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Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet

Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Benard convection, Faraday waves, liquid crystals, domain patterns in ferromagnetic films and skyrmion crystals recently observed in chiral magnets. Here we study a simple model of an anisotropic frustrated magnet and show that its zero-temperature phase diagram contains numerous multi-q states including the skyrmion crystal. We clarify the mechanism for stabilization of these states, discuss their multiferroic properties and formulate rules for finding new skyrmion materials. In addition to skyrmion crystal, we find stable isolated skyrmions with topological charge 1 and 2. Physics of isolated skyrmions in frustrated magnets is very rich. Their statical and dynamical properties are strongly affected by the new zero mode - skyrmion helicity.