Excessive energy dissipation in CMOS devices during switching is the primary threat to continued downscaling of computing devices in accordance with Moore’s law. In the quest for alternatives to traditional transistor based electronics, nanomagnet-based computing [1, 2] is emerging as an attractive alternative since: (i) nanomagnets are intrinsically more energy-efficient than transistors due to the correlated switching of spins [3], and (ii) unlike transistors, magnets have no leakage and hence have no standby power dissipation. However, large energy dissipation in the clocking circuit appears to be a barrier to the realization of ultra low power logic devices with such nanomagnets. To alleviate this issue, we propose the use of a hybrid spintronics-straintronics or straintronic nanomagnetic logic (SML) paradigm. This uses a piezoelectric layer elastically coupled to an elliptically shaped magnetostrictive nanomagnetic layer for both logic [4-6] and memory [7-8] and other information processing [9-10] applications that could potentially be 2-3 orders of magnitude more energy efficient than current CMOS based devices. This dissertation focuses on studying the feasibility, performance and reliability of such nanomagnetic logic circuits by simulating the nanoscale magnetization dynamics of dipole coupled nanomagnets clocked by stress. Specifically, the topics addressed are: 1. Theoretical study of multiferroic nanomagnetic arrays laid out in specific geometric patterns to implement a “logic wire” for unidirectional information propagation and a universal logic gate [4-6]. 2. Monte Carlo simulations of the magnetization trajectories in a simple system of dipole coupled nanomagnets and NAND gate described by the Landau-Lifshitz-Gilbert (LLG) equations simulated in the presence of random thermal noise to understand the dynamics switching error [11, 12] in such devices. 3. Arriving at a lower bound for energy dissipation as a function of switching error [13] for a practical nanomagnetic logic scheme. 4. Clocking of nanomagnetic logic with surface acoustic waves (SAW) to drastically decrease the lithographic burden needed to contact each multiferroic nanomagnet while maintaining pipelined information processing. 5. Nanomagnets with four (or higher states) implemented with shape engineering. Two types of magnet that encode four states: (i) diamond, and (ii) concave nanomagnets are studied for coherence of the switching process.

Since its inception, Moore's Law has been a reliable predictor of computational power. This steady increase in computational power has been due to the ability to fit increasing numbers of transistors in a single chip. A consequence of increasing the number of transistors is also increasing the power consumption. The physical properties of CMOS technologies will make this powerwall unavoidable and will result in severe restrictions to future progress and applications. A potential solution to the problem of rising power demands is to investigate alternative low power nanotechnologies for implementing logic circuits. The intrinsic properties of these emerging nanotechnologies result in them being low power in nature when compared to current CMOS technologies. This thesis specifically highlights quantum dot celluar automata (QCA) and nanomagnetic logic (NML) as just two possible technologies. Designs in NML and QCA are explored for simple arithmetic units such as full adders and subtractors. A new multilayer 5-input majority gate design is proposed for use in NML. Designs of reversible adders are proposed which are easily testable for unidirectional stuck at faults.

A recent International Technology Roadmap for Semiconductors (ITRS) report (2.0, 2015 edition) has shown that Moore’s law is unlikely to hold beyond 2028. There is a need for alternate devices to replace CMOS based devices, if further miniaturization and high energy efficiency is desired. The goal of this dissertation is to experimentally demonstrate the feasibility of nanomagnetic memory and logic devices that can be clocked with acoustic waves in an extremely energy efficient manner. While clocking nanomagnetic logic by stressing the magnetostrictive layer of a multiferroic logic element with with an electric field applied across the piezoelectric layer is known to be an extremely energy-efficient clocking scheme, stressing every nanomagnet separately requires individual contacts to each one of them that would necessitate cumbersome lithography. On the other hand, if all nanomagnets are stressed simultaneously with a global voltage, it will eliminate the need for individual contacts, but such a global clock makes the architecture non-pipelined (the next input bit cannot be written till the previous bit has completely propagated through the chain) and therefore, unacceptably slow and error prone. Use of global acoustic wave, that has in-built granularity, would offer the best of both worlds. As the crest and the trough propagate in space with a velocity, nanomagnets that find themselves at a crest are stressed in tension while those in the trough are compressed. All other magnets are relaxed (no stress). Thus, all magnets are not stressed simultaneously but are clocked in a sequentially manner, even though the clocking agent is global. Finally, the acoustic wave energy is distributed over billions of nanomagnets it clocks, which results in an extremely small energy cost per bit per nanomagnet. In summary, acoustic clocking of nanomagnets can lead to extremely energy efficient nanomagnetic computing devices while also eliminating the need for complex lithography. The dissertation work focuses on the following two topics: Acoustic Waves, generated by IDTs fabricated on a piezoelectric lithium niobate substrate, can be utilized to manipulate the magnetization states in elliptical Co nanomagnets. The magnetization switches from its initial single-domain state to a vortex state after SAW stress cycles propagate through the nanomagnets. The vortex states are stable and the magnetization remains in this state until it is ‘reset’ by an external magnetic field. 2. Acoustic Waves can also be utilized to induce 1800 magnetization switching in dipole coupled elliptical Co nanomagnets. The magnetization switches from its initial single-domain ‘up’ state to a single-domain ‘down’ state after SAW tensile/compressive stress cycles propagate through the nanomagnets. The switched state is stable and non-volatile. These results show the effective implementation of a Boolean NOT gate. Ultimately, the advantage of this technology is that it could also perform higher order information processing (not discussed here) while consuming extremely low power. Finally, while we have demonstrated acoustically clocked nanomagnetic memory and logic schemes with Co nanomagnets, materials with higher magnetostriction (such as FeGa) may ultimately improve the switching reliability of such devices. With this in mind we prepared and studied FeGa films using a ferromagnetic resonance (FMR) technique to extract properties of importance to magnetization dynamics in such materials that could have higher magneto elastic coupling than either Co or Ni.

