Anomalous diffusion on a hypersphere and time structure of two-point spin correlations in short-range-ordered doped oxides.

Recently, much attention was paid to exploring charge and spin- ordered phases in strongly correlated transition metal oxides, such as superconducting cuprates and related nickelates, manganites and cobaltites. Using elastic neutron scattering, we have investigated the nano-scale structure of short-range charge and spin ordering in a half-doped cobablite La1.5Sr0.5CoO4, and found that they can be understood in the framework of an effective anisotropic 3D random field Ising model. Here we report on the measurement of the time-dependence of the spin- spin correlation function in this material by means of Neutron Spin Echo (NSE) spectroscopy. Our high-precision NSE data exclude simple Arrhenius and stretched-exponential relaxations and can be best described by the model of anomalous diffusion on the appropriate hypersphere. We argue that such time dependence is generic for short-range-ordered spin systems.