Dynamic susceptibility of skyrmion crystal

Using stereographic projection approach, we develop a theory for calculation of dynamic susceptibility tensor of Skyrmion crystals (SkX), formed in thin ferromagnetic films with Dzyaloshinskii–Moriya interaction and in the external magnetic field. Staying whenever possible within analytical framework, we employ the model ansatz for static SkX configuration and discuss small fluctuations around it. The obtained formulas are numerically analyzed in the important case of uniform susceptibility, accessible in magnetic resonance experiments. We show that, in addition to three characteristic magnetic resonance frequencies discussed earlier both theoretically and experimentally, one should also expect several resonances of smaller amplitude at somewhat higher frequencies.