Micromagnetics simulation based on the classical Landau-Lifshitz-Gilbert (LLG) equation has long been a powerful method for modeling magnetization dynamics and reversal of three-dimensional (3D) magnets. For two-dimensional (2D) magnets, the magnetization reversal always accompanies the collapse of the magnetization even at low temperatures due to intrinsic strong spin fluctuation. We propose a micromagnetic theory that explicitly takes into account the rapid demagnetization and remagnetization dynamics of 2D magnets during magnetization reversal. We apply the theory to a single-domain magnet to illustrate fundamental differences in magnetization trajectories and reversal times for 2D and 3D magnets.
A mechanism of current-induced magnetization reversal based on the parametric resonance is described. The source of the magnetization reversal is a current-induced magnetic field, which is applied perpendicularly to the easy axis of magnetic anisotropy of a ferromagnetic nanomagnet. The current-induced magnetic field was measured in a FeCoB nanomagnet to be 60 Gauss at a current density of 65 mA/um2. Two mechanisms of the magnetization reversal are described and calculated. The first mechanism is the reversal by a RF electrical current, which modulated at a frequency close to the precession fr…
An effective method for ultrafast magnetization reversal of nanoclusters is suggested. The method is based on coupling a nanocluster to a resonant electric circuit. This coupling causes the appearance of a magnetic feedback field acting on the cluster, which drastically shortens the magnetization reversal time. The influence of the resonator properties, nanocluster parameters, and external fields on the magnetization dynamics and reversal time is analyzed. The magnetization reversal time can be made many orders shorter than the natural relaxation time. The reversal is studied for both the case…
Magnetization reversal of interconnected Kagome artificial spin ice was studied by the first-order reversal curve (FORC) technique based on the magneto-optical Kerr effect and magnetoresistance measurements. The magnetization reversal exhibits a distinct six-fold symmetry with the external field orientation. When the field is parallel to one of the nano-bar branches, the domain nucleation/propagation and annihilation processes sensitively depend on the field cycling history and the maximum field applied. When the field is nearly perpendicular to one of the branches, the FORC measurement reveal…
We demonstrate a quasi ballistic switching of the magnetization in a microscopic mag-neto resistive memory cell. By means of time resolved magneto transport we follow the large angle precession of the free layer magnetization of a spin valve cell upon applica-tion of transverse magnetic field pulses. Stopping the field pulse after a 180 degree precession rotation leads to magnetization reversal with reversal times as short as 165 ps. This switching mode represents the fundamental ultra fast limit of field induced magnetization reversal.
Local magnetic moments can be created in graphene by incorporating different defects. The possibility of regulating dynamics of magnetization in graphene, by employing the Purcell effect, is analyzed. The role of the system parameters in magnetization reversal is studied. The characteristics of such a reversal can be varied in a wide range, which can be used for various applications in spintronics. It is shown that fast magnetization reversal generates coherent radiation.
We investigate the magnetization reversal of single-domain magnetic nanoparticle driven by linear down-chirp microwave magnetic field pulse. Numerical simulations based on the Landau-Lifshitz-Gilbert equation reveal that solely down-chirp pulse is capable of inducing subnanosecond magnetization reversal. With a certain range of initial frequency and chirp rate, the required field amplitude is much smaller than that of constant-frequency microwave field. The fast reversal is because the down-chirp microwave field acts as an energy source and sink for the magnetic particle before and after cross…
We propose to accelerate reversal of the ferromagnetic order parameter in spin valves by electronic noise. By solving the stochastic equations of motion we show that the current-induced magnetization switching time is drastically reduced by a modest level of externally generated current (voltage) noise. This also leads to a significantly lower power consumption for the switching process.
