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Supriyo Bandyopadhyay

Publications and source records attributed to Supriyo Bandyopadhyay.

90 records · Page 5Linked to original sources
arXiv2011

Energy dissipation and switching delay in stress-induced switching of multiferroic devices 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 $\sim$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 $\sim$100% probability in less than 1 ns while dissipating less than 2 aJ at {\it 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 is ramped up or down.

cond-mat.mes-hall↗
arXiv2011

An ultrafast image recovery and recognition system implemented with nanomagnets possessing biaxial magnetocrystalline anisotropy

A circular magnetic disk with biaxial magnetocrystalline anisotropy has four stable magnetization states which can be used to encode a pixel's shade in a black/gray/white image. By solving the Landau-Lifshitz- Gilbert equation, we show that if moderate noise deflects the magnetization slightly from a stable state, it always returns to the original state, thereby automatically de-noising the corrupted image. The same system can compare a noisy input image with a stored image and make a matching decision using magneto-tunneling junctions. These tasks are executed at ultrahigh speeds (~2 ns for a 512\times512 pixel image).

cond-mat.mes-hall↗
arXiv2011

Magnetization Dynamics, Throughput and Energy Dissipation in a Universal Multiferroic Nanomagnetic Logic Gate with Fan-in and Fan-out

The switching dynamics of a multiferroic nanomagnetic NAND gate with fan-in/fan-out is simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation while neglecting thermal fluctuation effects. The gate and logic wires are implemented with dipole-coupled 2-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of ~50 mV applied to the piezoelectric layer generating 10 MPa stress in the magnetostrictive layers for switching. We show that a pipeline bit throughput rate of ~ 0.5 GHz is achievable with proper magnet layout and sinusoidal four-phase clocking. The gate operation is completed in 2 ns with a latency of 4 ns. The total (internal + external) energy dissipated for a single gate operation at this throughput rate is found to be only ~ 1000 kT in the gate and ~3000 kT in the 12-magnet array comprising two input and two output wires for fan-in and fan-out. This makes it respectively 3 and 5 orders of magnitude more energy-efficient than complementary-metal-oxide-semiconductor-transistor (CMOS) based and spin-transfer-torque-driven nanomagnet based NAND gates. Finally, we show that the dissipation in the external clocking circuit can always be reduced asymptotically to zero using increasingly slow adiabatic clocking, such as by designing the RC time constant to be 3 orders of magnitude smaller than the clocking period. However, the internal dissipation in the device must remain and cannot be eliminated if we want to perform fault-tolerant classical computing. Keywords: Nanomagnetic logic, multiferroics, straintronics and spintronics, Landau-Lifshitz-Gilbert equation.

cond-mat.mes-hall↗
arXiv2011

Magnetization Dynamics, Bennett Clocking and Associated Energy Dissipation in Multiferroic Logic

It has been recently shown that multiferroic logic - where logic bits are encoded in the magnetization orientation of a nanoscale magnetostrictive layer elastically coupled to a piezoelectric layer - can be Bennett clocked with small electrostatic potentials of few tens of mV applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by a large angle to carry out Bennett clocking. This method of clocking is far more energy-efficient than using spin transfer torque. In order to assess if such a clocking scheme can be also reasonably fast, we have studied the magnetization dynamics of a multiferroic logic array with nearest neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We find that switching delays of ~ 3 ns (clock rates of 0.33 GHz) can be achieved with proper design provided we clock non-adiabatically and dissipate ~48,000 kT (at room temperature) of energy per clock cycle per bit flip in the clocking circuit. This dissipation far exceeds the energy barrier separating the two logic states, which we assumed to be 32 kT to yield a bit error probability of . Had we used spin transfer torque to switch with the same ~ 3 ns delay, the energy dissipation would have been much larger (~ $6 \times 106$ kT). This shows that spin transfer torque, widely used in magnetic random access memory, is an inefficient way to switch a magnet, and multiferroic logic clocked with voltage-induced stress is a superior nanomagnetic logic scheme.

cond-mat.mes-hall↗
arXiv2011

An Energy-Efficient Bennett Clocking Scheme for 4-State Multiferroic Logic

Nanomagnets with biaxial magnetocrystalline anisotropy have four stable magnetization orientations that can encode 4-state logic bits (00), (01), (11) and (10). Recently, a 4-state NOR gate derived from three such nanomagnets, interacting via dipole interaction, was proposed. Here, we devise a Bennett clocking scheme to propagate 4-state logic bits unidirectionally between such gates. The nanomagnets are assumed to be made of 2-phase strain-coupled magnetostrictive/piezoelectric multiferroic elements, such as nickel and lead zirconate titanate (PZT). A small voltage of 200 mV applied across the piezoelectric layer can generate enough mechanical stress in the magnetostrictive layer to rotate its magnetization away from one of the four stable orientations and implement Bennett clocking. We show that a particular sequence of positive and negative voltages will propagate 4-state logic bits unidirectionally down a chain of such multiferroic nanomagnets for logic flow.

