Semi-classical Theories of Quantum Magnets

Recent progress in magnetism has been driven by embracing the complexity associated with entangled spin, orbital, and lattice degrees of freedom and by understanding the emergent quantum behaviors of magnetic systems. Over the past decades, intense efforts have been devoted to “extreme quantum materials” comprising low-dimensional lattices of spin S = 1/2 degrees of freedom, that are candidates to host quantum spin liquid phases with no classical counterpart. Finite-spin (S ≥ 1) systems that exhibit ground states with short-ranged entanglement have not been the center of much attention because they are expected to behave semi-classically. However, as we will demonstrate in this dissertation, the traditional classical limit (1/S expansion) does not work for large classes of finite-spin systems, which still admit an accurate classical or semi-classical treatment. To address this important problem, we will exploit the fact that N -level systems admit more than one classical limit. As we will demonstrate in this dissertation, different classical limits lead to different generalizations of the so-called Landau-Lifshitz dynamics. In particular, we will introduce generalized classical spin dynamics based on coherent states of SU(N ), where N is the dimension of the local Hilbert space. This new approach also allows generalizing the semi-classical spin dynamics (1/S-expansion) from SU(2) to SU(N ), providing a better approximation to incorporate quantum effects in the spin dynamics of large classes of realistic spin Hamiltonians, including S ≥ 1 systems with large single-ion anisotropy and weakly coupled multi-spin units, such as dimers, trimers or tetramers. Besides developing the mathematical formalism, we illustrate these ideas by comparing our theoretical predictions against inelastic neutron scattering data of two realistic effective S = 1 iron-based compounds. In the last part of this dissertation, we generalize the concepts of the magnetic skyrmions by taking alternative classical limits of quantum spin systems. In particular, we report the emergence of magnetic CP2 skyrmions in realistic spin-1 models based on SU(3) coherent states.