Micromagnetics at a finite temperature using the ridge optimization method

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Abstract
The thermally activated transitions of the magnetization are studied for a chain of three identical interacting ferromagnetic particles. The saddle points are located by implementation of the ridge method with an initial direction of search chosen at random using the statistical properties of small collective thermal excitations. The solution is refined using a technique that combines aspects of the conjugate gradient and a Newton-type optimization. The methodology used identifies the transitions of relatively high probability of occurrence and deduces the energy barrier of least height. From the study of the topology of the energy surface, it is shown that the irreversible response of the system to an external field is modified at finite temperature. The model predicts a reduction in the symmetry of the ‘‘fanning’’ mode of magnetic reversal and a finite probability for transitions to states other than the state of negative saturation that is attributed to the local uniaxial anisotropy of the particles. The field dependence of the energy barrier exhibits a discontinuity when the final state following the activation process is no longer stable.

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