High velocity vortex channeling in vicinal YBCO thin films.

We report on electrical transport measurements at high current densities on optimally doped YBa2Cu3O7-δ thin films grown on vicinal SrTiO3 substrates. Data were collected by using a pulsed-current technique in a four-probe arrangement, allowing to extend the current-voltage characteristics to high supercritical current densities (up to 24 MA cm-2) and high electric fields (more than 20 V/cm), in the superconducting state at temperatures between 30 and 80 K. The electric measurements were performed on tracks perpendicular to the vicinal step direction, such that the current crossed between ab planes, under magnetic field rotated in the plane defined by the crystallographic c axis and the current density. At magnetic field orientation parallel to the cuprate layers, evidence for the sliding motion along the ab planes (vortex channeling) was found. The signature of vortex channeling appeared to get enhanced with increasing electric field, due to the peculiar depinning features in the kinked vortex range. They give rise to a current-voltage characteristics steeper than in the more off-plane rectilinear vortex orientations, in the electric field range below approximately 1 V/cm. Roughly above this value, the high vortex channeling velocities (up to 8.6 km/s) could be ascribed to the flux flow, although the signature of ohmic transport appeared to be altered by unavoidable macroscopic self-heating and hot-electron-like effects.

Introduction

In the last few years there has been much interest in studying the anisotropic vortex transport behavior in high-T cuprate superconductors (HTSCs) under bias current nonparallel to the ab crystallographic planes [1-10]. When the magnetic field is applied parallel to these layers, the geometry of the experiment allows for a finite Lorentz force on the Josephson vortices, inducing their sliding motion along the ab-planes (vortex channeling) [1,2,5,7,10-14].

When the magnetic field direction is slightly tilted from the layers, the flux lines distort and kink into chain vortices consisting of alternating vortex “pancakes” located in the cuprate planes connected by Josephson vortex “strings” lying in the charge reservoir layers [15]. The Josephson string vortices are more weakly pinned than the pancake vortices, so that when the flux line is entirely string-like the available flux pinning is greatly reduced.

The vortex channeling was evidenced either through the appearance of a flux-flow voltage while reaching a vortex “lock-in” state in strongly anisotropic Bi2Sr2CaCu2O8+ single crystals under c-axis bias current [11,12,7], or through the minimum attained in critical current measurements when the magnetic field is oriented parallel to the ab-planes in YBa2Cu3O7− (YBCO) films grown on miscut (vicinal) substrates [1,2,14,5,10,16]. A small tilt of the flux line will rapidly nucleate many pancakes which will serve to strongly pin the flux line but a certain amount of dissipation continues nevertheless to occur through a flux cutting effect, especially in the angular region, where the Lorentz forces on the strings and pancakes are opposite [5,10]. The vortex string segments will bow out between the pancakes and will join the contiguous flux line. If the Lorentz force required to cause flux cutting is less than that required to de-pin the entire line, dissipation arises from flux cutting rather than from flux flow or flux creep [10].

It would be therefore interesting to investigate the anisotropic transport behavior by vortex motion in vicinal HTSC films also at higher levels of the Lorentz force and vortex velocity, that is at current densities much higher than in the previously published measurements. The purpose of the present paper is to provide such investigations at electric fields up to more than six orders of magnitude higher than the dissipation onset criterion for the critical current. Using a pulsed current technique allows for diminishing of self-heating and avoids possible damaging of the films at high dissipation levels.

Experimental technique

We report on electrical transport measurements at high current densities on thin films of optimally doped YBCO grown on vicinal SrTiO3 substrates. Thin films were prepared by pulsed laser deposition [17] and grown on single crystal SrTiO3 substrate, miscut by an angle α towards the (0 0 1) direction [5]. Current tracks were patterned by photolithography and Ar-ion milling to allow four terminal current–voltage (IV) measurements, and tracks were patterned both perpendicular and parallel to the vicinal step direction, as described in Ref. [5]. Contacts were prepared by sputtering Ag/Au bilayers. Our electric measurements were performed on tracks perpendicular to the vicinal step direction, such that the current crossed between ab planes. Data presented here were collected on a film with vicinal angle α ≈ 8°, 150 nm thickness, and the track was 10 μm wide and 120 μm long.

The experimental setup for the electric transport measurements was made up of a closed-cycle refrigerator and an electromagnet. The magnetic field of B = 1 T could be rotated in the plane defined by the crystallographic c axis and the current density j, as shown schematically in Fig. 1, where β is the angle between magnetic field B and current, α is the vicinal angle and θ = β − α is the angle between B and the ab plane of YBCO.

Fig. 1

Experimental geometry for the measurements in vicinal films and the respective coordinate systems.

Data were collected by using a pulsed-current technique in a four-probe arrangement, whose electric scheme is shown in Fig. 2, and that is described in detail elsewhere [18,19].

Fig. 2

Pulsed current technique.

The measurements were carried out at different discrete temperature values in the superconducting state, with a stability better than ±0.01 K, by using current pulse duration of the order of μs and with extremely low duty cycle (repetition rate ⩽10 Hz), so that the cumulative heating between subsequent pulses was avoided. The chosen pulse length was long enough to permit stabilization of the voltage signals after the high-frequency distortions at the pulse onset, so that the current and voltage values were measured in a very well resolved time-window in the last third of the pulse duration. The pulse length was also sufficiently short to avoid the effects of the heat wave propagation from the current contacts, and to keep very low the temperature increase due to the heat diffusion in the film substrate. For each data point, defined by (T, β, j), the current and voltage pulses were simultaneously sampled at a 200 MHz rate, digitized at high-resolution (14 bits), and recorded for averaging purposes in series of 1024 subsequent pulses. This technique allowed to extend the current–voltage characteristics to current densities above 20 MA cm−2, significantly higher than can be attained with the conventional dc method.

Measurement results and discussions

Current–voltage characteristics were recorded with the described method at several temperatures between 30 and 80 K and different orientations of the magnetic field. Typical measured IV curves are shown for a low temperature (40 K) in Fig. 3 and for a higher temperature (80 K) in Fig. 4.

Fig. 3

Current–voltage characteristics at 40 K in a magnetic field of 1 T oriented at different angles β with respect to the current direction.

Fig. 4

Current–voltage characteristics at 80 K in a magnetic field of 1 T oriented at different angles β with respect to the current direction.

In order to relate our pulsed current data to previous dc data from critical current measurements at very low electric field [1,5,10], we note that at a fixed voltage drop, the corresponding current density value can be interpreted as a “critical” current density j = j according to the respective criterion E = E. Results of such analysis are shown for T = 40 K in Fig. 5 at different voltage criteria.

Fig. 5

“Critical” current density at 40 K for different voltage criteria, as a function of the angle β between the magnetic field (B = 1 T) and the current direction.

In the “critical” current picture j(β) in Fig. 5 one can notice the two qualitative features already known from dc critical current measurements at a low voltage (of the order of 10−5 V/cm) criterion [1,5,10], namely the j peaks in the Lorentz-force free configuration (B∥j, β = 0), and the j minima attributed to the intrinsic channeling of vortices when the magnetic field is directed parallel to the CuO2 planes.

The more pronounced vortex channeling minimum at higher electric fields is yielded by the peculiar behavior of the current–voltage characteristics, which in the range below approximately 1 V/cm are steeper around the vicinal angle (see Figs. 3 and 4). We note that on reasonably small intervals, spanning at most two orders of magnitude in the electric field E, the IV curves can be approximated through power-law functions E ∝ j, and the exponent γ = (dE/dj)/(E/j) quantifies thus the steepness of the current–voltage characteristics.

The variation of the exponent γ corresponding to the electric field interval [10−2–1] V/cm is shown in Fig. 6 for different temperatures, as a function of the magnetic field orientation. A clear maximum around the vicinal angle can be noticed.

Fig. 6

Exponent γ in the power law approximation E ∝ j for the IV characteristics in the E range [0.01–0.5] V/cm at different temperatures.

The vortex channeling minimum is pronounced at low temperatures, for example at 40 K in Fig. 3, but diminishes with increasing temperature and completely disappears around 80 K, as one can see in Fig. 7, where the “critical current” is pictured at a constant voltage criterion for different temperatures. This feature was explained [1,5] in terms of the crossover [15] between the kinked vortex configuration and the anisotropic Abrikosov lattice which at higher temperatures persists for all angles of the applied magnetic field.

Fig. 7

“Critical” current density at different temperatures defined by a voltage criterion of 0.5 V/cm, as a function of the angle β between the magnetic field (B = 1 T) and the current direction.

Also in Fig. 6, one can notice an overall lower exponent γ as well as its less pronounced maximum at higher temperatures. The increase of power law exponent with decreasing temperatures is known to appear in vicinal films [3,4] as also in the more trivial geometry of a non-vicinal structure, that is with current flowing in the ab plane under a magnetic field parallel to the c-axis [20] or to the ab plane [21]. This behavior is usually attributed to a vortex glass transition and connected to the fact that the vortex movement becomes increasingly collective when temperature or magnetic field falls [22]. The lack of “universality” of such a transition in various samples was also signalized, namely the differences in magnitude and variation with magnetic field of the critical exponents [4].

While for electric field ranges below roughly 1 V/cm the exponent γ has a maximum approximately at the vicinal angle (β ≈ α, that is for ∥ab), it appears that at higher electric fields (E > 1 V/cm),γ is minimal at β ≈ α, as one can see in Fig. 3. While for the magnetic field orientations around ∥ab there is a strong decrease of the γ at higher electric fields, the current–voltage characteristics at orientations tilted far off the ab plane change only little their steepness at increasing vortex velocity. This difference in the transport features between oriented close to and far off the ab plane is qualitatively evidenced also in the dynamic resistivity picture from Fig. 8. One can notice the different curvature of the dynamic resistivity as a function of current density for angles β = 7°, 9°, 10.5°, 13° around the vicinal value with respect to the orientations farther from this angle. The tendency to saturation of the dynamic resistivity at orientations around ∥ab suggests that the flux flow would appear first for this orientation, where the vortex channeling occurs. However, for the current density and electric field ranges attained in our measurements, the ohmic regime of a free flux flow is apparently not reached, the lowest exponent value still being E ∝ j3.2 (see Fig. 3).

Fig. 8

Dynamic resistivity corresponding to data from Fig. 3 at 40 K in a magnetic field of 1 T oriented at different angles β with respect to the current direction.

The highest average vortex velocity attained in our measurements corresponds to the data points of highest electric field in Fig. 3 and is estimated through v = E/(B sin β) to be:

We can attempt to compare this value with estimations according to the free flux flow model for anisotropic Abrikosov vortices at ∥ab orientation under a bias current at vicinal angle with the ab plane, , where is the normal state resistivity in the out-of-plane direction and is the upper critical field parallel to the ab planes. If for optimally doped YBCO one assumes [23] and an almost constant extrapolated [24] , then the estimated flux flow velocity at the highest attained electric field would be vfff ≈ 4.7 km/s, that is roughly half of the velocity corresponding to the measured electric field values from Eq. (1). We can try to correct this discrepancy by taking into account the self-heating that could occur due to the high dissipation level. One contribution is the macroscopic (phononic) heating due to the thermal boundary resistance R at the film-substrate interface, which can be estimated through [25] T − T ≈ jE dR, with T the film lattice temperature, T the substrate temperature and d the film thickness. The second heating contribution could come from a hot-electron-like effect that is supposed to occur at temperatures substantially below T, where the electron–electron scattering time is small compared to the electron–phonon inelastic scattering time, so that the electron gas remains in internal equilibrium at a temperature higher than the lattice temperature [26]. This contribution can be estimated through with τ the electron–phonon energy relaxation time, T the electronic temperature and c the electronic specific heat. By taking as values for the mentioned parameters R ≈ 4.5 × 10−3 K cm2/W (evaluated directly by measuring the resistance increase due to self-heating far in the normal state), τ ≈ 0.1 ns from Ref. [26] and c(T) from Ref. [27], one finds for the data points corresponding to the highest attained electric fields in Fig. 3 the corrected temperature T ≈ 57.9 K and T ≈ 60.9 K. By estimating further from Ref. [24] and from Ref. [23], one finds eventually better approximations for the vortex velocity according to the free flux flow model:which is closer to the measured value from Eq. (1). Although the estimation made is rather rough, we may nevertheless assume that at the highest electric field values reached in our measurements for the vortex channeling configuration (∥ab) the almost free flux flow regime was attained. The γ exponent value still higher than one could be at least partially caused by the afore mentioned self-heating effects. The fact that at high electric fields (>1 V/cm) the IV characteristics are even steeper at field orientations far off the ab plane should be caused by the stronger flux pinning of rectilinear Abrikosov vortices in those orientations, so that the dynamic resistivity strongly increases with the current density.

The different behavior seen at low and moderately high electric fields (roughly below 1 V/cm), where the IV characteristics are the steepest for the vortex channeling orientation (∥ab), appears on the contrary in a dissipation range, where pinning is important also during the vortex channeling. Around this configuration, in the angular range of the kinked vortices, the dissipating vortex motion occurs mainly through cutting and rejoining of vortex string segments between more strongly pinned pancake vortices [5,10]. It appears that this kind of depinning gives not only a higher average vortex velocity responsible for channeling but it has also a stronger collective character than the flux creep and partial flux flow of the rectilinear Abrikosov vortices, so that steeper IV curves are to be found around the β = α orientation (Fig. 6). The higher γ exponent in the E ∝ j approximation for ∥ab yields in turn the enhanced channeling feature at higher vortex velocities pictured in Fig. 5.

Conclusions

In summary, we have investigated with the aid of a pulsed current technique the anisotropic transport behavior by vortex motion in vicinal YBCO films in the superconducting state at high supercritical current densities (up to 24 MA cm−2) and high electric fields (up to more than 20 V/cm), aiming to complement the critical current dc measurements that evidenced the vortex channeling at magnetic field orientation parallel to the cuprate layers. We have found the channeling signature to get enhanced with increasing electric field, due to the peculiar depinning features in the kinked vortex range, which give rise to a steeper current–voltage characteristics with respect to the more off-plane rectilinear vortex orientations, in the electric field range below approximately 1 V/cm. Roughly above this value, the high vortex channeling velocities can be ascribed to the free flux flow, although the signature of the ohmic transport appears to be altered by unavoidable macroscopic self-heating and hot-electron-like effects.