Three-dimensional magnetic domain structure in a model with exchange randomness

Surface magnetic domain structure can be different from internal one. Both of them are influenced by structural randomness. Three-dimensional numerical simulations are performed using a model with random exchange interactions and dipolar interactions on a lattice with the periodic boundary condition for the horizontal directions to simulate infinite system in the directions and with the free boundary condition for vertical direction (z) to represent the existence of surface. The lattice sizes are 64×64×(2Lz+1) for Lz=1,2,4 and 32×32×(2Lz+1) for Lz=8,16. To simulate highly anisotropic materials, time dependent Ginzburg-Landau equation using a model with Ising symmetry is solved numerically. Dependence of magnetic domain patterns on thickness of the system and the degree of disorder is investigated for systems with small thickness. Magnetic structure factor for the surface layer is compared with that for the internal layer. The inverse of the wave number that gives the maximum value of the magnetic structure factor depends on the thickness of the system T as T0.3 approximately. The distribution of the local magnetization depends on the disorder rather differently for different thicknesses of the system.