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We present results of the analysis of Brillouin Light Scattering (BLS) measurements of spin waves performed on ultrathin single and multirepeat CoFeB layers with adjacent heavy metal layers. From a detailed study of the spin-wave dispersion relation, we independently extract the Heisenberg exchange interaction (also referred to as symmetric exchange interaction), the Dzyaloshinskii-Moriya interaction (DMI, also referred to as antisymmetric exchange interaction), and the anisotropy field. We find a large DMI in CoFeB thin films adjacent to a Pt layer and nearly vanishing DMI for CoFeB films adjacent to a W layer. Furthermore, the residual influence of the dipolar interaction on the dispersion relation and on the evaluation of the Heisenberg exchange parameter is demonstrated. In addition, an experimental analysis of the DMI on the spin-wave lifetime is presented. All these parameters play a crucial role in designing skyrmionic or spin-orbitronic devices., Comment: 10 pages, 7 figures

Wave-based data processing by spin waves and their quanta, magnons, is a promising technique to overcome the challenges which CMOS-based logic networks are facing nowadays. The advantage of these quasi-particles lies in their potential for the realization of energy efficient devices on the micro- to nanometer scale due to their charge-less propagation in magnetic materials. In this paper, the frequency dependence of the propagation direction of caustic-like spin-wave beams in microstructured ferromagnets is studied by micromagnetic simulations. Based on the observed alteration of the propagation angle, an approach to spatially combine and separate spin-wave signals of different frequencies is demonstrated. The presented magnetic structure constitutes a prototype design of a passive circuit enabling frequency-division multiplexing in magnonic logic networks. It is verified that spin-wave signals of different frequencies can be transmitted through the device simultaneously without any interaction or creation of spurious signals. Due to the wave-based approach of computing in magnonic networks, the technique of frequency-division multiplexing can be the basis for parallel data processing in single magnonic devices, enabling the multiplication of the data throughput., Comment: 18 pages, 3 figures

The emerging field of magnonics employs spin waves and their quanta, magnons, to implement wave-based computing on the micro- and nanoscale. Multi-frequency magnon networks would allow for parallel data processing within single logic elements whereas this is not the case with conventional transistor-based electronic logic. However, a lack of experimentally proven solutions to efficiently combine and separate magnons of different frequencies has impeded the intensive use of this concept. In this Letter, the experimental realization of a spin-wave demultiplexer enabling frequency-dependent separation of magnonic signals in the GHz range is demonstrated. The device is based on two-dimensional magnon transport in the form of spin-wave beams in unpatterned magnetic films. The intrinsic frequency-dependence of the beam direction is exploited to realize a passive functioning obviating an external control and additional power consumption. This approach paves the way to magnonic multiplexing circuits enabling simultaneous information transport and processing., Comment: 16 pages, 3 figures

Brillouin light scattering measurements were performed in the backscattering geometry on a Bi-substituted rare earth iron garnet. We observed two different peaks, one attributed to a surface spin wave in the dipole-exchange regime. The other is referred to as a backscattering magnon mode, because the incident light in this case is scattered backward by exchange-dominated spin wave inside the material. We propose a method to estimate the exchange stiffness constant from the frequency of the backscattering magnon mode. The obtained value is comparable with the previously reported values for Y$ _3 $Fe$ _5 $O$ _{12} $., Comment: 11 pages, 6figures

We studied the transient behavior of the spin current generated by the longitudinal spin Seebeck effect (LSSE) in a set of platinum-coated yttrium iron garnet (YIG) films of different thicknesses. The LSSE was induced by means of pulsed microwave heating of the Pt layer and the spin currents were measured electrically using the inverse spin Hall effect in the same layer. We demonstrate that the time evolution of the LSSE is determined by the evolution of the thermal gradient triggering the flux of thermal magnons in the vicinity of the YIG/Pt interface. These magnons move ballistically within the YIG film with a constant group velocity, while their number decays exponentially within an effective propagation length. The ballistic flight of the magnons with energies above 20K is a result of their almost linear dispersion law, similar to that of acoustic phonons. By fitting the time-dependent LSSE signal for different film thicknesses varying by almost an order of magnitude, we found that the effective propagation length is practically independent of the YIG film thickness. We consider this fact as strong support of a ballistic transport scenario - the ballistic propagation of quasi-acoustic magnons in room temperature YIG.

