In this thesis we have developed electronic and spin model Hamiltonians to understand magnetism in molecule based magnets like photomagnets, high-nuclearity transition metal complexes and single molecule magnets. In chapter 1, we provide an overview of molecular magnets. Here, we present a survey on the literature available on molecule based magnets. The chapter throws light on various phenomena found in molecular magnetic systems that range in dimensions from 3D down to molecular dimension. This is followed by a brief introduction to high-nuclearity transition metal complexes and single molecule magnets (SMMs). In the last two sections of this chapter, we discuss Light Induced Excited Spin State Trapping (LIESST) and photomagnetism in some molecular systems. Chapter 2 discusses various theoretical models that have been developed for magnetism. We begin with an introduction to the spin Hamiltonian and the origin of direct and kinetic exchange in simple systems and extend it to larger systems. Then we introduce the concept of superexchange proposed by Goodenough and Kanamori, followed by introduction to anisotropic Dzyalashinskii-Moria (DM) exchange and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. We also discuss molecular magnetic anisotropy, long-range magnetic interactions and higher order exchange interactions. These are effective model Hamiltonians that do not provide microscopic origin of magnetism, hence electronic model Hamiltonians need to be invoked. We introduce electronic model Hamiltonians like Huckel, Hubbard and Pariser-Parr-Popple (PPP) models and then present numerical techniques like valencebond (VB) and constant MS techniques that are used to exactly solve these model Hamiltonians. We present a many-body electronic model involving the active orbitals on the transition metal ions for photomagnetism in MoCu6 cluster, in chapter 3. The model is exactly solved using a valence bond approach. The ground state solution of the model is highly degenerate and is spanned by five S=0 states, nine S=1 states, five S=2 states and one S=3 state. The orbital occupancies in all these states correspond to six Cu(II) ions and one diamagnetic Mo(IV ) ion. The optically excited chargetransfer (CT) state in each spin sector occurs at nearly the same excitation energy of 2.993 eV for physically reasonable parameter values. We find that the excitation cross sections in different spin manifolds are similar in magnitude. The lifetime of the S=3 excited states is expected to be the largest as the number of states below that energy is very sparse in this spin sector compared to other spin sectors. This shows that photomagnetism is not due to preferential excitation to the S = 3 state. The inputs from the electronic model allows us to develop a kinetic model. In this model, photomagnetism is attributed to a long lived S=3 charge transfer excited state for which there appears to be sufficient experimental evidence. Based on this postulate, we model photomagnetism by including internal conversions and intersystem crossings. The key feature of the model is the assumption of existence of two kinds of S=3 states; one of which has no direct pathway for internal conversion and the other characterized by slow kinetics for internal conversion to the lowenergy states. The trapped S=3 state can decay via a thermally activated barrier to the other S = 3 state. The experimental XMT vs. T variation for two different irradiation times are fitted using Arrhenius dependence of the rate constants in the model. Conventional superexchange rules predict ferromagnetic exchange interaction between Ni(II) and M (M = MoV ,WV , NbIV ). Recent experiments show that in some systems this superexchange is antiferromagnetic. To understand this feature, in chapter 4 we develop a microscopic model for Ni(II) - M systems and solve it exactly using a valence bond approach. We identify direct exchange coupling, splitting of the magnetic orbitals and interorbital electron repulsions, on the M site as the parameters which control the ground state spin of various clusters of the Ni(II) - M system. We present quantum phase diagrams which delineate the high-spin and low-spin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region in the parameter space where an intermediate spin state is the ground state. These results indicate that the spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian. The electronic model for A − B systems has been employed to reproduce the experimental magnetic data of the { NiW }2 system. In chapter 5, we present a theoretical approach to calculate the molecular magnetic anisotropy parameters, DM and EM for single molecule magnets in any eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as a perturbation. Neglecting inter-site dipolar interactions, we calculate molecular magnetic anisotropy in a given total spin state from the known single-ion anisotropies of the transition metal centers. The method is applied to Mn12Ac and Fe8 in their ground and first few excited eigenstates, as an illustration. We have also studied the effect of orientation of local anisotropies on the molecular anisotropy in various eigenstates of the exchange Hamiltonian. We find that, in case of Mn12Ac, the molecular anisotropy depends strongly on the orientation of the local anisotropies and the spin of the state. The DM value of Mn12Ac is almost independent of the orientation of the local anisotropy of the core Mn(IV ) ions. In the case of Fe8, the dependence of molecular anisotropy on the spin of the state in question is weaker. We have also calculated the anisotropy constants for several sets of exchange parameters and find that in Mn12Ac the anisotropy increases with spin excitation gap while in Fe8, the anisotropy is almost independent of the gap. We have modeled the magnetic property of Nb6Ni12 cluster using a spin Hamiltonian in chapter 6. From Goodenough-Kanamori rules we should expect a ferromagnetic exchange between Nb and Ni ions. However, the magnetic studies indicate that the interaction is antiferromagnetic. We give reasons for the anomaly and fit the XMT data using an antiferromagnetic Heisenberg model. The observed XMT value at 2 K however does not correspond to ferrimagnetic ground state of Stot=9 and we invoke intermolecular interaction to explain this feature.

