Topological Solitons in Magnetic Systems

A ferromagnet can often have inhomogeneous states that are protected from decaying into the uniform ground state due to topological reasons. Common examples of such states, known as topological solitons, are domain walls in a ferromagnetic wire and domain walls, vortices and skyrmions in two- and three-dimensional ferromagnets. In this dissertation, we study the statics and dynamics of multiple interacting topological solitons in one- and two-dimensional magnets. The ferromagnetic spin-1/2 Ising chain has domain walls, also known as kinks, as its elementary excitations. Adding a weak transverse magnetic field endows kinks with an ability to move; an additional weak longitudinal field leads to their confinement. In particular, this gives rise to a hierarchy of two-kink bound states. We show that in a two-dimensional system of parallel Ising chains with weak antiferromagnetic interchain coupling, two confined pairs on adjacent chains can form a composite bound state. This work supports the interpretation of an experimentally observed excitation in the spectrum of the quasi one-dimensional magnet CoNb2O6 as a four-kink bound state. Two domain walls in a classical ferromagnetic spin chain attract each other with a force that is exponentially weak at large separations but gets stronger as the domain walls approach each other. In the absence of energy dissipation this force simply causes a simultaneous precession of all magnetization vectors about the chain direction with a fixed angular velocity, owing to the gyrotropic nature of the dynamics of spins. Adding dissipation to the system then causes the two domain walls to approach each other and ultimately annihilate to create a uniform state. We develop an effective theory of the dynamics of the annihilation process by isolating four modes of the system, parametrized by four collective coordinates, that capture the essential physics of this process: the global position and orientation of the two domain walls and their relative position and orientation. The theoretical predictions are found to be in excellent agreement with micromagnetic simulations of the domain wall annihilation. Finally, we present a theory of the annihilation process of a vortex and an antivortex in a ferromagnetic thin film