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Complex microwave conductivity of YBa2Cu3O7 in magnetic fields up to 500 T
ELSEVIER
Physica B 211 (1995) 248-250
Complex microwave conductivity of YBa2Cu307 in magnetic fields up to 500 T A.I. Bykov a, M.I. Dolotenko a, C.M. Fowler b, B.L. Freeman b, J.D. Goettee b, J.C. King b, N.P. Kolokolchikov a, Yu.B. Kudasov a, W. Lewis c, B.R. Marshall c, B.J. Papatheofanis b, V.V. Platonov a, P.J. Rodriguez b, O.M. Tatsenko a'*, L.R. Veeser b, W.D. Zerwekh b aAll-Russia Scientific Research Institute of Experimental Physics, 607200, Arsamas-16, Russian Federation b Los Alamos National Laboratory, Los Alamos, NM 87545, USA ¢ EG&G Energy Measurements, 130 Robin Hill Rd., Goleta, CA 93117, USA
Abstract The complex microwave conductivity of thin, oriented YBazCu30 7 films was measured at 94 GHz in pulsed, ultrahigh-magnetic fields up to 500 T. The c-axis of the film was perpendicular to the magnetic field. We estimate the upper critical field of the film at absolute zero as B¢2 (0) = 340 + 40 T. Dynamics of the transition into a normal state and connection with previous measurements of the reversibility line are discussed.
The upper critical magnetic field (B¢2) of high temperature superconductors (HTSC) is known to be very high and strongly anisotropic [1,21. Where the magnetic field is perpendicular to the c-axis, as in this work, Bc2 in YBa2CuaO7 (YBCO) is well over 100 T for temperature significantly below the critical temperature, T¢. Thus the majority of direct measurements of B¢2 in YBCO have been conducted at higher temperatures, near Tc (about 90 K in this material), where B¢2 is low enough to be attainable in conventional experiments. Measurements of the magnetic hysteresis in monocrystaline YBCO showed that hysteresis disappears around 100T at T = 28 K, and it was speculated that it may be possible to relate the reversibility line to B¢2 [2]. However, comparison of this result with measurements in a static field [3] shows that the position of the reversibility line depends significantly on the time scale of the magnetic field rise [11. We have now been able to observe the exclusion
*Corresponding author.
of all superconductivity from a HTSC near zero temperature to provide a determination of Be2. In this experiment we have measured the complex conductivity to over 500 T, and we find that B~2 at zero temperature is well above the reversibility line [21, but far below the extrapolation of Be2 from the slope, dBc2/dT, near To. To produce the magnetic fields, we used explosivedriven flux compression generators. The very high fields, up to and above 500 T, were produced by MC1 magnetocumulative generators [41, which use explosive compression of a metallic liner to greatly increase an initial magnetic field. The compressed field rises from 100 T to over 500 T in a time of about 5 ~ts. For the experiment near Tc we used a lower field (140 T) two-stage generator [51, with magnetic field rise-time characteristics similar to the MC1. In this shot, the sample temperature was about 83 K, about 5 K below To. The 100 nm-thick YBCO films were grown on an AI20 3 (sapphire) substrate, 3.5 x 3.5 x 0.5 mm 3, by using a CeO2sublayer less than 50 nm thick. The c-axis was grown perpendicular to the substrate in the single-crystal
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 9 9 8 - 8
A.I. Bykov et al. / Physica B 211 (1995) 248-250 films and characterized by X-ray diffraction. Inductive measurements showed the onset of superconductivity at Tc = 88 K with a transition width ATe ~< 4 K. To determine the complex conductivity, we measured the transmission and reflection coefficients using a microwave interferometer with a carrier frequency of 94 GHz. This provides a diagnostic that is small and unobtrusive. About 100 laW of probing radiation was carried by rectangular dielectric waveguides into and out of a foam cryostat containing the sample. In a separate experiment, we determined that the imploding liner did not affect the microwave transmission equipment for fields up to 600 T. The samples were cooled by flowing cooled helium gas or liquid helium through the foamed-plastic cryostat. Temperatures were measured by monitoring the voltage across calibrated diodes. Because the film surface was parallel to the magnetic field, eddy-current heating was significantly lower than that for other film orientations. In addition, the excellent thermal conductivity of the sapphire substrate allows rapid absorption of the heat generated in the film. We estimated the temperature from heating for both the hard superconductor and flux flow regimes to be ~< 14 K for a field of 300 T and an initial sample temperature of 5 K. For initial temperatures more than 16 K, there is practically no temperature rise. The complex transmission and reflection coefficients of the film-substrate structure are related to the complex conductivity of the film. For a fiat, layered compound and an incident plane wave, the input impedance of layer x [6] is Zx(in) = Zx [Zx- 1(in) -- iZx tan q~x]/ [Zx - i Z ~ 1 tan ~x],
