Magnetization of multiple-quanta vortex lattices

We have studied sharp cusplike magnetization (M) anomalies, appearing at matching fields H-m=m phi(0)/S in superconducting films with sufficiently large antidots, forming a regular lattice with a unit-cell area S. Exactly at H=H-m each antidot pins the same quantized flux m phi(0). This m phi(0)-flux-line lattice has magnetization M(H-m) proportional to-m phi(0)/Lambda(2), where Lambda is the penetration depth in the film. Between the matching fields H-m<H<H-m+1 the M(H) curve follows a simple M infinity-1n(H-H-m) dependence. As a result, the whole magnetization curve M(H) can now be successfully described by the simple expression, derived for interacting multiquanta vortices in the London limit. In higher fields H>H-ns, when the occupancy of the antidots reaches the saturation number n(s)=r/2 xi(T), determined by the antidot radius r and temperature-dependent coherence length xi(T), the phi(0) vortices begin to fill interstices, thus forming composite flux-line lattices with m phi(0) vortices strongly pinned by antidots and phi(0) vortices weakly pinned by interstices.