Due to the particular geometry of the kagom\'e lattice, it is shown that antisymmetric Dzyaloshinsky-Moriya interactions are allowed and induce magnetic ordering. The symmetry of the obtained low-temperature magnetic phases are studied through mean field approximation and classical Mont\'e Carlo simulations. A phase diagram relating the geometry of the interaction and the ordering temperature has been derived. The order of magnitude of the anisotropies due to Dzyaloshinsky-Moriya interactions are more important than in nonfrustrated magnets, which enhances its appearance in real systems. Application to the jarosites compounds is proposed. In particular, the low-temperature behaviors of the Fe- and Cr-based jarosites are correctly described by this model.
Superconductivity in strongly correlated systems is a remarkable phenomenon that attracts a huge interest. The study of this problem is relevant for materials as the high $T_c$ oxides, pnictides and heavy fermions. In this work we study a realistic model that includes the relevant physics of superconductivity in the presence of strong Coulomb correlations. We consider a two-band model, since most of these correlated systems have electrons from at least two different atomic orbitals coexisting at their Fermi surface. The Coulomb repulsion is taken into account through a local repulsive interaction. Pairing is considered among quasi-particles in neighbouring sites and we allow for different symmetries of the order parameter. In order to deal with the strong local correlations, we use the well known slave boson approach that has proved very successful for this problem. Here we are interested in obtaining the zero temperature properties of the model, specifically its phase diagram and the existence and nature of superconducting quantum critical points. We show that these can arise by increasing the mixing between the two bands. Since this can be controlled by external pressure or doping, our results have a direct relation with experiments. We show that the superconductor-to-normal transition can be either to a metal, a correlated metal or to an insulator. Also we compare the relative stability of $s$ and $d$-wave paired states for different regions of parameter space and investigate the BCS-BEC crossover in the two-band lattice model as function of the strength of the pairing interaction.
A comparison of the quantum Heisenberg anti-ferromagnetic model on the pyrochlore lattice, the checkerboard lattice, and the square lattice with crossing interactions is performed. The three lattices are constructed with the same tetrahedral unit cell and this property is used to describe the low-energy spectrum by means of an effective Hamiltonian restricted to the singlet sector. We analyze the structure of the effective Hamiltonian and solve it within a mean-field approximation for the three lattices. PACS No.: 75.10Jm
The presence of spin-glass (SG) order in highly geometrically frustrated systems is analyzed in a cluster SG model. The model considers infinite-range disordered interactions among cluster magnetic moments and the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model couplings between Ising spins of the same cluster. This model can introduce two sources of frustration: one coming from the disordered interactions and another coming from the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ intracluster interactions (intrinsic frustration). The framework of one-step replica symmetry breaking is adopted to obtain a one-cluster problem that is exactly solved. As a main result we create phase diagrams of the temperature $T$ versus intensity of the disorder $J$, where the paramagnetic-SG phase transition occurs at ${T}_{f}$ when $T$ decreases for high-$J$ values. For low-$J$ values, the SG order is absent for antiferromagnetic clusters without intrinsic frustration. However, the SG order can be observed within the intracluster intrinsic frustration regime even for lower intensity of disorder. In particular, the results indicate that the presence of small clusters in geometrically frustrated antiferromagnetic systems can help stabilize the SG order within a weak disorder.
Dans certains reseaux cristallins, les energies des interactions entre aimants atomiques ou moleculaires ne peuvent etre minimalisees toutes a la fois. Cette frustration conduit a des proprietes inhabituelles, que les physiciens cherchent a verifier sur des materiaux reels. Avec quelques succes.
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