  The anisotropic spin glass transition, in which spin freezing is observed
only along the c-axis in pseudobrookite Fe$_2$TiO$_5$, has long been perplexing
because the Fe$^{3+}$ moments (d$^5$) are expected to be isotropic. Recently,
neutron diffraction demonstrated that surfboard-shaped antiferromagnetic
nanoregions coalesce above the glass transition temperature, T$_g$ $\approx$ 55
K, and a model was proposed in which the freezing of the fluctuations of the
surfboards' magnetization leads to the anisotropic spin glass state. Given this
new model, we have carried out high resolution inelastic neutron scattering
measurements of the spin-spin correlations to understand the temperature
dependence of the intra-surfboard spin dynamics on neutron (picosecond)
time-scales. Here, we report on the temperature-dependence of the spin
fluctuations measured from single crystal Fe$_2$TiO$_5$. Strong quasi-elastic
magnetic scattering, arising from intra-surfboard correlations, is observed
well above T$_g$. The spin fluctuations possess a steep energy-wave vector
relation and are indicative of strong exchange interactions, consistent with
the large Curie-Weiss temperature. As the temperature approaches T$_g$ from
above, a shift in spectral weight from inelastic to elastic scattering is
observed. At various temperatures between 4 K and 300 K, a characteristic
relaxation rate of the fluctuations is determined. Despite the freezing of the
majority of the spin correlations, an inelastic contribution remains even at
base temperature, signifying the presence of fluctuating intra-surfboard spin
correlations to at least T/T$_g$ $\approx$ 0.1 consistent with a description of
Fe$_2$TiO$_5$ as a hybrid between conventional and geometrically frustrated
spin glasses.

Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics