The control of nonthermal, all-optical magnetization switching under the regime with an independent state of laser polarization opens up new opportunities for ultrafast magnetic recording. Here, we investigate the photo-magnetic back-switching capabilities of the write and erase magnetic domain pattern using double-pump pulse excitations in an iron garnet film with pure cubic magnetocrystalline symmetry. It is essential to note that forward and backward magnetization switching is achievable in two distinctive scenarios: using identical linearly polarized laser pulses and with pulses having orthogonal polarization planes. By observing the switch of magnetization at domains independent of the initial state, one can nonthermally toggle the magnetization, equivalent to XOR logical operation, at frequencies reaching up to 50 GHz.

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