Magnetization of multiple-quanta vortex lattices

Abstract

We have studied sharp cusplike magnetization (M) anomalies, appearing at matching fields ${\mathit{H}}_{\mathit{m}}$=m${\mathrm{\ensuremath{\varphi}}}_{0}$/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${\mathrm{\ensuremath{\varphi}}}_{0}$. This m${\mathrm{\ensuremath{\varphi}}}_{0}$-flux-line lattice has magnetization M(${\mathit{H}}_{\mathit{m}}$) \ensuremath{\propto}-m${\mathrm{\ensuremath{\varphi}}}_{0}$/${\mathrm{\ensuremath{\Lambda}}}^{2}$, where \ensuremath{\Lambda} is the penetration depth in the film. Between the matching fields ${\mathit{H}}_{\mathit{m}}$H${\mathit{H}}_{\mathit{m}+1}$ the M(H) curve follows a simple M\ensuremath{\infty}-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\ensuremath{\gtrsim}${\mathit{H}}_{{\mathit{n}}_{\mathit{s}}}$, when the occupancy of the antidots reaches the saturation number ${\mathit{n}}_{\mathit{s}}$=r/2\ensuremath{\xi}(T), determined by the antidot radius r and temperature-dependent coherence length \ensuremath{\xi}(T), the ${\mathrm{\ensuremath{\varphi}}}_{0}$ vortices begin to fill interstices, thus forming composite flux-line lattices with m${\mathrm{\ensuremath{\varphi}}}_{0}$ vortices strongly pinned by antidots and ${\mathrm{\ensuremath{\varphi}}}_{0}$ vortices weakly pinned by interstices. \textcopyright{} 1996 The American Physical Society.