Validity of the N\'{e}el-Arrhenius model for highly anisotropic Co_xFe_{3-x}O_4 nanoparticles

We report a systematic study on the structural and magnetic properties of Co_{x}Fe_{3-x}O_{4} magnetic nanoparticles with sizes between $5$ to $25$ nm, prepared by thermal decomposition of Fe(acac){3} and Co(acac){2}. The large magneto-crystalline anisotropy of the synthesized particles resulted in high blocking temperatures ($42$ K \leqq $T_B$ $\leqq 345$ K for $5\leqq$ d $\leqq 13$nm)andlargecoercivefields($H_C \approxeq 1600$kA\mathrm{/}mfor$T = 5$ K). The smallest particles ($<d>=5$ nm) revealed the existence of a magnetically hard, spin-disordered surface. The thermal dependence of static and dynamic magnetic properties of the whole series of samples could be explained within the N'{e}el-Arrhenius relaxation framework without the need of ad-hoc corrections, by including the thermal dependence of the magnetocrystalline anisotropy constant $K_1(T)$ through the empirical Br"{u}khatov-Kirensky relation. This approach provided $K_1(0)$ values very similar to the bulk material from either static or dynamic magnetic measurements, as well as realistic values for the response times (${\tau }_0\simeq {10}^{-10}$ s). Deviations from the bulk anisotropy values found for the smallest particles could be qualitatively explained based on Zener'{}s relation between $K_1(T)$ and M(T).