This thesis will present the synthesis, characterization and magnetic measurements of lanthanide complexes with varying nuclearities (Ln, Ln2, Ln3 and Ln4). EuIII, GdIII, TbIII, DyIII, HoIII and YbIII have been selected as the metal centers. Eight polydentate Schiff-base ligands have been synthesized with N- and mostly O-based coordination environments which chelate 7-, 8- or 9-coordinate lanthanide ions. The molecular structures were characterized by single crystal X-ray crystallography and the magnetic properties were measured using a SQUID magnetometer. Each chapter consists of crystal structures and magnetic measurements for complexes with the same nuclearity. There are eight DyIII SMMs in this thesis which are discrete molecules that act as magnets below a certain temperature called their blocking temperature. This phenomenon results from an appreciable spin ground state (S) as well as negative uni-axial anisotropy (D), both present in lanthanide ions owing to their f electron shell, generating an effective energy barrier for the reversal of the magnetization (Ueff). The ab initio calculations are also included for the SMMs with high anisotropic energy barriers to understand the mechanisms of slow magnetic relaxation in these systems.

Due to the insecurity of the supply of raw materials needed for neodymium-iron-boron magnets, typically used in permanent magnet generators, the use of ferrite magnets as an alternative was investigated. The investigation was conducted by attempting to redesign a generator that previously used neodymium-iron-boron magnets for use with ferrite magnets. The major part of the redesign was to find an alternate rotor design with an electromagnetic design adapted to the characteristics of the ferrite magnets.It was found that  ferrite magnets can be used to replace neodymium-iron-boron magnets with changes to the electromagnetic design of the rotor. The changes of the electromagnetic design increase the amount of magnetically active material in the rotor and, therefore, require the mechanical design of the rotor to be changed. The new rotor design also requires some changes to the generator support structure. A design for a replacement rotor, using ferrite magnets, along with the required changes to the support structure, is presented.

Based on the form-invariant of Maxwell’s equations under coordinate transformations, we extend the theoryof transformation optics to transformation magneto-statics, which can design magnets through coordinatetransformations. Some novel DC magnetic field illusions created by magnets (e.g. rescaling magnets,cancelling magnets and overlapping magnets) are designed and verified by numerical simulations. Ourresearch will open a new door to designing magnets and controlling DC magnetic fields. / <p>QC 20141105</p>

Thesis (M.S.)--Michigan State University. Dept. of Physics and Astronomy, 2006. / Title from PDF t.p. (viewed on Nov. 20, 2008) Includes bibliographical references (p. 67-68). Also issued in print.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 115-116).

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Cesar A. Luongo, Florida State University, College of Engineering, Dept. of Mechanical Engineering. Title and description from dissertation home page (viewed Jan. 13, 2005). Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaves 134-138). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaves 134-138). Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, December 2000. / Includes bibliographical references. Also available on the Internet.