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Images of the minimum energy path. Images shown are at locations 0, 20, 40, 60, 80, 100 in the string. Red and blue (light and dark) represent downward and upward magnetization, respectively. Reversal occurs by nucleation of a domain on one corner and propagation of a domain wall across the material. The transition state is located close to image 20. The curve presents a kink near the 55th image. This occurs when the traveling domain wall reaches the opposite corners of the element and this feature has no effect on the magnitude of the transition rate.
Field dependence of activation energy for elements with two different sizes. The smaller samples follow more closely the predictions of the usual macrospin model ( ). For large samples, it can be seen that the activation energy is lower than that predicted by the macrospin model ( ) for a large range of values of the external field. In both cases, the small value of A permits nonuniform magnetization configurations and the smallest sample behaves more as a macrospin.
Comparison of two versions of the macrospin model: corresponds to the commonly used thin film limit and is a film with finite aspect ratio. Blue circles are calculated with the string method for a very large exchange constant.
Activation energy for square samples (blue/dark) and circular samples (red/light). Left inset shows the transition state configuration for a 150 nm diameter circular element. Right inset: energy barriers for a square of side 100 nm for different values of K, the points are obtained with the string method and the line obeys Eq. (8) .
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