  Polycrystalline samples of the half-metallic ferromagnet Heusler compound
Co$_2$TiSn have been prepared and studied using bulk techniques (X-ray
diffraction and magnetization) as well as local probes ($^{119}$Sn M\"ossbauer
spectroscopy and $^{59}$Co nuclear magnetic resonance spectroscopy) in order to
determine how disorder affects half-metallic behavior and also, to establish
the joint use of M\"ossbauer and NMR spectroscopies as a quantitative probe of
local ion ordering in these compounds. Additionally, density functional
electronic structure calculations on ordered and partially disordered
Co$_2$TiSn compounds have been carried out at a number of different levels of
theory in order to simultaneously understand how the particular choice of DFT
scheme as well as disorder affect the computed magnetization. Our studies
suggest that a sample which seems well-ordered by X-ray diffraction and
magnetization measurements can possess up to 10% of antisite (Co/Ti)
disordering. Computations similarly suggest that even 12.5% antisite Co/Ti
disorder does not destroy the half-metallic character of this material.
However, the use of an appropriate level of non-local DFT is crucial.
