Micromagnetic Simulations of Ferromagnetic Rings

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

Thermal Stability of the Magnetization in Perpendicularly Magnetized Thin Film Nanomagnets

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 leading-order dependence of magnetization reversal rates are governed by 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 the magnetization flipping as a rigid unit, 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.Comment: 5 pages, 4 Figure

Stability of 2pi domain walls in ferromagnetic nanorings

The stability of 2pi domain walls in ferromagnetic nanorings is investigated via calculation of the minimum energy path that separates a 2pi 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 2pi 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 2pi wall is compared to the activation energy for transitions between the two ring vortex states.Comment: 4 pages, 2 figure

Enhanced Stochastic Bit Rate for Perpendicular Magnetic Tunneling Junctions in a Transverse Field

Perpendicular magnetic tunneling junctions(pMTJs) as true random number generators (TRNGs) have been investigated by means of high-temperature micromagnetic simulations using MuMax3. An in-plane applied field, which lowers the energy barrier for thermally activated reversal, can be used to control and increase the bitrates. We study the attempt rate and the energy barrier for 10 and 40 nm diameter devices in various applied magnetic fields. At room temperature, the presence of the field leads to orders of magnitude increase in the bitrate, up to ∼ 100 MHz.QC 20230920</p

Energy Barriers for Thermally Activated Magnetization Reversal in Perpendicularly Magnetized Nanodisks in a Transverse Field

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 (Eb) to these transitions leading to faster fluctuations. In this study, we present analytical and numerical calculations of Eb 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 Eb 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.Under review process in Physical Review Applied by the American Physical Society</p

Enhanced Stochastic Bit Rate for Perpendicular Magnetic Tunneling Junctions in a Transverse Field

Perpendicular magnetic tunneling junctions(pMTJs) as true random number generators (TRNGs) have been investigated by means of high-temperature micromagnetic simulations using MuMax3. An in-plane applied field, which lowers the energy barrier for thermally activated reversal, can be used to control and increase the bitrates. We study the attempt rate and the energy barrier for 10 and 40 nm diameter devices in various applied magnetic fields. At room temperature, the presence of the field leads to orders of magnitude increase in the bitrate, up to ∼ 100 MHz.QC 20230920</p

Energy Barriers for Thermally Activated Magnetization Reversal in Perpendicularly Magnetized Nanodisks in a Transverse Field

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 journa