Electric field control of fixed magnetic Skyrmions for energy efficient nanomagnetic memory

To meet the ever-growing demand of faster and smaller computers, increasing number of transistors are needed in the same chip area. Unfortunately, Silicon based transistors have almost reached their miniaturization limits mainly due to excessive heat generation. Nanomagnetic devices are one of the most promising alternatives of CMOS. In nanomagnetic devices, electron spin, instead of charge, is the information carrier. Hence, these devices are non-volatile: information can be stored in these devices without needing any external power which could enable computing architectures beyond traditional von-Neumann computing. Additionally, these devices are also expected to be more energy efficient than CMOS devices as their operation does not involve translation of charge across the device. However, the energy dissipated in the clocking circuitry negates this perceived advantage and in practice CMOS devices still consume three orders of magnitudes less energy. Therefore, researchers have been looking for nanomagnetic devices that could be energy efficient in addition to being non-volatile which has led to the exploration of several switching strategies. Among those, electric field induced switching has proved to be a promising route towards scalable ultra-low power computing devices. Particularly Voltage Control of Magnetic Anisotropy (VCMA) based switching dissipates ~1 fJ energy. However, incoherence due to thermal noise and material inhomogeneity renders this switching error-prone. This dissertation is devoted towards studying VCMA induced switching of a spin spiral magnetic state, magnetic skyrmions, which can potentially alleviate this issue. Magnetic skyrmions has recently emerged as a viable candidate to be used in room temperature nanomagnetic devices. Most of the studies propose to utilize skyrmion motion in a magnetic track to implement memory devices. However, Magnetic Tunnel Junction (MTJ) devices based on skyrmions that are fixed in space might be advantageous in terms of footprint. To establish a new computing paradigm based on electrical manipulation of magnetization of fixed magnetic skyrmions we have studied: i) Purely VCMA induced reversal of magnetic skyrmions using extensive micromagnetic simulations. This shows sequential increase and decrease of Perpendicular Magnetic Anisotropy (PMA) can result into toggling between skyrmionic and ferromagnetic states. We also demonstrate VCMA assisted Spin Transfer Torque (STT) induced reversal of magnetic skyrmions. ii) Complete reversal of ferromagnets mediated by intermediated skyrmion state using rigorous micromagnetic simulation. We show that the switching can be robust by limiting the “phase space” of the magnetization dynamics through a controlled skyrmion state. Thus, the switching error can be lowered compared to conventional VCMA switching. iii) Finally, we perform preliminary experiments on VCMA induced manipulation of skyrmions. We demonstrate that skyrmions can be annihilated when Perpendicular Magnetic Anisotropy of the system is increased by applying a negative voltage pulse and can be recreated by decreasing PMA by applying a positive voltage pulse. The experimental observations are corroborated using micromagnetic simulation. Future research should focus on demonstrating reversal of skyrmions experimentally in MTJ like devices and study the downscaling of the proposed device. These can enable realization of energy efficient and robust nanomagnetic memory devices based on voltage control switching of fixed magnetic skyrmions as wells as other neuromorphic computing devices

Distortions, Endogenous Managerial Skills and Productivity Differences

We develop a span-of-control model where managerial skills are endogenous and the outcome of investments over the life cycle of managers. We calibrate this model to U.S plant-size data to quantify the effects of distortions that are correlated with the size of production units. These distortions lead to sharp reductions in plant productivity and the fraction of employment in large plants, with a quantitatively important role for managerial investments. We find that the model can account quite well for properties of Japanese size-distribution data, with a model-implied TFP of about 83% of the U.S. Distortions are critical in accounting for the differences in size distribution between the U.S. and Japan.distortions, size, skill investments, productivity differences

Resonate and Fire Neuron with Fixed Magnetic Skyrmions

In the brain, the membrane potential of many neurons oscillates in a subthreshold damped fashion and fire when excited by an input frequency that nearly equals their eigen frequency. In this work, we investigate theoretically the artificial implementation of such "resonate-and-fire" neurons by utilizing the magnetization dynamics of a fixed magnetic skyrmion in the free layer of a magnetic tunnel junction (MTJ). To realize firing of this nanomagnetic implementation of an artificial neuron, we propose to employ voltage control of magnetic anisotropy or voltage generated strain as an input (spike or sinusoidal) signal, which modulates the perpendicular magnetic anisotropy (PMA). This results in continual expansion and shrinking (i.e. breathing) of a skyrmion core that mimics the subthreshold oscillation. Any subsequent input pulse having an interval close to the breathing period or a sinusoidal input close to the eigen frequency drives the magnetization dynamics of the fixed skyrmion in a resonant manner. The time varying electrical resistance of the MTJ layer due to this resonant oscillation of the skyrmion core is used to drive a Complementary Metal Oxide Semiconductor (CMOS) buffer circuit, which produces spike outputs. By rigorous micromagnetic simulation, we investigate the interspike timing dependence and response to different excitatory and inhibitory incoming input pulses. Finally, we show that such resonate and fire neurons have potential application in coupled nanomagnetic oscillator based associative memory arrays