Vortex Breaking and Cutting in Type II Superconductors A. Palau, R. Dinner, J. H. Durrell, and M. G. Blamire Department of Materials Science, Cambridge University, Pembroke Street, Cambridge CB2 3QZ, United Kingdom (Received 10 March 2008; published 26 August 2008) In technological superconductors, the Lorentz force on the flux vortices is opposed by inhomogeneous pinning and so the critical current may be controlled by a combination of vortex entanglement, cutting, and cross-joining. To understand the roles of these processes we report measurements of structures in which a weak pinning layer is sandwiched between two strongly pinning leads. Quantitative modeling of the results demonstrates that in such systems the critical current is limited by the deformation of individual vortices and not by subsequent cross-joining processes. DOI: 10.1103/PhysRevLett.101.097002 PACS numbers: 74.25.Qt, 74.25.Fy, 74.78.Fk, 74.78.Na The commercialization of high temperature supercon- ductors (HTS), particularly YBa 2 Cu 3 O 7x , is limited by the field dependence of the critical current density (J c ). At J c , the Lorentz force (LF) on magnetic vortices is balanced by pinning forces, which can be strongly inhomogeneous along the length of a vortex. Theory predicts that in this case, vortices could cut and cross-join in the weakly pinned regions between strong pins, allowing dissipation without depinning entire vortices [1]. Such inhomogeneous pinning abounds in HTS conductors, arising from surface currents [2], point pinning [1], and planes of weak pinning, such as grain boundaries [3,4] and twin boundaries [5]. The recent introduction of second-phase nanoparticles pinning centers [6] provide another source of inhomogeneity. Despite its relevance, cutting remains poorly under- stood, principally because direct comparison of calcula- tions to experiments is precluded by the statistical spread of the strengths and spatial distribution of pinning centers in HTS. An open question is whether an energy barrier to vortex cutting causes vortex entanglement [7], which might actually enhance critical current density [8,9]. Although entanglement has been modeled for isolated vortices [9,10], the collective behavior of an entangled lattice is much less tractable [11], and, since no experi- mental technique can probe the three-dimensional struc- ture of such systems, the role and energetics of vortex cutting remains unknown. Here we report experiments on heterostructures which restrict vortex deformation to an engineered volume which simulates a naturally occurring HTS weak pinning plane such as a grain boundary or the space between two strong pinning centers. The cutting force can be directly measured and we obtain for the first time quantitative agreement between calculated and ex- perimentally measured values. We show that vortex-vortex interactions do not enhance J c but represent a mechanism by which strong pinning centers may be bypassed. Our measurements are performed on superconducting trilayer devices consisting of a layer of relatively weakly pinning amorphous Mo 82 Si 18 sandwiched by strongly pin- ning Nb layers. The two materials chosen (whose transition temperatures, T c , are 7 K and 9 K, respectively) differ in pinning strength by more than a factor of 10. As thin films they also have a large upper critical field,  0 H c2 , of at least 0.8 T and so we can avoid low fields where the local vortex angle can diverge strongly from the applied field direction [12]. As a result, vortices pass through the three layers and, under the influence of a current, will deform in the Mo 82 Si 18 channel while remaining pinned in the surround- ing Nb. Steady-state dissipation under these conditions requires that vortex segments within the channel cut and cross-join. Our experiment therefore probes the forces necessary for vortex deformation and cutting. The films were grown on oxidized Si substrates by ultrahigh vacuum dc magnetron sputtering. X-ray diffrac- tion of plain Mo 82 Si 18 films shows no crystalline peaks, verifying that the layers are amorphous. Heterostructures with different Mo 82 Si 18 thicknesses (t ¼ 0, 50, and 100 nm) and fixed Nb thicknesses, 400 nm, were grown in the same sputtering run by varying the deposition time for each of several substrates. The films are patterned to define a 4 m track with four contacts. Using a focused- ion beam (FIB), a portion of the track is narrowed to 500 nm, then lateral cuts force the current to flow vertically through the weak pinning channel, as shown in Fig. 1 and detailed in Ref. [13]. We measure J c as a function of , the angle between the film normal and the applied magnetic field, using a crite- rion of 0:5 V. Although the voltage contacts are outside the narrowed portion of the track, any voltage measured must arise from this constriction because of its much smaller area and therefore higher current density than the leads. Figure 2(a) presents J c ðÞ for a set of samples with different t at 0.5 T and 5 K. The pure Nb sample (t ¼ 0) behavior is qualitatively different from the others. The fit to this is derived purely from geometrical factors: the chang- ing cross-sectional area of the current path along the structure coupled with the changing relative angle (and PRL 101, 097002 (2008) PHYSICAL REVIEW LETTERS week ending 29 AUGUST 2008 0031-9007= 08=101(9)=097002(4) 097002-1 Ó 2008 The American Physical Society