_
~ -10.01
W (+lOdBm)
’
0.60in.
YeCO
1’ LaA103
cu
sensitivity, we have chosen to bypass the HP 8517B test set with its built-in directional couplers. 1 W (f30 dBm) of input power was available from an H P 83020A broadband amplifier.
\
a\
YBCO: 100 x 0.38 Km
-zx
-30
-2 5
-I 5
-0 5
05
I 5
25
Frequency (MHz)
Fig. 3. Resonances as a function of rf input power at T = 84 K. Curves are shown for input powers of 0.01 W, 0.1 W and 1 W Fig. 2. Cross sectional view of the resonator.
111. RESULTS A N D DISCUSSION
Typically, discussions of the Bean critical state are restricted to bulk geometries such as cylinders or thick slabs[4], and the critical state is induced by means of externally applied magnetic fields. Recent theoretical advances[5], [6] have renewed interest in applying the a critical state approach to thin films with fields applied perpendicular to the film as well as current driven geometries such as the one we are concerned with here. The existence of a critical state is due to the fact that the current density is limited by J,, and thus saturates when it reaches this value. Thus, for a rectangular current carrying thin strip, a current distribution which minimizes the incursion of flux has a current profile which saturates to J , at the edges and decays as we approach the center of the strip. Another consequence of the critical state is the nonlinear response to ac currents[7]. Since the response of the critical state is inherently history-dependent] the ac response is inherently nonlinear. Such a nonlinear response is best studied at high frequencies] since the effects increase with frequency. We have studied the nonlinear surface impedance as a function of microwave power or microwave magnetic field H,f in the same experimental setup where we have carried out dc field measurements. Here we increase the input power while maintaining a fixed temperature and keep Hdc = 0. In order to take full advantage of the available power and at the same time gain
The strong nonlinear response of the YBCO film is evident from Fig. 3, where the transmitted power near the resonance is shown for different input powers at T = $4 K . There is a dramatic broadening of the resonance, implying increased dissipation and accompanied by a shift of the resonant frequency to lower frequencies, implying a corresponding increase of the reactance. The dependence of surface resistance R, on H,f was obtained from the Q in terms of the 3 dB bandwidth, although we have verified that similar results are obtained if the Q is determined from the insertion loss. The peak surface magnetic field, H,f. was obtained from absolute measurements of the absorbed power as well as the known geometric factors. The results are displayed in Fig. 4. (At lower temperatures, <E 70 K the available power was inadequate to observe any significant deviations from linearity). The plot shows an upward curvature] and close examination shows that the leading behavior is H:f, followed by a faster increase. The nonlinearities increase rapidly with increasing temperature. We do not see any indications of H c l , such as sharp breaks in the R,(H,f) curves (in contrast to Ref. [SI). Recently one of us [a] has proposed that a model based on the ac response of a current-induced critical state in a strip of rectangular cross-section describes the essential features of the microwave nonlinear response. Here the microwave field induces a oscillating current. For an infinite strip, the model yields a nonlinear surface resis/ z 2 , fo(z) = tance & , s t n p ( H r f ) = ( 8 ~ p 0 ~ / ~ ) . f 0 ( z )where (1+z)ln(l+z)+(1-z)ln(l-a)-z2 and z = H ~ / H , .The key result that emerges is that for small H,f. the model yields R , ( H , f ) K H,2,, and increases faster at higher fields.
1755
IV. CONCLUSIONS
n
C
E
w ~
K
8:
0.6
%
4
al 4
0.4 4
4
81 K n80 K +77 K
.r(
v1
2
4
al 0.2 m U-l
5 VI
4
a R
4
+
a
70 E >>$do+ *:+ + e%a 4
0.0
0
0 . 0
0
Microwave Field
0,
H,,
O
O
,
(Oe)
Fig. 4. Nonlinear response represented by R, vs. H,f a t various temperatures (T = 70 K , 77 K , 80 K , 81 K and 83 K , the slopes of the lines increase with increasing T .
