George Mias

This dissertation explores different theoretical aspects of domains in quantum magnetism. In the first part, domain seeding is discussed in the context of spinor Bose-Einstein condensates. The underlying theory is described and developed for an F = 1 spinor condensate in connection with experimental results. The dynamical quantum fluctuations of a sample that begins as a condensate of N atoms in a pure F=1, mF = 0 state are discussed in analogy to the theory of squeezed quantum states. In such a system the initial mF = 0 condensate acts as a source for the creation pairs of mF = ±1 atoms. The quantum fluctuations of the initial dynamics of the system are found to provide the seeds for the formation of the domains of ferromagnetically aligned spins.

In the second part of the thesis, the roughening of domain interfaces in equilibrium systems is introduced for crystals and developed in the context of transverse Ising models. The roughening of interfaces for Ising models with short range interactions is discussed. Roughening in an Ising model with long-range interactions is also investigated in connection with the insulator LiHoF4. This system has naturally formed domain walls, arising from the combination of strong Ising anisotropy and long-range forces. The long-range forces are shown to affect the morphology of the domain walls and lead to the absence the roughening transition, causing the domain interfaces to remain smooth.