Thesis presented November 10, 2015

Abstract:
Competing interactions are an essential feature of frustrated magnetic systems, they stand behind a large degeneracy of classical or mean-field ground states. In many cases such degeneracy can be lifted by thermal and quantum fluctuations, this mechanism is commonly called order from disorder.
Experimentally studied magnetic systems inevitably contain a finite amount of structural disorder. In this work the influence of defects, namely vacancies and bond disorder, on a degenerate ground state manifold is studied for various frustrated systems. We find that quenched disorder is also capable of consistently lifting the degeneracy, moreover, it has in a wide range of frustrated systems. Moreover, the effect of quenched disorder leads to an opposite tendency, compared to the order by disorder mechanism, produced by fluctuations. For every considered model, analytic energy corrections are derived in the form of effective anisotropic terms, which act on the manifold of degenerate ground states. Analytical arguments are confirmed by numerical calculations, which include energy minimization and classical Monte Carlo simulations. The detected sequences of ordered states is attributed to competition of fluctuations and structural disorder. The observed effect can open additional possibilities in tuning magnetic structure of the system.
Finally, the effect of external magnetic field is investigated for the pure XY pyrochlore antiferromagnet. Depending on the field orientation we observe phase transitions, which do not exist within the mean-field description of the system. They are generalizations of the spin-flop transition for the case of broken discrete _k symmetry with k > 2.

Keywords:
Orbital models, Impurities, Monte Carlo Simulation, Frustrated magnets

On-line thesis.