Date of Award


Degree Type


Degree Name

Doctor of Philosophy



Major Professor

Ted Barnes

Committee Members

Elbio Dagotto, Pengcheng Dai, Robert Hinde


In this thesis, small quantum spin systems, known as nano-magnets or molecular magnets, have been investigated. This is an area of great interest in the development of nanotechnology and quantum computers. Previous research on molecular magnets has concentrated on large, complex materials, which have many magnetic ions competing for superexchange pathways. Due to the large number of magnetic ions, the Hamiltonians resulted in very large Hilbert spaces, which makes it difficult for the magnetic interactions to be characterized and analyzed. Through the analysis of smaller and simpler magnetic clusters, insight can be gained from the interactions of the magnetic ions in these systems. Because many quantum spin systems can be accurately modeled using an antiferromagnetic Heisenberg Hamiltonian, we will assume this as a starting point for the theoretical description of molecular magnets.

Our previous work on these systems considered only clusters of S=1/2 ions. Here, we derived closed form results for the magnetothermal properties and inelastic neutron scattering structure factors for dimers, trimers, and tetramers in various geometries, and in several cases were able to compare these calculations to known molecular magnets, and assist in the identification of the dominant magnetic interaction pathways.

Using similar methods, these results are extended to clusters of two to six ions of spin S. An analysis of magnetic properties and observables for these clusters reveal a distinct pattern for that may be useful for the understanding of large clusters that cannot be determined analytically. From the specific case examined, the analysis of data from experiments on some magnetic materials shows the use and need for these calculations. This study of magnetic interactions in small quantum magnets develops clearer insight into the nature of excitations of larger, more complicated systems, which at present can only be investigated phenomenologically or through the use of numerical methods.

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