Hofstadter butterflies in a modulated magnetic field - APS Link ...

IYE et al. PHYSICAL REVIEW B 70, 144524 (2004)FIG. 10. Structure of the samples. (a) Sample A for the checkerboardfield. (b) Sample B for the stripe field. The external fieldparallel to the network plane controls the magnetization of the ferromagneticarray. The amplitude of the spatially modulated magneticfield can be changed by the azimuthal angle of the parallelfield.III. EXPERIMENT WITH SUPERCONDUCTINGWIRE NETWORKSA. Experimental methodThe samples used in the present study were fabricated onsilicon substrates by the following steps.(i) Electrode pads were first formed by electron beam lithographyand gold evaporation.(ii) The network pattern (square lattice) was defined byelectron beam lithography and the niobium wire networkwas formed by ion-beam sputtering deposition and the liftoffprocess.(iii) A protecting layer of germanium was deposited ontop of the wire network, so as to prevent oxidation of niobiumand to keep it from direct contact with the ferromagneticmaterial to be deposited next.FIG. 11. Magnetoresistance traces at different temperatures forsample A. These data were taken at =0, i.e., =0.FIG. 12. Evolution of the Little-Parks oscillation for sample Awith the value of (checkerboard field). The traces are verticallyoffset for clarity.(iv) An array of mesoscopic ferromagnets (cobalt ornickel) was placed on top by electron beam lithography, ionbeamsputter deposition, and liftoff.The crucial point in the fabrication was to achievegood positional and angular registration between thesuperconducting network and the overlaid ferromagnetarray.Two samples (A and B) were intensively studied. Thesesamples represent the checkerboard field case (sample A)and the stripe field case (sample B), respectively. Thesuperconductor part of the sample consisted of a squarenetwork of 100100 unit cells, made of niobium wire150 nm wide and 40 nm thick. The lattice period was500 nm for sample A and 750 nm for sample B. For sampleA, 150200 nm 2 rectangular dots of 80-nm-thick cobaltwere placed on top of the center of every other bond wiresin the y direction, as shown in Fig. 10(a). For sample B,250-nm-wide strips of 60-nm-thick nickel were placedon top of every other lines in the y direction as shown inFig. 10(b).Measurements of the superconducting properties wereconducted by use of a cross-coil superconducting magnetsystem, consisting of a 6 T Helmholtz coil and a 1 Tsolenoid. The horizontal field was used to fix the magnetizationof the ferromagnetic array and thereby controlthe strength of the spatially varying field (parameter or ).The vertical field supplied the uniform field (parameter )for the network. The four-terminal resistance of the networkwas measured by a standard ac lock-in technique. Cryogeniccontrol was achieved by a variable temperature insert Dewar144524-6