Thesis presented June 29, 2022

Abstract:
Degeneracy of frustrated magnets makes them highly sensitive to fluctuations. Quantum zero-point fluctuations or entropic contribution may select certain spin structures from the degenerate classical ground state manifold. This phenomenon goes by the name of order by disorder (OBD). In this thesis we study various instances of OBD in frustrated quantum spin systems using spin-wave theory.
Firstly, we study fractional magnetization plateaus - an emblematic feature of frustrated magnets - in the kagome and pyrochlore antiferromagnets. We calculate full magnetization curves that allow us to predict a large fractional plateau for both systems, solely within linear spin-wave theory. The predicted plateau width agrees well with available numerical data for the kagome lattice.
In the second part of the thesis, we focus on ground state selection in the face-centered-cubic Heisenberg antiferromagnet. The classical degeneracy is broken at the harmonic level in spin-wave theory and there is selection of a given state at zero temperature. Surprisingly, at low temperature, thermal population of low-lying magnons results in a different selection. To complement the study, we go to higher order in spin-wave theory and include the effects of magnon-magnon interactions self-consistently. We find that the ground state selected at zero temperature is different from what was found in the harmonic approximation, even at large spin. This problem gives a nice illustration of how subtle the OBD mechanism can be in highly frustrated magnets, and demonstrates as well the power of spin-wave theory.

Keywords:
Order by disorder, Frustrated magnetism , Fcc lattice, Magnetization plateaus, Spin wave theory, Quantum