Gabriel Chaves-O'Flynn

Micromagnetic study of magnetization reversal in ferromagnetic nanorings

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 rings 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.

Stability of

The stability of 2π domain walls in ferromagnetic nanorings is investigated via calculation of the minimum energy path that separates a 2π domain wall from the vortex state of a ferromagnetic nanoring. Trapped domains are stable when they exist between certain types of transverse domain walls, i.e., walls in which the edge defects on the same side of the magnetic strip have equal sign and thus repel. Here the energy barriers between these configurations and vortex magnetization states are obtained using the string method. Due to the geometry of a ring, two types of 2π walls must be distinguished that differ by their overall topological index and exchange energy. The minimum energy path corresponds to the expulsion of a vortex. The energy barrier for annihilation of a 2π wall is compared to the activation energy for transitions between the two ring vortex states.

2\pi

Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The magnetization reversal rate depends primarily on the energy barrier the system needs to surmount in order for reversal to proceed. In this paper, we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than all parts of the element switching simultaneously, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements, the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements, the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases, the energy barriers are smaller than those expected for coherent magnetization reversal.

Domain Walls in Ferromagnetic Nanorings

We present the results of zero temperature macrospin and micromagnetic simulations of spin transfer switching of thin film nanomagnets in the shape of an ellipse with a spin-polarization tilted out of the layer plane. The perpendicular component of the spin-polarization is shown to increase the reversal speed, leading to a lower current for switching in a given time. However, for tilt angles larger than a critical angle, the layer magnetization starts to precess about an out-of-plane axis, which leads to a final magnetization state that is very sensitive to simulation conditions. As the ellipse lateral size increases, this out-of-plane precession is suppressed, due to the excitation of spatially non-uniform magnetization modes.

Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane magnetization angle in a weakly damped regime. We then apply this model to study the experimentally relevant problem of switching of an elliptical element when the spin polarization has a component perpendicular to the film plane, restricting the reduced model to a macrospin approximation. The macrospin ordinary differential equation is treated analytically as a weakly damped Hamiltonian system, and an orbit-averaging method is used to understand transitions in solution behaviors in terms of a discrete dynamical system. The predictions of our reduced model are compared to those of the full Landau-Lifshitz-Gilbert-Slonczewski equation for a macrospin.

Micromagnetic study of spin transfer switching with a spin polarization tilted out of the free layer plane

We present the switching characteristics of a spin-transfer device that incorporates a perpendicularly magnetized spin-polarizing layer with an in-plane magnetized free and fixed magnetic layer, known as an orthogonal spin transfer spin valve device. This device shows clear switching between parallel (P) and antiparallel (AP) resistance states and the reverse transition (AP → P) for both current polarities. Further, hysteretic transitions are shown to occur into a state with a resistance intermediate between that of the P and AP states, again for both current polarities. These unusual spin-transfer switching characteristics can be explained within a simple macrospin model that incorporates thermal fluctuations and considers a spin-polarized current that is tilted with respect to the free layers plane, due to the presence of the spin-transfer torque from the polarizing layer.

Reduced model for precessional switching of thin-film nanomagnets under the influence of spin torque

Numerical simulations were performed for thin ferromagnetic nanorings with non-negligible anisotropy. In a thin film, the cubic crystalline anisotropy reduces to a four-fold symmetric term favoring magnetization along the ±x̂ and ±ŷ directions. Our numerical studies use an extension of the previously proposed algorithm for thin film micromagnetic simulations based on optimal grids for the calculation of the stray field. The relative strength of the magnetostatic energy was varied with respect to the crystalline and exchange energies. The remanent magnetization configurations were obtained for a variety of ring geometries and initial saturation orientations. The magnetocrystalline contribution causes the appearance of distinct domains in the annular structure, resulting in a new variety of magnetization configurations. Based on energetic considerations we provide a classification of possible remanent states.