VOLUME 79, NUMBER 10 PHYSICAL REVIEW LETTERS 8SEPTEMBER 1997 Flux Pinning in a Superconductor by an Array of Submicrometer Magnetic Dots J. I. Martı ´n,* M. Vélez,* J. Nogués, ² and Ivan K. Schuller Physics Department, University of California-San Diego, La Jolla, California 92093-0319 (Received 10 March 1997) Triangular arrays of submicrometer magnetic dots, with typical spacing of 400–600 nm and diameters close to 200 nm, have been fabricated by electron beam lithography to study pinning effects on Nb thin films. The resistivity versus magnetic field curves exhibit regular structure. Minima appear at constant field intervals, given by the lattice parameter of the dot array. The angular, current, and temperature dependencies of the resistivity imply synchronized pinning by the magnetic array which is relevant at high vortex velocities, when the order in the vortex lattice increases. [S0031-9007(97)03979-3] PACS numbers: 74.60.Ge, 85.40.Ux Flux pinning has been the subject of much interest both in high and low temperature superconductors because of their relevance for applications as well as from the fun- damental point of view [1,2]. A rich variety of phenom- ena in vortex dynamics can be found depending on the type, strength, and correlation of the defects present in the superconducting material. A very useful tool to un- derstand the interaction between vortices and material im- perfections, and in this way enhance the critical current, consists in the introduction of controlled artificial pinning centers in the superconductor. Many types of random im- perfections such as secondary-phase precipitates [3], cold work induced dislocations and strain [4], several kinds of radiation induced defects like heavy-ion columnar tracks [5], etc. can be used to address this problem. A different approach is the fabrication of ordered defect arrays of well defined size and geometry, as, for example, spatially modulated superconducting alloys [6], thickness modulation [7], holes in superconducting networks [8], arrays of holes [9], or magnetic particles [10]. In this way, a whole range of new phenomena may appear associated with the matching of the vortex lattice and the artificial structure. However, only recently submicrometer litho- graphic techniques have been developed that allow reduc- ing the size of pinning centers to a scale comparable to coherence lengths of conventional superconductors. Some possibilities that have been explored include regular lat- tices of holes on low T C superconducting films [11] or spatially modulated e-beam irradiation damage in YBa 2 Cu 3 O 7 [12]. In all these cases normal regions are created throughout the material. In this Letter, for the first time the pinning interac- tion between the vortex lattice and ordered arrays of sub- micrometer magnetic dots has been studied. Therefore, the superconducting thin film is continuous and pinning arises from the interaction with a periodic array of pin- ning centers not from the multiply connected geometry of the system. In this case, in a narrow temperature range, an evenly spaced regular array of minima appears in the resistivity versus perpendicular magnetic field. The peri- odicity of the minima is given by the field corresponding to the spacing of the array of magnetic dots. This indi- cates a collective locking of the flux lattice to the mag- netic dot array. The detailed vortex arrangement has not been uniquely identified. Comparison with available theo- retical models indicates a synchronized pinning by the magnetic dot array at high vortex velocities. Magnetic dots approximately 200 nm in diameter and 40 nm in thickness were prepared on oxidized Si(100) sub- strates using the electron beam lithography. The desired pattern was defined on a PMMA resist layer; then the mag- netic (Fe or Ni) layer was sputtered on top. This was fol- lowed by a lift-off process to obtain the triangular array (50 mm 3 50 mm) of magnetic dots. The lattice constant (d) of the triangular array was varied in the range 400– 600 nm. Figure 1 shows a scanning electron microscopy (SEM) image of a triangular Fe array with d › 600 nm. After this, a 100 nm thick Nb film was sputtered on top. Optical lithography and reactive ion etching were used to define a 40 mm wide bridge with a distance between the voltage contacts of 50 mm for transport measurements [see Fig. 1(b)]. Note that in this geometry the Nb film is con- tinuous so the pinning dots are not embedded within the Nb, but are outside. The dc measurements were performed in a helium cryo- stat with an 80 kG superconducting magnet and a rotatable sample holder with a precision of 1 ± . The magnetic field is always applied perpendicular to the transport current, while the angle u between the field and the film normal was varied to study the angular dependence. The lithographed Nb film on top of the magnetic array of dots exhibits metallic behavior from room temperature to the onset of superconductivity at T › 8.3 K. Figure 2 shows rsBd for a sample with an array of Ni dots (d › 410 nm, J › 2.5 3 10 4 Aycm 2 ) at T › 8.2 K. In the mixed state (8.1 , T , 8.3 K), the resistivity ver- sus magnetic field shows a set of minima regularly spaced at values (B n ) of field. The intervals between two con- secutive minima (DB 0 ) are constant, as shown in the in- set of Fig. 2, with DB 0 › 141 6 4 G. This value may be related with the lattice parameter d of the triangular mag- netic array through the well known relation a 0 › 1.075 sF 0 yBd 1y2 [13], between the magnetic induction (B), and the corresponding triangular vortex lattice constant (a 0 ) 0031-9007y 97y 79(10) y1929(4)$10.00 © 1997 The American Physical Society 1929