Magnetization of multiple-quanta vortex lattices

We have studied sharp cusplike magnetization (M) anomalies, appearing at matching fields ${\mathit{H}}_{\mathit{m}}$=m${\mathrm{\phi }}_0$/S in superconducting films with sufficiently large antidots, forming a regular lattice with a unit-cell area S. Exactly at H=${\mathit{H}}_{\mathit{m}}$ each antidot pins the same quantized flux m${\mathrm{\phi }}_0$. This m${\mathrm{\phi }}_0$-flux-line lattice has magnetization M(${\mathit{H}}_{\mathit{m}}$) ∝-m${\mathrm{\phi }}_0$/${\mathrm{\Lambda }}^2$, where Λ is the penetration depth in the film. Between the matching fields ${\mathit{H}}_{\mathit{m}}$<H<${\mathit{H}}_{\mathit{m}+1\mathrm{}}$ the M(H) curve follows a simple M∞-ln(H-${\mathit{H}}_{\mathit{m}}$) 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≳${\mathit{H}}_{{\mathit{n}}_{\mathit{s}}}$, when the occupancy of the antidots reaches the saturation number ${\mathit{n}}_{\mathit{s}}$=r/2ξ(T), determined by the antidot radius r and temperature-dependent coherence length ξ(T), the ${\mathrm{\phi }}_0$ vortices begin to fill interstices, thus forming composite flux-line lattices with m${\mathrm{\phi }}_0$ vortices strongly pinned by antidots and ${\mathrm{\phi }}_0$ vortices weakly pinned by interstices. © 1996 The American Physical Society.