Proprietes de basse energie et anisotropies d'interactions de systemes magnetiques geometriquement frustres
Résumé
The work presented in this thesis is divided in two parts, both related to geometrically frustrated spins systems. In some highly frustrated lattices (pyrochlore,...) with an antiferromagnetic interaction between nearest neighbour S=1/2 spins, the ground state as well as the first excited states are singlets (S=0). Furthermore, the spin-spin correlations in these spin-liquids are short ranged. In order to study the low temperature behaviour of these systems we derive an effective hamiltonian restricted to the singlet sector and which takes into account the local caracter of the singlets as well as the lattice geometry. Solving this hamiltonian within the mean field approximation, we are able to extract the singlet structure of the ground state. The kagome antiferromagnet has been widely studied for its peculiar magnetic properties and disordered ground state. However, some experimental realizations of the kagome lattice (jarosites compounds) have an ordered low temperature magnetic structure. Taking into account the geometry of the kagomé lattice (or the related jarosites compounds), we show that Dzyaloshinsky-Moriya interactions are relevant for these systems, and a microscopic derivation of this interaction is done. On the other hand, we show by mean-field calculations as well as Monté Carlo simulations that this interaction explains the magnetic structure of the jarosites. Monté Carlo simulations are also used to study the magnetic properties at finite temperature. Quantum fluctuations are considered through a spin-wave expansion. A similar work is done for the pyrochlore lattice. We explicit the Dzyaloshinsky-Moriya interactions allowed by the symmetry of this lattice and the magnetic ordering which appears. We propose that the ordering of some pyrochlore compounds might be due to Dzyaloshinsky-Moriya interactions.
Cette these est consacree a l'etude de quelques aspects theoriques de systemes geometriquement frustres. Dans certains reseaux (pyrochlore,...) ou les interactions antiferromagnetiques entre spins (S=1/2) plus proches voisins sont fortement frustrees l'etat fondamental ainsi que les premiers etats excites sont des singulets (S=0). Par ailleurs, les correlations spin-spin sont a courte portee dans ces liquides de spins. En prenant en compte ces deux caracteristiques, ainsi que la geometrie du reseau pyrochlore, on derive un hamiltonien effectif pour decrire ce systeme a basse temperature. En resolvant cet hamiltonien a l'approximation du champ moyen, on obtient la structure singulet de l'etat fondamental. Le reseau kagome a ete l'objet de nombreuses etudes qui montrent que l'hamiltonien de Heisenberg conduit a un etat desordonné liquide de spins sur ce reseau. Ceci est en desaccord avec l'ordre magnetique observe dans certaines realisations experimentales du reseau kagome (de la famille des jarosites). On montre que les interactions Dzyaloshinsky-Moriya sont autorisees par la geometrie du reseau kagome (et des jarosites), on en precise la structure et une derivation microscopique de ces interactions est faite. Les proprietes magnetiques qui en decoulent sont etudiees dans l'approximation du champ moyen et par simulations Monte Carlo. Les fluctuations quantiques sont sondees par un developpement en ondes de spins. On montre que les interactions de Dzyaloshinsky-Moriya expliquent la mise en ordre de certains composes jarosites. Le cas du reseau pyrochlore est egalement considere : on explicite les interactions Dzyaloshinsky-Moriya autorisees par la geometrie de ce reseau et les structures magnetiques qui en decoulent. Cette interaction pourrait expliquer l'ordre magnetique qui apparai t dans certains composes pyrochlores.
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