  Surface based geometries of microfabricated wires or patterned magnetic films
can be used to magnetically trap and manipulate ultracold neutral atoms or
Bose-Einstein condensates. We investigate the magnetic properties of such atom
chips using a scanning magnetoresistive (MR) microscope with high spatial
resolution and high field sensitivity. We show that MR sensors are ideally
suited to observe small variations of the magnetic field caused by
imperfections in the wires or magnetic materials which ultimately lead to
fragmentation of ultracold atom clouds. Measurements are also provided for the
magnetic field produced by a thin current-carrying wire with small geometric
modulations along the edge. Comparisons of our measurements with a full numeric
calculation of the current flow in the wire and the subsequent magnetic field
show excellent agreement. Our results highlight the use of scanning MR
microscopy as a convenient and powerful technique for precisely characterizing
the magnetic fields produced near the surface of atom chips.
