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(a) The magnetization vector and four different states A, B, C and B′ defined by the magnetization orientation in a nanomagnet shaped like an elliptical disk. (b) Energy profile of a shape anisotropic nanomagnet (shaped like an elliptical disk) as a function of magnetization orientation in the plane of the nanomagnet. The potential energy is plotted as a function of the azimuthal angle ϕ. (c) Modified energy profile with an applied magnetic field H, (d) spin transfer torque mediated switching from state A to state C, (e) modified energy profile with uniaxial compressive stress along the major axis for a magnet with positive magnetostriction (the same would be true for uniaxial tensile stress along the major axis for a magnet with negative magnetostriction), (f) introduction of asymmetry in the energy profile with a dipole coupled nanomagnet.
Source publication
Micromagnetic studies of the magnetization change in magnetostrictive
nanomagnets subjected to stress are performed for nanomagnets of different
sizes. The interplay between demagnetization, exchange and stress anisotropy
energies is used to explain the rich physics of size-dependent magnetization
dynamics induced by modulating stress anisotropy in...
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Citations
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... These simulations consider switching errors caused only by thermal noise (not defects) and are usually based on the Landau-Lifshitz-Gilbert-Langevin (or stochastic Landau-Lifshitz-Gilbert) equation. [50][51][52][53][54][55][56] They have shown that straintronic switching error probability can range between 10 À3 and 10 À8 at room temperature (owing to thermal noise alone), which is, of course, too high for logic where the error probability might need to be no larger than 10 À15 . 57 The stochastic Landau-Lifshitz-Gilbert equation is ...
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... There are many possible reasons why defects can exacerbate switching errors. One very likely possibility is that defects promote incoherent switching, which is known to increase error rate [13,51]. Another possibility is, of course, that they can spawn metastable states that pin the magnetization and hinder switching. ...
Magnetoelastic (straintronic) switching of bistable magnetostrictive nanomagnets is an extremely energy-efficient switching methodology for (magnetic) binary switches that has recently attracted widespread attention because of its potential application in ultra-low-power digital computing hardware. Unfortunately, this modality of switching is also very error prone at room temperature. Theoretical studies of switching error probability of magnetoelastic switches have predicted probabilities ranging from 10−8 to 10−3 at room temperature for ideal, defect-free nanomagnets, but experiments with real nanomagnets show a much higher probability that exceeds 0.1 in some cases. The obvious spoilers that can cause this large difference are defects and nonidealities. We theoretically study the effect of common defects (that occur during fabrication) on magnetoelastic switching probability in the presence of room-temperature thermal noise. Surprisingly, we find that even small defects increase the switching error probabilities by orders of magnitude. There is usually a critical stress that leads to the lowest error probability and its value increases enormously in the presence of defects. All this could limit or preclude the application of magnetoelastic (straintronic) binary switches in either Boolean logic or memory, despite their excellent energy efficiency, and restrict them to non-Boolean (e.g., neuromorphic, stochastic) computing applications. We also study the difference between magnetoelastic switching with a stress pulse of constant amplitude and sinusoidal time-varying amplitude (e.g., due to a surface acoustic wave) and find that the latter method is more reliable and generates lower switching error probabilities in most cases provided the time variation is reasonably slow.
... (2) Secondly, there can be rough edges due to lithographic imperfections and material defects that can introduce incoherency in the switching dynamics and metastable states that pin the magnetization. While incoherency is not a big issue in STT switching, it severely affects the switching probability of strain induced switching [118,119]. Additionally, experiments were performed with 200-400 nm sized magnets. The single domain limit of a magnet can be 10×exchange length which is about 50 nm. ...
... (b) Energy profile of a shape anisotropic nanomagnet (shaped like an elliptical disk) plotted as a function of the azimuthal angle. Reprinted with permission from[118], Copyright (2017), Institute of Physics. ...
... (a) Schematic of a straintronic switching device, (b) modified energy profile plotted as a function of the azimuthal angle with uniaxial compressive stress along the major axis for a magnet with positive magnetostriction (the same would be true for uniaxial tensile stress along the major axis for a magnet with negative magnetostriction), (c) introduction of asymmetry in the energy landscape due to dipole coupling plotted as a function of the azimuthal angle. Reprinted with permission from[118], Copyright (2017), Institute of Physics. ...
... We will study the switching of the magnetization of the test nanomagnet (with a hole in its center) due to the combined effect of the bias magnetic field (representing dipole coupling with the neighbor) and stress in the presence of thermal noise using the micromagnetic simulator MuMax3 [34]. The procedure for incorporating stress and thermal noise in the simulations has been described in [35] and will not be repeated here. The switching error probability is found as follows: At time t = 0, the magnetization points antiparallel to the bias magnetic field representing dipole coupling. ...
We theoretically study the effect of a material defect (material void) on switching errors associated with magneto-elastic switching of magnetization in elliptical magnetostrictive nanomagnets having in-plane magnetic anisotropy. We find that the error probability increases significantly in the presence of the defect, indicating that magneto-elastic switching is particularly vulnerable to material imperfections. Curiously, there is a critical stress value that gives the lowest error probability in both defect-free and defective nanomagnets. The critical stress is much higher in defective nanomagnets than in defect-free ones. Since it is more difficult to generate the critical stress in small nanomagnets than in large nanomagnets (having the same energy barrier for thermal stability), it would be a challenge to downscale magneto-elastically switched nanomagnets in memory and other applications where reliable switching is required. This is likely to be further exacerbated by the presence of defects.
... The logic operation and data propagation in NML are realised by dipole-dipole interaction between neighbour magnets. The study in [14][15][16] researched the magnetisation dynamics in a single multiferroic nanomagnet. To propagate the binary information unidirectionally, we usually use a linear chain of magnets aligned horizontally or vertically, which is called binary wires [17][18][19][20]. ...
The error rates of multiferroic majority logic gate (MLG) in the presence of thermal noise fluctuation are evaluated via solving the Landau-Lifshitz-Gilbert equations. It is found that in the pre-stress condition, magnetisation orientations of nanomagnets in the MLG denote an initial 4°-10° departure from the easy axis direction due to random thermal noise field. This phenomenon may be the main origin of switching errors of multiferroic logic gates at high temperature. Specifically, in the post-stress condition, it has been seen that larger spacing between nanomagnets leads to a high error rate, up to 50%, which arises from weak dipolar coupling interactions and strong thermal fluctuations. However, opposed to their expected, small spacing between nanomagnets leads to a higher error rate, up to 90%, which mainly arises from spontaneous magnetisation reversal induced by weak stress anisotropy energy. Therefore, moderate spacing is very important to MLG switching at room temperature, for example the optimal spacing is 250-310 nm for MLG constructed with nanomagnets having shape anisotropy energy of 623 kT. These findings can provide guides on multiferroic logic circuit design.
