Kuntal Roy

Hybrid spintronics and straintronics: A magnetic technology for ultra low energy computing and signal processing

The authors show that the magnetization of a 2-phase magnetostrictive/piezoelectric multiferroic single-domain shape-anisotropic nanomagnet can be switched with very small voltages that generate strain in the magnetostrictive layer. This can be the basis of ultralow power computing and signal processing. With appropriate material choice, the energy dissipated per switching event can be reduced to ∼45 kT at room temperature for a switching delay of ∼100 ns and ∼70 kT for a switching delay of ∼10 ns, if the energy barrier separating the two stable magnetization directions is ∼32 kT. Such devices can be powered by harvesting energy exclusively from the environment without the need for a battery.

Energy dissipation and switching delay in stress-induced switching of multiferroic nanomagnets in the presence of thermal fluctuations

Switching the magnetization of a shape-anisotropic 2-phase multiferroic nanomagnet with voltage-generated stress is known to dissipate very little energy (<1 aJ for a switching time of ∼0.5 ns) at 0 K temperature. Here, we show by solving the stochastic Landau-Lifshitz-Gilbert equation that switching can be carried out with ∼100% probability in less than 1 ns while dissipating less than 1.5 aJ at room temperature. This makes nanomagnetic logic and memory systems, predicated on stress-induced magnetic reversal, one of the most energy-efficient computing hardware extant. We also study the dependence of energy dissipation, switching delay, and the critical stress needed to switch, on the rate at which stress on the nanomagnet is ramped up or down.

Magnetization dynamics, Bennett clocking and associated energy dissipation in multiferroic logic

It has been recently shown that the magnetization of a multiferroic nanomagnet, consisting of a magnetostrictive layer elastically coupled to a piezoelectric layer, can be rotated by a large angle if a tiny voltage of a few tens of millivolts is applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by ~90° to implement Bennett clocking in nanomagnetic logic chains. Because of the small voltage needed, this clocking method is far more energy efficient than those that would employ spin transfer torque or magnetic fields to rotate the magnetization. In order to assess if such a clocking scheme can also be reasonably fast, we have studied the magnetization dynamics of a multiferroic logic chain with nearest-neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We find that clock rates of 2.5 GHz are feasible while still maintaining the exceptionally high energy efficiency. For this clock rate, the energy dissipated per clock cycle per bit flip is ~52,000 kT at room temperature in the clocking circuit for properly designed nanomagnets. Had we used spin transfer torque to clock at the same rate, the energy dissipated per clock cycle per bit flip would have been ~4 x 10⁸ kT, while with current transistor technology we would have expended ~10⁶ kT. For slower clock rates of 1 GHz, stress-based clocking will dissipate only ~200 kT of energy per clock cycle per bit flip, while spin transfer torque would dissipate about 10⁸ kT. This shows that multiferroic nanomagnetic logic, clocked with voltage-generated stress, can emerge as a very attractive technique for computing and signal processing since it can be several orders of magnitude more energy efficient than current technologies.

Switching dynamics of a magnetostrictive single-domain nanomagnet subjected to stress

The temporal evolution of the magnetization vector of a single-domain magnetostrictive nanomagnet, subjected to in-plane stress, is studied by solving the Landau-Lifshitz-Gilbert equation. The stress is ramped up linearly in time and the switching delay, which is the time it takes for the magnetization to flip, is computed as a function of the ramp rate. For high levels of stress, the delay exhibits a non-monotonic dependence on the ramp rate, indicating that there is an {\it optimum} ramp rate to achieve the shortest delay. For constant ramp rate, the delay initially decreases with increasing stress but then saturates showing that the trade-off between the delay and the stress (or the energy dissipated in switching) becomes less and less favorable with increasing stress. All of these features are due to a complex interplay between the in-plane and out-of-plane dynamics of the magnetization vector induced by stress.

Ultra-low-energy non-volatile straintronic computing using single multiferroic composites

The primary impediment to continued downscaling of traditional charge-based electronic devices in accordance with Moores law is the excessive energy dissipation that takes place in the device during switching of bits. One very promising solution is to utilize multiferroic heterostructures, comprised of a single-domain magnetostrictive nanomagnet strain-coupled to a piezoelectric layer, in which the magnetization can be switched between its two stable states while dissipating minuscule amount of energy. However, no efficient and viable means of computing is proposed so far. Here we show that such single multiferroic composites can act as universal logic gates for computing purposes, which we demonstrate by solving the stochastic Landau-Lifshitz-Gilbert (LLG) equation of magnetization dynamics in the presence of room-temperature thermal fluctuations. The proposed concept can overwhelmingly simplify the design of large-scale circuits and portend a highly dense yet an ultra-low-energy computing paradigm for our future information processing systems.