cond-mat.mes-hall↗
arXiv2011

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.

cond-mat.mes-hall↗
arXiv2011

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

The authors show that the magnetization of a 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 $\sim$45 $kT$ at room temperature for a switching delay of $\sim$100 ns and $\sim$70 $kT$ for a switching delay of $\sim$10 ns, if the energy barrier separating the two stable magnetization directions is $\sim$32 $kT$. Such devices can be powered by harvesting energy exclusively from the environment without the need for a battery.

cond-mat.mes-hall↗
arXiv2011

Four-state nanomagnetic logic using multiferroics

The authors show how to implement a 4-state universal logic gate (NOR) using three strain-coupled magnetostrictive-piezoelectric multiferroic nanomagnets (e.g. Ni/PZT) with biaxial magnetocrystalline anisotropy. Two of the nanomagnets encode the 2-state input bits in their magnetization orientations and the third nanomagnet produces the output bit via dipole interaction with the input nanomagnets. A voltage pulse alternating between -0.2 V and +0.2 V is applied to the PZT layer of the third nanomagnet and generates alternating tensile and compressive stress in its Ni layer to produce the output bit, while dissipating ~ 57,000 kT (0.24 fJ) of energy per gate operation.

cond-mat.mes-hall↗
arXiv2010

Energy-efficient mixed mode switching of a multiferroic nanomagnet for logic and memory

In magnetic memory and logic devices, a magnet's magnetization is usually flipped with a spin polarized current delivering a spin transfer torque (STT). This mode of switching consumes too much energy and considerable energy saving can accrue from using a multiferroic nanomagnet switched with a combination of STT and mechanical stress generated with a voltage (VGS). The VGS mode consumes less energy than STT, but cannot rotate magnetization by more than 90?, so that a combination of the two modes is needed for energy-efficient switching.

cond-mat.mes-hall↗
arXiv2010

The dominant spin relaxation mechanism in compound organic semiconductors

Despite the recent interest in "organic spintronics", the dominant spin relaxation mechanism of electrons or holes in an organic compound semiconductor has not been conclusively identified. There have been sporadic suggestions that it might be hyperfine interaction caused by background nuclear spins, but no confirmatory evidence to support this has ever been presented. Here, we report the electric-field dependence of the spin diffusion length in an organic spin-valve structure consisting of an Alq3 spacer layer, and argue that this data, as well as available data on the temperature dependence of this length, contradict the notion that hyperfine interactions relax spin. Instead, they suggest that the Elliott-Yafet mechanism, arising from spin-orbit interaction, is more likely the dominant spin relaxing mechanism.

cond-mat.mes-hall↗
arXiv2009

Comment on "Control of Spin Precession in a Spin-Injected Field Effect Transistor" [Science, 325, 1515 (2009)]

A recently published report in the journal Science claims that the Datta-Das Spin Field Effect Transistor has been demonstrated because an exact agreement was found between the voltage modulation in a fabricated structure and a theoretical equation that supposedly describes the voltage modulation of the Datta-Das Transistor. Here, I show that the said theoretical equation holds only for a one-dimensional transistor, or perhaps a quasi one-dimensional transistor, and is certainly not applicable to the two-dimensional transistor studied. Hence, the exact agreement is meaningless and does not substantiate the claim.

cond-mat.mes-hall↗
arXiv2009

Electron Spin for Classical Information Processing: A Brief Survey of Spin-Based Logic Devices, Gates and Circuits

In electronics, information has been traditionally stored, processed and communicated using an electron's charge. This paradigm is increasingly turning out to be energy-inefficient, because movement of charge within an information-processing device invariably causes current flow and an associated dissipation. Replacing charge with the "spin" of an electron to encode information may eliminate much of this dissipation and lead to more energy-efficient "green electronics". This realization has spurred significant research in spintronic devices and circuits where spin either directly acts as the physical variable for hosting information or augments the role of charge. In this review article, we discuss and elucidate some of these ideas, and highlight their strengths and weaknesses. Many of them can potentially reduce energy dissipation significantly, but unfortunately are error-prone and unreliable. Moreover, there are serious obstacles to their technological implementation that may be difficult to overcome in the near term. This review addresses three constructs: (1) single devices or binary switches that can be constituents of Boolean logic gates for digital information processing, (2) complete gates that are capable of performing specific Boolean logic operations, and (3) combinational circuits or architectures (equivalent to many gates working in unison) that are capable of performing universal computation.

cond-mat.mes-hall↗
arXiv2006

Spin relaxation of "upstream" electrons in quantum wires: Failure of the drift diffusion model

