Sign change of the vortex Hall effect in superconducting YBCO thin films with a square pattern of ion-irradiated defect columns

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Physica C: Superconductivity and its applications 0 0 0 (2016) 1–4

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Sign change of the vortex Hall effect in superconducting YBCO thin films with a square pattern of ion-irradiated defect columns G. Zechner a, L.T. Haag a, W. Lang a,∗, M. Dosmailov b, M.A. Bodea b, J.D. Pedarnig b a b

Faculty of Physics, Electronic Properties of Materials, University of Vienna, Boltzmanngasse 5, A-1090, Wien, Austria Johannes-Kepler-University Linz, Institute of Applied Physics, Altenbergerstrasse 69, A-4040 Linz, Austria

a r t i c l e

i n f o

Article history: Received 8 January 2016 Accepted 1 June 2016 Available online xxx Keywords: Superconductors Vortex Hall effect Vortex matching Pinning

a b s t r a c t The Hall effect in the mixed state of thin films of the high-temperature superconductor YBa2 Cu3 O7−δ (YBCO) that were patterned with a square array of regions with suppressed superconducting order parameter is investigated. Cylindrical defect columns penetrating the entire thin YBCO film along its crystallographic c−axis have been created by irradiation with He+ ions through a silicon stencil mask. Distinct peaks of the critical current at commensurate arrangements of magnetic flux quanta with the artificial defect lattice confirm enhanced vortex pinning. Vortex motion not only leads to a dissipative voltage along the current direction but also to a transverse voltage, termed vortex Hall effect. We report on the observation of a novel commensurability effect in the transverse Hall signal. A sign change and a positive peak of the Hall coefficient appear in a narrow magnetic field range around the matching field. The feature appears in the temperature range below the critical temperature, where the Hall effect usually is negative in underdoped and optimally-doped cuprate superconductors. The results indicate that the Hall matching effect originates from enhanced pinning of the vortices along the regular defect columns. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The dissipative effect of vortex motion is almost omnipresent in superconductivity research and is commonly associated with a voltage drop along the current direction. It is not so evident that also a transverse voltage appears in this situation that resembles the Hall effect and is, thus, frequently called vortex Hall effect. Due to the complicated equation of motion of a vortex in a real system with pinning and other forces, and the even more subtle situation in a vortex ensemble, this vortex Hall effect is not well understood. In particular, in the copper-oxide superconductors, the Hall effect in the superconducting state exhibits several anomalies that are in contrast to traditional models for vortex dynamics [1,2]. The most frequently discussed observation is a sign reversal of the Hall coefficient RH below the critical temperature Tc . Several theoretical models have attempted to explain this observation and a phenomenological interpretation based on a renormalized Ginzburg-Landau model for superconducting order parameter fluctuations provides a satisfactory fit to the experimental observations, but still a well-accepted microscopic explanation is missing [3, 4, and references therein].

∗

Corresponding author. E-mail address: [email protected] (W. Lang).

Careful experiments under more extreme experimental conditions have revealed double, even triple, sign reversals of the vortex Hall effect. On one hand they appear in highly anisotropic, weak-pinning high-temperature superconductors (HTS), like in Bi2 Sr2 CaCu2 Ox (BSCCO) [5,6] and are probably an intrinsic electronic property of the layered material. On the other hand, it was intensively discussed [7,8], whether vortex pinning can cause a 2 + ρ 2 ), where the change of the Hall conductivity σxy = ρyx /(ρxx yx Hall resistivity ρyx = RH B and B the magnetic field. It could ultimately lead to a sign reversal of the Hall effect below Tc [9,10] that can be dependent on the dimensionality of the pinning centers near a Bose or vortex glass transition, respectively [11]. Indeed, the intrinsic strong pinning in near-optimally doped thin films of YBa2 Cu3 O7−δ (YBCO) leads to a second sign reversal that emerges in low magnetic fields only, when the vortex density is low enough to enable efficient pinning on twin boundaries (see Fig. 1). Note that this second sign reversal emerges for B < 100 mT only and is canceled by depinning of vortices in high current densities or by tilting the magnetic field off the crystallographic c-axis and, thus, off the twin-boundary direction, rendering them less efficient for pinning [12]. Only with the recent emergence of advanced nanopatterning methods that allow for the fabrication of regular arrays of many thousands holes with (sub)-μm distance in a thin superconducting film it became possible that artificial structures can compete with

http://dx.doi.org/10.1016/j.physc.2016.06.001 0921-4534/© 2016 Elsevier B.V. All rights reserved.

