Ground states and excitations of frustrated magnetic systems, from the classical limit to the quantum case

The first part of this thesis is devoted to classical magnetic systems. A method for an exhaustive search of states that do not break any spatial symmetry on a given lattice is presented. New Néel states on the kagome lattice are described. Their static structure factors give a way to analyze experimental results. Some non-coplanar spin orders are the only ground states of Heisenberg Hamiltonians. The chirality is a discrete order parameter and give rise to a finite temperature phase transition, studied on a toy model. We show that Z2 topological defects proliferate near chirality domain walls. The order of the transition (first order or Ising like) depends on the spin interactions. The Schwinger boson mean-field theory (SBMFT) allows us to link classical and quantum spin physics: long-range ordered and disordered phases as topological spin liquids can be described in this frame. Symmetry and the way to impose them are analyzed. Different phases are distinguished by their fluxes. These are gauge invariant quantities having a signification as well in a quantum system as in the classical limit. Visons are quantum excitations that change fluxes. Thus, the Z2 vorticies are their classical limit. By relaxing some symmetry constraints, chiral phases are obtained, whose classical limit sends back to the first chapter of this thesis, and whose disordered phase gives chiral spin liquids. The example of the Dzyaloshinskii-Moriya interaction on the kagome lattice is studied.


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