(1)
where Z , = Axv/~/e~ is the input impedance of the layer material,/~x and e~ are the permeability and permittivity, Zx- a(in) is the input impedance of the next layer through which the radiation propagates, ~ = Axk~d~, kx = tn/cx~//~x is the wave number, to is the circular radiation frequency, d~ is the layer thickness, and Ax is a coefficient depending on the incident angle and wave polarization. Using Eq. (1) it is possible to obtain the transmission coefficient of the film-substrate system 1-6] D = Do + 2(Zs{in} + Zf)(Zf{in} -F 1) x e x p [ - i(4~f + q~)](1 + Z~)(Z~{in} + Z~) x (Zf{in} + Zf).
(2)
The reflection coefficient is given by V = Vo + (Zf{in} - 1)/(Zf{in} + 1).
(3)
249
Indices f and s in Eqs. (2) and (3) refer to the film and the substrate. In our case, #f = 1 and/~s = 1. In Eqs. (2) and (3), the only variable that depends on the magnetic field is ef = i4~trf/to, where af is the complex conductivity of the film. In our system there exist some small stray coupling and reflection, which lead to the coefficients/)o in Eq. (2) and V0 in Eq. (3). At high magnetic fields the conductivity of ia HTSC is governed by vortices. Their behavior depends on the temperature, the field strength and rise time, and the frequency of the penetrating radiation used t~ probe the sample to measure the conductivity. At low frequencies, vortex movement is confined by pinning for~es, and in this case the imaginary part of the complex conductivity prevails. At high frequencies, viscous vortex imovement (flux flow) is achieved, and at this point the deal part of the conductivity becomes larger than the imaginary part. The cross-over from the pinning regime to flu~ flow takes place at a frequency, top, which is estimated [7] to be around 3 × l011 s - l for YBCO in weak fields and zero temperature. Since this frequency is very c!ose to the microwave probe frequency in our experimen i, we expect the conductivity here to be due to both ~eakly and strongly pinned vortices [7,8]: trf 1 = aw 1 + a s 1. Here trw = tlc2/CboBf(T) is the conductivity of the weaklypinned vortices, trs = iqc2/~boB[top/to{1 - f ( T ) } ] is the conductivity of the strongly-pinned ones, t / i s t h e viscosity, and q~0 is the flux quantum. The fraction of the vortices that is weakly pinned is f ( T ) = exp[ - U(T)/kBT], where U(T) is the Anderson Kim activation energy. For YBCO, U(T) was found experimentally [-7] to be about 0.8ka Tc for microwaves unless T is very close to T c. Our results are consistent with this model. At T = Tc - 5 K, (the experiment with the two-Stage generator) the conductivity is defined by motion of the weaklypinned vortices. The measured imaginary part of the conductivity was small, and around 15 T it disappeared completely. Above 15 T the conductivity is o f the flux flow type until the real part stopped changing, indicating Be2 = 45 _ 10 T. We determined the real and imaginary t~arts of the 94 GHz conductivity independently from the transmission and reflection measurements. The conductivity for this point is shown as a function of the field it~ Fig. 1 (the 30 K transmission data are similar). For tMds below 75 T, the conductivity is almost purely imagir~ary, implying that all the vortices are strongly pinned. From 75 T to 210T, the magnetic field increasingly suppresses the pinning potential, and the fraction of the vortices that are weakly pinned increases rapidly. This leads tO a rotation of the complex conductivity vector, of. Above 210 T some strongly-pinned vortices remain, but tile sample is largely in the flux-flow regime. At a certain Value of the
250
A.I. Bykov et al. / Physica B 211 (1995) 248-250
2 4 0
3 0
100
200
300
400
Field
500
600
(T)
Fig. 1. The dependence of complex conductivity of YBCO film on magnetic field. Curves (1) and (3) show, respectively, the real and imaginary parts of the conductivity determined from the reflection. Curves (2) and (4) show the real and imaginary conductivity determined independently from the transmission.
