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Microwave attenuation in CuO superconducting powders
PflYSICA[
Physica B 194-196 (1994) 1361-1362 North-Holland
Microwave attenuation in CuO superconducting powders Partha Bhattacharyya Theoretical Physics Group, T a t a Institute of Fundamental l~esearch, Homi Bhabha P~oad, Colaba, Bombay 400 005, India We give an explanation in terms of k ---- 0 mode response of the observed magnetic field dependence of the microwave absorption
AP(H) = P ( H ) -P(O)
seen in recent experiments
on powdered samples of YbCo. A uniform magnetic field in a (flavor) singlet representation of a
QHOtV/'-H corresponding to weak pinning. The field dependence AP(H)/Q2H = O(h~}/'OlnQ2,(h 9~) ¢x ln(Q 2 + Q~)in superconductor (SDW) induces a modulation at wave number
agreement with experiment, Q being the wave number of the thermal shear.
A number of recent experiments have revealed striking anomalies in the microwave absorption characterist.ics of CuO superconductors. Among them, the significant dependence of the microwave power absorption on the magnetic field in powdered samples of YbCo. It is given by a virgin curve
main wall separating regions of opposite parity can be translated at no extra cost in energy. Although there are some similarities to the models discussed already [4], the vortex glass model described is relevant in three dimensions not in two.
THEORY A finite system necessarily requires an in~ P ( n ) = P ( n ) - P(O) variance of its modular characteristics that can = (n/Ho)/(1 + H/no)) (1) be thought of as an invariance of the partition that seems to be a feature of samples prepared function with the interchange of the two reby m a n y different techniques. We show that gions of opposite parity. A pseudoscalar boson, the LO mode connects state of oppothe requirement of absence of convection [2] in classical fluids is the requirement that equilib- site parity implying a drop in resistivity at Tc rium :is maintained in a system of finite size [3] whereas the dissipation is the result of the excitation of shear modes. by requiring the interfacial tension [3] between We describe in this section a theory of an insuperconducting regions to drive a dislocation terface separating two different superconductloop transition. ing regions. It seeks to represent a vortex glass As regards H0, the following points are nomodel where a distortion of interface incurs a table: (i) H0 "~ a + b(1 - t) where t = T/Tc; (ii) there is no systematics between H0 and cost in free energy otanAA where an is the microwave conductance and AA the change in the grain size; and (iii) H0 is a weak function area induced by the distortion. The interface of frequency. configuration m a y be described by a variable The k = 0 mode response shows that in h(y) characterizing a local flux. equilibrium a finite system requires that a do0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)E1261-J
1362 A theory of the SNS interface asserts, therefore, that the long wave length properties can be obtained from an effective Hamiltonian of the form
where Q2 = Q~ + Q~ where Q~ : const, and Q~(t) =- b(1 - t ) from comparison with experiment. The transition from the superconducting to the normal state is the roughening transition.
Her f o¢. O"n
DISCUSSION We show that the microwave attenuation is (2) dominated by a k = 0 mode that manifests itself as a pseudoscalar boson inducing tunneling between equivalent vacuua across a norwhere a , is the area conductance as a result of mal state domain (SNS). As the phase winds the scattering from the dislocation loop in the through x at the boundary of the sample a phase slip mechanism, A,q being a magnetic kink-antikink pair exists harmonic oscillations penetration depth. along the line of disclinations with a wave Since we are interested in the zero mode number Q2 = Q~ + Q~(t), where Q~ = const., dominated response, it is justified to neglect Q~(t) = b(1 - t). It causes the resonant mode the higher order terms (h.o.t.) in a gradient to move with respect to the fermi level. The expansion: temperature dependence of the resonant level makes it interesting to think in terms of a description in terms of two level systems (TLS). Her f = ( ,/2)fdy[1Vh(u)t 2 We note that in a calculation [5] of the mag+ 2] + (h.o.t.) (3) netic field penetration in grain boundaries the linear regime of the weak link ]osephson juncHell is known to admit of a zero mode where tion corresponding to restoration of symmetry a line of disclinations (domain wall) can move by a boson is considered adequate. The conat no excess cost in energy. dition f de = 0 is, in our context, nothing but Some care is needed in calculating the mag- the phase slip mechanism. netization as it involves the change in energy when a boson tunnels across regions of oppo- R E F E R E N C E S site parity. A uniform magnetic field induces . S.M. Bhagat, M.X. Huang, J.S. Raa modulation of the vortex lattice at a wave machandran, K. Kish and S. Tyagi, Physnumber Q n ~ v/ft. To calculate the power ica C202 (1992) absorption it is enough to calculate the mean square displacement . Fluid mechanics by L.D. Landau and
(h 2) o¢ (TIa.)#.n [(Q~ + Q2)IQ:]
(4)
where the change in energy 5E is given by the contribution from a single bosonic mode and Q = 1/X,q. The regularisation ensures a r a n d o m distribution of microscopic magnetic fields when QH ~ 0. It is a feature of the modulation that the dissipation in energy proportional to square of the core energy is obtained by an infinitesimal variation of Q, i.e.
AP(H)/Q2H- al0(h Q---2)
1/(Q
+ Q2) (5)
E.M. Lifshitz, Vol. 6 of Course of Theoretical Physics, Pergamon Press. 3. M.P. Gelfand and Michael E. Fisher, preprint. A.C. Maggs, S. Leibler, M.E. Fisher and C.J. Camacho, Phys. Rev. A42 (1992) 691. 4. J. Toner, Phys. 2537
t~ev. Lett.
