Magnetization of multiple-quanta vortex lattices

We have studied sharp cusplike magnetization ({ital M}) anomalies, appearing at matching fields {ital H}{sub {ital m}}={ital m}{phi}{sub 0}/{ital S} in superconducting films with sufficiently large antidots, forming a regular lattice with a unit-cell area {ital S}. Exactly at {ital H}={ital H}{sub {ital m}} each antidot pins the same quantized flux {ital m}{phi}{sub 0}. This {ital m}{phi}{sub 0}-flux-line lattice has magnetization {ital M}({ital H}{sub {ital m}}) {proportional_to}{minus}{ital m}{phi}{sub 0}/{Lambda}{sup 2}, where {Lambda} is the penetration depth in the film. Between the matching fields {ital H}{sub {ital m}}{lt}{ital H}{lt}{ital H}{sub {ital m}+1} the {ital M}({ital H}) curve follows a simple {ital M}{infinity}{minus}ln({ital H}{minus}{ital H}{sub {ital m}}) dependence. As a result, the whole magnetization curve {ital M}({ital H}) can now be successfully described by the simple expression, derived for interacting multiquanta vortices in the London limit. In higher fields {ital H}{approx_gt}{ital H}{sub {ital n}{sub {ital s}}}, when the occupancy of the antidots reaches the saturation number {ital n}{sub {ital s}}={ital r}/2{xi}({ital T}), determined by the antidot radius {ital r} and temperature-dependent coherence length {xi}({ital T}), the {phi}{sub 0} vortices begin to fill interstices, thus forming composite flux-line lattices with {ital m}{phi}{sub 0} vortices strongly pinned by antidots and {phi}{sub 0} vortices weakly pinned by interstices. {copyright} {ital 1996 The American Physical Society.}