Linear magnetic susceptibility of a finite XY chain model with magnetic helices as metastable states

•A finite-size chain of N classical spins with helical metastable states is investigated.•The model is representative of a soft ferromagnetic film sandwiched by two hard films.•The effect of a weak in-plane magnetic field or uniaxial anisotropy is studied.•Analytical expressions are obtained for the corrections to the helical states and the susceptibility.•The magnetic susceptibility of the chain is found to scale as N3 or N2 depending on the helix mode.