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The tilt-to-length coupling during the LISA Pathfinder mission has been numerically and analytically modeled for particular timespans. In this work, we investigate the long-term stability of the coupling coefficients of this noise. We show that they drifted slowly (by 1\,$\mu$m/rad and 6$\times10^{-6}$ in 100 days) and strongly correlated to temperature changes within the satellite (8\,$\mu$m/rad/K and 30$\times10^{-6}$/K). Based on analytical TTL coupling models, we attribute the temperature-driven coupling changes to rotations of the test masses and small distortions in the optical setup. Particularly, we show that LISA Pathfinder's optical baseplate was bent during the cooldown experiment, which started in late 2016 and lasted several months.

A precise characterization of the magnetic properties of LISA Pathfinder free falling test-masses is of special interest for future gravitational wave observatory in space. Magnetic forces have an important impact on the instrument sensitivity in the low frequency regime below the millihertz. In this paper we report on the magnetic injection experiments performed throughout LISA Pathfinder operations. We show how these experiments allowed a high precision estimate of the instrument magnetic parameters. The remanent magnetic moment was found to have a modulus of $(0.245\pm0.081)\,\rm{nAm}^2$, the x-component of the background magnetic field within the test masses position was measured to be $(414 \pm 74)$ nT and its gradient had a value of $(-7.4\pm 2.1)\,\mu$T/m. Finally, we also measured the test mass magnetic susceptibility to be $(-3.35\pm0.15)\times$10$^{-5}$ in the low frequency regime. All results are in agreement with on-ground estimates.

LISA Pathfinder was a mission designed to test key technologies required for gravitational wave detection in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime, which corresponds to the measurement band of interest for future space-borne gravitational wave observatories. Magnetic-induced forces couple to the test mass motion, introducing a contribution to the relative acceleration noise between the free falling test masses. In this Letter we present the first complete estimate of this term of the instrument performance model. Our results set the magnetic-induced acceleration noise during the February 2017 noise run of $\rm 0.25_{-0.08}^{+0.15}\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz and $\rm 1.01_{-0.24}^{+0.73}\, fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz. We also discuss how the non-stationarities of the interplanetary magnetic field can affect these values during extreme space weather conditions.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find that: 1) the evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies $f\gtrsim 1\,\text{mHz}$, is consistent with the decaying pressure due to the outgassing of a single gaseous species. 2) between $f=36\,\mu\text{Hz}$ and $1\,\text{mHz}$, the acceleration ASD shows a $1/f$ tail in excess of the Brownian noise of almost constant amplitude, with $\simeq 20\%$ fluctuations over a period of a few days, with no particular time pattern over the course of the mission; 3) at the lowest considered frequency of $f=18\,\mu\text{Hz}$, the ASD significantly deviates from the $1/f$ behavior, because of temperature fluctuations that appear to modulate a quasi-static pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement, or a quantitative estimate from dedicated experiments. These sources account for approximately $40\%$ of the noise power in the $1/f$ tail. Finally, we analyze the possible sources of the remaining unexplained fraction, and identify the possible measures that may be taken to keep those under control in LISA.

We investigate anomalous spin and orbital Hall phenomena in antiferromagnetic (AF) materials via orbital pumping experiments. Conducting spin and orbital pumping experiments on YIG/Pt/Ir20Mn80 heterostructures, we unexpectedly observe strong spin and orbital anomalous signals in an out-of-plane configuration. We report a sevenfold increase in the signal of the anomalous inverse orbital Hall effect (AIOHE) compared to conventional effects. Our study suggests expanding the Orbital Hall angle ({\theta}_OH) to a rank 3 tensor, akin to the Spin Hall angle ({\theta}_SH), to explain AIOHE. This work pioneers converting spin-orbital currents into charge current, advancing the spin-orbitronics domain in AF materials., Comment: 5 pages and 4 figures

