The possible use of spin rather than charge as a state variable in devices for processing and storing information has been widely discussed, because it could allow low-power operation and might also have applications in quantum computing. However, spin-based experiments and proposals for logic applications typically use spin only as an internal variable, the terminal quantities for each individual logic gate still being charge-based. This requires repeated spin-to-charge conversion, using extra hardware that offsets any possible advantage. Here we propose a spintronic device that uses spin at every stage of its operation. Input and output information are represented by the magnetization of nanomagnets that communicate through spin-coherent channels. Based on simulations with an experimentally benchmarked model, we argue that the device is both feasible and shows the five essential characteristics for logic applications: concatenability, nonlinearity, feedback elimination, gain and a complete set of Boolean operations.

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

The need to find low power alternatives to digital electronic circuits has led to increasing interest in alternative switching schemes like the magnetic quantum cellular automata(MQCA) that store information in nanomagnets which communicate through their magnetic fields. A recent proposal called all spin logic (ASL) proposes to communicate between nanomagnets using spin currents which are spatially localized and can be conveniently routed. The objective of this paper is to present a model for ASL devices that is based on established physics and is benchmarked against available experimental data and to use it to investigate switching energy-delay of ASL devices.Digital electronic circuits store information in the form of capacitor charges that are manipulated using transistor-based switches. Switches of this type currently operate with a supply voltage of one volt involving ≈ 10 4 − 10 5 electrons, requiring 1 − 10 femto-Joules (fJs), dissipating 1-10 µW per switch if operating at 1 GHz. This dissipation per switch is believed to be the single most important impediment to continued miniaturization and there is a serious attempt to "reinvent the transistor" 1 so as to operate at lower voltages.A more radical approach is to replace the entire chargebased architecture with an architecture based on some other state variable such as spin 2 . For example, MQCA 3 uses nanomagnets to represent digital information (0 and 1). Recently an all spin logic (ASL) device 4 has been proposed whereby information is similarly stored in nanomagnets but is communicated via spin currents that are spatially localized and can be conveniently routed within a spin-coherence length which can be 100's of nanometers 5 to microns 6 .It has been argued that ASL devices could potentially lead to ultralow power switches since a stable nanomagnet with an activation barrier of 40 kT could be switched with less than an attoJoule (aJ) 4 . Experimentally, however, nanomagnet memory devices typically require tens of fJs to switch at speeds that are a factor of 100 to 1000 lower, raising questions about the potential of ASL devices to provide a low-power alternative to today's transistors. This is because most of the dissipation in switching magnets is associated not with the dynamics of magnets but with the spin transport process and we need a suitable model that incorporates both to make reliable predictions. This paper presents such a model that is based on established physics and is benchmarked against the recent experimental result of Yang et al. 7 .In general, the switching energy and energy-delay can be written as:V and I are the charge voltage and current respectively and t sw is the switching delay. Q tot = It sw is the total charge involved in a switching event. Equation 1 permits a simple comparison with charge-based devices likeFIG. 1: (a) An ASL device consisted of input and output magnets. (b) Illustrates the self-consistent model. (c) Shows the conductance matrices describing the spin-transport.today's transistors where Q tot is the amou...

We show that the established physics of spin valves together with the recently discovered giant spin-Hall effect could be used to construct Read and Write units that can be integrated into a single spin switch with input-output isolation, gain and fan-out similar to CMOS inverters, but with the information stored in nanomagnets making it nonvolatile. Such spin switches could be interconnected, with no external amplification, just with passive circuit elements, to perform logic operations. Moreover, since the digitization and storage occurs naturally in the magnets, the voltages can be used to implement analog "weighting" for non-Boolean logic.

We present a Non-Equilibrium Green"s Function (NEGF)-based model for spin torque transfer (STT) devices which provides quantitative agreement with experimentally measured (1) differential resistances, (2) Magnetoresistance (MR), (3) In-plane torque and (4) out-of-plane torque over a range of bias voltages, using a single set of three adjustable parameters. We believe this is the first theoretical model that is able to cover this diverse range of experiments and a key aspect of our model is the inclusion of multiple transverse modes. We also provide a simple explanation for the asymmetric bias dependence of the in-plane torque, based on the polarization of the two contacts in energy range of transport. DOI:PACS:Spin Torque Transfer (STT) devices that can switch the magnetization of a soft ferromagnetic layer through spin polarized electrons without any external field have generated significant interest from both basic and applied points of view (See for example Ref. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Although the concept of spin torque has been demonstrated by a number of experiments [14,15], quantitative measurement of bias dependence of spin torque has been achieved only very recently [16][17][18][19][20]. Note that these experiments show considerable dispersions in measuring the bias dependence of inplane torque [16,17,19,20]. Currently, there is no consensus as to a microscopic model that accounts for this discrepancy. Moreover, the existing theoretical models based on effective mass, tightbinding [21][22][23] and Ab-initio [24,25] band structures do not provide quantitative agreements with the experiments. Therefore, we need a model which can simultaneously explain all of the diverse aspects of STT devices namely i) differential resistances R(V), ii) TMR, iii) in-plane/spin-transfer (  ) and iv) out-ofplane/field-like (  ) components of spin torque. This paper presents a simple effective mass model with five parameters: a) equilibrium Fermi level E f , b) Spin-splitting ∆, c) Barrier height of the insulator U b , d) effective masses for electrons inside FM contacts (m FM, * = m FM, * = m FM * ) and e) effective mass for electrons inside insulator m ox * in terms of which we can understand all of the aforementioned characteristics (i-iv) of STT devices. Note that we view U b , m FM * and m ox * as parameters that account for a wide variety of factors including imperfection at ferromagnet/insulator interfaces. As such we consider these three parameters adjustable from one structure from another. On the other hand, E f and  are material parameters. Although this is an effective mass model that does not include bandstructure effects explicitly, we believe that the quantitative agreement with such a diverse set of experiments shows that it captures much of the essential physics at least in the structures analyzed. One such effect our model tries to capture is the role of transverse modes on the TMR, R(V) and bias asymmetry of the in-plane torque. This last point is currently a topic of d...