| In this thesis, we study the effect of quantum fluctuations on the half-polarized magnetization plateau of a pyrochlore antiferromagnet. We argue that an expansion around the easy axis limit is appropriate for discussing the ground state selection amongst the classically degenerate manifold of collinear states with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A general approach to the necessary degenerate perturbation theory is presented, and an effective quantum dimer model within this degenerate manifold is derived for arbitrary spin s. We show that under rather general conditions, the first non-constant terms in the effective Hamiltonian for s ≥ 1 occur only at sixth order in the transverse exchange coupling. For s ≥ 5/2, the dominant terms in the effective Hamiltonian are those of a classical dimer model, which predicts a magnetically ordered state. For s ≤ 2, more exotic possibilities may be realized. The effective dimer Hamiltonian then is strongly quantum. We describe 2 likely ground states in that regime---one a U(1) spin liquid phase, and the other a magnetically ordered state. |
