Manipulation of the magnetization by external energies other than magnetic field, such as spin-polarized current1-4, electric voltage5,6 and circularly polarized light7-11 gives a paradigm shift in magnetic nanodevices. Magnetization control of ferromagnetic materials only by circularly polarized light has received increasing attention both as a fundamental probe of the interactions of light and magnetism but also for future high-density magnetic recording technologies. Here we show that for granular FePt films, designed for ultrahigh-density recording, the optical magnetic switching by circularly polarized light is an accumulative effect from multiple optical pulses. We further show that deterministic switching of high anisotropy materials by the combination of circularly polarized light and modest external magnetic fields, thus revealing a pathway towards technological implementation.