Paramagnetic Meissner effect in YBa2Cu3O7−δ

Physica C 219 (1994) 87-92 North-Holland

Paramagnetic Meissner effect in YBa2Cu3O7_~ A non-resonant microwave absorption study S.V. B h a t =, A. Rastogi a, N. K u m a r a, R. N a g a r a j a n b a n d C.N.R. R a o b,l • Department of Physics, Indian Institute of Science, Ban&alore560 012, India b S•lidStateandStructuralChemistryUnit••ndian•nstitute•fScience•Bangal•re56••12••ndia

Received 25 May 1993 Revised manuscript received4 October 1993

The low-field dependence of non resonant microwave absorption (MWA) in polycrystallinesamples of YBa2Cu3Ov_awith 0.1 1 (hysteretic junctions), there is a currentcarrying ground state and that for p:*, 1, as is expected to be the case for mesoscopic defect structures of micron size, g ~ n in the ground state. Thus, the operating point of the Josephson junction changes from ~ = 0 to ~---n. Now, independent of the microscopic loss mechanism, the power absorption when a small (miUigauss) microwave field modulates the static field ( ~ 1 G), the absorption must be proportional to the square of the incremental response d~/dC}~t: d~

2

or

PMWA(g~e,,) 1--pCOS[@(0)] ]2 P-- PMWA(0) -- l-/~cos[@(l@oxtl)][ '

(2)

where cp(g~t) is function of g~e~tgiven implicitly by eq. ( 1 ). (Inasmuch as there is no preferred direction for the static external magnetic field, the MWA in eq. (2) must be invariant with respect to the reversal of the static magnetic field. Hence the modulus sign I~ t I in eq. (2).) More specif~ally, the prefactor in the expression for PMWAdepends on the specific mechanism of dissipation. A ubiquitous mechanism of dissipation involves the normal component of the current through the Josephson junction. If ~ is the phase difference across the junction and R, is the junction resistance for the normal current, then the instantaneous power loss is given by

S. V. Bhat et al. / Paramagnetic Meissner effect in YBazCu3OT_a

,2

(d__O2

4e2R-----~× \ dt ,I ' as follows from the fundamental relation between the voltage across the junction and the rate of change of the phase. Now the phase difference is directly related to the total flux • enclosed, i.e. dO dO 0 0 dO~t dO dt pc dt - 0Oe~t dt °Cd-~e~t for a O,~t of given amplitude and frequency. From this our eq. (2) follows immediately. Here we have assumed the RF field to be along the static field direction for simplicity. This is, however, an inessential point inasmuch as the Josephson-junction ( J J ) loops in the sample are randomly oriented and all that matters is the component of the flux (the static and the RF) normal to the plane of the loop. Thus, for the orthogonal configuration of the static and the RF fields (the usual EPR configuration) this introduces geometrical factors involving direction cosines. This in no way affects the basic mechanism discussed above. (It may be noted that in principle this highly nonlinear response problem must be solved as a problem of resistively shunted JJ's following the well known analysis of Silver and Zimmerman [ 11 ].) However, for a low-loss junction (large shunt resistance R~) one can, as indeed we have done, fast calculate the voltage (h/2e) ( d O / d t ) across the junction ignoring R~ and then use that voltage to calculate the loss as h2 4e2R~

91

zero-field minimum to the zero-field maximum. In fig. 6, we have plotted p as function of O~t for a typical value of p. The MWA clearly shows two minima at O~t~-~ symmetrical about the central maximum at O~,t--0. The central cusp-like maximum should be expected to be rounded off in a real system because of a distribution of random internal fields. In the actual plots we have smeared out O~t over a box distribution of __0.1. Recalling that the junction Jc decreases with the decreasing concentration of the isolated moments (on the chain Cu 2+ ) and indeed goes negative for a suberitical concentration of spins [ 6 ], we should expect the anomalous MWA absorption to disappear with or even before the total disappearance of the EPR signal (assuming that the EPR signal originates from the same magnetic-impurity spins that make up the ~ junctions). This trend is clearly seen in our experimental findings as J decreases to 0.1. We can understand the origin of the g junctions in YBa2CU3OT_a samples based on the above discussion. In YBa2Cu306.9 ( J = 0 . 1 ) , the coordination of the chain coppers is four-fold with respect to the oxygens. Thus there is a negligible concentration of Cu 2+ impurities and therefore no local moments and hence the normal MWA. However, for a higher oxygen deficiency (especially J = 0 . 3 - 0 . 4 ) we would have a finite concentration of impurity Cu 2+ ions with local moments (unpaired spins) giving ~ junctions. In view of the high degree of anisotropy, we can, for example, imagine the supercurrent to flow

/dO~ 2

XL-~j

•

This is in the spirit of a first-order perturbation. Also, to calculate the voltage we have taken the RF magnetic flux ( ~: static magnetic field) to just modulate the static external flux; that is, the 0 is determined by the instantaneous external flux (static plus RF) through eq. ( 1 ). Such a quasistatic approximation is quite reasonable for a low junction capacitance and a loop inductance characteristic of mesoscopic defects. In any case, these are quantitative approximations. The main qualitative point of our simple treatment is that the change of the operative point from 0 = 0 to O-~Tr (i.e. a normal g junction) can change the behavior of the MWA qualitatively, from

o

0-

<

I

-10

I

f

I

I

0

i

I

I

I

10

cxt

Fi~ 6. Plot of absorbed power p as a function of Oat obtained from eq. (2), by smearing out Oat over a box distribution of _ 0.1.

92

S. V. Bhat et al. / Paramagnetic Meissner effect in YBazCu3Oz_6

along the sheet interrupted by a defect forcing the pairs to tunnel across via the chains containing the local moments. We cannot be more specific about the nature of these mesoscopic defects at this stage. While our experimental observations are strongly suggestive of the correlation between anomalous MWA and the presence of paramagnetic moments (as revealed by EPR), there are other systematics that we would like to point out. These relate to the detailed temperature and composition (J) dependence oftbe intensity and the shape o f the MWA signals. For J = 0 . 3 and 0.4 (oxygen-disordered samples) the MWA goes through a maximum as the temperature decreases below To. However, for J--0.5 (oxygen-ordered sample), MWA increases monotonically as the temperature decreases below To. Also, samples with J = 0 . 3 and 0.4 show a rich lineshape variation as a function of temperature, which is not the case for the J = 0 . 5 sample. We believe that these temperature/composition effects are due to the parametric changes of the ~ junction loops in our samples. Thus, for example, the critical current of a 7c junction depends on temperature and on the possible configurations of the impurity spins in the junction. These effects call for further study. In conclusion, we have provided experimental evidence that the anomalous MWA with a zero-field maximum is correlated with the unpaired spins on Cu-I. This observation is theoretically consistent with the existence of g junctions normally implicated in PME studies.

Acknowledgement The authors would like to thank the Council of Scientific and Industrial Research, India and the National Superconductivity Programme for support.

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