Switching of Dipole Coupled Multiferroic Nanomagnets in the Presence of Thermal Noise: Reliability of Nanomagnetic Logic

Fashami, Mohammad Salehi; Munira, Kamaram; Bandyopadhyay, Supriyo; Ghosh, Avik W.; Atulasimha, Jayasimha

doi:10.1109/tnano.2013.2284777

Cited by 43 publications

(15 citation statements)

References 27 publications

(29 reference statements)

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“…The error rate is an important feature in the ME memory. The simulation and calculation displayed that the error rate in ME switching was high, but could be reduced via modest theoretical design [ 121 , 122 , 123 ]. The relevant experimental outcome of error rate is waiting to be verified.…”

Section: Challenges and Perspectivesmentioning

confidence: 99%

Magnetoelectric Memory Based on Ferromagnetic/Ferroelectric Multiferroic Heterostructure

Wang

Chen

et al. 2021

Materials

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Electric-field control of magnetism is significant for the next generation of large-capacity and low-power data storage technology. In this regard, the renaissance of a multiferroic compound provides an elegant platform owing to the coexistence and coupling of ferroelectric (FE) and magnetic orders. However, the scarcity of single-phase multiferroics at room temperature spurs zealous research in pursuit of composite systems combining a ferromagnet with FE or piezoelectric materials. So far, electric-field control of magnetism has been achieved in the exchange-mediated, charge-mediated, and strain-mediated ferromagnetic (FM)/FE multiferroic heterostructures. Concerning the giant, nonvolatile, and reversible electric-field control of magnetism at room temperature, we first review the theoretical and representative experiments on the electric-field control of magnetism via strain coupling in the FM/FE multiferroic heterostructures, especially the CoFeB/PMN–PT [where PMN–PT denotes the (PbMn1/3Nb2/3O3)1−x-(PbTiO3)x] heterostructure. Then, the application in the prototype spintronic devices, i.e., spin valves and magnetic tunnel junctions, is introduced. The nonvolatile and reversible electric-field control of tunneling magnetoresistance without assistant magnetic field in the magnetic tunnel junction (MTJ)/FE architecture shows great promise for the future of data storage technology. We close by providing the main challenges of this and the different perspectives for straintronics and spintronics.

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Section: Challenges and Perspectivesmentioning

confidence: 99%

Magnetoelectric Memory Based on Ferromagnetic/Ferroelectric Multiferroic Heterostructure

Wang

Chen

et al. 2021

Materials

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“…The magnetisation dynamics of any nanomagnet is described by the Landau–Lifshitz–Gilbert equation [27]

\begin{matrix} right leftthickmathspace.5em \\ \frac{d M}{dt} & = - γ M \times {bold-italicH}_{eff} \\ - \frac{α γ}{M_{normals}} false[bold-italicM \times false(bold-italicM \times H_{normaleff} false) false] \end{matrix}

where H eff is the effective magnetic field on one nanomagnet, accordingly [28]

H_{normaleff} = - \frac{1}{μ_{0} V} \frac{d E}{d M} + H_{normalthermal}

In (1) and (2), M s is the saturation magnetisation of the magnetostrictive layer, μ 0 is the permeability of vacuum, γ is the gyromagnetic ratio, V is the volume of the nanomagnet, α is the Gilbert damping factor. The total energy of any element due to the shape anisotropy, stress anisotropy and dipole coupling energy with the neighbour nanomagnet is given as [18]

E = E_{normaldipole} + E_{normalshape} + E_{normalstress}

Let θ be the polar angle and φ is the azimuthal angle of the magnetisation vector (see Fig.…”

Section: Modelling Of Majority Gatementioning

confidence: 99%

Characteristics of signal propagation in multiferroic majority logic gates subjected to thermal noise

Wei

Cai

Liu

et al. 2018

Micro & Nano Letters

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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.

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“…[7] studied room-temperature error probabilities in dipole-coupled NML logic clocked with magnetic fields instead of strain and found them to be impractically high (> 1%). We showed that SML with intermagnet dipole-coupling is similarly error prone [8] owing to the out-of-plane excursion of the magnetization vector during switching that produces a detrimental torque which hinders correct switching [9]. Here, we will address the question of improving the reliability of dipole-coupled SML by making information transfer between two multiferroic nanomagnets (NMs) interacting via dipole coupling more robust.…”

Section: Introductionmentioning

confidence: 99%

Reducing error rates in straintronic multiferroic nanomagnetic logic by pulse shaping

Munira¹,

Xie²,

Nadri³

et al. 2015

Nanotechnology

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Dipole-coupled nanomagnetic logic (NML), where nanomagnets (NMs) with bistable magnetization states act as binary switches and information is transferred between them via dipole-coupling and Bennett clocking, is a potential replacement for conventional transistor logic since magnets dissipate less energy than transistors when they switch in a logic circuit. Magnets are also 'non-volatile' and hence can store the results of a computation after the computation is over, thereby doubling as both logic and memory-a feat that transistors cannot achieve. However, dipole-coupled NML is much more error-prone than transistor logic at room temperature [Formula: see text] because thermal noise can easily disrupt magnetization dynamics. Here, we study a particularly energy-efficient version of dipole-coupled NML known as straintronic multiferroic logic (SML) where magnets are clocked/switched with electrically generated mechanical strain. By appropriately 'shaping' the voltage pulse that generates strain, we show that the error rate in SML can be reduced to tolerable limits. We describe the error probabilities associated with various stress pulse shapes and discuss the trade-off between error rate and switching speed in SML.The lowest error probability is obtained when a 'shaped' high voltage pulse is applied to strain the output NM followed by a low voltage pulse. The high voltage pulse quickly rotates the output magnet's magnetization by 90° and aligns it roughly along the minor (or hard) axis of the NM. Next, the low voltage pulse produces the critical strain to overcome the shape anisotropy energy barrier in the NM and produce a monostable potential energy profile in the presence of dipole coupling from the neighboring NM. The magnetization of the output NM then migrates to the global energy minimum in this monostable profile and completes a 180° rotation (magnetization flip) with high likelihood.

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Switching of Dipole Coupled Multiferroic Nanomagnets in the Presence of Thermal Noise: Reliability of Nanomagnetic Logic

Cited by 43 publications

References 27 publications

Magnetoelectric Memory Based on Ferromagnetic/Ferroelectric Multiferroic Heterostructure

Magnetoelectric Memory Based on Ferromagnetic/Ferroelectric Multiferroic Heterostructure

Characteristics of signal propagation in multiferroic majority logic gates subjected to thermal noise

Reducing error rates in straintronic multiferroic nanomagnetic logic by pulse shaping

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