Ice is a common material that has unusual properties. The hydrogen ions in ice keep in disordered states even at the extremely low temperatures. Thus ice has the socalled zero point entropy. The disordered states in ice are a consequence of geometrical frustration, a fascinating phenomenon that attracts not only considerable interest in basic physics but also provides a novel platform for important applications, such as data storage and neural networks.

Geometrical frustration also occurs in magnetic materials, in which the geometry of an ordered lattice prohibits simultaneous minimization of all magnetic interactions. Spin ice is a class of geometrically frustrated materials in which the magnetic ions mimic the frustration of hydrogen ion positions in frozen water. However, such chemically synthesized materials put severe limitations on probing the individual magnetic ions and tuning the magnetic interactions.

We used electron beam lithographic patterning to create square arrays of singledomain permalloy (Ni_0.8Fe_0.2) nanomagnets in which the dipolar interactions displayed two-dimensional frustration analogous to spin ice. Magnetic force microscopic (MFM) images of individual magnetic moments directly displayed the local accommodation of frustration. We saw both ice-like short-range correlations and an absence of long-range correlations, behavior which is strikingly similar to the low-temperature state of spin ice.

The second part of this thesis is about our investigations on demagnetization on the nanometer scale. We studied demagnetization protocols for artificial spin ice by rotating it in a changing magnetic field. To demagnetize the sample, we find that the most effective demagnetization is achieved by not only stepping the field strength down while the sample is rotating, but by combining each field step with an alternation in the field direction. By contrast, linearly decreasing the field strength or stepping the field down without alternating the field direction leaves the arrays with a larger remanent magnetic moment. These results suggest that non-monotonic variations in field magnitude around and below the coercive field are important for the demagnetization process.