Physica C 332, 353 (2000)

Enhanced critical currents in high-temperature superconductors with splayed pins

C. J. Olson*, R.T. Scaletter, G.T. Zimanyi
Department of Physics, University of California, Davis, CA 95616, USA

Abstract

Using realistic three-dimensional computer simulations, we consider the effects of point, columnar, and splayed columnar pinning on vortex transport. We find an enhancement in the critical current when columnar pins are placed in a splayed configuration rather than parallel to each other, but that this enhancement is limited to the vortex creep regime at the lowest measurable applied currents. At higher currents, in the vortex flow regime, the enhancement by splay is lost. 200 Elsevier Science B.V. All rights reserved.

Keywords: Critical current; Splayed configuration; Vortex transport; Flux creep; Flux pinning

Heavy-ion irradiation is known to enhance enhance critical currents in superconductors through the creation of extended columnar defects that localize individual vortices much more effectively than naturally occurring point defects [1]. Due to thermal fluctuations, however, significant creep of flux lines from one columnar pin to the next occurs, reducing the achievable critical current [18,19]. In Ref. [2] it was suggested that the motion of a vortex between columnar pins that are tilted with respect to each other costs more energy than motion between parallel pins, implying that pinning by artificial columnar defects could be further improved by irradiating the sample at a range of angles rather than at a fixed angle as considered previously [1]. In recent experiments [3-16], splay pinning has been created directly through multiple-step irradiation of the sample, or indirectly by irradiation through thin foils. Up to an order of magnitude enhancement of the critical current relative to parallel columnar pins has been reported [3].

Although the beneficial effects of splay have been carefully studied experimentally, the particular microscopic mechanism responsible for the enhancement of the critical current by splay has not been determined. Several mechanisms were suggested in Ref. [2], but none of these can be directly observed experimentally. In spite of the importance of splay for critical current enhancement, no realistic numerical simulations of vortices interacting with splayed pinning have been reported up until this time. In this paper we demonstrate the suppression of vortex creep due to splayed pinning using a realistic, three-dimensional London Langevin simulation. We find that small splay angles strongly suppress vortex creep at low applied currents, due to the difference in the energy barrier for the movement of double kinks.

To address this problem from a microscopic level, we use computer simulations based on a realistic London Langevin model [17]. The simulations shown here are for samples 106 long on each side (where is the coherence length) containing 49 vortices and 80 layers. We integrate the overdamped Langevin equation of vortex motion, given by: (z,t)= (z,t) + FL +Fint +Fel + Fpin. Here, is the velocity of vortex element in layer z at time t. is the Langevin thermal force for T=0.78Tc, which corresponds to 77K in YBCO. FL is the Lorentz force. Fint is the interaction force between vortices [17], and Fel is the elastic bending forces acting between elements belonging to a single vortex. The pinning force Fpin representing irradiated areas is modeled by short-range attractive parabolic wells of radius rp = 0.5 which are spatially correlated between layers to form columnar pins. All of the wells belonging to a single columnar defect have the same energy Upi chosen from a Gaussian distribution with mean Up=0.08 and standard deviation = 0.012. The number of pins, Np = 225, is much larger than the number of vortices, Nv= 49, so each vortex can be trapped by a pin. The vortex lattice is heavily distorted by the strong random pins.


Fig. 1. Resistivity, versus j/j0 for columnar (filled circles) and splayed (open squares) defects.

In Fig. 1, we compare two samples with an equal density of columnar pins. In the first sample the pins are aligned parallel to the z-axis, and in the second, the pins are splayed at =5.7o from the z-axis, perpendicular to the direction of vortex motion. As shown in Fig. 1, we find a suppression of the creep of vortices by splay in the small current regime. Furthermore, we observe an enhancement in the critical current, but only if defined via a threshold criterion with xxthreshold<0.05. At resistivities (or equivalently, currents) above these values the enhancement by splay is lost.

The microscopic mechanism that we observe causing the enhancement of Jc by the splayed pinning in our simulations is the suppression of vortex kink spreading by the splayed pinning. At low applied currents j/j0 < 0.09, vortices move between pins by thermally activated double kinks [18-21]. For parallel columnar pins, extending an already formed double kink does not cost extra energy. For splayed pins, double kinks between pairs of pins tilted in opposite directions can become localized due to the energy cost for continued expansion as the vortex attempts to move between two pins of opposite tilt.


Fig. 2. Resistivity versus applied current j/j0 for equal densities of: point pinning (plus signs), columnar pinning (filled circles), bimodal splay pinning (open squares), and Gaussian splay pinning with = 5o (open up triangles).

To explore the effect of pinning geometry on vortex motion in the creep regime, we have simulated resistivity measurements on samples with equal numbers of pinning elements placed in point, columnar, bimodal splay, or Gaussian splay arrangements. As seen in Fig. 2, we find the highest resistivity for point pins, lower for columnar, and the lowest for splayed. We find that the Gaussian splay produces a higher resistivity than columnar pins, consistent with experiments [3,9-11].

In conclusion, we have used realistic simulations to show an enhancement of superconducting transport properties by splayed pinning configurations. This enhancement is limited to regimes of vortex creep. At low currents, vortices move by means of double kinks, and the existence of a higher energy barrier for kink motion in the splayed sample leads to lower vortex mobility. At higher applied currents when vortices no longer move by means of kinks, the resistivity in the splayed sample becomes as large as that in a sample with columnar pins.

Acknowledgments

We thank G. Crabtree, N. Gronbech-Jensen, T. Hwa, L. Krusin-Elbaum, W. Kwok, D. Nelson, and V. Vinokur for useful discussions. Funding was provided by NSF-DMR028535, CLC, and CULAR.

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