Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions

It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.Comment: 6 pages. 9 figure

Weak antiferromagnetism and dimer order in quantum systems of coupled tetrahedra

We analyze the phases of an S=1/2 spin model on a lattice of coupled tetrahedra. The presence of both Heisenberg and antisymmetric, Dzyaloshinsky-Moriya interactions can lead to two types of symmetry-broken states: non-magnetic dimer order and, unexpectedly, exotic 4 sub-lattice weak antiferromagnetic order - a state with a generically small ordered moment and non-zero chirality. External magnetic field also induces weak antiferromagnetism co-existing with strong dimer correlations in the ground state. These states are formed as a result of broken Ising symmetries and exhibit a number of unusual properties.Comment: 5 pages, 4 figures; final version to appear in Phys. Rev.

Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions

The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI) may be present in pyrochlore compounds as is shown, and the consequences of such interactions on the magnetic properties are investigated through mean field approximation and monte carlo simulations. It is found that DMI (if present) tremendously change the low temperature behaviour of the system. At a temperature of the order of the DMI a phase transition to a long range ordered state takes place. The ordered magnetic structures are explicited for the different possible DMI which are introduced on the basis of symmetry arguments. The relevance of such a scenario for pyrochlore compounds in which an ordered magnetic structure is observed experimentally is dicussed

Ising transition driven by frustration in a 2D classical model with SU(2) symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for $J_2/J_1 > 1/2$, thermal fluctuations give rise to an effective $Z_2$ symmetry leading to a {\it finite-temperature} phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that $T_c\to 0$ with an infinite slope when $J_2/J_1\to 1/2$.Comment: 4 pages with 4 figure

Proprietes de basse energie et anisotropies d'interactions de systemes magnetiques geometriquement frustres

President du jury: L.P. Levy, Rapporteurs: PCW Holdswoth et P. Sindzingre, Examinateur: P. Monod, Directeurs de these: B. Canals et C. LacroixThe 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