Qualititatively this is indeed the case in the present experiments, since the leading behavior at low fields in Fig. 4 is Hi. Note that the theory naturally implies a scaled response in terms of the scaled field 2 , as shown in Fig. 5 the experimental data can also be represented in such a fashion. For a quantitative comparison, the above expression is shown in Fig. 5 as a solid line. Evidently the theory coincides almost exactly with the experiment. However it should be noted that the data continue to increase even beyond saturation field which is the same as H , ( T ) , and that we have introduced a temperature dependent scaling factor R O ,0: ~ H , which is not predicted by the theory. This may be due to the failure of the assumption that the critical state “follows” the microwave field even at 3.7 GHz. Further work is currently under way to understand the dynamics. However it is evident that the essential physics is captured by the description in terms of the ac response of the critical state. Also, it must be noted that the field scales required for the scaling correspond to critical currents Jc(77 K) x 2 x lo6 A/cm2, comparable with independent dc measurements on similar films. n
b
2
1.0
P?
E
0.8
0.6
LI
5
rn a
0.4 0.2
0
rn
n -.-n 0.00
0.25
0.50
0.75
1.00
1.25
S c a l e d Field Hr,/HS,=*(T) Fig. 5. Scaled plot of the R,(H,f) data from Fig. 4. The solid line represents the theory.
Our work implies that a single mechanism is responsible for the nonlinear response, namely ac hysteretic losses related to penetration of magnetic flux. This is in contrast to other analyses which require two distinct mechanisms above and below H,1[8]. The ac response of the critical state induced by a current thus provides an excellent description of the nonlznear response measured at high frequencies, although further work is needed to understand the dynamics of penetration. In separate work we have shown that the dc field dependence at fields comparable to J,d is also well described in terms a critical state model[9]. This work shows that high frequency experiments can provide a unique probe of electrodynamic phenomena in superconductors. In turn the analysis presented in this work provides a unified understanding of a variety of apparently complex phenomena at high frequencies in superconducting films.
REFERENCES “Raising the power[l] Zhi-Yuan Shen and Charles Wilker, handling capacity of hts circuits”, Microwaves 8 RF, pp. 129138, April 1994. [2] S. Sridhar, “Nonlinear microwave impedance of superconductors and ac response of the critical state”, A p p l . Phys. Lett., vol. 65, no. 8, pp. 1054-1056, August 1994. [3] Balam A. Willemsen, John S. Derov, JosC H. Silva, and S. Sridhar, “Vortex dynamics in patternedYBazCu307-& thin films”, A p p l . Phys. Lett., submitted, 1994. [4] C. P. Bean, “Magnetization of hard superconductors”, Phys. Rev. Lett., vol. 8 , pp. 250-253, 1962. [5] Ernst Helmut Brandt, “Dynamics of flat superconductors in a perpendicular magnetic field”, Phys. Rev. Lett., vol. 71, pp. 2821-2824,1993. [SI E. Zeldov, John R. Clem, M. M. McElfresh, and M. Darwin, “Magnetization and transport currents in thin superconducing films.”, Phys. Rev. B, vol. 49, pp. 9802, 1994. [7] W. T. Norris, “Calculation of hysteresis losses in hard superconductors carrying ac: isolated conductors and edges of thin sheets”, J. Phys. D,vol. 3 , pp. 489, 1970. [8] P. P. Nguyen, D. E. Oates, G. Dresselhaus, and M. S. Dresselhaus, “Nonlinear surface impedance for Y B a z C ~ 3 0 7 - thin ~ films: Measurements and a coupled-grain model”, Phys. Rev. B , vol. 48, pp. 6400, 1993. [9] Balam A. Willemsen, John S. Derov, JosC H. Silva, and S. Sridhar, “Critical state flux penetration and linear microwave response in YBa~Cu307-6 thin films”, in preparation, 1995.
