Size dependence of the spin-flop transition in hematite nanoparticles

The spin-flop transition of acicular hematite nanoparticles of different size synthesized by chemical route and annealed at different temperatures has been investigated as a function of temperature. Transmission electron microscopy (TEM) measurements show that particles have an ellipsoidal shape, with a major axis of $330\ifmmode\pm\else\textpm\fi{}50\mathrm{nm}$ and a minor axis of $70\ifmmode\pm\else\textpm\fi{}10\mathrm{nm}.$ TEM and x-ray diffraction experiments show that nanoparticles are made of hematite crystallites, which grow on increasing the annealing temperature. Both the Morin transition temperature ${(T}_{M})$ and the spin-flop transition field ${(H}_{\mathrm{sf}})$ have been found to increase for increasing crystallite size $(d):$ for instance, for $d=36\mathrm{nm}$ particles ${T}_{M}=164\mathrm{K}$ and the value of ${H}_{\mathrm{sf}}$ extrapolated at $T=0$ ${(H}_{\mathrm{sf}0})$ is 1.7 T, whereas for bulk hematite ${T}_{M}=263\mathrm{K}$ and ${H}_{\mathrm{sf}0}=6.5\mathrm{T}.$ Both ${H}_{\mathrm{sf}0}$ and ${T}_{M}$ follow a $1/d$ dependence (at a faster rate for ${H}_{\mathrm{sf}0}),$ indicating that their variation is mainly driven by surface effects.