Geometrical frustration is known to significantly modify the properties of many materials. Pyrochlore spin ice and hexagonal water ice are canonical systems that show the effects of frustration in both heat capacity and dynamical response. In both instances, microscopic ordering principles on the lattice lead to a macroscopic degeneracy of configurations. This degeneracy in spin ice may also be modified or lifted by lattice imperfections, external pressure, or magnetic field. Unfortunately, these effects are difficult to model or predict, because existing experimental techniques cannot directly observe the local ordering, near lattice defects or otherwise. To address this long outstanding problem, recent interest has focused on fabricating systems that allow the effects of frustration to be physically modeled and the resulting local configurations to be directly observed.

In this dissertation, I present an artificial approach to kagome lattice. The kagome lattice is a two-dimensional structure composed of corner-sharing triangles and is an essential component of the pyrochlore spin ice structure. Our artificial kagome spin ice, constructed by magnetic nano-bar elements, mimics spin ice in 2D. The realized system rigorously obeys the ice rule (2-in 1-out or 1-in 2-out configuration at a vertex of three elements), thus providing a sought-after model system appropriate for further studies.

To study the ground state of the artificial kagome system and to validate the artificial approach for spin ice study, we demagnetize the samples using rotating field and observe spin configurations using Lorentz TEM. The ice rule, short-range ordering and absence of long-range disorder, as well as the relatively low remnant magnetization are found in the system, which are signatures of spin ice materials in their ground states. To model our system and relate it to other spin study, we introduce magnetic charge model and Shannon entropy concept. The calculated charge correlation (charge ordering coefficient) and Shannon entropy suggest that the degeneracy of our lattice is lifted from a completely disordered kagome spin ice system, and close to a "true" ground state that is usually found as the kagome plateau in pyrochlore spin ice when applying a field in <111> direction. We also study the effects of external perturbations. When applying a magnetic field, chain-like spin flipping is found in the system, which can be explained by the magnetic charge model. When distorting the lattice by introducing an artificial strain, we observe partial ordering or symmetry breaking in the system, which is similar to the pressure effects in real spin ice.

In the Appendix, I also introduce another study I have done, i.e. multiferroic thin film measurements.  The focus of that chapter is the dielectric measurement for BaTiO3 (BTO) -CoFe2O4 (CFO) thin film material using a microwave microscope. The measurement has a quantitative spatial resolution of approximately 5 m, and it provides a method for film quality check and the basis for a proposed ME coupling measurement.