Magnetization dynamics in the system of magnetic nanoclusters with randomly distributed properties are studied by means of computer simulations. The main attention is paid to the possibility of coherent magnetization reversal from a strongly nonequilibrium state with a mean cluster magnetization directed opposite to an external magnetic field. Magnetic nanoclusters are known to be characterized by large magnetic anisotropy and strong dipole interactions. It is also impossible to produce a number of nanoclusters with identical properties. As a result, any realistic system of nanoclusters is com…
The nature of magnetization reversal in an isolated cylindrical nanomagnet has been studied employing time-resolved magnetoresistance measurement. We find that the reversal mode is highly stochastic, occurring either by multimode or single-step switching. Intriguingly, the stochasticity was found to depend on the alignment of the driving magnetic field to the long axis of the nanowires, where predominantly multimode switching gives way to single-step switching behavior as the field direction is rotated from parallel to transverse with respect to the nanowire axis.
We have considered the effect of different spin-orbit interaction mechanisms on the process of demagnetization under the influence of short-pulse lasers. All-optical magnetization reversal of perpendicularly magnetized thin films can occur if there are sufficient strong spin-Hall, skew scattering, and Rashba interactions. In the presence of spin-orbit interactions, the transient charge currents provide the generation of transverse-spin currents and accumulations, which eventually exert spin-transfer torque on the magnetization. By combining the optically excited spin-dependent diffusive transp…
The magnetization reversal process in thin-film ferromagnetic elements with surface anisotropy of various shapes and sizes is investigated by means of numerical simulation. The dependence of the perpendicular and in-plane hysteresis loops on the element thickness and the value of the surface anisotropy constant is obtained. For sufficiently large values of the surface anisotropy constant the magnetization reversal of thin-film elements is shown to occur due to the nucleation of the buckling mode. For an elongated rectangular element the nucleation field of the buckling mode is proportional to …
We demonstrate the current-induced complete magnetization reversal of the free layer in lateral nanowires patterned from metallic pseudo spin valve stacks. The reversal is induced by Oersted fields in conjunction with a dipolar coupling via the lateral stray fields of the two magnetic layers. Starting from the parallel state the Oersted field rotates the magnetization vectors of both magnetic layers in opposite directions so far off the wire axis that the dipolar coupling becomes strong enough to stabilize an antiparallel configuration. As simulations and experiments show this coupling is only…
The reversal of a uniform axial magnetization in a ferromagnetic nanotube (FNT) has been predicted to nucleate and propagate through vortex domains forming at the ends. In dynamic cantilever magnetometry measurements of individual FNTs, we identify the entry of these vortices as a function of applied magnetic field and show that they mark the nucleation of magnetization reversal. We find that the entry field depends sensitively on the angle between the end surface of the FNT and the applied field. Micromagnetic simulations substantiate the experimental results and highlight the importance of t…
We report that the irreversible magnetization switching process in ferromagnetic nanoparticles is governed by the formation and dynamics of topological point-defects in the form of hedgehog-antihedgehog pairs. After nucleation, these pairs rapidly separate with speeds exceeding domain wall velocities, and they generate an emergent electric field of solenoidal character and substantial magnitude.
The reversal condition of magnetization in a nanomagnet under the effect of rotating magnetic field generated by a microwave is theoretically studied based on the Landau-Lifshitz-Gilbert equation. In a rotating frame, the microwave produces a dc magnetic field pointing in the reversed direction, which energetically stabilizes the reversed state. We find that the microwave simultaneously produces a torque preventing the reversal. It is pointed out that this torque leads to a jump in the reversal field with respect to the frequency. We derive the equations determining the reversal fields in both…
Computational and experimental results on the thermally-induced magnetization reversal in single-domain magnetic nanoparticles are reported. The simulations are based on the direct integration of the Fokker-Planck equation that governs the dynamics of the magnetic moment associated with the nanoparticles. A mean field approximation is used to account for the influence of the dipolar interaction between nanoparticles. It is shown that the interactions can either speed up or slow down the reversal process, depending on the angle between the external magnetic field and the axis of easy magnetizat…
We study dynamics of the magnetization coupled to the surface Dirac fermions of a three di- mensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of charge current, we find current induced magnetization dynamics and discuss the possibility of mag- netization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The mag- netization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unne…
