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Thermally-induced transitions between bistable magnetic states of magnetic tunnel junctions (MTJ) are of interest for generating random bitstreams and for applications in stochastic computing. An applied field transverse to the easy axis of a perpendicularly magnetized MTJ (pMTJ) can lower the energy barrier ($E_b$) to these transitions leading to faster fluctuations. In this study, we present analytical and numerical calculations of $E_b$ considering both coherent (macrospin) reversal and non-uniform wall-mediated magnetization reversal for a selection of nanodisk diameters and applied fields. Non-uniform reversal processes dominate for larger diameters, and our numerical calculations of $E_b$ using the String method show that the transition state has a sigmoidal magnetization profile. The latter can be described with an analytical expression that depends on only one spatial dimension, parallel to the applied field, which is also the preferred direction of profile motion during reversal. Our results provide nanodisk energy barriers as a function of the transverse field, nanodisk diameter, and material characteristics, which are useful for designing stochastic bitstreams., Comment: 10 pages, 8 figures, 1 table. It will be submitted to a peer-reviewed journal

We review work by the authors on thermal activation in nanoscopic magnetic systems. These systems present unique difficulties in analyzing noise-induced escape over a barrier, including the presence of nonlocal interactions, nongradient terms in the energy functional, and dynamical textures as initial or saddle states. We begin with a discussion of magnetic reversal between single-domain configurations of the magnetization. Here the transition (saddle) state can be either a single-domain or a spatially varying (instanton-like) configuration, and depending on the system parameters can exhibit either Arrhenius or non-Arrhenius reversal rates. We then turn to a discussion of transitions between magnetic textures, which can be either static and topologically protected or dynamic and not topologically protected. An example of the latter case is the droplet soliton, a rotating nontopologically-protected configuration, which we find can occur either as a metastable or transition state in a nanoscopic magnetic system. After discussing various issues in calculating transition rates, we present results for the activation barriers for creation and annihilation of these magnetic textures. We conclude with a discussion of activated transitions between topologically protected skyrmion textures and other configurations, on which work is ongoing.

We study noise-induced creation and annihilation of magnetic droplet solitons in experimental parameter regions in which they are linearly stable against drift. Exploiting the rotational symmetry of the problem, we transform to the reference frame rotating with the droplet soliton and introduce an effective potential energy that accounts for the work done against spin-transfer torque to rotate the magnetization between two different orientations. We use this function to compute the activation barrier in both directions between the uniform magnetization state and the droplet soliton state for a variety of nanocontact radii and currents. We investigate droplet soliton structures with both zero and nonzero spin-torque asymmetry parameter. Our approach can be applied to estimate activation barriers for dynamical systems where non-gradient terms can be absorbed by changes of reference frames, and suggests a technique applicable to extended systems that may not be uniformly magnetized., Comment: 12 figures, 22 pages

We present results of micromagnetic simulations of thin ferromagnetic rings undergoing magnetization reversal. This geometry is one of few examples in micromagnetics in which the transition states have been found analytically in a 1D model. According to this model, at low fields and large ring sizes, the energetically preferred transition state is a localized magnetization fluctuation (instanton saddle). At high fields and small ring size, the preferred saddle state is a uniformly rotated magnetization (constant saddle). In the first part of this paper, we use numerical micromagnetic simulations to test these predictions of the 1D analytical model for more realistic situations, including a variety of ring radii, annular widths and magnetic fields. The predicted activation energies for magnetization reversal are found to be in close agreement with numerical results, even for rings with a large annular width where the 1D approximation would be expected to break down. We find that this approximation breaks down only when the ring's annular width exceeds its radius. In the second part, we present new metastable states found in the large radius limit and discuss how they provide a more complete understanding of the energy landscape of magnetic nanorings., Comment: 12 pages, 16 figures. Bibtex file for references, correct author order

Thin nanomagnetic rings have generated interest for fundamental studies of magnetization reversal and also for their potential in various applications, particularly as magnetic memories. They are a rare example of a geometry in which an analytical solution for the rate of thermally induced magnetic reversal has been determined, in an approximation whose errors can be estimated and bounded. In this work, numerical simulations of soft ferromagnetic rings are used to explore aspects of the analytical solution. The evolution of the energy near the transition states confirms that, consistent with analytical predictions, thermally induced magnetization reversal can have one of two intermediate states: either constant or soliton-like saddle configurations, depending on ring size and externally applied magnetic field. The results confirm analytical predictions of a transition in thermally activated reversal behavior as magnetic field is varied at constant ring size. Simulations also show that the analytic one dimensional model continues to hold even for wide rings.