In this work, we explore the intriguing spin-momentum locking phenomenon within the Rashba states of antimony (Sb) films. By combining spin pumping with the flow of an external charge current, we reveal the topological properties of surface states in Sb films. Taking advantage of the well-defined spin polarization of both spin-momentum-locked charge currents and spin-pumped currents, we demonstrate precise manipulation over the direction and magnitude of the resulting charging current, generated through the inverse Rashba-Edelstein effect. This fascinating phenomenon is attributed to the dynamic interaction between the accumulation of out-of-equilibrium pumped spins and the flowing spins, intrinsically locked perpendicular to the direction of the charge current. The results show that Sb as a promising material for basic and applied investigation of spintronics phenomena. We believe that the nanostructures investigated here open the way for the development of low-power logic gates operating in the range of a few tens of microamperes., Comment: 25 pages, 11 figures

Our investigation reveals a groundbreaking discovery of a negative inverse orbital Hall effect (IOHE) in Ge thin films. We employed the innovative orbital pumping technique where spin-orbital coupled current is injected into Ge films using YIG/Pt(2)/Ge($t_{Ge}$) and YIG/W(2)/Ge($t_{Ge}$) heterostructures. Through comprehensive analysis, we observe significant reductions in the signals generated by coherent (RF-driven) and incoherent (thermal-driven) spin-orbital pumping techniques. These reductions are attributed to the presence of a remarkable strong negative IOHE in Ge, showing its magnitude comparable to the spin-to-charge signal in Pt. Our findings reveal that although the spin-to-charge conversion in Ge is negligible, the orbital-to-charge conversion exhibits large magnitude. Our results are innovative and pioneering in the investigation of negative IOHE by the injection of spin-orbital currents., Comment: 6 pages and 4 figures

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

We present a novel approach to determine the optical properties of materials in the nanoscale range using optical tweezers (OT). Fluorescent polymer-based nanostructures (pdots) are optically trapped in a Gaussian beam OT and the trap stiffness is studied as a function of various parameters of interest. We explicitly show that properties such as the refractive index and the optical anisotropy of these nanostructures can be determined with high accuracy by comparing the experimental data to an optical force model. In particular, we demonstrate that the effective optical properties of these pdots can be modulated by changing the light wavelength that excites the sample, opening the door for a fine tuning of their optical response, with possible applications in the development of new sensors and/or other optoelectronic devices.

We investigated how different materials affect the orbital-charge conversion in heterostructures with the naturally oxidized cooper capping layer. When we added a thin layer of $CuOx(3nm)$ onto yttrium iron garnet $(YIG)/W$ stacks, we observed a significant reduction in the charge current signal measured by means the spin pumping effect technique. This finding contrasts with the results of a prior study conducted on YIG/Pt/CuOx, which reported the opposite effect. On the other hand, when we added the same $CuOx(3nm)$ layer to $YIG/Ti(4nm)$ structures, there was not much change in the spin pumping signal. This occurred because Ti does not generate much orbital current at the $Ti/CuOx$ interface, unlike Pt, due to its weaker spin-orbit coupling. Interestingly, when we added the $CuOx(3nm)$ layer to $SiO_{2}/Py(5nm)/Pt(4nm)$ structures, the spin pumping signal increased. However, in $SiO_{2}/CuOx(3nm)/Pt(4nm)/Py(5nm)$ structures, the signal decreased. Finally, we delve into a theoretical analysis of the spin (orbital) Hall effect in YIG/Heavy-metal systems. These findings have the potential to advance research in the innovative field of orbitronics and contribute to the development of new technologies based on spin-orbital conversion., Comment: 21 pages, 6 figures

The spin-to-charge conversion phenomena is investigated in a trilayer structure consisting of Co(12 nm)/Sb(t)/Py(12 nm), where the thickness t of the antimony layer is varied. Using the spin-pumping technique, a pure spin current is injected from both FM layers into the middle layer, the DC voltage is then measured. We observe a spin-to-charge mechanism in the Sb layer that exhibits striking similarities to the inverse Rashba-Edelstein effect (IREE), driven by surface states., Comment: 6 pages, 4 figures

