In this thesis we investigate the frustrated spin liquid Tb$_2$Ti$_2$O$_7$ theoretically.
The low-energy effective Hamiltonian of this compound is derived
by integrating out
the excited crystal field states. It is shown that the pairwise interaction
in the effective Hamiltonian is renormalized by all the other Tb$_2$Ti$_2$O$_7$ ions
in the system and dynamically generate frustration. The phase diagram
of Tb$_2$Ti$_2$O$_7$ in the single tetrahedron approximation
is calculated. It is shown that Tb$_2$Ti$_2$O$_7$
is in a singlet state which is a linear combination of all
frustrated two-in/two-out states. Motivated by experimental results,
the diffuse neutron scattering of Tb$_2$Ti$_2$O$_7$ is obtained within the single tetrahedron
approximation. This diffuse neutron scattering captures semi-quantitatively most of
the experimental neutron scattering features. The
magnetization of Tb$_2$Ti$_2$O$_7$ in the single tetrahedron approximation is calculated.
Two experiments based on diffuse neutron scattering and
magnetization in high symmetry directions are proposed
to verify the spin ice like ground state of Tb$_2$Ti$_2$O$_7$.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3091 |
| Date | 05 1900 |
| Creators | Molavian Jazi, Hamidreza |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | 2016754 bytes, application/pdf |
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