Spin dynamics of half-doped La3/2Sr1/2NiO4

We report polarized- and unpolarized-neutron inelastic-scattering measurements of the magnetic excitation spectrum in the spin-charge ordered phase of ${\mathrm{La}}_{3∕2}{\mathrm{Sr}}_{1∕2}\mathrm{Ni}{\mathrm{O}}_{4}$. Up to energies of $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ we observe broad magnetic modes characteristic of a near checkerboard ordering. A linear spin-wave model for an ideal checkerboard ordering with a single antiferromagnetic exchange interaction ${J}^{\ensuremath{'}}=5.8\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ between next-nearest-neighbor spins on ${\mathrm{Ni}}^{2+}$ sites, together with a small $XY$-like single-ion anisotropy, provides a reasonable description of the measured dispersion. Above $30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ the excitations are not fully consistent with the linear spin-wave model, with modes near the two-dimensional reciprocal space wave vector (0.5, 0.5) having an anomalously large intensity. Furthermore, two additional dispersive modes not predicted by spin-wave theory were observed, both of which are probably magnetic. One disperses away from (0.5, 0.5) in the energy range between $50\char21{}56\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, and the other appears around $(h,k)$ type positions $(h,k=\text{integer})$ in the energy range $31\char21{}39\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We propose a model in which these anomalous features are explained by the existence of discommensurations in the checkerboard ordering. At low energies there is additional diffuse scattering centred on the magnetic ordering wave vector. We associate this diffuse scattering with dynamic antiferromagnetic correlations between spins attached to the doped holes.