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

A finite-size ferromagnetic chain of classical XY spins, where each of the two edge spins is exchange-coupled to a fictitious fully-pinned spin, is investigated in the presence of a weak in-plane perturbation (external magnetic field or uniaxial anisotropy). Within a macrospin approximation, the above chain model can be representative of a soft ferromagnetic film consisting of N parallel atomic layers, sandwiched between two magnetically hard films. In zero field, the model has a ferromagnetic collinear ground state and admits a class of metastable helical states containing an integer number of twists. Analytical expressions are obtained for the linear corrections to the helical magnetic configuration and for the local magnetic susceptibility tensor. The dependence of the integral susceptibility of the chain, chi , on the number of spins in the chain, N, is also calculated. It is found that chi is proportional to N^3 for small values of the helix mode (m <<N), while chi is proportional to N^2 for large values of the helix mode ( m approx (N+1)/4 ).