We delve into the statistical properties of regions within complex networks that are distant from vertices with high centralities, such as hubs or highly connected clusters. These remote regions play a pivotal role in shaping the asymptotic behaviours of various spreading processes and the features of associated spectra. We investigate the probability distribution $P_{\geq m}(s)$ of the number $s$ of vertices located at distance $m$ or beyond from a randomly chosen vertex in an undirected network. Earlier, this distribution and its large $m$ asymptotics $1/s^2$ were obtained theoretically for undirected uncorrelated networks [S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin, Nucl. Phys. B 653 (2003) 307]. Employing numerical simulations and analysing empirical data, we explore a wide range of real undirected networks and their models, including trees and loopy networks, and reveal that the inverse square law is valid even for networks with strong correlations. We observe this law in the networks demonstrating the small-world effect and containing vertices with degree $1$ (so-called leaves or dead ends). We find the specific classes of networks for which this law is not valid. Such networks include the finite-dimensional networks and the networks embedded in finite-dimensional spaces. We notice that long chains of nodes in networks reduce the range of $m$ for which the inverse square law can be spotted. Interestingly, we detect such long chains in the remote regions of the undirected projection of a large Web domain., Comment: 13 pages, 10 figures, 2 tables, 1 ancillary file

We present a study of the tilt-to-length coupling noise during the LISA Pathfinder mission and how it depended on the system's alignment. Tilt-to-length coupling noise is the unwanted coupling of angular and lateral spacecraft or test mass motion into the primary interferometric displacement readout. It was one of the major noise sources in the LISA Pathfinder mission and is likewise expected to be a primary noise source in LISA. We demonstrate here that a recently derived and published analytical model describes the dependency of the LISA Pathfinder tilt-to-length coupling noise on the alignment of the two freely falling test masses. This was verified with the data taken before and after the realignments performed in March (engineering days) and June 2016, and during a two-day experiment in February 2017 (long cross-talk experiment). The latter was performed with the explicit goal of testing the tilt-to-length coupling noise dependency on the test mass alignment. Using the analytical model, we show that all realignments performed during the mission were only partially successful and explain the reasons why. In addition to the analytical model, we computed another physical tilt-to-length coupling model via a minimising routine making use of the long cross-talk experiment data. A similar approach could prove useful for the LISA mission.

A comprehensive summary of the measurements made to characterize test mass charging due to the space environment during the LISA Pathfinder mission is presented. Measurements of the residual charge of the test mass after release by the grabbing and positioning mechanism, show that the initial charge of the test masses was negative after all releases, leaving the test mass with a potential in the range $-12$ mV to $-512$ mV. Variations in the neutral test mass charging rate between $21.7$ e s$^{-1}$ and $30.7$ e s$^{-1}$ were observed over the course of the 17-month science operations produced by cosmic ray flux changes including a Forbush decrease associated with a small solar energetic particle event. A dependence of the cosmic ray charging rate on the test mass potential between $-30.2$ e s$^{-1}$ V$^{-1}$ and $-40.3$ e s$^{-1}$ V$^{-1}$ was observed and this is attributed to a contribution to charging from low-energy electrons emitted from the gold surfaces of the gravitational reference sensor. Data from the on-board particle detector show a reliable correlation with the charging rate and with other environmental monitors of the cosmic ray flux. This correlation is exploited to extrapolate test mass charging rates to a 20-year period giving useful insight into the expected range of charging rate that may be observed in the LISA mission., Comment: 17 pages, 10 figures

We study how available data on COVID-19 cases and deaths in different countries are reliable. Our analysis is based on a modification of the law of anomalous numbers, the Newcomb-Benford law, applied to the daily number of deaths and new cases in each country. We first revisit the Newcomb-Benford law and show how to avoid false negative compliance of the data. We then compared deviation from this law, to a number of social and economic indices for each country by computing the Spearman rank order correlation between each index and the \c{hi}2 deviation of COVID- 19 data to the modified NB law. A similar analysis for excess deaths for the same countries with sufficient available data was performed. We conclude that in general less democratic, less transparent and more corrupt countries tend to have data of lesser quality. We also discuss the limitations of the present approach., Comment: 20 pages, 13 figures

