Correlation length and time in the vortex-glass critical regime in YBa2Cu3O7−x films

Physica C 235-240 (1994) 2661-2662

PHYSICA

North-Holland

Correlation length and time in the vortex-glass critical regime in YBa2Cu307. x films D.G. Xenikos a,b, T.R. Lembergera, L. Hou c, M.W. McElfreshc aDepartment of Physics, Ohio State University, 174 West 18th Ave, Columbus, OH 43210, USA. bpresent address: CRTBT-C.N.R.S., BP 166, 38042 Grenoble-CEdex 9, France. eDepartment of Physics, Purdue University, West Lafayette, IN 47907, USA.

We report on the complex conductivity of a YBa2Cu307. x (YBCO) microbridge in the presence of magnetic field 0.5 Tg+, the critical scaling laws break down when the diverging vortex correlaLon length matches the film thickness of our sample and the correlation time exceeds I0 lxs.

1.

INTRODUCTION The signature of the critical slowing down of the vortex system on the complex conductivity in YBCO films, along a phase boundary T g ( B ) separating a vortex-liquid from a glass phase, has triggered considerable controversy. In particular, transport measurements at frequencies 1-600 MHz are inconclucive about the exponent of the power law followed by the in-phase and the out-of-phase components of the a c electrical conductivity at T g ( B ) . I , 2 In our work, we study the film a c conductivity at relatively lower frequencies 0.05 < f < 20 MHz, thus recording the critical slowing down at temperatures closer to Tg. A careful analysis to estimate the width of the critical region in the vicinity of the phase boundary is obtained by comparing the ac-conductivity results to currentvoltage (I-V) characteristics in the dc limit, and then extracting the vortex correlation length and time of the transition. 2.

CRITICAL SCALING Our measurements are performed on an epitaxial YBCO film deposited by laser ablation onto a heated SrTiO3 substrate. The film was 2500-2"_400 A thick, with its c-axis normal to the substrate, and exhibited a 2 K-wide transition at 88.5 K. It was patterned

into a 4-contact 35 mm x 600 mm microbridge by photolithographic techniques. A square wave transport current of frequency 10 < f < 2 × 106 Hz was then passed through the bridge and the resulting a c voltage was measured using a lock-in. For frequencies f>50 KHz, the sample response was heterodyned into audio frequency signal to be detected by the lock-in. Fig. 1 (top) shows typical nonlinear I-V curves at f=102 Hz ( d c limit), at B=6T. Following established procedures 3"6, we define Tg =74.0 K, i.e., the highest T with I-V close to linear in the log-log plot. Furthermore, when we require the I-V curves to collapse on a set of scaling functions, we obtain from our data an uncertainty in determining Tg, ATg=+0.7 K. The in-phase Vi (out-of-phase V o) components of the a c voltage are shown in middle of Fig. 1 (bot.). The amplitude of the excitation current is kept small I=40 mA, so that Vi, Vo are linear in I. We notice that the f-dependence of the Vi and Vo are quite different: Vo follows a power law Vo~ f~, with oc switching from cz=l below Tg, to ~=0.75 at T>>Tg, while V i deviates from power law at all T > T g . At Tg however, Vi ~ Vo o~ f~, with ~=0.82+0.05. A single power law for both V i, Vo is consistent with a phase transition at Tg. 7 Our value for ct at Tg is in excellent agreement with ref.

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2662

D.G. Xenikos et al./Physica C 235-240 (1994) 2661-2662

1, but clearly at odds with the reported one in ref. 2. I ~

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CORRELATION LENGTH AND TIME Our data allow us to estimate the vortex correlation length ~o and time x as T - ~ T g +. Scaling analysis of the curvature of the I-Vs at T>75 K in Fig. 1 (top) indicates that the crossover current In from linear to nonlinear conductivity descends to lower values. Taking I o = 8 X l 0 " 5 A [the corresponding current density is Jo = 0.9x107 A/m 2] for T=75.3 K the temperature closest to Tg with a prominent linear component at low I, we estimate 5" 7 ~o = (kT/Jo~o)l/2 = 2000 A. As expected, this indicates that the scaling of the I-Vs persists to the temperature T-~Tg + where ~o approximately equals the film thickness. This result is consistent with measurements in Al-doped YBCO films.5, 6 Finally, since V o in the vicinity of Tg follows a power law down to -at least- frequency fo" 105 Hz, we conclude that the critical slowing down persists to temperatures where the vortex correlation time exceeds x_> lifo = 10 Its.

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We acknowledge support primarily by grant AFOSR-91-0188, and also by DOE grant DE-FG0290ER45427 through MISCON.

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REFERENCES

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Figure 1. Electrodynamic response of the YBCO microbridge at B=6 T around Tg (dashed lines). Top: I-V curves in the dc limit for T=77.7, 77.2, 76.9, 76.7, 76.2, 75.9, 75.3, 74.3, 73.6, 72.6, 71.6, 70.0, 69.7, 68.8 K. M i d d l e : Frequency dependence of the in-phase (Bot.: out-of-phase) component of the voltage when the amplitude of the current passing through the bridge is I=40 ~tA, corresponding to the I-Vs at the higher 9 temperature values. All the logarithms are on base l0 and all the quantities shown are in MKS units.

3. 4. 5. 6. 7.

H.K. Olsson et al., Phys. Rev. Lett. 66, 2661 (1991). Hut Wu et al., Phys. Rev. Lett. 71, 2642 (1993). R.H. Koch et al., Phys. Rev. Lett. 63, 1511 (1989). P.L. Gammel et al., Phys. Rev. Lett. 66, 953 (1991). D.G. Xenikos et al., Phys. Rev. B 48, 7742 (1993). D.G. Xenikos et al., Physica B 194-196, 1913 (1994). D.S. Fisher et al., Phys. Rev. B 43, 130 (1991).