An extension of the Néel-Brown model for systems with multiple switching pathways

The Néel-Brown model is the most widely accepted model for the description of magnetization reversal by thermal excitation. This model predicts a decreasing average switching field and an increasing width ΔH of switching field distribution as the temperature is increased, and has been found to hold good on several occasions. However, for a few classes of systems, the temperature dependence of ΔH shows the opposite trend, and so far no satisfactory explanation exists. We present here an experimental study of switching field statistics of permalloy (Ni₈₀Fe₂₀) thin films on Si(100) grown by pulsed laser ablation. It was seen that the sample deviates from the Neel-Brown behavior in the manner described above. We performed calculations based on a natural extension of the Néel-Brown model, which incorporated multiple reversal pathways characterized by a Gaussian distribution of coercive fields. Calculations based on this model for different values of the width parameter σ_HSW show two distinct kinds of behavior. At low values of σ_HSW, the total width ΔH is limited by thermal broadening according to the traditional Neel-Brown expression. This regime is characterized by an increasing ΔH with temperature. For high σ_HSW, the broadening is dominated by σ_HSW, which masks thermal broadening. In this regime, ΔH decreases with increasing temperature. Whereas the experimentally observed temperature dependence of the average switching field was found to be in good agreement with this model, qualitative agreement with regard to the temperature dependence of ΔH could be observed only for relaxation times lower than ~10⁻⁴⁰ s, which is much smaller than Néel-Brown relaxation times (10⁻⁹–10⁻¹⁹ s) usually encountered in the literature.