The use of superconducting films having low flux pinning density in a vortex storage region (VSR) of an Abrikosov vortex memory was assessed. Flux pinning densities in MoSi thin films were examined with particular attention to parallel field behavior. Pinning force densities in the perpendicular field decreased with decreasing film thickness. On the other hand these values for thinner films in the parallel field were one order of magnitude larger than those in the perpendicular field. This indicated the need for increasing the perpendicular conponent in the magnetic field generated by the write current line in order to enhance low write current operation. An improved cell structure was devised in which the write current line is located adjacent to the VSR. This arrangement proved to be effective in stable low current operation in a vortex memory.