A novel method to study the fundamental problem of quantum double well potential systems that display magnetic hysteresis is proposed. The method, coined quantum-first-order reversal curve (QFORC) analysis, is inspired by the conventional first-order reversal curve (FORC) protocol, based on the Preisach model for hysteretic phenomena. We successfully tested the QFORC method in the peculiar hysteresis of the Mn12Ac molecular magnet, which is governed by macroscopic quantum tunneling of magnetization. The QFORC approach allows one to quickly reproduce well the experimental magnetization behavior…
We investigate the magnetization reversal of single-domain magnetic nanoparticle driven by the circularly polarized cosine chirp microwave pulse (CCMP). The numerical findings, based on the Landau-Lifshitz-Gilbert equation, reveal that the CCMP is by itself capable of driving fast and energy-efficient magnetization reversal. The microwave field amplitude and initial frequency required by a CCMP are much smaller than that of the linear down-chirp microwave pulse. This is achieved as the frequency change of the CCMP closely matches the frequency change of the magnetization precession which leads…
The magnetization reversal in a single molecular magnet (SMM) weakly coupled to an electrode with spin-dependent splitting of chemical potentials (spin bias) is theoretically investigated by means of the rate equation. A microscopic mechanism for the reversal is demonstrated by the avalanche dynamics at the reversal point. The magnetization as a function of the spin bias shows hysteresis loops tunable by the gate voltage and varying with temperature. The nondestructive measurement to the orientation of giant spin in SMM is presented by measuring the fully polarized electric current in the resp…
It has been shown that a single-domain magnetic nanoparticle can be effectively switched by a linear down-chirp microwave field pulse (DCMWP) in zero temperature limit. However, finite temperature is ubiquitous in practice. Here, we study the effect of finite temperature on the DCMWP-induced magnetization reversal based on the stochastic Landau-Lifshitz-Gilbert equation. It is found that any one of the three controlling parameters of a DCMWP, i.e. the amplitude, chirp rate, or initial frequency, decreases with increasing temperature while the other two are fixed. The maximal temperature at whi…
The half antivortex, a fundamental topological structure which determines magnetization reversal of submicron magnetic devices with domain walls, has been suggested also to play a crucial role in spin torque induced vortex core reversal in circular disks. Here we report on magnetization reversal in circular disks with nanoholes through consecutive metastable states with half antivortices. In-plane anisotropic magnetoresistance and broadband susceptibility measurements accompanied by micromagnetic simulations reveal that cobalt disks with two and three linearly arranged nanoholes directed at 45…
We simulate the stochastic Landau-Lifshitz-Gilbert (LLG) dynamics of a uniaxial nanomagnet out to sub-millisecond timescales using a graphical processing unit based micromagnetic code and determine the effect of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted reversal dynamics. The asymptotic behavior of the switching time ($I\rightarrow 0$, $<τ>\propto\exp(-ξ(1-I)^2)$) is approached gradually, indicating a broad crossover regime between ballistic and thermally assisted spin transfer reversal. Interestingly, the mean switching time is shown to …
We show that a slowly decaying current pulse can lead to nearly deterministic precessional switching in the presence of noise. We consider a biaxial macrospin, with an easy axis in the plane and a hard axis out-of-the plane, typical of thin film nanomagnets patterned into asymmetric shapes. Out-of-plane precessional magnetization orbits are excited with a current pulse with a component of spin polarization normal to the film plane. By numerically integrating the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation we show that thermal noise leads to strong dephasing of the magnetization orb…
Nanometer-sized magnetic particles have generated continuous interest as the study of their properties has proved to be scientifically and technologically very challenging. In this article we reviewed the most important theories and experimental results concerning the magnetization reversal of single-domain particles,clusters and molecular clusters. Sect.1 reviews briefly the commonly used measuring techniques. Among them, electrical transport measurements, Hall probes and micro-SQUID techniques seem to be the most convenient techniques for low temperature measurements. Sect.2 discusses the me…
We report here the results of two-dimensional electron gas based micro-Hall magnetometry measurements and micromagnetic simulations of dipolar coupled nanomagnets of Ni80Fe20 arranged in a double ring-like geometry. We observe that although magnetic force microscopy images exhibit single domain like magnetic states for the nanostructures, their reversal processes may undergo complex behavior. The details of such reversal behavior is observed as specific features in micro-Hall magnetometry data which compares well with the micromagnetic simulation data.