We investigate the amplification of externally excited spin waves via the Spin-Transfer-Torque (STT) effect in combination with the Spin-Hall-Effect (SHE) employing short current pulses. The results reveal that, in the case of an overcompensation of the spin wave damping, a strong nonlinear shift of the spin wave frequency spectrum occurs. In particular, this shift affects the spin wave amplification using the SHE-STT effect. In contrast, this effect allows for the realization of a spin wave switch. By determining the corresponding working point, an efficient spin wave excitation is only possible in the presence of the SHE-STT effect yielding an increased spin wave intensity of a factor of 20 compared to the absence of the SHE-STT effect.

We present a time-resolved study of the magnetization dynamics in a microstructured Cr$|$Heusler$|$Pt waveguide driven by the Spin-Hall-Effect and the Spin-Transfer-Torque effect via short current pulses. In particular, we focus on the determination of the threshold current at which the spin-wave damping is compensated. We have developed a novel method based on the temporal evolution of the magnon density at the beginning of an applied current pulse at which the magnon density deviates from the thermal level. Since this method does not depend on the signal-to-noise ratio, it allows for a robust and reliable determination of the threshold current which is important for the characterization of any future application based on the Spin-Transfer-Torque effect., Comment: 5 pages, 3 figures. arXiv admin note: text overlap with arXiv:1701.02094

A number of high-level languages and libraries have been proposed that offer novel and simple to use abstractions for concurrent, asynchronous, and distributed programming. The execution models that realise them, however, often change over time---whether to improve performance, or to extend them to new language features---potentially affecting behavioural and safety properties of existing programs. This is exemplified by SCOOP, a message-passing approach to concurrent object-oriented programming that has seen multiple changes proposed and implemented, with demonstrable consequences for an idiomatic usage of its core abstraction. We propose a semantics comparison workbench for SCOOP with fully and semi-automatic tools for analysing and comparing the state spaces of programs with respect to different execution models or semantics. We demonstrate its use in checking the consistency of properties across semantics by applying it to a set of representative programs, and highlighting a deadlock-related discrepancy between the principal execution models of SCOOP. Furthermore, we demonstrate the extensibility of the workbench by generalising the formalisation of an execution model to support recently proposed extensions for distributed programming. Our workbench is based on a modular and parameterisable graph transformation semantics implemented in the GROOVE tool. We discuss how graph transformations are leveraged to atomically model intricate language abstractions, how the visual yet algebraic nature of the model can be used to ascertain soundness, and highlight how the approach could be applied to similar languages., Comment: Accepted by Formal Aspects of Computing

We present the temperature dependence of the thermal magnon density in a thin ferromagnetic layer. By employing Brillouin light scattering and varying the temperature, an increase of the magnon density accompanied by a lowering of the spin-wave frequency is observed with increasing temperature. The magnon density follows the temperature according to the Bose-Einstein distribution function which leads to an approximately linear dependency. In addition, the influence of this effect in spin-transfer-torque-driven systems is presented. In particular, the increase in the magnon density with temperature sets the limit for a suppression of magnons in charge current-driven systems. Hence, the maximum possible suppression of thermal magnons occurs at a finite current., Comment: 5 pages, 4 figures

We present a time-resolved study of the DC-current driven magnetization dynamics in a microstructured Cr/Heusler/Pt waveguide by means of Brillouin light scattering. A reduction of the effective spin-wave damping via the spin-transfer-torque effect leads to a strong increase in the magnon density. This is accompanied by a decrease of the spin-wave frequencies. By evaluating the time scales of these effects, the origin of this frequency shift can be identified. However, recently, we found that the experimental setup partially influences the decay of the spin-wave intensity after the current pulse is switched off. Thus, further investigations on the presented effect are needed to allow for a more detailed analysis. For this reason, we need to withdraw the manuscript at this point and might publish an updated version later., Comment: Recently, we found that the experimental setup partially influences the decay of the spin-wave intensity after the current pulse is switched off. Thus, further investigations on the presented effect are needed to allow for a more detailed analysis. For this reason, we need to withdraw the manuscript at this point and might publish an updated version later

