Magnetically actuated lab-on-a-chip (LOC) technologies have enabled rapid, highly efficient separation of specific biomarkers and cells from complex biological samples. Nonlinear magnetophoresis (NLM) is a technique that uses a microfabricated magnet array (MMA) and a time varying external magnetic field to precisely control the transport of superparamagnetic (SPM) beads on the surface of a chip based on their size and magnetization. We analyze the transport and separation behavior of SPM monomers and dimers on four MMA geometries, i.e., circular, triangular, square and rectangular shaped micromagnets, across a range of external magnetic field rotation frequencies. The measured critical frequency of the SPM beads on an MMA, i.e., the velocity for which the hydrodynamic drag on a bead exceeds the magnetic force, is closely related to the local magnetic flux density landscape on a micromagnet in the presence of an external magnetic field. A set of design criteria has been established for the optimization of MMAs for NLM separation, with particular focus on the shape of the micromagnets forming the array. The square MMA was used to detect a model protein biomarker and gene fragment based on a magnetic bead assembly (MBA) assay. This assay uses ligand functionalized SPM beads to capture and directly detect an analyte through the formation of SPM bead aggregates. These beads aggregates were detected through NLM separation and microscopic analysis resulting in a highly sensitive assay that did not use carrier fluid.