In this paper we present spin-to-charge current conversion properties in the Weyl semimetal TaP by means of the inverse Rashba-Edelstein effect (IREE) with the integration of this quantum material with the ferromagnetic metal Permalloy $(Py=Ni_{81}Fe_{19})$. The spin currents are generated in the Py layer by the spin pumping effect (SPE) from microwave-driven ferromagnetic resonance and are detected by a dc voltage along the TaP crystal, at room temperature. We observe a field-symmetric voltage signal without the contamination of asymmetrical lines due to spin rectification effects observed in studies using metallic ferromagnets. The observed voltage is attributed to spin-to-charge current conversion based on the IREE, made possible by the spin-orbit coupling induced intrinsically by the bulk band structure of Weyl semimetals. The measured IREE coefficient ${\lambda}_{IREE}=(0.30 \pm{0.01})$ nm is two orders of magnitude larger than in graphene and is comparable to or larger than the values reported for some metallic interfaces and for several topological insulators., Comment: 15 pages, 4 figures

The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse networks that contain an arbitrary finite subgraph. Assuming the local tree-likeness of the enclosing network, and that branches emanating from the finite subgraph do not intersect at finite distances, we show that the largest eigenvalue of the nonbacktracking matrix of the composite network is equal to the highest of the two largest eigenvalues: that of the finite subgraph and of the enclosing network. In the localized state, when the largest eigenvalue of the subgraph is the highest of the two, we derive explicit expressions for the NBCs of nodes in the subgraph and other nodes in the network. In this state, nonbacktracking centrality is concentrated on the subgraph and its immediate neighbourhood in the enclosing network. We obtain simple, exact formulas in the case where the enclosing network is uncorrelated. We find that the mean NBC decays exponentially around the finite subgraph, at a rate which is independent of the structure of the enclosing network, contrary to what was found for the localization of the principal eigenvector of the adjacency matrix. Numerical simulations confirm that our results provide good approximations even in moderately sized, loopy, real-world networks., Comment: 11 pages, 7 figures

We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a weaker condition than for a mutually connected component in interdependent networks, in which any two vertices must be connected by a path within each of the layers. The effect of the overlaps on weak percolation turns out to be opposite to that on the giant mutually connected component. While for the giant mutually connected component, overlaps do not change the critical phenomena, our theory shows that in two layers any (nonzero) concentration of overlaps drives the weak percolation transition to the ordinary percolation universality class. In three layers, the phase diagram of the problem contains two lines -- of a continuous phase transition and of a discontinuous one -- connected in various ways depending on how the layers overlap. In the case of only doubled overlapped edges, two of the end points of these lines coincide, resulting in a tricritical point like that seen in heterogeneous $k$-core percolation., Comment: 21 pages, 8 figures

While current-induced torque by orbital current has been experimentally found in various structures, evidence for its reciprocity has been missing so far. Here, we report experimental evidence of strong inverse orbital torque in YIG/Pt/CuOx (YIG = Y3Fe5O12) mediated by spin-orbital entangled electronic states in Pt. By injecting spin current from YIG to Pt by the spin pumping via ferromagnetic resonance and by the spin Seebeck effect, we find a pronounced inverse spin Hall effect-like signal. While a part of the signal is explained as due to the inverse spin-orbital Hall effect in Pt, we also find substantial increase of the signal in YIG/Pt/CuOx structures compared to the signal in YIG/Pt. We attribute this to the inverse orbital Rashba-Edelstein effect at Pt/CuOx interface mediated by the spin-orbital entangled states in Pt. Our work paves the way toward understanding of spin-orbital entangled physics in nonequilibrium and provides a way for electrical detection of the orbital current in orbitronic device applications., Comment: 14 pages, four figures

We study a model of non-identical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortex-like phase-waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotors, and groups of drones. A generalized Ott-Antonsen ansatz provides the first analytic description of these states and conditions for their existence. We show how this approach may be used in studies of active matter and related disciplines.

