There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

Redox‐Based Resistive Switching Memories – Nanoionic Mechanisms, Prospects, and Challenges

Recent developments in the controlled movement of domain walls in magnetic nanowires by short pulses of spin-polarized current give promise of a nonvolatile memory device with the high performance and reliability of conventional solid-state memory but at the low cost of conventional magnetic disk drive storage. The racetrack memory described in this review comprises an array of magnetic nanowires arranged horizontally or vertically on a silicon chip. Individual spintronic reading and writing nanodevices are used to modify or read a train of ∼10 to 100 domain walls, which store a series of data bits in each nanowire. This racetrack memory is an example of the move toward innately three-dimensional microelectronic devices.

http://science.sciencemag.org/content/sci/320/5873/190.full.pdf

Magnetic Domain-Wall Racetrack Memory

Memristive devices are electrical resistance switches that can retain a state of internal resistance based on the history of applied voltage and current. These devices can store and process information, and offer several key performance characteristics that exceed conventional integrated circuit technology. An important class of memristive devices are two-terminal resistance switches based on ionic motion, which are built from a simple conductor/insulator/conductor thin-film stack. These devices were originally conceived in the late 1960s and recent progress has led to fast, low-energy, high-endurance devices that can be scaled down to less than 10 nm and stacked in three dimensions. However, the underlying device mechanisms remain unclear, which is a significant barrier to their widespread application. Here, we review recent progress in the development and understanding of memristive devices. We also examine the performance requirements for computing with memristive devices and detail how the outstanding challenges could be met.

Memristive devices for computing

Nonvolatile RAM using resistance contrast in phase-change materials [or phase-change RAM (PCRAM)] is a promising technology for future storage-class memory. However, such a technology can succeed only if it can scale smaller in size, given the increasingly tiny memory cells that are projected for future technology nodes (i.e., generations). We first discuss the critical aspects that may affect the scaling of PCRAM, including materials properties, power consumption during programming and read operations, thermal cross-talk between memory cells, and failure mechanisms. We then discuss experiments that directly address the scaling properties of the phase-change materials themselves, including studies of phase transitions in both nanoparticles and ultrathin films as a function of particle size and film thickness. This work in materials directly motivated the successful creation of a series of prototype PCRAM devices, which have been fabricated and tested at phase-change material cross-sections with extremely small dimensions as low as 3 nm × 20 nm. These device measurements provide a clear demonstration of the excellent scaling potential offered by this technology, and they are also consistent with the scaling behavior predicted by extensive device simulations. Finally, we discuss issues of device integration and cell design, manufacturability, and reliability.

Phase-change random access memory: a scalable technology

Extension of nuclear magnetic resonance (NMR) to nanoscale samples has been a longstanding challenge because of the insensitivity of conventional detection methods. We demonstrated the use of an individual, near-surface nitrogen-vacancy (NV) center in diamond as a sensor to detect proton NMR in an organic sample located external to the diamond. Using a combination of electron spin echoes and proton spin manipulation, we showed that the NV center senses the nanotesla field fluctuations from the protons, enabling both time-domain and spectroscopic NMR measurements on the nanometer scale.

http://science.sciencemag.org/content/sci/339/6119/557.full.pdf

Nanoscale Nuclear Magnetic Resonance with a Nitrogen-Vacancy Spin Sensor

The controlled motion of a series of domain walls along magnetic nanowires using spin-polarized current pulses is the essential ingredient of the proposed magnetic racetrack memory, a new class of potential non-volatile storage-class memories. Using permalloy nanowires, we achieved the successive creation, motion, and detection of domain walls by using sequences of properly timed, nanosecond-long, spin-polarized current pulses. The cycle time for the writing and shifting of the domain walls was a few tens of nanoseconds. Our results illustrate the basic concept of a magnetic shift register that relies on the phenomenon of spin-momentum transfer to move series of closely spaced domain walls.

https://science.sciencemag.org/content/sci/320/5873/209.full.pdf

Current-controlled magnetic domain-wall nanowire shift register.

We have combined ultrasensitive magnetic resonance force microscopy (MRFM) with 3D image reconstruction to achieve magnetic resonance imaging (MRI) with resolution <10 nm. The image reconstruction converts measured magnetic force data into a 3D map of nuclear spin density, taking advantage of the unique characteristics of the “resonant slice” that is projected outward from a nanoscale magnetic tip. The basic principles are demonstrated by imaging the 1H spin density within individual tobacco mosaic virus particles sitting on a nanometer-thick layer of adsorbed hydrocarbons. This result, which represents a 100 million-fold improvement in volume resolution over conventional MRI, demonstrates the potential of MRFM as a tool for 3D, elementally selective imaging on the nanometer scale.

/pdf/nanoscale-magnetic-resonance-imaging-2diz73sqsk.pdf

Nanoscale magnetic resonance imaging

Several decades ago computers used devices called magnetic bubble memories, in which information was stored in small magnetized areas defined by domain walls. The domain walls, where the magnetization changes its direction, were moved by magnetic fields. This otherwise attractive technology had problems with reliability and scaling and gradually fell out of favour. Today an entirely new way of moving domain walls, using short pulses of electrical current, could make bubble memory devices feasible at the nanoscale. Thomas et al. use this technique to move domain walls in ferromagnetic wires on very short timescales, by applying nanosecond-long pulses. They also observe an intriguing 'boomerang' effect, where the domain walls are driven out of their confining potential, in the opposite direction to the current pulse. Experiments show that domain walls in ferromagnetic wires can be moved on very short timescales, by applying nanosecond-long pulses, and also detail a so-called 'boomerang' effect, where the domain walls are driven out of their confining potential, in the opposite direction of the current pulse. Magnetic domain walls, in which the magnetization direction varies continuously from one direction to another, have long been objects of considerable interest1. New concepts for devices based on such domain walls are made possible by the direct manipulation of the walls using spin-polarized electrical current2,3 through the phenomenon of spin momentum transfer4,5. Most experiments to date have considered the current-driven motion of domain walls under quasi-static conditions6,7,8,9,10,11,12, whereas for technological applications, the walls must be moved on much shorter timescales. Here we show that the motion of domain walls under nanosecond-long current pulses is surprisingly sensitive to the pulse length. In particular, we find that the probability of dislodging a domain wall, confined to a pinning site in a permalloy nanowire, oscillates with the length of the current pulse, with a period of just a few nanoseconds. Using an analytical model13,14,15,16,17 and micromagnetic simulations, we show that this behaviour is connected to a current-induced oscillatory motion of the domain wall. The period is determined by the wall's mass18 and the slope of the confining potential. When the current is turned off during phases of the domain wall motion when it has enough momentum, the domain wall is driven out of the confining potential in the opposite direction to the flow of spin angular momentum. This dynamic amplification effect could be exploited in magnetic nanodevices based on domain wall motion.

Charles T. Rettner

Papers

Phase-change random access memory: a scalable technology

Nanoscale Nuclear Magnetic Resonance with a Nitrogen-Vacancy Spin Sensor

Current-controlled magnetic domain-wall nanowire shift register.

Nanoscale magnetic resonance imaging

Oscillatory dependence of current-driven magnetic domain wall motion on current pulse length