First order devices, hybrid memristors, and the frontiers of nonlinear circuit theory

Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices seem to be beyond the, say, classical scope of circuit theory, which is formulated in terms of resistors, capacitors, inductors, and voltage and current sources. We explore in this paper the potential extent of nonlinear circuit theory by classifying such mem-devices in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. Within this framework, the frontier of first order circuit theory is defined by so-called hybrid memristors, which are proposed here to accommodate a characteristic relating all four fundamental circuit variables. Devices with differential order two and mem-systems are discussed in less detail. We allow for fully nonlinear characteristics in all circuit elements, arriving at a rather exhaustive taxonomy of C^1-devices. Additionally, we extend the notion of a topologically degenerate configuration to circuits with memcapacitors, meminductors and all types of memristors, and characterize the differential-algebraic index of nodal models of such circuits.Comment: Published in 2013. Journal reference included as a footnote in the first pag

Dynamical properties of electrical circuits with fully nonlinear memristors

The recent design of a nanoscale device with a memristive characteristic has had a great impact in nonlinear circuit theory. Such a device, whose existence was predicted by Leon Chua in 1971, is governed by a charge-dependent voltage-current relation of the form $v=M(q)i$. In this paper we show that allowing for a fully nonlinear characteristic $v=\eta(q, i)$ in memristive devices provides a general framework for modeling and analyzing a very broad family of electrical and electronic circuits; Chua's memristors are particular instances in which $\eta(q,i)$ is linear in $i$. We examine several dynamical features of circuits with fully nonlinear memristors, accommodating not only charge-controlled but also flux-controlled ones, with a characteristic of the form $i=\zeta(\varphi, v)$. Our results apply in particular to Chua's memristive circuits; certain properties of these can be seen as a consequence of the special form of the elastance and reluctance matrices displayed by Chua's memristors.Comment: 19 page

The tractability index of memristive circuits: branch-oriented and tree-based models

The memory-resistor or memristor is a new electrical element characterized by a nonlinear charge-flux relation. This device poses many challenging problems, in particular from the circuit modeling point of view. In this paper we address the index analysis of certain differential-algebraic models of memristive circuits; specifically, our attention is focused on so-called branch-oriented models, which include in particular tree-based formulations of the circuit equations. Our approach combines results coming from DAE theory, matrix analysis and the theory of digraphs. This framework should be useful in future studies of dynamical aspects of memristive circuits

Spintronic device modeling and evaluation using modular approach to spintronics

Spintronics technology finds itself in an exciting stage today. Riding on the backs of rapid growth and impressive advances in materials and phenomena, it has started to make headway in the memory industry as solid state magnetic memories (STT-MRAM) and is considered a possible candidate to replace the CMOS when its scaling reaches physical limits. It is necessary to bring all these advances together in a coherent fashion to explore and evaluate the potential of spintronic devices. This work creates a framework for this exploration and evaluation based on Modular Approach to Spintronics, which encapsulate the physics of transport of charge and spin through materials and the phenomenology of magnetic dynamics and interaction in benchmarked elemental modules. These modules can then be combined together to form spin-circuit models of complex spintronic devices and structures which can be simulated using SPICE like circuit simulators. In this work we demonstrate how Modular Approach to Spintronics can be used to build spin-circuit models of functional spintronic devices of all types: memory, logic, and oscillators. We then show how Modular Approach to Spintronics can help identify critical factors behind static and dynamic dissipation in spintronic devices and provide remedies by exploring the use of various alternative materials and phenomena. Lastly, we show the use of Modular Approach to Spintronics in exploring new paradigms of computing enabled by the inherent physics of spintronic devices. We hope that this work will encourage more research and experiments that will establish spintronics as a viable technology for continued advancement of electronics

Skyrmion lattice hosted in synthetic antiferromagnets and helix modes

Thin ferromagnetic films can possess unconventional magnetic properties, opening a new road for using them in spintronic technologies. In the present work exploiting three different methods, we comprehensively analyze phason excitations of a skyrmion lattice in synthetic antiferromagnets. To analyze phason excitations of the skyrmion lattice, we have constructed an analytical model based on three coupled helices and found a linear gapless mode. Micromagnetic simulations also support this result. Moreover, a similar result has been achieved within the rigid skyrmion lattice model based on the coupled Thiele's equations, when the coupling between skyrmions in different layers of the synthetic antiferromagnetic is comparable to or larger than the intralayer coupling. In addition, we also consider the orbital angular momentum and spin pumping current associated with phason excitations. Due to the gapless excitations in the case of skyrmion lattice, the pumping current is nonzero for the arbitrary frequency of pumping microwaves. In the case of individual skyrmions, no current is pumped when microwave frequency is inside the gap of the spectrum of individual skyrmions.Comment: 12 pages, 8 figures, accepted in Phys. Rev.

Excitation of picosecond magnetisation dynamics by spin transfer torque

\chapter*{Abstract} This thesis presents the results from investigations of ultrafast magnetisation dynamics driven by pure spin currents. Spin orbit coupling in heavy metal layers - such as tungsten, tantalum or platinum - allows for the generation of pure spin currents, whereby spin up and spin down electrons move in opposite directions. Hence, a flow of angular momentum can be controlled through the manipulation of charge current through a heavy metal layer. When a spin current is injected into a ferromagnet, a torque is exerted on its magnetisation, with the potential to induce a wide variety of ultrafast dynamics. The experimental investigation of these phenomena employed a variety of high-frequency electrical techniques and time-resolved scanning Kerr microscopy (TRSKM) methods. In addition, various simulative and analytical approaches were used to gain insight into the underlying mechanisms. Spin Hall nano-oscillators (SHNOs) have recently been shown to support a tunable GHz spin wave `bullet’ under injection of direct current (DC), making it an exciting candidate for microwave communication applications. This thesis will show how TRKSM can be used to measure the torques within these devices, revealing that radio frequency (RF) current does not possess the same distribution as the DC. The competition between self-inductance and focusing within the device geometry results in a modified distribution of spin current. Further TRSKM measurements show the modified torque landscape to promote the mobility of the `bullet' within the magnetic layer. Devices that exploit spin currents for magnetisation reversal have received interest from academia and industry for their potential use as memory elements. The perpendicular magnetic anisotropy present in Ta/CoFeB/MgO leads to lower write currents and higher thermal stability. However, ultrafast processes have not been previously observed in such devices. TRSKM measurements of Hall bar devices were compared with a macrospin model to understand the underlying torques, and to investigate the conditions required to promote switching. Square elements built from the same stack structure exhibited contrasting static and dynamic behaviour. Pulsed currents drove differing dynamics at the edge and center of the device, while enabling the realignment of magnetic domains. The domains themselves could be driven directly by the spin current leading to domain wall dynamics. Measurements with a bipolar electrical pulse demonstrated that meta-stable switching can be achieved in micron-scale elements