Particle-size effects on the value of Tc of MnFe2O4: Evidence for finite-size scaling

Abstract

${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer measurements show that the ${\mathit{T}}_{\mathit{c}}$ of 〈12〉-nm particles of ${\mathrm{MnFe}}_2$ ${\mathrm{O}}_4$ is higher than that of the 〈33〉-nm particles, which exhibit the bulk ${\mathit{T}}_{\mathit{c}}$ value (573 K). The ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ isomer shift as well as the internal field are, however, independent of the particle size, as is the cation distribution determined by Mn and Fe extended x-ray absorption fine structure and Mn x-ray absorption near-edge structure measurements at different temperatures. The results confirm that the higher ${\mathit{T}}_{\mathit{c}}$ of the 〈12〉-nm particles arises from finite-size scaling.