The classical drift diffusion (DD) model of spin transport treats spin relaxation via an empirical parameter known as the ``spin diffusion length''. According to this model, the ensemble averaged spin of electrons drifting and diffusing in a solid decays exponentially with distance due to spin dephasing interactions. The characteristic length scale associated with this decay is the spin diffusion length. The DD model also predicts that this length is different for ``upstream'' electrons traveling in a decelerating electric field than for ``downstream'' electrons traveling in an accelerating field. However this picture ignores energy quantization in confined systems (e.g. quantum wires) and therefore fails to capture the non-trivial influence of subband structure on spin relaxation. Here we highlight this influence by simulating upstream spin transport in a multi-subband quantum wire, in the presence of D'yakonov-Perel' spin relaxation, using a semi-classical model that accounts for the subband structure rigorously. We find that upstream spin transport has a complex dynamics that defies the simplistic definition of a ``spin diffusion length''. In fact, spin does not decay exponentially or even monotonically with distance, and the drift diffusion picture fails to explain the qualitative behavior, let alone predict quantitative features accurately. Unrelated to spin transport, we also find that upstream electrons undergo a ``population inversion'' as a consequence of the energy dependence of the density of states in a quasi one-dimensional structure.

cond-mat.mes-hall↗
arXiv2005

Spin relaxation of "upstream" electrons: beyond the drift diffusion model

The classical drift diffusion (DD) model of spin transport treats spin relaxation via an empirical parameter known as the ``spin diffusion length''. According to this model, the ensemble averaged spin of electrons drifting and diffusing in a solid decays exponentially with distance due to spin dephasing interactions. The characteristic length scale associated with this decay is the spin diffusion length. The DD model also predicts that this length is different for ``upstream'' electrons traveling in a decelerating electric field than for ``downstream'' electrons traveling in an accelerating field. However this picture ignores energy quantization in confined systems (e.g. quantum wires) and therefore fails to capture the non-trivial influence of subband structure on spin relaxation. Here we highlight this influence by simulating upstream spin transport in a multi-subband quantum wire, in the presence of D'yakonov-Perel' spin relaxation, using a semi-classical model that accounts for the subband structure rigorously. We find that upstream spin transport has a complex dynamics that defies the simplistic definition of a ``spin diffusion length''. In fact, spin does not decay exponentially or even monotonically with distance, and the drift diffusion picture fails to explain the qualitative behavior, let alone predict quantitative features accurately. Unrelated to spin transport, we also find that upstream electrons undergo a ``population inversion'' as a consequence of the energy dependence of the density of states in a quasi one-dimensional structure.

cond-mat.mes-hall↗
arXiv2005

Spin transport in self assembled all-metal nanowire spin valves: A study of the pure Elliott-Yafet mechanism

We report experimental study of spin transport in all-metal nanowire spin valve structures. The nanowires have a diameter of 50 nm and consist of three layers - cobalt, copper and nickel. Based on the experimental observations, we conclude that the primary spin relxation mechanism in the paramagnet copper is the Elliott-Yafet mode associated with frequent interface roughness scattering. This mode is overwhelmingly dominant over all other modes, so that we are able to study the pure Elliott-Yafet mode in isolation. We deduce that the effective spin relaxation length associated with this mechanism is about 16 nm in our nanowires and is fairly independent of temperature in the range 1 - 100 K. The corresponding spin relaxation time is about 100 femtoseconds. We also find that the spin relaxation length or time is fairly independent of the electric field driving the current in the range 0.75 - 7.5 kV/cm.

cond-mat.mes-hall↗
arXiv2005

Can the interface between a non-ideal ferromagnet and a semiconductor quantum wire acts as an ideal spin filter?

The problem of spin injection across the interface between a non-ideal ferromagnet (less than 100% spin polarization) and a semiconductor (paramagnetic) quantum wire is examined in the presence of Rashba spin orbit coupling and an axial magnetic field along the wire axis. The field is caused by the ferromagnet magnetized along the wire axis. At low temperatures and for certain injection energies, the interface can act as an ideal spin filter allowing injection only from the majority spin band of the ferromagnet. Thus, 100% spin filtering can take place even if the ferromagnet itself is less than 100% spin polarized. Below a critical value of the magnetic field, there are two injection energies for which ideal (100%) spin filtering is possible; above this critical field, there is only one such injection energy.

cond-mat.mes-hall↗
arXiv2000

A Self Assembled Nanoelectronic Quantum Computer Based on the Rashba Effect in Quantum Dots

Quantum computers promise vastly enhanced computational power and an uncanny ability to solve classically intractable problems. However, few proposals exist for robust, solid state implementation of such computers where the quantum gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I present a new approach whereby a complete computer with nanoscale gates might be self-assembled using chemical synthesis. Specifically, I demonstrate how to self-assemble the fundamental unit of this quantum computer - a 2-qubit universal quantum controlled-NOT gate - based on two exchange coupled multilayered quantum dots. Then I show how these gates can be wired using thiolated conjugated molecules as electrical connectors. A qubit is encoded in the ground state of a quantum dot spin-split by the Rashba interaction. Arbitrary qubit rotations are effected by bringing the spin splitting energy in a target quantum dot in resonance with a global ac magnetic field by applying a potential pulse of appropriate amplitude and duration to the dot. The controlled dynamics of the 2-qubit controlled-NOT operation (XOR) can be realized by exploiting the exchange coupling with the nearest neighboring dot. A complete prescription for initialization of the computer and data input/output operations is presented.

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