Scaling behavior at the vortex glass transition

Physiea C 185-189 (1991) 1815-1816 North-Holland

SCALING BEHAVIOR AT THE VORTEX GLASS TRANSITION H.K. Olsson, R. H. Koch*, W. Eidelloth*, and R. Robertazzi* Physkcs Department, Chalmers University of Technology, S-412 96 Grteborg, Sweden, *IBM Research Division, Yorktown Heights, NY 10598, USA. We find scaling behavior of the linear ac-impedance consistent with a phase transition from a normal or vortex fluid state into a superconducting or vortex glass state in measurements on cuprate YBa2Cu307 superconducting thin films in strong fields (, 0.55 T ). At the vortex glass transition temperature, Tg--86.1 K, as determined from de IV-curves we find scaling with frequency of the impedance amplitude, I Z I ~ 000.83, and a frequency independent phase, ~=74o. In addition a critical slowing down of the vortex dynamics consistent with a diverging correlation time is observed as Tg is approached, x - (T-Tg)-5.8.

1. INTRODUCTION The possible existence of a vortex glass phase below the mean-field transition for a superconductor in a large magnetic field H>Hcl has recently been suggested 1. IV-curve measurements 2 confirm the existence of a truly superconducting state with zero linear resistance below a well defined phase transition temperature and are consistent with scaling theory3. The phase transition is characterized by a diverging correlation length, ~ - IT-TgI-~ and a diverging correlation time, x ~ IT-Tgl-~z, where v and z are critical scaling exponents . We report measurements of the linear at-impedance 4 in the frequency range from 100 kHz to 500 MHz that are consistent with the vortex glass model.

3. RESULTS Figure 1 shows a set of IV-curves for different temperatures both above and below Tg. A well defined transition temperature separates a normal region from a superconducting region with exponentially vanishing voltage, V- exp{J c/J }~t , where Jc is the critical current and ~t (0~2), see figure 2. Also here do we f'md a power law dependence

10-3 ~1~

2. EXPERIMENTAL Measurements were made on 250 nm thin YBa2Cu307 films on LaA103 substrates that were patterned into 8 by 600 ~tm large stripes. The critical current density was i.6xi06 A/cm 2 at 77K. A two terminal method using a networkanalyzer with matched coax-lines was used for the measurements. The calculated impedance is proportional to the sample resistivity for these thin films. Close to T g , the condition of film thickness being small compared to two London penetration depths is well satisfied. IV-curves were mcasured at 11 Hz using a four-terminal method.

i

I

i

.,o_: ]

/

T=T,

I

1

W

'i 10 -6

10 -7

10 -7

10 -6

|j

I0 -s

10 -4

10 -3

1

10 -2

Current (a)

Figure 1. IV-curves for different temperatures. A power law is obtained for T=Tg=86.1 K.

0921-4534/91/$0a.50 © 1991 - Elsevier Science Publishers B.V. All dghls reserved.

1t.1(. Oisson et al. / Scaling behavior at the vortex glass transition

1816

103

102 ~. ¢,. O Q) ¢',t

I

I

I

I

I

I

90 80

. . . . . . .

,

.....

I

I

I

I

_

_ A

70 6O

v

50 40

10 100 O-

30 20

_E 10-1 T =

10

'

10-2 -I ,." , I I I 105 10s 107 108 Frequency (Hz)

I

109

05

lOs 107 108 Frequency (Hz)

109

Figure 2. Impedance amplitude for a set of temperatures. A slope of 0.83 is measured at T= 86.1 K.

Figure 4. The phase for different temperatures. A frequency independent phase of 740 is measured at Tg.

at 86.1 K, IZI-- (o0.83, where Z is the complex sample impedance and (o the frequency. The impedance is dominated by a frequency independent part above the mean-field transition and approaches the two-fluid result, IZl-. col.0, below Tg. The transition region is a critical scaE~g regime, and has a temperature dependent cross-over frequency, f4=llx. Q has a power law dependence ~-(T-Tg)5.8 giving the exponents z=5.2 and v=l.1, see figure 3. In other words, we measure a diverging correlation time as the sample is cooled down and the vortex glass phase is approached. From the extent of the linear regime in the IV-curve measurements we get values for typical correlation lengths (in the film c-direction) ranging from 50 to 200 nm and v=l.1. For comparison, these values are larger than the distance between vortices (40 nm ) but

smaller than the film thickness. The phase, defined as ¢p= arctan Im{Z}/Re{Z}, is plotted in figure 4 for the same temperature range. Temperatures well above Tg approach cp=0o or being dominated by resistive losses whereas below Tg, q)=90o and a vortex glass or superconducting state dominated by the kinetic inductance is approached. At Tg we measure ~p=74o. This value gives z=5.6 (¢p=~(z-1)/2z) in good agreement with the value obtained from IZ(c0)l, z=5.9 ( 0.83=(z-1)/z ). Power dependence measurements confirm that the 101xA at-current used was not too large and therefor confined the measurements to within the linear regime.

•

,

r

I

1

p /*

10 8

.}j

¥ / /.'@ /

107

t

/

¢

/

I I

106 0,01

(t-tg)/rq

0.05

Figure 3. Crossover frequency, f2=l/x-(T-Tg)5.8, as a function of temperature.

4. CONCLUSION In conclusion we find a qualitative and quantitative agreement with the vortex glass theory. Both dc and ac measurements give consistent critical exponents for a field of 0.55 T: z= 5.2+0.7 and v= 1.1+0.4. REFERENCES 1. M.P.A. Fisher, Phys.Rev.Lett. 62, 1415 (1989). 2. R.H. Koch, V. Foglietti, W.J. Gallagher, G. Koren, A. Gupta, and M.P.A. Fisher, Phys.Rev.Lett. 63, 1511 (1989). 3. D.S. Fisher, M.P.A. Fisher, and D.A. Huse, Phys.Rev B 43, 7575 (1991). 4. H.K. Olsson, R.H. Koch, W. Eidelloth, and R.P. Robertazzi, Phys.Rev.Lett. 66, 2661 (1991).