Magnetization of multiple-quanta vortex lattices

We have studied sharp cusplike magnetization (M) anomalies, appearing at matching fields Hₘ=mφ₀/S in superconducting films with sufficiently large antidots, forming a regular lattice with a unit-cell area S. Exactly at H=Hₘ each antidot pins the same quantized flux mφ₀. This mφ₀-flux-line lattice has magnetization M(Hₘ) {∝}-mφ₀/Λ², where {Λ} is the penetration depth in the film. Between the matching fields HₘHHₘ₊₁ the M(H) curve follows a simple M{∞}-ln(H-Hₘ) 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 nₛ=r/2{ξ}(T), determined by the antidot radius r and temperature-dependent coherence length {ξ}(T), the φ₀ vortices begin to fill interstices, thus forming composite flux-line lattices with mφ₀ vortices strongly pinned by antidots and φ₀ vortices weakly pinned by interstices. {} 1996 The American Physical Society.