Nanoscale single-domain bar magnets are building blocks for a variety of fundamental and applied mesoscopic magnetic systems, such as artificial spin ices, magnetic shape-morphing microbots as well as magnetic majority logic gates. The magnetization reversal switching field of the bar nanomagnets is a crucial parameter that determines the physical properties and functionalities of their constituted artificial systems. Previous methods on tuning the magnetization reversal switching field of a bar nanomagnet usually rely on modifying its aspect ratio, such as its length, width and/or thickness. …
Modulation of stress anisotropy of magnetostrictive nanomagnets with strain offers an extremely energy-efficient method of magnetization reversal. The reversal process, however, is often incoherent and hence error-prone in the presence of thermal noise at room temperature. Occurrence of incoherent metastable states in the potential landscape of the nanomagnet can further exacerbate the error. Stochastic micromagnetic simulations at room temperature are used to understand and calculate energy dissipations and switching error probabilities in this important magnetization switching methodology. W…
The diversity of various manganese types and its complexes in the Mn-doped ${\rm A^{III}B^V}$ semiconductor structures leads to a number of intriguing phenomena. Here we show that the interplay between the ordinary substitutional Mn acceptors and interstitial Mn donors as well as donor-acceptor dimers could result in a reversal of electron magnetization. In our all-optical scheme the impurity-to-band excitation via the Mn dimers results in direct orientation of the ionized Mn-donor $d$ shell. A photoexcited electron is then captured by the interstitial Mn and the electron spin becomes parallel…
In this work, and by means of micromagnetic simulations, we study the magnetic properties of toroidal nanomagnets. The magnetization ground state for different values of the aspect ratio between the toroidal and polar radii of the nanotorus has been obtained. The hysteresis curves are also obtained, evidencing the existence of two reversal modes depending on the geometry: a vortex mode and a coherent rotation. A comparison between toroidal and cylindrical nanoparticles has been performed evidencing that nanotori can accommodate a vortex as the ground state for smaller volume than cylindrical n…
We study the influence of the spin torque, which depends on the space and time derivative of magnetization, on magnetization reversal time in a ferromagnetic fine particle. The spin torque operates to dissipate the angular momentum of the magnetization precession, and the torque increases in a spin vortex structure. We calculate the magnetization reversal time under a DC magnetic field using the Landau-Lifshitz-Gilbert equation containing a spin torque term. We found that the spin torque changes the magnetization switching speed significantly during the reversal process by maintaining a spin v…
We investigate the influence of shape anisotropy on the magnetization reversal of a single-domain magnetic nanoparticle driven by a circularly polarized linear down-chirp microwave field pulse (DCMP). Based on the Landau-Lifshitz-Gilbert equation, numerical results show that the three controlling parameters of DCMP, namely, microwave amplitude, initial frequency and chirp rate, decrease with the increase of shape anisotropy. For certain shape anisotropy, the reversal time significantly reduces. These findings are related to the competition of shape anisotropy and uniaxial magnetocrystalline an…
Current-induced magnetization dynamics in Co/Cu/Co trilayer nanopillars (~100nm in diameter) has been studied experimentally for large applied fields perpendicular to the layers. An abrupt and hysteretic increase in dynamic resistance is observed at high current densities for one polarity of the current, comparable to the giant magnetoresistance effect observed at low fields. A micromagnetic model, that includes a spin-transfer torque, suggests that the current induces a complete reversal of the thin Co layer to alignment antiparallel to the applied field-that is, to a state of maximum magneti…
The large arrays of magnetic dots are the building blocks of magnonic crystals and the emerging bit patterned media for future recording technology. In order to fully utilize the functionalities of high density magnetic nanodots, a method for the selective reversal of a single nanodot in a matrix of dots is desired. We have proposed a method for magnetization reversal of a single nanodot with microwave excitation in a matrix of magneto-statically interacting dots. The method is based on the excitation of collective modes and the spatial anomaly in the microwave power absorption. We perform num…
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 simulatio…
We report on room temperature magnetoresistance and low frequency noise in sub-100nm elliptic CoFeB/MgO/CoFeB magnetic tunnel junctions with ultrathin (0.9nm) barriers. For magnetic fields applied along the hard axis, we observe current induced magnetization switching between the antiparallel and parallel alignments at DC current densities as low as 4*106A/cm2. We attribute the low value of the critical current to the influence of localized reductions in the tunnel barrier, which affects the current distribution. The analysis of random telegraph noise, which appears in the field interval near …
Magnetization reversal mechanisms and impact of magnetization direction are studied in square arrays of interconnected circular permalloy nanorings using MOKE, local imaging, numerical simulations and transport techniques.
