Characterization thermal magnetization switching behavior under arbitrary short time pulse field with magnitude below medium coercivity is an important issue in many applications. One scenario is describing magnetic recording erasure feature, which is generated by passing head fields over media millions of times. The other example is studying thermal stability of magnetic elements in MRAM. Since in general direct Langevin simulation for long time thermal switching is too time consuming, the widely used approach in studying long time thermal switching of magnetic gains under time varying field is master equation with time dependent energy barrier. Although it is well known that the approach based upon energy barrier can not be extended to relatively short time region where dynamics of magnetization becomes important [1], less clear is the method's limitation in describing long time thermal reversal with time varying fields below medium coercivity. In this paper, we show a scale dilemma in using time dependent energy barrier approach to describe long time thermal reversal of magnetic grains under time varying pulse field. Figure 1 shows an independent magnetic grain under two periodic pulse fields with different excitation frequencies. The field magnitude is well below grain coercivity. In this case, master equation with time dependent energy barrier predicts the same magnetization decay behavior for high frequency and low frequency excitations, independent of grain magnetic properties, temperature and exact field pulse shape. However the averaged thermal transition rate obtained from stochastic dynamics of the magnetization depends upon pulse frequency. Depending upon excitation frequency, exact pulse shape etc, there can be an order of magnitude difference in transition rate between high and low frequency field pulse.
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