We consider magnetization reversal due to thermal fluctuations in thin, submicron-scale rings. These mesoscopic ferromagnetic particles are of particular interest as potential information storage components in magnetoelectronic devices, because their lack of sharp ends result in a magnetization density that is significantly more stable against reversal than in thin needles and other geometries. Their two-dimensional nature and rotational symmetry allow us to incorporate long-range magnetostatic forces in a fully analytic treatment, which is not possible in most geometries. We uncover a type of 'phase transition' between different activation regimes as magnetic field is varied at fixed ring size. Previous studies of such transitions in classical activation behavior have found that they occur as length is varied, which cannot be realized easily or continuously for most systems. However, the different activation regimes in a single mesoscopic ferromagnet should be experimentally observable by changing the externally applied magnetic field, and by tuning this field the transition region itself can be studied in detail.
We introduce a continuum approach to studying the lifetimes of monovalent metal nanowires. By modelling the thermal fluctuations of cylindrical nanowires through the use of stochastic Ginzburg-Landau classical field theories, we construct a self-consistent approach to the fluctuation-induced "necking" of nanowires. Our theory provides
quantitative estimates of the lifetimes for alkali metal nanowires
in the conductance range 10 < G/G0 < 100 (where G0 = 2e/h is the conductance quantum), and allows us to account for qualitative differences in the
conductance histograms of alkali vs. noble metal nanowires.
We treat analytically a model that captures several features of the
phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial domain, perturbed by weak spatiotemporal noise having a flat power spectrum in time and space. Our analysis extends the Kramers theory of noise-induced transitions to the case when the system acted on by the noise has nonzero spatial extent, and the noise itself is spatially dependent. By extending the Langer-Coleman theory of the noise-induced decay of a metastable state, we determine the dependence of the activation barrier and the Kramers reversal rate prefactor on the size
of the spatial domain. As this is increased from zero and passes through a certain critical value, a transition between activation regimes occurs, at which the rate prefactor diverges. Beyond the transition, reversal preferentially takes place in a spatially inhomogeneous rather than in a homogeneous way. Transitions of this sort were not discovered by Langer or Coleman, since they treated only the infinite-volume limit. Our analysis uses higher ranscendental functions to handle the case of finite volume.
Similar transitions between activation regimes should occur in other models of metastable systems with nonzero spatial extent, perturbed by weak noise, as the size of the spatial domain is varied.