Dynamical studies of antiferromagnetic exchange interactions in low dimensional quantum spin systems

Various forms of antiferromagnetic (AF) exchange interactions among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Sodium vanadate, NaV₂O₅, a quarter-filled two-leg ladder compound, can be mapped to a spin-1/2 chain with the spins on molecular orbitals of V-O-V rungs. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the “zig-zag” charge density as well as the magnetic stabilization of the low temperature phase.; The inorganic spin-Peierls compound copper germanate CuGeO ₃, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J₁ competes with an antiferromagnetic next nearest neighbor interaction J₂. Below T_SP = 14K, a dimerization of the nearest neighbor coupling occurs, precipitating the spin-Peierls transition. In this study, the dynamical structure factor is used to fit J₂ and the dimerization δ of J₁ to the inelastic neutron scattering data of CuGeO₃ at _T = 10_K. It is found that both δ and α increase significantly at lower temperatures.; It is shown that the effects of spin-1 impurities in dimerized AF spin-1/2 chains are similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The signature of this decoupling is seen in the dynamical structure factor, the magnetic susceptibility and the AF correlations near the impurity.