A magnetic sensor with increased sensitivity, lower noise, and improved frequency response is described. The sensor's free layer is ribbon shaped and is closely flanked at each long edge by a ribbon of magnetically soft, high permeability material. The side stripes of soft magnetic material absorb external field flux and concentrate the flux to flow into the sensor's edges to promote larger MR sensor magnetization rotation. The free layer may be deposited simultaneously with the soft magnetic layer when they are aligned in the same plane. When the flux absorbing stripes are positioned above or below the MR sensor, then the free layer and flux absorbing stripes are deposited in separate steps.