Influence of the temperature dependence of anisotropy on the magnetic behavior of nanoparticles

The influence of the temperature dependence of magnetic anisotropy on the superparamagnetic behavior and on the coercivity of nanostructured materials is theoretically investigated in Fe, Co, and Ni. These metals---Fe, Co, and Ni---show a more marked decrease of the magnetocrystalline anisotropy from low to room temperature. The thermal-driven demagnetization process is analyzed using the Arrhenius expression, in which the magnetic barrier is described in terms of the bulk temperature dependence of the magnetocrystalline anisotropy of each material. In the case of cobalt, the effect of considering the second order, K₁, and the fourth order, K₂, magnetocrystalline constants is investigated. The blocking temperatures, T₁, have been calculated for a range of particle volumes, V, and for different measurement times. The temperature dependence of the anisotropy produces that the blocking temperature-to-particle volume is not constant for all sizes and that the relaxation times and the magnetic anisotropies values, calculated from the analysis of the measurement time dependence of the T₁, have no relationship with the theoretical ones. In particular, the calculated relaxation time can be strongly reduced. The analysis of the coercivity was accomplished considering oriented cobalt nanoparticles with uniaxial anisotropy. In the temperature region where the magnetic anisotropy changes, the field dependence of the effective magnetic anisotropy follows a (1-H∕{H₂ₑ) }^ dependence where H₂ₑ and depend on the K₁ (T) and K₂ (T) values, with being smaller than 2 (that is, the value obtained with the Stoner-Wohlfarth model). The temperature dependence of the coercive field does not follow the classical 1- (T∕{T₁) }^ expression, or it follows but with the factor much larger than the 0. 5 value. The results are discussed to evidence how the influence of the temperature dependence of the anisotropy or other features of the nanostructured materials influence the interpretation of magnetic measurements.