Ordered ferromagnetic nanowire arrays are widely studied due to the diversity of possible applications. However, there is still no complete understanding of the relation between the array's parameters and its magnetic behavior. The effect of vortex states on the magnetization reversal of large-diameter nanowires is of particular interest. Here, we compare analytical and micromagnetic models with experimental results for three arrays of iron nanowires with diameters of 33, 52 and 70 nm in order to find the balance between the number of approximations and resources used for the calculations. The…
We inject current pulses into uniformly magnetized patterns of thin films of the itinerant ferromagnet SrRuO3, while monitoring the effective temperature of the patterns during the current injection. We gradually increase the amplitude of the pulses until magnetization reversal occurs. We observe magnetization reversal induced by current above a temperature-dependent threshold and show that this effect is not simply due to sample heating or Oersted fields. We discuss the applicability of the current-induced spin-wave instability scenario.
The magnetization reversal in ordered arrays of iron oxide nanotubes of 50 nm outer diameter grown by atomic layer deposition is investigated theoretically as a function of the tube wall thickness, $d_{w}$. In thin tubes ($d_{w}<13$ nm) the reversal of magnetization is achieved by the propagation of a vortex domain boundary, while in thick tubes ($d_{w}>13$ nm) the reversal is driven by the propagation of a transverse domain boundary. Magnetostatic interactions between the tubes are responsible for a decrease of the coercive field in the array. Our calculations are in agreement with recently r…
Microwave assisted magnetization reversal are studied in the bulk bilayer exchange coupled system. We investigate the nonlinear magnetization reversal dynamics in a perpendicular exchange spring media using Landau-Lifshitz equation. In the limit of the infinite thickness of the system, the propagation field leads the reversal of the system. The reduction of the switching field and the magnetization profile in the extended system are studied numerically. The possibility to study the dynamics analytically is discussed and an approximation where two P-modes are coupled by an interaction field is …
Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary Stoner particle under an external magnetic field and a spin-polarized electric current, differential equations for the optimal reversal trajectory, along which the magnetization reversal is the fastest one among all possible reversal routes, are obtained. We show that this is a Euler-Lagrange problem with constrains. The Euler equation of the optimal trajectory is useful in designing a magnetic field pulse and/or a polarized electric current pulse in magnetization reversal for two reasons. 1) It is straightforward to obtai…
It is shown that a pulsed current driven through Ni nanowires provokes an irreversible magnetization reversal at a field distant from the spontaneous switching field $H_{sw}$ by $ΔH$ of as much as 40 % of $H_{sw}$. The state of the magnetization is assessed by magnetoresistive measurements carried out on single, isolated nanowires. The reversible part of the magnetization follows that of a uniform rotation. The switching occurs between the two states accessible otherwise by normal field ramping. $ΔH$ is studied as a function of the angle between the applied field and the wire, and also of the …
We investigate magnetization reversal processes of magnetic nanorings. Using a recently developed efficient cartesian coordinates fast multipole method, magnetization switching phase diagrams are constructed for such structures. We find that the dominant switching mechanisms strongly depend on the relative spatial dimensions of the rings, i.e. height, width and radius. Furthermore, they are found to depend on a characteristic exchange length scale, which is determined by the competing short-range ferromagnetic and long-range dipolar interactions in these systems. Detailed simulations allow us …
We demonstrate the magnetization reversal features in NiFe/IrMn/NiFe thin-film structures with 40% and 75% relative content of Ni in Permalloy in the temperature range from 80 K to 300 K. At the descending branches of the hysteresis loops, the magnetization reversal sequence of the two ferromagnetic layers is found to depend on the type of NiFe alloy. In the samples with 75% relative content of Ni, the bottom ferromagnetic layer reverses prior to the top one. On the contrary, in the samples with 40% of Ni, the top ferromagnetic layer reverses prior to the bottom one. These tendencies of magnet…
