Size effect on the ordering ofL10FePt nanoparticles

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We have studied the size effect on the $\mathrm{L}{1}_{0}$ ordering of FePt (001) nanoparticles epitaxially grown on MgO (001). From the dark field images using 110 superlattice spots excited by incident electron beam along $[\overline{1}1l]$ $(l=4--6)$, the critical size for $\mathrm{L}{1}_{0}$ ordering has been evaluated to be $d=1.5--2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ below which no ordering occurs. Further, we have taken an electron diffraction pattern of each FePt nanoparticle using a nanometer-sized electron beam and determined the respective long-range order parameter $S$ by analyzing the superlattice/fundamental diffraction intensity ratio based on the multislice method. It is found that the order parameter $S$ sharply drops below $d\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and decreases to zero for $dl2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the result is almost consistent with thermodynamic calculations previously reported. The present work unambiguously shows that the ordering of $\mathrm{L}{1}_{0}$ FePt is entirely inhibited when its size is less than $d\ensuremath{\sim}2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Such size effect is not so serious for practical applications of FePt to permanent magnets or magnetic recording media because the effect is significant only for $dl2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ where the $\mathrm{L}{1}_{0}$ FePt would be magnetically unstable due to severe thermal agitation.