Semiclassical Theory of the Magnonic Isospin in Antiferromagnets

In this dissertation, we introduce the concept of magnonic isospin, an internal degree of freedom for antiferromagnetic spin waves which carries spin but acts as a charge in reacting to the emergent electromagnetic fields of the underlying ground state. The isospin vector parameterizes the degenerate subspace of the two antiferromagnetic spin wave modes in the unperturbed Heisenberg model. To derive the dynamics of this isospin vector, we extend the nonabelian wavepacket theory by accounting for the unusual properties of the pseudo-Hermitian Hamiltonian generating the spin wave dynamics. Using the emergent
Schrödinger equation governing the isospin, we make several predictions about possible magnonic devices utilizing this new, nonabelian degree of freedom.