Analytical determination of the LLG zero-damping critical switching field

Previous numerical studies based on the Landau-Lifshitz-Gilbert (LLG) equation have considered the magnetisation reversal of a uniaxial, single-domain particle due to an applied field pulse with a short rise time. When the LLG damping constant alpha < 1, these studies have observed coherent switching for applied field magnitudes below the Stoner-Wohlfarth limit. The switching field computed in these studies decreases as alpha --> 0, with apparent convergence to a limiting value. In this paper, analytic methods determine the value of the switching field in the zero-damping limit for an applied field pulse with zero rise time. The locus of normalized switching fields in parametric form is h(y) = - sin theta(cos theta - 1)/2; h(z) = -cos theta(cos theta + 1)/2; \theta\ less than or equal to 2 pi/3. A non-parametric form is also derived. One surprising implication is that magnetization reversal may be caused by an applied field with easy axis component in the same direction as the initial magnetization (h(z) > 0).