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, $P(0)=0$. Above a critical value of a control parameter, the removal of a tiny fraction $\Delta$ of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, $\Pi=P(1)$. We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point $\Pi_c$, respectively. In the limit $\Delta\to0$ the total collapse for $\Pi>\Pi_\text{c}$ takes a time $T \propto 1/(\Pi-\Pi_\text{c})$, while there is an exponential relaxation below $\Pi_\text{c}$ with a relaxation time $\tau \propto 1/[\Pi_\text{c}-\Pi]$., Comment: 12 pages, 6 figures

Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the number of communities. Here we propose an efficient hypothesis test for community detection based on quantifying dissimilarities between graphs. Given a random graph, the null hypothesis is that it is of degree-corrected Erd\"{o}s-R\'{e}nyi type. We compare the dissimilarity between them by a measure incorporating the vertex distance distribution, the clustering coefficient distribution, and the alpha-centrality distribution, which is used for our hypothesis test. We design a two-stage bipartitioning algorithm to uncover the number of communities and the corresponding structure simultaneously. Experiments on synthetic and real networks show that our method outperforms state-of-the-art ones., Comment: a algorithm has been added

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups., Comment: 10 pages, 7 figures

Message-passing theories have proved to be invaluable tools in studying percolation, non-recurrent epidemics and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix whose largest eigenvalue, the corresponding eigenvector, and the closely related nonbacktracking centrality play a central role in determining how the given dynamical model behaves. Here we propose a degree-class-based method to approximate these quantities using a smaller matrix related to the joint degree-degree distribution of neighbouring nodes. Our findings suggest that in most networks degree-degree correlations beyond nearest neighbour are actually not strong, and our first-order description already results in accurate estimates, particularly when message-passing itself is a good approximation to the original model in question, that is when the number of short cycles in the network is sufficiently low. We show that localization of the nonbacktracking centrality is also captured well by our scheme, particularly in large networks. Our method provides an alternative to working with the full nonbacktracking matrix in very large networks where this may not be possible due to memory limitations., Comment: 11 pages, 6 figures; supplemental material

A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show that the phase diagram predicted by this analysis is incomplete. Our numerical analysis of the equations reveals that the model can also undergo an abrupt phase transition from oscillations to wobbly rotations of the order parameter under increasing field frequency or decreasing field strength. This transition was not revealed by bifurcation analysis because it is not caused by a bifurcation, and can neither be classified as first nor second-order since it does not display critical phenomena characteristic of either transition. We discuss the topological origin of this transition and show that it is determined by a singular point in the order-parameter space., Comment: 5 pages, 4 figures

The function and performance of neural networks is largely determined by the evolution of their weights and biases in the process of training, starting from the initial configuration of these parameters to one of the local minima of the loss function. We perform the quantitative statistical characterization of the deviation of the weights of two-hidden-layer ReLU networks of various sizes trained via Stochastic Gradient Descent (SGD) from their initial random configuration. We compare the evolution of the distribution function of this deviation with the evolution of the loss during training. We observed that successful training via SGD leaves the network in the close neighborhood of the initial configuration of its weights. For each initial weight of a link we measured the distribution function of the deviation from this value after training and found how the moments of this distribution and its peak depend on the initial weight. We explored the evolution of these deviations during training and observed an abrupt increase within the overfitting region. This jump occurs simultaneously with a similarly abrupt increase recorded in the evolution of the loss function. Our results suggest that SGD's ability to efficiently find local minima is restricted to the vicinity of the random initial configuration of weights., Comment: 12 pages, 8 figures

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. We describe a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. We fully describe the critical phenomena of this process. In particular, in two layers, with finite second moments of the degree distributions, an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers we find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+ 1/(M-1)$ for $M$ layers., Comment: 42 pages, 8 figures

The control of pure spin currents carried by magnons in magnetic insulator (MI) garnet films with a robust perpendicular magnetic anisotropy (PMA) is of great interest to spintronic technology as they can be used to carry, transport and process information. Garnet films with PMA present labyrinth domain magnetic structures that enrich the magnetization dynamics, and could be employed in more efficient wave-based logic and memory computing devices. In MI/NM bilayers, where NM being a normal metal providing a strong spin-orbit coupling, the PMA benefits the spin-orbit torque (SOT) driven magnetization's switching by lowering the needed current and rendering the process faster, crucial for developing magnetic random-access memories (SOT-MRAM). In this work, we investigated the magnetic anisotropies in thulium iron garnet (TIG) films with PMA via ferromagnetic resonance measurements, followed by the excitation and detection of magnon-mediated pure spin currents in TIG/Pt driven by microwaves and heat currents. TIG films presented a Gilbert damping constant {\alpha}~0.01, with resonance fields above 3.5 kOe and half linewidths broader than 60 Oe, at 300 K and 9.5 GHz. The spin-to-charge current conversion through TIG/Pt was observed as a micro-voltage generated at the edges of the Pt film. The obtained spin Seebeck coefficient was 0.54 {\mu}V/K, confirming also the high interfacial spin transparency.

