Motivated by the geometry of the materials Na2Ti2As2O and Na2Ti2Sb2O, we study a square-lattice Heisenberg antiferromagnet, with spins located at the bond-centers. The largest exchange constant J couples neighboring spins in a given row or column. This leads to a mesh of isolated spin-chains running along the X and Y axes. A weaker exchange constant J ′ couples the nearest-neighbor spins on the lattice. Classically, J ′ fails to fix the relative spin orientation for different chains and hence the ground state is highly degenerate. Quantum order by disorder effect is studied by spin-wave theory and numerical methods. It is shown that a 4-sublattice order is favored by quantum fluctuations. However, several arguments are presented that suggest that the ground state of the system remains disordered, thus providing us with a paradigm for a two-dimensional spin-liquid.PACS numbers: 75.10. Jm, 75.40.Cx, 75.40.Gb, 75.50.Ee In recent years many new materials have been discovered which exhibit novel magnetic behavior. Various aspects of quantum magnetism, including quantum critical phenomena and existence of spin-disordered ground states with spin-gaps have been observed in a variety of Cuprates, Germanates, Vanadates and other low-dimensional materials. One interesting fact that has come to light in these studies is that the geometrical arrangement of the transition metal and Oxygen ions can have a dramatic impact on the underlying microscopic spin-Hamiltonian and hence on the macroscopic magnetic properties of the system. For example in various Cuprates, the Cu-O-Cu bond angle is crucial for determining the effective exchange constant between Copper spins. Thus, Strontium Cuprates with certain stoichiometry behave as virtually decoupled spin-ladders [1], even though the separation of the Copper spins between neighboring ladders maybe smaller than their separation within a given ladder. In the CuGeO 3 [2] and CaV n O 2n+1 [3] it is also believed that superexchange between the transition metal ions is mediated by Oxygen and because of the geometry of various bond angles and occupied orbitals the second neighbor interactions are substantial compared to nearest neighbor ones. This leads to various interesting quantum phase transitions and spin-gap behavior in these materials.Here, we consider a Heisenberg model with spins at the bond-centers of a square lattice:with J ′ << J. The interactions are shown in Fig. 1. The exchange J couples neighboring spins in a given row or column, whereas J ′ is the nearest neighbor coupling between rows and columns. In the absence of J ′ the system consists of a square mesh of decoupled spinchains running along the X and Y axes. The motivation for studying such a model comes from the materials Na 2 Ti 2 Sb 2 O ( and also Na 2 Ti 2 As 2 O) [4,5]. These layered Titanates consist of planes of (Ti 2 Sb 2 O) 2− , where the Oxygen atoms form a square-lattice and the Titanium atoms sit at the bond centers of the lattice. The Antimony atoms sit above and below the centers of the elementary squar...

Calculations of Raman scattering intensities in spin 1/2 square-lattice Heisenberg model, using the Fleury-Loudon-Elliott theory, have so far been unable to describe the broad line shape and asymmetry of the two magnon peak found experimentally in the cuprate materials. Even more notably, the polarization selection rules are violated with respect to the Fleury-Loudon-Elliott theory. There is comparable scattering in B1g and A1g geometries, whereas the theory would predict scattering in only B1g geometry. We review various suggestions for this discrepency and suggest that at least part of the problem can be addressed by modifying the effective Raman Hamiltonian, allowing for two-magnon states with arbitrary total momentum. Such an approach based on the Sawatzsky-Lorenzana theory of optical absorption assumes an important role of phonons as momentum sinks. It leaves the low energy physics of the Heisenberg model unchanged but substantially alters the Raman line-shape and selection rules, bringing the results closer to experiments. 78.30, 42.65.D, 75.10.J, 75.50.E

We discuss ways in which the ratio of exchange constants along the rungs and legs of a spinladder material influences the two-magnon Raman scattering spectra and hence can be determined from it. We show that within the Fleury-Loudon-Elliott approach, the Raman line-shape does not change with polarization geometries. This lineshape is well known to be difficult to calculate accurately from theory. However, the Raman scattering intensities do vary with polarization geometries, which are easy to calculate. With some assumptions about the Raman scattering Hamiltonian, the latter can be used to estimate the ratio of exchange constants. We apply these results to Sugai's recent measurements of Raman scattering from spin-ladder materials such as La6Ca8Cu24O41 and Sr14Cu24O41.

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Infrared reflectivity results of YBa2Cu3O7x and SmBa2Cu3O7−x, in the tetragonal semiconducting phase, are reported. At least 10 of the 11 group theoretically allowed modes are observed, and the 11th may be observed in the Sm-material. Due to the fact that the modes are clearly resolved from each other, and, in some cases, have large shifts when Y is replaced by Sm, severial these modes can be assigned to definate vibrations. This and other aspects of the data are discussed.