Finite-size scaling law in single-crystalline Fe3O4 hollow nanostructures

Abstract

Single-crystalline Fe3O4 hollow nanostructures (nanoring and nanotube) have been successfully synthesized by a hydrothermal method along with a heat treatment process. The temperature dependences of the magnetization of the hollow nanostructures were measured under a high vacuum ([Formula: see text] Torr) from 300[Formula: see text]K to 900[Formula: see text]K. The Curie temperatures of the nanoring and nanotube samples were found to decrease with decreasing the mean wall thickness. The Curie temperatures of the hollow magnetite nanostructures follow a finite-size scaling relation with the scaling exponent [Formula: see text]. By comparison with those of the zero-dimensional Fe3O4 particles and two-dimensional Fe3O4 films, we show that the scaling relation for our hollow nanostructures is in better agreement with the quasi-two-dimensional finite-size scaling law.