Please cite this article as: G. Zechner et al., Sign change of the vortex Hall effect in superconducting YBCO thin films with a square pattern of ion-irradiated defect columns, Physica C: Superconductivity and its applications (2016), http://dx.doi.org/10.1016/j.physc.2016.06.001

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Fig. 1. Hall coefficient of a pristine (unpatterned) YBCO film near the superconducting transition in low magnetic fields. The arrow indicates the sequence of reduced magnetic fields according to the indicated values. Adapted from [12].

the intrinsic pinning of twin boundaries in YBCO. A common proof for the capability of artificial structures to pin vortices is the socalled “vortex matching” effect, where at particular magnetic fields a commensurate relation exists between the vortex lattice and the lattice of holes (antidots) or defect columns imprinted in the sample. For a square array of pinning sites the (first) matching field is given by

Bm =

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φ0 d2

,

(1)

where φ 0 is the flux quantum, and d the lattice constant of the square array. In principle, vortex matching can also occur at fields nBm with n a rational number. The various arrangements of vortices with respect to the defect lattice for integer and fractional values of n have been demonstrated with Lorentz microscopy in a superconducting Nb film [13]. Whereas the reports on various manifestations of vortex matching are numerous for clean and, hence, weak-pinning metallic superconductors [14], there are only few observations of such an effect in the strong-pinning limit of thin YBCO films [15–19]. In this paper, we report on investigations of the field matching effect in the Hall signal in very low magnetic fields. We shall demonstrate that a second sign reversal of the Hall effect in artificially patterned YBCO films appears only in close vicinity to the matching field, thus, providing a hallmark of enhanced pinning. 2. Experimental techniques Thin films of YBa2 Cu3 O7−δ were grown epitaxially on (100) MgO single-crystal substrates by pulsed-laser deposition using 248 nm KrF-excimer-laser radiation at a fluence of 3.2 J/cm2 . The thickness of the film used for the present work was 210 nm after 60 0 0 laser pulses. For the electrical transport measurements the films were patterned to bridges with dimensions 240 × 60 μm2 by photolithography and wet chemical etching. Contacts were established in a four-probe geometry using sputtered Au-pads with a distance of 100 μm for the voltage probes. The patterned sample had a critical temperature Tc ∼ 90 K, a transition width Tc ∼ 1 K, and a critical current density jc ∼ 3 MA/cm2 at 77 K and zero magnetic field. Periodic arrays of defect columns were prepared by a masked ion beam shadowing technique, described in more detail elsewhere Please cite

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G.

Zechner et

Fig. 2. Critical current density as a function of the applied magnetic field B. To avoid hysteretic effects the sample was heated to T = 100 K and then field-cooled for every data point. The upper horizontal axis is scaled to multiples of the matching field Bm = 22.7 mT. The insert shows a scanning electron microscopy picture of the sample surface, where the black areas indicate the irradiated nonsuperconducting defect columns.

[20–22]. Briefly, a thin Si stencil mask with a square array of about 670 × 270 holes with diameters 180 ± 5 nm and 302 ± 2 nm lattice constant was placed on top of the YBCO film. A well-defined distance of the mask to the surface of the YBCO film was established by a layer of 1.5 μm-thick photoresist that was applied to the sample area aside from the bridge. By this procedure any contact of the Si surface with the YBCO surface was avoided. The ion beam can only reach the YBCO sample through the mask holes, all other parts of the sample, as well as the contact areas are protected from the irradiation. The irradiation was performed with 75 keV He+ ions in a commercial ion implanter (High Voltage Engineering Europa B. V.) on a cooled sample stage and with dose monitoring by Faraday cups. The beam direction was parallel to the sample’s c-axis. The measurements of the Hall effect were performed in a closed-cycle refrigerator with temperature control by a Cernox resistor [23]. The magnetic field was supplied by an electromagnet and monitored by a calibrated Hall probe with an accuracy better than ± 1%. The fixed current through the sample was generated by a Keithley 2400-LV constant-current source in both polarities to exclude thermoelectric signals and the voltage drop along the probes measured by a Keithley 2182A nanovoltmeter. For every data point the sample was slowly cooled from the normal state with applied magnetic field down to the respective measurement temperature at which reversals of the polarity of the excitation current (30 times) and the magnetic field (4 times) were performed to improve the signal to noise ratio. The standard error of the mean values of these multiple measurements are displayed as error bars in Fig. 4. 3. Results and discussion The commensurate arrangement of the vortices in superconducting samples with a periodic array of pinning centers can be demonstrated by a pronounced enhancement of the critical current jc [15,16,19,24]. The jc of our irradiated YBCO film at 34.3 K as a function of the magnetic field B oriented perpendicular to the sample surface is shown in Fig. 2. To allow for a quasi-equilibrium arrangement of vortices the data were collected with the respective magnetic field applied at 100 K before cooling the sample below

al., Sign change of the vortex Hall effect in superconducting YBCO thin

films with a square pattern of ion-irradiated defect columns, Physica C: Superconductivity and its applications (2016), http://dx.doi.org/10.1016/j.physc.2016.06.001

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RH (10-4 cm3/C)

1

0

-1

19.7 mT 20.3 mT 23.0 mT 23.6 mT 24.8 mT

-2

-3 32

33

34

35

36

Temperature (K) Fig. 3. Hall coefficient of the irradiated YBCO film at temperatures below the superconducting transition in various small magnetic fields. The matching field Bm = 22.7 mT according to Eq. (1). For the sake of clarity, only data at selected representative values of the magnetic field are displayed.

1.4

2.8

1.2

2.7

1.0

2.6

0.6 0.4

2.5

0.2

2.4

0.0 -0.2

2.3

-0.4

RH (35.0 K)

-0.6

2.2

jc (34.3 K)

-0.8

2.1

-1.0 -1.2

jC (kA/cm2)

RH (10-4 cm3/C)

0.8

20

21

22

23

24

25

2.0

B (mT) Fig. 4. Comparison of two different manifestations of the vortex matching effect in the irradiated YBCO film. Blue squares show the peak of the critical current at 34.3 K and green triangles the magnitude of the Hall coefficient at 35.0 K near the matching field. Error bars indicate the standard error of the mean value. The sign change of RH from negative to positive values is attributed to enhanced pinning.

Tc [19]. The distinct maxima in jc (B) are positioned exactly at the matching fields nBm = n(22.7 ± 0.2 ) mT according to Eq. (1) where a commensurate relation exists between the vortex lattice and the square lattice of irradiated regions defined by the geometrical parameters of the stencil mask. Note that the largest maximum reflects the fact that the critical current is highest in zero magnetic field. A scanning electron microscopy picture of the irradiated areas (dark spots) is shown in the insert of Fig. 2. It should be mentioned that the midpoint of the superconducting transition is lowered to Tc ∼ 47 K after irradiation what we attribute to a certain straggling of the ions after passing through the holes in the stencil mask and within the YBCO film itself. This leads to an, although minor, number of defects in the areas of the YBCO film that are protected by the stencil mask and, thus, a reduction of Tc . A similar observation was reported by other authors [16]. Hence, the fixed temperatures employed in Figs. 2 and 4 correspond to a reduced temperature t = T /Tc ≈ 0.75. In principle, one would expect that the commensurate matching of vortices with the defect array should have influence on the transverse transport properties, too. Please cite

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G.