References
I00
+
300
~200
1oo
magnetic field, the imaginary part of the conductivity disappears, and we interpret this field as the critical magnetic field B¢2 = 340 _ 40 T. No further features are seen in the data between 340 T and the field at which the microwave line was struck by the imploding liner, above 550 T. The uncertainty in the determination of Be2 arises mainly from the difficulty in determining when the imaginary (inductive) conductivity reaches zero in Fig. 1, as the slope is very small near Be2. Fig. 2 shows the dependence of Be2 on temperature for YBCO. The points and the solid curve connecting them are our data. In addition to the points at 5 and 83 K, we made a measurement at 30 K, for which the data were similar to those at 5 K. It is seen that B¢2 is far above the reversibility line [2], shown as the dashed curve. According to the model discussed above, the onset of irreversibility is caused by the suppression of the pinning potential by the magnetic field. In fact the reversibility line is at about the field where the magnetic field begins to strongly suppress the pinning potential. The slope of the solid curve near Tc is in rough agreement with the value - 10 T / K [3]. However our Be2 measurements near zero temperature show about half the value calculated from the W H H formula [8] in the orbital limit, Be2(0) = 0 . 7 T ¢ [ d B c 2 ( T c ) / d T ] ~ 650 T.
i
0 0
i 20
,
i
,
,
F i 40
,-,
,
' 60
'
'
,
i 80
i
~3 i - ~ q 100
T,(~t Fig. 2. Measured values of the upper critical magnetic field Be2 (points) in the YBCO as a function of temperature. The open point is from Ref. [9], and the closed points are from this work. The dashed curve is the reversibility line [2]. For points near Tc we scaled the abscissas to T c = 88 K.
[1] A.P. Malozemoff, in: Physical Properties of High Temperature Superconductors, ed. D. Ginzberg (World Scientific, Singapore, 1989) ch. 3. [2] K. Nakao, N. Miura, K. Tatsuhara, H. Takeya and H. Takei, Phys. Rev. Lett. 63 (1989) 97. [3] U. Welp, W.K. Kwok, G.W. Crabtree, K.G. Vandervoort and J.Z. Liu, Phys. Rev. Lett. 62 (1989) 1908. I-4] A.I. Pavlovskii and R.Z. Ludaev, Magnetic Cumulation (Nauka, Moscow, 1984). [5] C.M. Fowler, B.R. Freeman, W.L. Hults, J.C. King, F.M. Mueller and J.L. Smith, Phys. Rev. Lett. 68 (1992) 534. 1-6] L.M. Brekhovskih, Waves in Layered Substances (Academic Press, Moscow, 1957). I-7] R. Marcon, R. Fastamps, M. Giurs and E. Silva, Phys. Rev. B 43 (1991) 2940. I-8] N.R. Werthamer, E. Helfand and P.C. Hohenberg, Phys. Rev. 147 (1966) 295. [9] J. D. Goettee, J.S. Brooks, D.G. Rickel, B.L. Freeman, C.M. Fowler, J.C. King, P.M. Mankiewich, W.J. Skocpol, E.I. De Obaldia, M.L. O'Malley and J.L. Smith, preprint of LANL, LA-UR-92-3100 (1992).