67 (1991)
. T.L. Hylton and M.tL Beasley, Phys. Rev. B39 1990) 9042
Physica B 194-196 (1994) 1361-1362 North-Holland
Microwave attenuation in CuO superconducting powders Partha Bhattacharyya Theoretical Physics Group, T a t a Institute of Fundamental l~esearch, Homi Bhabha P~oad, Colaba, Bombay 400 005, India We give an explanation in terms of k ---- 0 mode response of the observed magnetic field dependence of the microwave absorption
AP(H) = P ( H ) -P(O)
seen in recent experiments
on powdered samples of YbCo. A uniform magnetic field in a (flavor) singlet representation of a
QHOtV/'-H corresponding to weak pinning. The field dependence AP(H)/Q2H = O(h~}/'OlnQ2,(h 9~) ¢x ln(Q 2 + Q~)in superconductor (SDW) induces a modulation at wave number
agreement with experiment, Q being the wave number of the thermal shear.
A number of recent experiments have revealed striking anomalies in the microwave absorption characterist.ics of CuO superconductors. Among them, the significant dependence of the microwave power absorption on the magnetic field in powdered samples of YbCo. It is given by a virgin curve
main wall separating regions of opposite parity can be translated at no extra cost in energy. Although there are some similarities to the models discussed already [4], the vortex glass model described is relevant in three dimensions not in two.
THEORY A finite system necessarily requires an in~ P ( n ) = P ( n ) - P(O) variance of its modular characteristics that can = (n/Ho)/(1 + H/no)) (1) be thought of as an invariance of the partition that seems to be a feature of samples prepared function with the interchange of the two reby m a n y different techniques. We show that gions of opposite parity. A pseudoscalar boson, the LO mode connects state of oppothe requirement of absence of convection [2] in classical fluids is the requirement that equilib- site parity implying a drop in resistivity at Tc rium :is maintained in a system of finite size [3] whereas the dissipation is the result of the excitation of shear modes. by requiring the interfacial tension [3] between We describe in this section a theory of an insuperconducting regions to drive a dislocation terface separating two different superconductloop transition. ing regions. It seeks to represent a vortex glass As regards H0, the following points are nomodel where a distortion of interface incurs a table: (i) H0 "~ a + b(1 - t) where t = T/Tc; (ii) there is no systematics between H0 and cost in free energy otanAA where an is the microwave conductance and AA the change in the grain size; and (iii) H0 is a weak function area induced by the distortion. The interface of frequency. configuration m a y be described by a variable The k = 0 mode response shows that in h(y) characterizing a local flux. equilibrium a finite system requires that a do0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)E1261-J
1362 A theory of the SNS interface asserts, therefore, that the long wave length properties can be obtained from an effective Hamiltonian of the form
where Q2 = Q~ + Q~ where Q~ : const, and Q~(t) =- b(1 - t ) from comparison with experiment. The transition from the superconducting to the normal state is the roughening transition.
Her f o¢. O"n
DISCUSSION We show that the microwave attenuation is (2) dominated by a k = 0 mode that manifests itself as a pseudoscalar boson inducing tunneling between equivalent vacuua across a norwhere a , is the area conductance as a result of mal state domain (SNS). As the phase winds the scattering from the dislocation loop in the through x at the boundary of the sample a phase slip mechanism, A,q being a magnetic kink-antikink pair exists harmonic oscillations penetration depth. along the line of disclinations with a wave Since we are interested in the zero mode number Q2 = Q~ + Q~(t), where Q~ = const., dominated response, it is justified to neglect Q~(t) = b(1 - t). It causes the resonant mode the higher order terms (h.o.t.) in a gradient to move with respect to the fermi level. The expansion: temperature dependence of the resonant level makes it interesting to think in terms of a description in terms of two level systems (TLS). Her f = ( ,/2)fdy[1Vh(u)t 2 We note that in a calculation [5] of the mag+ 2] + (h.o.t.) (3) netic field penetration in grain boundaries the linear regime of the weak link ]osephson juncHell is known to admit of a zero mode where tion corresponding to restoration of symmetry a line of disclinations (domain wall) can move by a boson is considered adequate. The conat no excess cost in energy. dition f de = 0 is, in our context, nothing but Some care is needed in calculating the mag- the phase slip mechanism. netization as it involves the change in energy when a boson tunnels across regions of oppo- R E F E R E N C E S site parity. A uniform magnetic field induces . S.M. Bhagat, M.X. Huang, J.S. Raa modulation of the vortex lattice at a wave machandran, K. Kish and S. Tyagi, Physnumber Q n ~ v/ft. To calculate the power ica C202 (1992) absorption it is enough to calculate the mean square displacement . Fluid mechanics by L.D. Landau and
(h 2) o¢ (TIa.)#.n [(Q~ + Q2)IQ:]
(4)
where the change in energy 5E is given by the contribution from a single bosonic mode and Q = 1/X,q. The regularisation ensures a r a n d o m distribution of microscopic magnetic fields when QH ~ 0. It is a feature of the modulation that the dissipation in energy proportional to square of the core energy is obtained by an infinitesimal variation of Q, i.e.
AP(H)/Q2H- al0(h Q---2)
1/(Q
+ Q2) (5)
E.M. Lifshitz, Vol. 6 of Course of Theoretical Physics, Pergamon Press. 3. M.P. Gelfand and Michael E. Fisher, preprint. A.C. Maggs, S. Leibler, M.E. Fisher and C.J. Camacho, Phys. Rev. A42 (1992) 691. 4. J. Toner, Phys. 2537
t~ev. Lett.
67 (1991)
. T.L. Hylton and M.tL Beasley, Phys. Rev. B39 1990) 9042