Dynamical properties of the spin-Peierls compound ${\alpha }^{\prime }-{\mathrm{NaV}}_2{\mathrm{O}}_5$

Dynamical properties of the inorganic spin-Peierls compound ${\alpha }^{\prime }-{\mathrm{NaV}}_2{\mathrm{O}}_5$ are investigated using a one-dimensional dimerized Heisenberg model. By exact diagonalizations of chains with up to 28 sites, supplemented by a finite-size scaling analysis, the dimerization parameter δ is determined by requiring that the model reproduces the experimentally observed spin gap Δ. The dynamical and static spin structure factors are calculated. As for ${\mathrm{CuGeO}}_3,$ the existence of a low-energy magnon branch separated from the continuum is predicted. The present calculations also suggest that a large magnetic Raman scattering intensity should appear above an energy threshold of 1.9Δ. The predicted photoemission spectrum is qualitatively similar to results for an undimerized chain due to the presence of sizable short-range antiferromagnetic correlations.