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Etude des excitations de basse énergie dans des systèmes magnétiques frustrés de basse dimensionnalité: gap de spin et singulets de basse énergie

Matthieu Mambrini 1
1 Groupe de Physique Théorique (LPQ)
LPQ - Laboratoire de Physique Quantique
Abstract : Low energy physics of the two-dimensional spin-1/2 Heisenberg antiferromagnet display a wide range of behaviours. Most of them are only partially understood especially in the case of frustrated magnets. These models not only raise theoretical questions, but are also relevant to describing physical properties of many recently synthesized compounds. In this thesis, both aspects --- theory and relation to experiments --- are analysed. Theoretically, we use a numerical approach to study the Heisenberg model on the kagomé lattice, one of the most frustrated lattices. We show that strong signatures of frustration in this model (spin gap and exponential proliferation of singlets inside the gap) can be faithfully described in terms of short range RVB states (<< Resonating Valence Bond >>). Such states also provide a relatively simple picture of the low energy physics of the model. Even if the unusual properties of the kagomé antiferromagnet spectrum are believed to be the consequences of the strong frustration of this model, no other similar system was known to exhibit such a behaviour. In fact, we show exactly that these properties (spin gap filled with low lying singlets) indeed occur in a one-dimensional model of coupled tetrahedra. Lastly, we consider connections between experimental aspects of frustration and numerical studies of frustrated models. For the vanadate compound CaV4O9 --- which is the first half-filled two-dimensional system with a spin gap --- we show that the analysis of the symmetry of the first excited state, obtained by neutron scattering experiments, provides strong constraints on the parameters of the model and emphasizes the role of frustration. For Li2VO(Si,Ge)O4, susceptibility measurements compared to exact diagonalisation results allow us to identify this compound as the prototype of the J_1 - J_2 model on the square lattice and to give estimations of J_2/J_1.
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Submitted on : Monday, November 4, 2002 - 6:00:22 PM
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Matthieu Mambrini. Etude des excitations de basse énergie dans des systèmes magnétiques frustrés de basse dimensionnalité: gap de spin et singulets de basse énergie. Matière Condensée [cond-mat]. Université Paul Sabatier - Toulouse III, 2000. Français. ⟨tel-00001912⟩

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