The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mechanism of external injection of bosons by irradiation is required. Here, we present a novel and universal approach to enable BEC of quasi-particles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose-Einstein condensation., Comment: In contrast to the previous version additional information has been added. The chemical potential was derived from BLS measurements, the influence of the spin Seebeck effect is discussed more extensively in the Supplement with respect to the theoretical model and the rapid cooling has been realized in Au/Al/YIG structures where no substantial contribution of the spin Seebeck effect is expected

Graphs are used as models in all areas of computer science: examples are state space graphs, control flow graphs, syntax graphs, UML-type models of all kinds, network layouts, social networks, dependency graphs, and so forth. Once such graphical models are constructed, they can be analysed and transformed to verify their correctness within a domain, discover new properties, or produce new equivalent and/or optimised versions. Graphs as Models' main focus is the exchange and collaboration of researchers from different backgrounds. The workshop serves as platform to boost inter- and transdisciplinary research and wants to serve as leeway for new ideas. Thus, besides classical research presentations, the workshop is highly geared toward numerous interactive sessions. The second edition of the Graphs as Models workshop was held on 2-3 June 2016 in Eindhoven, The Netherlands, colocated with the 19th European Joint Conferences on Theory and Practice of Software (ETAPS 2016).

The temporal evolution of pulsed Spin Hall Effect - Spin Transfer Torque (SHE-STT) driven auto-oscillations in a Yttrium Iron Garnet (YIG) / platinum (Pt) microdisc is studied experimentally using time-resolved Brillouin Light Scattering (BLS) spectroscopy. It is demonstrated that the frequency of the auto-oscillations is different in the center and at the edge of the investigated disc that is related to the simultaneous STT excitation of a bullet and a non-localized spin-wave mode. Furthermore, the magnetization precession intensity is found to saturate on a time scale of 20 ns or longer, depending on the current density. For this reason, our findings suggest that a proper ratio between the current and the pulse duration is of crucial importance for future STT-based devices., Comment: 4 pages, 3 figures

A number of novel programming languages and libraries have been proposed that offer simpler-to-use models of concurrency than threads. It is challenging, however, to devise execution models that successfully realise their abstractions without forfeiting performance or introducing unintended behaviours. This is exemplified by SCOOP---a concurrent object-oriented message-passing language---which has seen multiple semantics proposed and implemented over its evolution. We propose a "semantics workbench" with fully and semi-automatic tools for SCOOP, that can be used to analyse and compare programs with respect to different execution models. We demonstrate its use in checking the consistency of semantics by applying it to a set of representative programs, and highlighting a deadlock-related discrepancy between the principal execution models of the language. Our workbench is based on a modular and parameterisable graph transformation semantics implemented in the GROOVE tool. We discuss how graph transformations are leveraged to atomically model intricate language abstractions, and how the visual yet algebraic nature of the model can be used to ascertain soundness., Comment: Accepted for publication in the proceedings of FASE 2016 (to appear)

To harness the power of multi-core and distributed platforms, and to make the development of concurrent software more accessible to software engineers, different object-oriented concurrency models such as SCOOP have been proposed. Despite the practical importance of analysing SCOOP programs, there are currently no general verification approaches that operate directly on program code without additional annotations. One reason for this is the multitude of partially conflicting semantic formalisations for SCOOP (either in theory or by-implementation). Here, we propose a simple graph transformation system (GTS) based run-time semantics for SCOOP that grasps the most common features of all known semantics of the language. This run-time model is implemented in the state-of-the-art GTS tool GROOVE, which allows us to simulate, analyse, and verify a subset of SCOOP programs with respect to deadlocks and other behavioural properties. Besides proposing the first approach to verify SCOOP programs by automatic translation to GTS, we also highlight our experiences of applying GTS (and especially GROOVE) for specifying semantics in the form of a run-time model, which should be transferable to GTS models for other concurrent languages and libraries., Comment: In Proceedings GaM 2015, arXiv:1504.02448

We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate prepared in a room temperature yttrium-iron-garnet magnetic film and subject to a thermal gradient. The magnon condensate is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-, frequency- and wavector-resolved Brillouin light scattering spectroscopy. It has been found that local heating in the focal point of a probing laser beam enhances the temporal decrease in the density of the freely evolving magnon condensate after the termination of the pumping pulse, but it does not alter the relaxation dynamics of the gaseous magnon phase. This phenomenon is understood as the appearance of a magnon supercurrent within the condensate due to a temperature- and, consequently, magnetisation-gradient induced phase gradient in the condensate wave function.