Even though silicon technology is dominant today, the physics (quantum electron tunneling effect), design (power dissipation, wire delays) and the manufacturing (lithography resolution) limitations of CMOS technology are pushed towards the scaling end. These issues motivated us towards a new paradigm that contributes to a continued advancement in terms of performance, density, and cost. The magnetic field coupled computing (MFC) paradigm, which is one of the regimes where we leverage and utilize the neighbor interaction of the nanomagnets to order the single-domain magnetic cells to perform computational tasks. The most important and attractive features of this technology are: 1) room temperature operation, which has been a limitation in electrostatic field coupled devices, 2) high density and nonetheless 3) low static power dissipation. It will be intriguing to address queries like, what are the challenges posed by the technology with such exotic features? Answer to such questions would become the focus of this doctoral research. The fundamental problem with magnetic field coupled devices is the directional flow of information from input to output. In this work, we have proposed a novel spatially moving Landauer clock system for MFC nanomagnet array which has an advantage over existing adiabatic clock system. Extensive simulation studies were done to model and validate the clock for different length, size, and shape of nanomagnet array. Another key challenge is the manufacturing defect, which leads to uncertainty and unreliability issues. We studied the different dominant types of geometric defects (missing material, missing cell, spacing, bulge, and merging) in array (used as interconnects) based on our fabrication experiments. We also studied effect of these defects on different segments (locations) of the array with spatially moving clock. The study concluded that a spatially moving clock scheme constitutes a robust MFC architecture as location of defect and length of arrays does not play any role in error masking as opposed to conventional clock. Finally, the work presents the study on the 2D nanomagnet array for boolean logic computation and vision logic computation. The effect of dipole-dipole interaction on magnetization state transition in closely spaced 2D array of ferromagnetic circular nanomagnet was explored. The detailed design space to demarcate the boundary between single domain state and vortex state reveals that the single domain state space is desirable for Boolean logic computation while the space around the boundary would be appropriate for vision logic computing.

Nanomagnetic logic, incorporating logic bits in the magnetization orientations of single-domain nanomagnets, has garnered attention as an alternative to transistor-based logic due to its non-volatility and unprecedented energy-efficiency. The energy efficiency of this scheme is determined by the method used to flip the magnetization orientations of the nanomagnets in response to one or more inputs and produce the desired output. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field or spin-transfer-torque inhibit the promised energy-efficiency. Another technique offering superior energy efficiency, “straintronics”, involves the application of a voltage to a piezoelectric layer to generate a strain which is transferred to an elastically coupled magnetrostrictive layer, causing magnetization rotation. The functionality of this scheme can be enhanced further by introducing magnetocrystalline anisotropy in the magnetostrictive layer, thereby generating four stable magnetization states (instead of the two stable directions produced by shape anisotropy in ellipsoidal nanomagnets). Numerical simulations were performed to implement a low-power universal logic gate (NOR) using such 4-state magnetostrictive/piezoelectric nanomagnets (Ni/PZT) by clocking the piezoelectric layer with a small electrostatic potential (~0.2 V) to switch the magnetization of the magnetic layer. Unidirectional and reliable logic propagation in this system was also demonstrated theoretically. Besides doubling the logic density (4-state versus 2-state) for logic applications, these four-state nanomagnets can be exploited for higher order applications such as image reconstruction and recognition in the presence of noise, associative memory and neuromorphic computing. Experimental work in strain-based switching has been limited to magnets that are multi-domain or magnets where strain moves domain walls. In this work, we also demonstrate strain-based switching in 2-state single-domain ellipsoidal magnetostrictive nanomagnets of lateral dimensions ~200 nm fabricated on a piezoelectric substrate (PMN-PT) and studied using Magnetic Force Microscopy (MFM). A nanomagnetic Boolean NOT gate and unidirectional bit information propagation through a finite chain of dipole-coupled nanomagnets are also shown through strain-based "clocking". This is the first experimental demonstration of strain-based switching in nanomagnets and clocking of nanomagnetic logic (Boolean NOT gate), as well as logic propagation in an array of nanomagnets.