With the feature of low-power magnetization manipulation at an ultrashort time scale, all optical switching (AOS) has been propelled to the forefront in investigations. To further speed up the magnetization reversal by manipulating ultrashort optical pulses, in this paper, one single square-wave laser pulse (SWLP) vie the combination of heating and Inverse Faraday Effect (IFE) is explored to excite the reversal of magnetization in a Co/Pt system. Simulation results show that the switching time of magnetization is 3 times faster than the using of a traditional Gaussian wave laser pulse (GWLP) u…
We report numerical and analytical studies of the reversal of the magnetic moment of a single-domain magnetic particle by a circularly polarized ac field of time-dependent frequency. For the time-linear frequency sweep, the phase diagrams are computed that illustrate the dependence of the reversal on the frequency sweep rate v, the amplitude of the ac field h, the magnetic anisotropy field d, and the damping parameter alpha. It is shown that the most efficient magnetization reversal requires a non-linear time dependence of the frequency, omega(t), for which an exact analytical formula is deriv…
We investigate magnetization reversal of two-body uniaxial Stoner particles, by injecting spin-polarized current through a spin-valve structure. The two-body Stoner particles perform synchronized dynamics and can act as an information bit in computer technology. In the presence of magnetic dipole-dipole interaction (DDI) between the two particles, the critical switching current $I_c$ for reversing the two dipoles is analytically obtained and numerically verified in two typical geometric configurations. $I_c$ bifurcates at a critical DDI strength, where $I_c$ can be decreased to about 70% of th…
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 sp…
Features of thermally-activated magnetization switching have been studied in a FeCoB nanomagnet using the Néel model. A method of a high-precision measurement of the coercive field, retention time, Δ and the size of the switching nucleation domain has been proposed and experimentally demonstrated using a Hall-probe setup. A high measurement precision, repeatability and reliability are the features of the proposed method. The dependency of the parameters of thermally-activated magnetization switching on the gate voltage and the bias current were studied.
We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, Kagome artificial spin ice (ASI). The number of strong modes in the FMR spectra depend on the orientation of the applied DC magnetic field. In addition, discontinuities observed in the FMR field-frequency dispersion curves also depend on DC field orientation, and signal a multi-step DC magnetization reversal, which is caused by the reduced energy degeneracy of Fibonacci-distorted vertices. The results suggest the orientation of applied magnetic field and severity of Fibonacci distortion co…
A new strategy is proposed aimed at substantially reducing the minimal magnetization switching field for a Stoner particle. Unlike the normal method of applying a static magnetic field which must be larger than the magnetic anisotropy, a much weaker field, proportional to the damping constant in the weak damping regime, can be used to switch the magnetization from one state to another if the field is along the motion of the magnetization. The concept is to constantly supply energy to the particle from the time-dependent magnetic field to allow the particle to climb over the potential barrier b…
We investigate magnetic anisotropy and magnetization reversal mechanism in chromium telluride thin films grown by molecular beam epitaxy. We report existence of strong perpendicular anisotropy in these thin films, along with a relatively strong second order anisotropy contribution. The angular variation of the switching field observed from the magnetoresistance measurement is explained quantitatively using a one-dimensional defect model. The model reveals the relative roles of nucleation and pinning in the magnetization reversal, depending on the applied field orientation. Micromagnetic simula…
The asymptotic behavior of switching time as a function of current for a uniaxial macrospin under the effects of both spin-torque and thermal noise is explored analytically by focusing on its diffusive energy space dynamics. The scaling dependence ($I\rightarrow 0$, $<τ\propto\exp(-ξ(1-I)^2)$) is shown to confirm recent literature results. The analysis shows the mean switching time to be functionally independent of the angle between the spin current and magnet's uniaxial axes. These results have important implications for modeling the energetics of thermally assisted magnetization reversal of …
