Size and interface effects on ferromagnetic and antiferromagnetic transition temperatures

A simple and unified model, which is based on the energy-equilibrium criterion between the spin-spin exchange interactions and the thermal vibration energy of atoms at the transition temperature and a size-dependent Debye temperature function Theta(D)(D), has been established for the size, dimension, and interface effects on the Curie temperature T-c(D) and the Neel temperature T-N(D) of low-dimensionally ferromagnetic and antiferromagnetic nanocrystals, where D denotes the diameter of nanoparticles and nanorods or the thickness of thin films. In terms of this model, T-c(D) and T-N(D) functions are predicted to increase or decrease with dropping D, depending on the interaction strength at the film/substrate interface when the interface exists. The predicted results are consistent with available experimental measurements for Fe, Co, Ni, Gd, Ho, Co1Ni1, Co1Ni3, Co1Ni9, Fe3O4, MnFe2O4, CoO, NiO, and CuO low-dimensional nanocrystals.