Zechner et al.,

3

A substantial misfit angle between the axis of the square array of defect columns and the current direction in the sample should give rise to vortex channeling equivalent to oblique microchannels for easy vortex flow that evoke a transverse voltage [25]. In fact, an additional component to the Hall voltage, comparable in magnitude to the anomalous (negative) Hall effect, was observed in YBCO films with a square array of antidots tilted at γ = −35◦ and attributed to guided vortex motion [26]. In our experimental design, however, care was taken to align the defect lattice parallel to the current (better than ±1°), so that an easy flow of vortices would be perpendicular to the current direction and induce a longitudinal voltage only. The Hall effect in the patterned YBCO film at moderate field B = 0.8 T has similar features like it is displayed in Fig. 1 for the pristine YBCO except for a lower Tc as discussed before. Notably, only one sign reversal with a negative peak of RH = −1.5 × 10−4 cm−3 /C can be observed. In sharp contrast to the previous observations in unpatterned YBCO, the second (positive) sign reversal does not evolve continually with lower B but occurs only in a limited field range around the matching field Bm (see Fig. 3). The magnitude of the positive maximum at Bm is RH ≈ 1.1 × 10−4 cm−3 /C and, hence, comparable to the value observed in unpatterned YBCO films at B = 32 mT. The above observations are strong indications that the second sign change in the irradiated YBCO film is caused by enhanced pinning at a commensurate arrangement of the vortices. The intriguing similarity between the well-established signature of vortex matching as a peak in jc and our novel observation of a sign reversal and a peak in RH are compared in Fig. 4 for the same sample. The confinement of the observed effect to magnetic fields near Bm is an additional indication that it is not caused by guided vortex motion. First, guided vortex motion should be observable in a wide range of magnetic fields, and, second, it should not coincide with a maximum of pinning, as reflected in the jc (B) behavior, but rather with a minimum. A possible explanation is that enhanced pinning of vortices at commensurate vortex arrangement leads to a change of the Hall conductivity that may be decomposed into

σxy = σxyN + σxyS + σxyP ,

(2)

N represents a quasiparticle or vortex-core contribution, where σxy S σxy a superconducting contribution, resulting from hydrodynamic P vortex effects and superconducting fluctuations [27–31], and σxy N allows for a pinning-dependence of σ xy . The sign of σxy is the same as that of the normal-state Hall effect, i.e., positive in YBCO, but S depends on details of the Fermi surface [28–30,32]. the sign of σxy Assuming that it is negative, the Hall effect’s sign reversal and behavior in a wide range of magnetic fields can be quantitatively P can evoke a second sign modeled [4]. The pinning contribution σxy S and a reversal of RH , provided that it has the opposite sign of σxy P | can similar magnitude. Kopnin et al. [8] have proposed that |σxy S |, leading eventually to an additional sign reversal of exceed |σxy the vortex Hall effect due to strong pinning. Ikeda [11] has emphaP does depend on the dimensionality of the sized that the sign of σxy P S ) for nearly three-dimensional pinning, namely sgn(σxy ) = sgn(σxy P ) = systems with point-like disordered pinning sites and sgn(σxy S sgn(σxy ) when line-like pinning disorder dominates. The latter pinning situation prevails in our YBCO films with B oriented parallel to the defect columns. Finally, we note that the second sign reversal and the positive peak of RH are washed out in elevated current densities, when pinning effects are overcome by the larger Lorentz force on the

Sign change of the vortex Hall effect in superconducting YBCO thin

films with a square pattern of ion-irradiated defect columns, Physica C: Superconductivity and its applications (2016), http://dx.doi.org/10.1016/j.physc.2016.06.001

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vortices, contrary to the negative anomalous Hall effect that is enhanced in high currents [6,33]. 4. Conclusions The commensurate arrangement of vortices at a regular array of defect columns that were produced by masked ion-beam irradiation in thin YBCO films not only gives rise to maxima in the critical current, but also to a novel manifestation of a commensurability effect in the transverse Hall signal. A second sign change and a positive peak of the Hall coefficient apart from the well-known negative Hall anomaly in YBCO appears in a narrow magnetic field range around the matching field. In line with previous theoretical results we propose that it originates from pinning of the vortices along line-like defects.

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Acknowledgments [21]

We appreciate the help of Klaus Haselgrübler with the ion implanter. This work was supported by the COST Action MP-1201. M.D. acknowledges the European Erasmus Mundus (Target II) program for financial support. References

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al., Sign change of the vortex Hall effect in superconducting YBCO thin

films with a square pattern of ion-irradiated defect columns, Physica C: Superconductivity and its applications (2016), http://dx.doi.org/10.1016/j.physc.2016.06.001