The characterization of the material properties of Single Molecule Magnets (SMMs) has grown in importance over the last few decades with the rise of novel applications such as high-density magnetic storage and quantum computation. Many of the applications require the probing of SMMs with spectroscopic methods that make use of electromagnetic radiation. The interaction with these time-dependent fields leads to energy shifts, which can be attributed to the geometric phase acquired by the system or the Bloch-Siegert shift. We model an SMM by a giant spin Hamiltonian, and use Floquet perturbation theory to find the geometric phase shifts. The locations where the phase shift between two levels is zero is useful for performing accurate spectroscopies, whereas the regions where relative phase differences exist are useful in applications like quantum computing. Using the same giant spin Hamiltonian, we can use Floquet theory and Salwen perturbation theory to determine the Bloch-Siegert shift and derive a modified version of the Rabi formula for transition probabilities between the energy states E(alpha) -> E(alpha)±1, E(alpha) -> E(alpha) ±3, and E(alpha) -> E(alpha) ±5, where alpha is the index of an arbitrary initial state. The shifted eigenvalues and modified transition probabilities can be useful in spectroscopies where accurate values for the energy-splitting between magnetic states needs to be determined.

Library of Congress Subject Headings

Nanostructured materials--Magnetic properties; Magnetic materials; Quantum theory

Publication Date


Document Type


Student Type


Degree Name

Materials Science and Engineering (MS)

Department, Program, or Center

School of Chemistry and Materials Science (COS)


Mishkatul Bhattacharya

Advisor/Committee Member

Moumita Das

Advisor/Committee Member

Stefan Preble


Physical copy available from RIT's Wallace Library at TA418.9.N35 C36 2015


RIT – Main Campus

Plan Codes