Influence of particle size, stoichiometry, and degree of long-range order on magnetic susceptibility of titanium monoxide

In situ measurements of the magnetic susceptibility of ordered and disordered titanium monoxides TiO$_{y}$ in the temperature range from 300 to 1200 K have revealed that it depends on the size of crystals, their stoichiometry, and long-range order parameters. Analysis of the data for both the ordered and disordered TiO$_{y}$ has demonstrated that the dependence of the Van Vleck paramagnetism on the nanocrystal size is inversely proportional due to the breaking of symmetry of the local environment of titanium and oxygen atoms near the surface of nanocrystals. It has been found that the Van Vleck contribution from the atomic vacancy disorder in monoxide nanocrystals of superstoichiometric composition, as well as in the crystalline stoichiometric monoxide, is proportional to the deviation of the degree of long-range order from the maximum value.