Size Dependence of Metal-Insulator Transition in Stoichiometric Fe3O4 Nanocrystals

Magnetite (Fe3O4) is one of the most actively studied materials with a famous metal-insulator transition (MIT), so-called the Verwey transition at around 123 K. Despite the recent progress in synthesis and characterization of Fe3O4 nanocrystals (NCs), it is still an open question how the Verwey transition changes on a nanometer scale. We herein report the systematic studies on size dependence of the Verwey transition of stoichiometric Fe3O4 NCs. We have successfully synthesized stoichiometric and uniform-sized Fe3O4 NCs with sizes ranging from 5 to 100 nm. These stoichiometric Fe3O4 NCs show the Verwey transition when they are characterized by conductance, magnetization, cryo-XRD, and heat capacity measurements. The Verwey transition is weakly size-dependent and becomes suppressed in NCs smaller than 20 nm before disappearing completely for less than 6 nm, which is a clear, yet highly interesting indication of a size effect of this well-known phenomena. Our current work will shed new light on this ages-old problem of Verwey transition.Comment: 18 pages, 4 figures, Nano Letters (accepted

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary