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A skyrmion crystal (SkX) expressed as a multiple number of spiral modulationsmanifests itself not only in its peculiar magnetic texture but also innontrivial transport properties originating from an emergent magnetic field. Wehere report our numerical results for multiple SkXs in a centrosymmetrictetragonal crystal system. By performing simulated annealing for an effectivespin model for itinerant magnets, we find that three types of the SkXs with theskyrmion numbers of one and two, which are characterized by differentsuperpositions of helices, are stabilized in the ground state, and aretransformed by an external magnetic field. The essence of the emergent multipleSkXs is lied in itinerant frustration where exchange interactions are competedin momentum space due to the nature of itinerant electrons.

Multiple skyrmion crystal phases by itinerant frustration in centrosymmetric tetragonal magnets