Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences


Physics and Astronomy

First Advisor

Dr. Lance E. De Long


In recent years, the topic of magnetic frustration in systems and the effect that frustration can have on system dynamics has been a rich environment for study. One such system that lends itself directly to this study are systems of single domain ferromagnetic bars in two dimensions. These ferromagnetic bars can be fabricated from a thin film using current lithography techniques. The bars are fabricated in such a way that their shape anisotropy dictates the magnetization of the bar will be a single domain, Ising-like magnetic moment. These single domain magnetic bars scan be arranged to introduce frustration of their contained magnetic moments. Collections of these arranged single domain magnets are often referred to as an artificial spin ice (ASI). The use of this test bed was first reported in 2006 by Wang et al., where frustrated correlations in a square lattice arrangement of these single domain magnets were investigated. In 2008, Qi et al. reported novel experimental results on connected ferromagnetic wires arranged on a hexagonal lattice and the geometric frustration embedded in that system.

Much of the initial interest in the artificial spin ice came with the realization that the vertices of these arrangements can be represented as clusters of magnetic charge that can be interpreted as quasi-particles of magnetic charge. These quasi-particles of magnetic charge are often thought of as an analog to the yet undiscovered magnetic monopole. These quasi-particles can be manipulated by magnetic fields to form chains of aligned spins that form an analog for Dirac Strings [01]. The study of these dynamics can give insights into the complicated magnetically driven reversal and how these events are governed by the competing constraints of ferromagnetic domain wall behavior versus the magnetic frustration of the system.

Previous work on these systems of Ising-like arranged on a hexagonal lattice has focused on the specifics of the magnetic reversal of the permalloy segments by domain wall creation and propagation through the system. The overall nature of the magnetoresistance (MR) signal in an applied magnetic field is dominated by the anisotropic magnetoresistance (AMR). It has also been reported that the anisotropic magnetoresistance is insufficient to describe the magnetic reversal and that the internal energies of the vertices have a large influence. The charge order of the vertices can affect the nature of the magnetic reversal of the entire system. In Le et al. the energetics of the vertices were shown to have a substantial effect on the magnetic reversal at low fields [02]. The full explanation of the magnetoresistance signal of the magnetic reversal of the system can only be explained by understanding the impact of each of these competing influences.

In this work, we look to compare the magnetic reversal behavior of a periodic hexagonal lattice with one that has undergone a Fibonacci Sequence based distortion. This distortion allows the continuous distortion of the periodic hexagonal lattice to an aperiodic hexagonal lattice. Through this distortion we change the lengths of the segments and the coordination of the vertices that connect the segments. In doing that we change the magnitude of the Ising-like moment in each segment and the energy of their corresponding vertices. This distortion will then directly affect the underlying forces that mediates the resulting magnetic reversal.

We present a brief overview of the key concepts of these artificial spin ice systems. Both connected and disconnected artificial spin ices.

We then discuss the development and implementation of the Fibonacci Distortion on the hexagonal artificial spin ice. The details of the application of the distortion explain how it is used to continuously distort a periodic lattice into an aperiodic lattice and how those are qualitatively different.

We review past work done on the undistorted, periodic, hexagonal lattice and contrast that work with results on the Fibonacci Hexagonal distorted aperiodic hexagonal lattice. We compare these experimental results to magnetotransport experiment simulations done with Object Oriented Micromagnetic Framework (OOMMF). We discuss the nature of magnetotransport results and simulated magnetization images work used to describe the magnetic reversal of the artificial spin ice segments. Results show that the Fibonacci Distortion affects the reversal nature of the system and the critical field value at which these reversal events occur.

Finally, we conclude this thesis with a summary of the results established in this research and discuss other avenues of future research associated with similar systems and possible magnetotransport experiments.

Digital Object Identifier (DOI)

Funding Information

Department of Energy, Basic Energy Sciences, “Magnetization Dynamics and Soft X-Ray Vortex Beam Formation in Nanoscale Magnetic Metamaterials,” DE-SC0016519. 2016-2021.