Spin correlations on the pyrochlore lattice

Pyrochlores have the chemical formula A₂B₂O₇ with A, B, or both A and B magnetic. It has corner-sharing tetrahedra in the structure, therefore, frustration phenomena naturally occurs in these systems. Because of the frustration, pyrochlore have many interesting properties, including the spin glass in Y₂Mo₂O₇, spin liquid in Tb₂Ti₂O₇, disordered spin ice in Ho₂Ti₂O₇, and ordered spin ice in Tb₂Sn₂O₇. In this thesis we will focus on Tb₂Ti₂O₇. Our goal is to find the spin correlation functions between different sites of Tb ions. The Hamiltonian of Tb ions is an anisotropic nearest neighbour exchange interaction. We apply perturbation theory to the Hamiltonian, and it will separate the Hamiltonian into two parts. The unperturbed part of Hamiltonian is the spin ice Hamiltonian, and other parts of the Hamiltonian are perturbative. The perturbative parts of Hamiltonian can be written in the local coordinates to give three different terms X₂, X₃, X₄. In order to find the spin correlation function, we calculate time dependent spin operators in the interaction picture. Then we apply them to the unperturbed and perturbed terms of Hamiltonian to calculate the spin correlation functions. Finally, we discuss the neutron scattering experiment and how to apply it to test our results