The Matrix Product Approach to Quantum Spin Ladders

We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the exchange coupling constants, which can be ferromagnetic or antiferromagnetic along the legs and the rungs of the ladder We compute ground state energy densities, correlation lengths and string order parameters. We present numerical evidence of the duality properties of the 3 different non ferromagnetic spin 1/2 ladders. We show that the long range topological order characteristic of isolated spin 1 chains is broken by the interchain coupling. The string order correlation function decays exponentially with a finite correlation length that we compute. A physical picture of the spin 1 ladder is given in terms of a collection of resonating spin 1 chains. Finally for ladders with spin equal or greater than 3/2 we define a class of AKLT states whose matrix product coefficients are given by 9-j symbols.Comment: REVTEX file, 16 pages, 12 figures, 6 Table

Analysis of magnetic and structural properties in La0.6Sr 0.4MnO3 ferromagnetic particles under the influence of mechanical ball milling effect

We have investigated the magnetic, structural and morphological properties of La0.6Sr0.4MnO3 (LSMO-40) manganite particles, synthesized by solid state reaction method. The resulting LSMO-40 powders were milled in air atmosphere during 3, 6 and 12 hours, by using a planetary ball milling. Samples obtained were characterized by X-ray diffraction, scanning electron microscopy – SEM and magnetization measurements as a function of temperature and magnetic field. A Rietveld analysis was carried on each XRD pattern, and was observed a reduction in crystallite average size (Dv) with increased ball milling time, tM. This is associated with a decrease in particle size. A characteristic rhombohedral crystal structure for the LSMO-40 phase was identified (space group R3C), independent of the milling time of the powders. However, from SEM microstructure was observed more homogeneity in the grain distribution by milling process. The results of magnetic characterization, showed that samples with higher tM (smaller grain size), presented the lowest value of the saturation magnetization, which is attributed to surface effects that induce magnetically disordered states with decreasing particle sizes. This magnetic anisotropy surface is evidenced also on the changes of coercive fields, HC, measured at low temperatures, which increased with increasing tM

Dualities in Spin Ladders

We introduce a set of discrete modular transformations $T_\ell,U_\ell$ and $S_\ell$ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder we show that the $RVB$ phase is invariant under the $S_\ell$ transformation, while the Haldane phase is invariant under $U_\ell$. These two phases are related by $T_\ell$. Moreover there is a "mixed" phase, that is invariant under $T_\ell$, and which under $U_\ell$ becomes the RVB phase, while under $S_\ell$ becomes the Haldane phase. For odd ladders there exists only the $T_\ell$ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.Comment: REVTEX file, 5 pages, 2 EPS figure