We report an investigation of the spin- to charge-current conversion in sputter-deposited films of topological insulator $Bi_2Se_{3}$ onto single crystalline layers of YIG $(Y_{3}Fe_{5}O_{12})$ and polycrystalline films of Permalloy $(Py = Ni_{81}Fe_{19})$. Pure spin current was injected into the $Bi_{2}Se_{3}$ layer by means of the spin pumping process in which the spin precession is obtained by exciting the ferromagnetic resonance of the ferromagnetic film. The spin-current to charge-current conversion, occurring at the $Bi_{2}Se_{3}/$ferromagnet interface, was attribute to the inverse Rashba-Edelstein effect (IREE). By analyzing the data as a function of the $Bi_{2}Se_{3}$ thickness we calculated the IREE length used to characterize the efficiency of the conversion process and found that 1.2 pm $\leq|{\lambda}_{IREE}|\leq$ 2.2 pm. These results support the fact that the surface states of $Bi_{2}Se_{3}$ have a dominant role in the spin-charge conversion process, and the mechanism based on the spin diffusion process plays a secondary role. We also discovered that the spin- to charge-current mechanism in $Bi_{2}Se_{3}$ has the same polarity as the one in Ta, which is the opposite to the one in Pt. The combination of the magnetic properties of YIG and Py, with strong spin-orbit coupling and dissipationless surface states topologically protected of $Bi_{2}Se_{3}$ might lead to spintronic devices with fast and efficient spin-charge conversion.

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph's degree., Comment: 21 pages, 8 figures, 3 tables

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several non-typical phenomena. In two layers, the giant component emerges with a continuos phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent $\gamma$, the discontinuity vanishes but at $\gamma=1.5$ in three layers, more generally at $\gamma = 1+ 1/(M-1)$ in $M$ layers., Comment: 11 pages, 6 figures

LISA Pathfinder (LPF) has been a space-based mission designed to test new technologies that will be required for a gravitational wave observatory in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime (mHz and below), the measurement band of interest for a space-based observatory. The magnetic field can couple to the magnetic susceptibility and remanent magnetic moment from the test masses and disturb them from their geodesic movement. LISA Pathfinder carried on-board a dedicated magnetic measurement subsystem with noise levels of 10 $ \rm nT \ Hz^{-1/2}$ from 1 Hz down to 1 mHz. In this paper we report on the magnetic measurements throughout LISA Pathfinder operations. We characterise the magnetic environment within the spacecraft, study the time evolution of the magnetic field and its stability down to 20 $\mu$Hz, where we measure values around 200 $ \rm nT \ Hz^{-1/2}$ and identify two different frequency regimes, one related to the interplanetary magnetic field and the other to the magnetic field originating inside the spacecraft. Finally, we characterise the non-stationary component of the fluctuations of the magnetic field below the mHz and relate them to the dynamics of the solar wind., Comment: 16 pages, 17 figures. MNRAS LaTeX style file version 3.0

We report on the results of the LISA Pathfinder (LPF) free-fall mode experiment, in which the control force needed to compensate the quasistatic differential force acting on two test masses is applied intermittently as a series of "impulse" forces lasting a few seconds and separated by roughly 350 s periods of true free fall. This represents an alternative to the normal LPF mode of operation in which this balancing force is applied continuously, with the advantage that the acceleration noise during free fall is measured in the absence of the actuation force, thus eliminating associated noise and force calibration errors. The differential acceleration noise measurement presented here with the free-fall mode agrees with noise measured with the continuous actuation scheme, representing an important and independent confirmation of the LPF result. An additional measurement with larger actuation forces also shows that the technique can be used to eliminate actuation noise when this is a dominant factor.

