Journal of Magnetism and Magnetic Materials 113 (1992) 132-136 North-Holland Memory effect in a labyrinth domain structure in bubble materials M. Portes de Albuquerque ~ and P. Molho Laboratoire Louis N~el, CNRS-UJF, 25 at'. des Martyrs, 166X, 38042 Grenoble-Cedex, France A cellular pattern, obtained from a magnetic bubble lattice, shows memory effect after one field cycle, H m-0- H m. We analyze the loss of memory, occurring after many cycles, using image processing to characterize the patterns. We study the evolution of the number of vertices, the mean distance and the total length between them. The excess of length due to curvature of cell edges is proportional, on average, to the cells area, and this can be related to dipolar interactions. The loss of memory, seen in the evolution of the total length between vertices, can be described by the after-effect model, where "degrees of freedom" acquired when the edge of the cells wind up in decreasing field are analogous to thermal fluctuations. 1. Introduction An amorphous lattice of bubbles is one of the possible domain structures, in zero field, in "bub- ble materials". Such a lattice is an hexagonal packing of bubbles, but with many defects, small bubbles with 5 neighbors and large ones with 7 neighbors. When the magnetic field is applied in the direction of the magnetization in the bubbles, one can see an evolution of the pattern, driven by the collapse of small bubbles, leading to a disor- dered cellular pattern, with a large distribution of size of cells (fig. 1) [1-3]. When the field is decreased to zero, the edges of the cells wind up in order to increase the reverse domain, leading to a labyrinth type structure, with zero magneti- zation in zero field. But the labyrinth keeps the topology of the cellular pattern, and if the field is increased back to its maximum previous value, the cellular pattern is almost exactly recoveced (fig. 2). This memory effect results from the sta- bility of the vertices in the pattern. Nevertheless, when many cycles of the field, Hmax-0-Hmax, are alOlOttkzu, tllClC lb i:l blOW CXOlUtlOn of the pattern (a) (b) ........ ~c) Fig. 1. Evolution of the bubble lattice with increasing mag- netic field: (a) H = 0; (b) 70.50e: (c) 82.50e. (fi~. 3). We analyze this "lns~ cff rnornc~rv" hv quantifying the evolution. Correspondence to: Dr. P. Molho, Laboratoire Louis N~el, CNRS-UJF, 25 av. des Martyrs, 166X, 38042 Grenoble-Cedex, France. i On leave from: Centro ~rasileiro de Pesquisas Fisicas, CBPF/CNPq, Brazil. 2. Experiment We used a sample provided by LETI-CEN Grenoble. It is a thin layer (5 ~m) of single 0304-8853/92/$05.00 (~5 1992 - Elsevier Science Publishers B.V. All rights reserved