Physica B 211 (1995) 248-250
Complex microwave conductivity of YBa2Cu307 in magnetic fields up to 500 T A.I. Bykov a, M.I. Dolotenko a, C.M. Fowler b, B.L. Freeman b, J.D. Goettee b, J.C. King b, N.P. Kolokolchikov a, Yu.B. Kudasov a, W. Lewis c, B.R. Marshall c, B.J. Papatheofanis b, V.V. Platonov a, P.J. Rodriguez b, O.M. Tatsenko a'*, L.R. Veeser b, W.D. Zerwekh b aAll-Russia Scientific Research Institute of Experimental Physics, 607200, Arsamas-16, Russian Federation b Los Alamos National Laboratory, Los Alamos, NM 87545, USA ¢ EG&G Energy Measurements, 130 Robin Hill Rd., Goleta, CA 93117, USA
Abstract The complex microwave conductivity of thin, oriented YBazCu30 7 films was measured at 94 GHz in pulsed, ultrahigh-magnetic fields up to 500 T. The c-axis of the film was perpendicular to the magnetic field. We estimate the upper critical field of the film at absolute zero as B¢2 (0) = 340 + 40 T. Dynamics of the transition into a normal state and connection with previous measurements of the reversibility line are discussed.
The upper critical magnetic field (B¢2) of high temperature superconductors (HTSC) is known to be very high and strongly anisotropic [1,21. Where the magnetic field is perpendicular to the c-axis, as in this work, Bc2 in YBa2CuaO7 (YBCO) is well over 100 T for temperature significantly below the critical temperature, T¢. Thus the majority of direct measurements of B¢2 in YBCO have been conducted at higher temperatures, near Tc (about 90 K in this material), where B¢2 is low enough to be attainable in conventional experiments. Measurements of the magnetic hysteresis in monocrystaline YBCO showed that hysteresis disappears around 100T at T = 28 K, and it was speculated that it may be possible to relate the reversibility line to B¢2 [2]. However, comparison of this result with measurements in a static field [3] shows that the position of the reversibility line depends significantly on the time scale of the magnetic field rise [11. We have now been able to observe the exclusion
*Corresponding author.
of all superconductivity from a HTSC near zero temperature to provide a determination of Be2. In this experiment we have measured the complex conductivity to over 500 T, and we find that B~2 at zero temperature is well above the reversibility line [21, but far below the extrapolation of Be2 from the slope, dBc2/dT, near To. To produce the magnetic fields, we used explosivedriven flux compression generators. The very high fields, up to and above 500 T, were produced by MC1 magnetocumulative generators [41, which use explosive compression of a metallic liner to greatly increase an initial magnetic field. The compressed field rises from 100 T to over 500 T in a time of about 5 ~ts. For the experiment near Tc we used a lower field (140 T) two-stage generator [51, with magnetic field rise-time characteristics similar to the MC1. In this shot, the sample temperature was about 83 K, about 5 K below To. The 100 nm-thick YBCO films were grown on an AI20 3 (sapphire) substrate, 3.5 x 3.5 x 0.5 mm 3, by using a CeO2sublayer less than 50 nm thick. The c-axis was grown perpendicular to the substrate in the single-crystal
0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 9 9 8 - 8
A.I. Bykov et al. / Physica B 211 (1995) 248-250 films and characterized by X-ray diffraction. Inductive measurements showed the onset of superconductivity at Tc = 88 K with a transition width ATe ~< 4 K. To determine the complex conductivity, we measured the transmission and reflection coefficients using a microwave interferometer with a carrier frequency of 94 GHz. This provides a diagnostic that is small and unobtrusive. About 100 laW of probing radiation was carried by rectangular dielectric waveguides into and out of a foam cryostat containing the sample. In a separate experiment, we determined that the imploding liner did not affect the microwave transmission equipment for fields up to 600 T. The samples were cooled by flowing cooled helium gas or liquid helium through the foamed-plastic cryostat. Temperatures were measured by monitoring the voltage across calibrated diodes. Because the film surface was parallel to the magnetic field, eddy-current heating was significantly lower than that for other film orientations. In addition, the excellent thermal conductivity of the sapphire substrate allows rapid absorption of the heat generated in the film. We estimated the temperature from heating for both the hard superconductor and flux flow regimes to be ~< 14 K for a field of 300 T and an initial sample temperature of 5 K. For initial temperatures more than 16 K, there is practically no temperature rise. The complex transmission and reflection coefficients of the film-substrate structure are related to the complex conductivity of the film. For a fiat, layered compound and an incident plane wave, the input impedance of layer x [6] is Zx(in) = Zx [Zx- 1(in) -- iZx tan q~x]/ [Zx - i Z ~ 1 tan ~x],