Critical analysis and remedy of switching failures in straintronic logic using Bennett clocking in the presence of thermal fluctuations

Straintronic logic is a promising platform for beyond Moores law computing. Using Bennett clocking mechanism, information can propagate through an array of strain-mediated multiferroic nanomagnets, exploiting the dipolar coupling between the magnets without having to physically interconnect them. Here, we perform a critical analysis of switching failures, i.e., error in information propagation due to thermal fluctuations through a chain of such straintronic devices. We solved stochastic Landau-Lifshitz-Gilbert equation considering room-temperature thermal perturbations and show that magnetization switching may fail due to inherent magnetization dynamics accompanied by thermally broadened switching delay distribution. Avenues available to circumvent such issue are proposed.

ULTRA-LOW-ENERGY STRAINTRONICS USING MULTIFERROIC COMPOSITES

This paper reviews the recent developments on building nanoelectronics for our future information processing paradigm using multiferroic composites. With appropriate choice of materials, when a tiny voltage of few tens of millivolts is applied across a multiferroic composite, i.e., a piezoelectric layer stain-coupled with a magnetostrictive layer, the piezoelectric layer gets strained and the generated stress in the magnetostrictive layer switches the magnetization direction between its two stable states. We particularly review the switching dynamics of magnetization and calculation of associated metrics like switching delay and energy dissipation. Such voltage-induced magnetization switching mechanism dissipates a minuscule amount of energy of only ~ 1 attojoule in sub-nanosecond switching delay at room-temperature. The performance metrics for such nonvolatile straintronic devices make them very attractive for building not only memory devices but also building logic, so that they can be deemed suitable for computational purposes. Hence, multiferroic straintronics has profound promise of contributing to beyond Moores law technology, i.e., of being possible replacement of conventional charge-based electronics, which is reaching its performance limit specifically due to excessive energy dissipation.

Electric field-induced magnetization switching in interface-coupled multiferroic heterostructures: a highly-dense, non-volatile, and ultra-low-energy computing paradigm

Electric field-induced magnetization switching in multiferroic magnetoelectric devices is promising for computing purposes in beyond Moores law era. We show here that interface-coupled multiferroic heterostructures, i.e., a ferroelectric layer coupled with a ferromagnetic layer, are particularly suitable for highly-dense, non-volatile, and ultra-low-energy computing. By solving the stochastic Landau–Lifshitz–Gilbert equation of magnetization dynamics in the presence of room-temperature thermal fluctuations, we demonstrate that error-resilient switching of magnetization is possible with a sub-nanosecond delay while expending only a minuscule amount of energy, of ~1 attojoule. Such devices can be operated by drawing energy from the environment without the need for an external battery.

Separating read and write units in multiferroic devices.

Strain-mediated multiferroic composites, i.e., piezoelectric-magnetostrictive heterostructures, hold profound promise for energy-efficient computing in beyond Moore’s law era. While reading a bit of information stored in the magnetostrictive nanomagnets using a magnetic tunnel junction (MTJ), a material selection issue crops up since magnetostrictive materials in general cannot be utilized as the free layer of the MTJ. This is an important issue since we need to achieve a high magnetoresistance for technological applications. We show here that magnetically coupling the magnetostrictive nanomagnet and the free layer e.g., utilizing the magnetic dipole coupling between them can circumvent this issue. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics in the presence of room-temperature thermal fluctuations, we show that such design can eventually lead to a superior energy-delay product.

Ultra-low-energy computing paradigm using giant spin Hall devices

Spin Hall effect converts charge current to spin current, which can exert spin-torque to switch the magnetization of a nanomagnet. Recently, it is shown that the ratio of spin current to charge current using spin Hall effect can be made more than unity by using the areal geometry judiciously, unlike the case of conventional spin-transfer-torque switching of nanomagnets. This can enable energy-efficient means to write a bit of information in nanomagnets. Here, we study the energy dissipation in such spin Hall devices. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics in the presence of room temperature thermal fluctuations, we show a methodology to simultaneously reduce switching delay, its variance and energy dissipation, while lateral dimensions of the spin Hall devices are scaled down.