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The complex-field approach is developed to derive analytical expressions ofthe magnetic field distributions around superconducting strips on ferromagneticsubstrates (SC/FM strips). We consider the ferromagnetic substrates as idealsoft magnets with an infinite magnetic permeability, neglecting theferromagnetic hysteresis. On the basis of the critical state model for asuperconducting strip, the ac susceptibility $\chi_1'+i\chi_1''$ of a SC/FMstrip exposed to a perpendicular ac magnetic field is theoreticallyinvestigated, and the results are compared with those for superconductingstrips on nonmagnetic substrates (SC/NM strips). The real part $\chi_1'$ for$H_0/j_cd_s\to 0$ (where $H_0$ is the amplitude of the ac magnetic field, $j_c$is the critical current density, and $d_s$ is the thickness of thesuperconducting strip) of a SC/FM strip is 3/4 of that of a SC/NM strip. Theimaginary part $\chi_1''$ (or ac loss $Q$) for $H_0/j_cd_s<0.14$ of a SC/FMstrip is larger than that of a SC/NM strip, even when the ferromagnetichysteresis is neglected, and this enhancement of $\chi_1''$ (or $Q$) is due tothe edge effect of the ferromagnetic substrate.

Analytical investigation of magnetic field distributions around superconducting strips on ferromagnetic substrates