(1)
where Z , = Axv/~/e~ is the input impedance of the layer material,/~x and e~ are the permeability and permittivity, Zx- a(in) is the input impedance of the next layer through which the radiation propagates, ~ = Axk~d~, kx = tn/cx~//~x is the wave number, to is the circular radiation frequency, d~ is the layer thickness, and Ax is a coefficient depending on the incident angle and wave polarization. Using Eq. (1) it is possible to obtain the transmission coefficient of the film-substrate system 1-6] D = Do + 2(Zs{in} + Zf)(Zf{in} -F 1) x e x p [ - i(4~f + q~)](1 + Z~)(Z~{in} + Z~) x (Zf{in} + Zf).
(2)
The reflection coefficient is given by V = Vo + (Zf{in} - 1)/(Zf{in} + 1).
(3)
249
Indices f and s in Eqs. (2) and (3) refer to the film and the substrate. In our case, #f = 1 and/~s = 1. In Eqs. (2) and (3), the only variable that depends on the magnetic field is ef = i4~trf/to, where af is the complex conductivity of the film. In our system there exist some small stray coupling and reflection, which lead to the coefficients/)o in Eq. (2) and V0 in Eq. (3). At high magnetic fields the conductivity of ia HTSC is governed by vortices. Their behavior depends on the temperature, the field strength and rise time, and the frequency of the penetrating radiation used t~ probe the sample to measure the conductivity. At low frequencies, vortex movement is confined by pinning for~es, and in this case the imaginary part of the complex conductivity prevails. At high frequencies, viscous vortex imovement (flux flow) is achieved, and at this point the deal part of the conductivity becomes larger than the imaginary part. The cross-over from the pinning regime to flu~ flow takes place at a frequency, top, which is estimated [7] to be around 3 × l011 s - l for YBCO in weak fields and zero temperature. Since this frequency is very c!ose to the microwave probe frequency in our experimen i, we expect the conductivity here to be due to both ~eakly and strongly pinned vortices [7,8]: trf 1 = aw 1 + a s 1. Here trw = tlc2/CboBf(T) is the conductivity of the weaklypinned vortices, trs = iqc2/~boB[top/to{1 - f ( T ) } ] is the conductivity of the strongly-pinned ones, t / i s t h e viscosity, and q~0 is the flux quantum. The fraction of the vortices that is weakly pinned is f ( T ) = exp[ - U(T)/kBT], where U(T) is the Anderson Kim activation energy. For YBCO, U(T) was found experimentally [-7] to be about 0.8ka Tc for microwaves unless T is very close to T c. Our results are consistent with this model. At T = Tc - 5 K, (the experiment with the two-Stage generator) the conductivity is defined by motion of the weaklypinned vortices. The measured imaginary part of the conductivity was small, and around 15 T it disappeared completely. Above 15 T the conductivity is o f the flux flow type until the real part stopped changing, indicating Be2 = 45 _ 10 T. We determined the real and imaginary t~arts of the 94 GHz conductivity independently from the transmission and reflection measurements. The conductivity for this point is shown as a function of the field it~ Fig. 1 (the 30 K transmission data are similar). For tMds below 75 T, the conductivity is almost purely imagir~ary, implying that all the vortices are strongly pinned. From 75 T to 210T, the magnetic field increasingly suppresses the pinning potential, and the fraction of the vortices that are weakly pinned increases rapidly. This leads tO a rotation of the complex conductivity vector, of. Above 210 T some strongly-pinned vortices remain, but tile sample is largely in the flux-flow regime. At a certain Value of the
250
A.I. Bykov et al. / Physica B 211 (1995) 248-250
2 4 0
3 0
100
200
300
400
Field
500
600
(T)
Fig. 1. The dependence of complex conductivity of YBCO film on magnetic field. Curves (1) and (3) show, respectively, the real and imaginary parts of the conductivity determined from the reflection. Curves (2) and (4) show the real and imaginary conductivity determined independently from the transmission.
