Unconventional mechanisms of magnetic ordering in frustrated models of quantum magnetism

In this thesis we investigate in the semiclassical approximation how unconventional magnetic ordering, that is magnetic ordering which is not predicted at the classical level, emerges in a variety of frustrated models of quantum magnetism. The first part of this thesis presents our semiclassical investigation of the magnetization processes of the anisotropic triangular lattice Heisenberg antiferromanget and of the J1 − J2 square lattice Heisenberg antiferromanget. Existing analytical, numerical and experimen- tal evidences report that these systems exhibit a magnetization plateau respectively at 1/3 and 1/2 of the saturation value and whose structure can be understood in simple terms as a collinear spin structure. We develop a strategy to estimate the semiclassical energy of collinear spin structures away from their classical stability point. In this framework we are able to predict the stabilization of a collinear up-up-down structure with a magnetization equal to one third of the saturation value in a wide anisotropy range for the triangular lattice Heisen- berg antiferromanget. Similarly we find that the four sublattice up-up-up-down structure with magnetization equal to 1/2 of the saturation value is stabilized deep into the classically striped ordered region of the J1 − J2 square lattice Heisenberg antiferromanget. In the case of the anisotropic triangular lattice Heisenberg antiferromagnet a brief digression is made to the zero field case. The semiclassical approach confirms that quantum fluctuations favor collinear structures over the classical spiral states in either the weakly and strongly coupled chain regimes. The second part of the thesis is devoted to the study of fully frustrated transverse field Ising models. These models have emerged as an alternative tool to access the physics of the quan- tum dimer models (QDM) of Rokhsar and Kivelson at the purely kinetic point. We studied the classical phase diagram of this model for the square and honeycomb lattice geometries. In either case the effect of quantum fluctuations and the relevance to the physics of the QDM is discussed. In the case of the honeycomb lattice geometry we find that the classical phase diagram is rather involved with columnar and plaquette states separated by an infinite series of states of mixed nature. From the study of quantum fluctuations we conjecture that the sqrt(12) × sqrt(12) plaquette phase dominates over the columnar structure down to zero transverse field in the limit S = 1/2. In the case of the square lattice geometry we find that at the classical level the plaquette state is stabilized below the polarized state down to zero transverse field. In agreement with the most recent quantum Monte Carlo results, we show that for S = 1/2 quantum fluctuations favor columnar oder in the whole field range below saturation even though this structure is never classically stable in this parameter range.