We present the experimental observation of the localized amplification of externally excited spin waves in a transversely in-plane magnetized Ni$_{81}$Fe$_{19}$ magnonic waveguide by means of parallel pumping. By employing microfocussed Brillouin light scattering spectroscopy, we analyze the dependency of the amplification on the applied pumping power and on the delay between the input spin-wave packet and the pumping pulse. We show that there are two different operation regimes: At large pumping powers, the spin-wave packet needs to enter the amplifier before the pumping is switched on in order to be amplified while at low powers the spin-wave packet can arrive at any time during the pumping pulse., Comment: 11 pages, 3 figures

Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those that can test whether the topmost counter value is zero and those which cannot. We show that control-state reachability for level $k$ \HOCS with $0$-test is complete for \mbox{$(k-2)$}-fold exponential space; leaving out the $0$-test leads to completeness for \mbox{$(k-2)$}-fold exponential time. Restricting \HOCS (without $0$-test) to level $2$, we prove that global (forward or backward) reachability analysis is $\PTIME$-complete. This enhances the known result for pushdown systems which are subsumed by level $2$ \HOCS without $0$-test. We transfer our results to the formal language setting. Assuming that $\PTIME \subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}$, we apply proof ideas of Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS form strictly interleaving hierarchies. Interestingly, Engelfriet's constructions also allow to conclude immediately that the hierarchy of collapsible pushdown languages is strict level-by-level due to the existing complexity results for reachability on collapsible pushdown graphs. This answers an open question independently asked by Parys and by Kobayashi., Comment: Version with Full Proofs of a paper that appears at MFCS 2013

We introduce {\omega}-Petri nets ({\omega}PN), an extension of plain Petri nets with {\omega}-labeled input and output arcs, that is well-suited to analyse parametric concurrent systems with dynamic thread creation. Most techniques (such as the Karp and Miller tree or the Rackoff technique) that have been proposed in the setting of plain Petri nets do not apply directly to {\omega}PN because {\omega}PN define transition systems that have infinite branching. This motivates a thorough analysis of the computational aspects of {\omega}PN. We show that an {\omega}PN can be turned into an plain Petri net that allows to recover the reachability set of the {\omega}PN, but that does not preserve termination. This yields complexity bounds for the reachability, (place) boundedness and coverability problems on {\omega}PN. We provide a practical algorithm to compute a coverability set of the {\omega}PN and to decide termination by adapting the classical Karp and Miller tree construction. We also adapt the Rackoff technique to {\omega}PN, to obtain the exact complexity of the termination problem. Finally, we consider the extension of {\omega}PN with reset and transfer arcs, and show how this extension impacts the decidability and complexity of the aforementioned problems., Comment: 37 pages, 6 figures, submitted

The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability problem restricted to eager runs (i.e., runs where messages are either received immediately after being sent, or never received). The problem is EXPTIME-complete in the decidable case. The second result is a doubly exponential time algorithm for bounded context analysis in this setting, together with a matching lower bound. Both results extend and improve previous work from La Torre et al.

To make the development of efficient multi-core applications easier, libraries, such as Grand Central Dispatch, have been proposed. When using such a library, the programmer writes so-called blocks, which are chunks of codes, and dispatches them, using synchronous or asynchronous calls, to several types of waiting queues. A scheduler is then responsible for dispatching those blocks on the available cores. Blocks can synchronize via a global memory. In this paper, we propose Queue-Dispatch Asynchronous Systems as a mathematical model that faithfully formalizes the synchronization mechanisms and the behavior of the scheduler in those systems. We study in detail their relationships to classical formalisms such as pushdown systems, Petri nets, fifo systems, and counter systems. Our main technical contributions are precise worst-case complexity results for the Parikh coverability problem for several subclasses of our model., Comment: 38 pages, submitted for publication