References
I00
+
300
~200
1oo
magnetic field, the imaginary part of the conductivity disappears, and we interpret this field as the critical magnetic field B¢2 = 340 _ 40 T. No further features are seen in the data between 340 T and the field at which the microwave line was struck by the imploding liner, above 550 T. The uncertainty in the determination of Be2 arises mainly from the difficulty in determining when the imaginary (inductive) conductivity reaches zero in Fig. 1, as the slope is very small near Be2. Fig. 2 shows the dependence of Be2 on temperature for YBCO. The points and the solid curve connecting them are our data. In addition to the points at 5 and 83 K, we made a measurement at 30 K, for which the data were similar to those at 5 K. It is seen that B¢2 is far above the reversibility line [2], shown as the dashed curve. According to the model discussed above, the onset of irreversibility is caused by the suppression of the pinning potential by the magnetic field. In fact the reversibility line is at about the field where the magnetic field begins to strongly suppress the pinning potential. The slope of the solid curve near Tc is in rough agreement with the value - 10 T / K [3]. However our Be2 measurements near zero temperature show about half the value calculated from the W H H formula [8] in the orbital limit, Be2(0) = 0 . 7 T ¢ [ d B c 2 ( T c ) / d T ] ~ 650 T.
i
0 0
i 20
,
i
,
,
F i 40
,-,
,
' 60
'
'
,
i 80
i
~3 i - ~ q 100
T,(~t Fig. 2. Measured values of the upper critical magnetic field Be2 (points) in the YBCO as a function of temperature. The open point is from Ref. [9], and the closed points are from this work. The dashed curve is the reversibility line [2]. For points near Tc we scaled the abscissas to T c = 88 K.
[1] A.P. Malozemoff, in: Physical Properties of High Temperature Superconductors, ed. D. Ginzberg (World Scientific, Singapore, 1989) ch. 3. [2] K. Nakao, N. Miura, K. Tatsuhara, H. Takeya and H. Takei, Phys. Rev. Lett. 63 (1989) 97. [3] U. Welp, W.K. Kwok, G.W. Crabtree, K.G. Vandervoort and J.Z. Liu, Phys. Rev. Lett. 62 (1989) 1908. I-4] A.I. Pavlovskii and R.Z. Ludaev, Magnetic Cumulation (Nauka, Moscow, 1984). [5] C.M. Fowler, B.R. Freeman, W.L. Hults, J.C. King, F.M. Mueller and J.L. Smith, Phys. Rev. Lett. 68 (1992) 534. 1-6] L.M. Brekhovskih, Waves in Layered Substances (Academic Press, Moscow, 1957). I-7] R. Marcon, R. Fastamps, M. Giurs and E. Silva, Phys. Rev. B 43 (1991) 2940. I-8] N.R. Werthamer, E. Helfand and P.C. Hohenberg, Phys. Rev. 147 (1966) 295. [9] J. D. Goettee, J.S. Brooks, D.G. Rickel, B.L. Freeman, C.M. Fowler, J.C. King, P.M. Mankiewich, W.J. Skocpol, E.I. De Obaldia, M.L. O'Malley and J.L. Smith, preprint of LANL, LA-UR-92-3100 (1992).