In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant information contained in inputs (arrays of zeroes and ones). This problem serves as a reference model for the statistics of filtering and related sampling problems. The filter patterns in this problem conveniently allow a microscopic, combinatorial consideration. This allows us to find the statistics of outputs, namely the exact distribution of output degeneracies, for arbitrary input sizes. We observe that the resulting degeneracy distribution of outputs decays as $e^{-c\log^\alpha \!d}$ with degeneracy $d$, where $c$ is a constant and exponent $\alpha>1$, i.e. faster than a power law. Importantly, its form essentially depends on the size of the input data set, appearing to be closer to a power-law dependence for small data set sizes than for large ones. We demonstrate that for sufficiently small input data set sizes typical for empirical studies, this distribution could be easily perceived as a power law. We extend our results to filter patterns of various sizes and demonstrate that the shortest filter pattern provides the maximum informative representations of the inputs., Comment: 17 pages, 8 figures, 1 table, Supplementary Material

LISA Pathfinder (LPF) was a technology pioneering mission designed to test key technologies required for gravitational wave detection in space. In the low frequency regime (milli-Hertz and below), where space-based gravitational wave observatories will operate, temperature fluctuations play a crucial role since they can couple into the interferometric measurement and the test masses' free-fall accuracy in many ways. A dedicated temperature measurement subsystem, with noise levels in 10$\,\mu$K$\,$Hz$^{-1/2}$ down to $1\,$mHz was part of the diagnostics unit on board LPF. In this paper we report on the temperature measurements throughout mission operations, characterize the thermal environment, estimate transfer functions between different locations and report temperature stability (and its time evolution) at frequencies as low as 10$\,\mu$Hz, where typically values around $1\,$K$\,$Hz$^{-1/2}$ were measured., Comment: 13 pages, 16 figures. MNRAS LaTeX style file version 3.0

The zodiacal dust complex, a population of dust and small particles that pervades the Solar System, provides important insight into the formation and dynamics of planets, comets, asteroids, and other bodies. Here we present a new set of data obtained using a novel technique: direct measurements of momentum transfer to a spacecraft from individual particle impacts. This technique is made possible by the extreme precision of the instruments flown on the LISA Pathfinder spacecraft, a technology demonstrator for a future space-based gravitational wave observatory that operated near the first Sun-Earth Lagrange point from early 2016 through Summer of 2017. Using a simple model of the impacts and knowledge of the control system, we show that it is possible to detect impacts and measure properties such as the transferred momentum (related to the particle's mass and velocity), direction of travel, and location of impact on the spacecraft. In this paper, we present the results of a systematic search for impacts during 4348 hours of Pathfinder data. We report a total of 54 candidates with momenta ranging from 0.2$\,\mu\textrm{Ns}$ to 230$\,\mu\textrm{Ns}$. We furthermore make a comparison of these candidates with models of micrometeoroid populations in the inner solar system including those resulting from Jupiter-family comets, Oort-cloud comets, Hailey-type comets, and Asteroids. We find that our measured population is consistent with a population dominated by Jupiter-family comets with some evidence for a smaller contribution from Hailey-type comets. This is in agreement with consensus models of the zodiacal dust complex in the momentum range sampled by LISA Pathfinder., Comment: 22 pages, 14 figures, accepted in ApJ

Non-recurrent short term variations of the galactic cosmic-ray (GCR) flux above 70 MeV n$^{-1}$ were observed between 2016 February 18 and 2017 July 3 aboard the European Space Agency LISA Pathfinder (LPF) mission orbiting around the Lagrange point L1 at 1.5$\times$10$^6$ km from Earth. The energy dependence of three Forbush decreases (FDs) is studied and reported here. A comparison of these observations with others carried out in space down to the energy of a few tens of MeV n$^{-1}$ shows that the same GCR flux parameterization applies to events of different intensity during the main phase. FD observations in L1 with LPF and geomagnetic storm occurrence is also presented. Finally, the characteristics of GCR flux non-recurrent variations (peaks and depressions) of duration $<$ 2 days and their association with interplanetary structures are investigated. It is found that, most likely, plasma compression regions between subsequent corotating high-speed streams cause peaks, while heliospheric current sheet crossing cause the majority of the depressions.

Oscillatory dynamics is a key tool in optical tweezers applications. It is usually implemented by mechanical interventions that cannot be optically controlled. In this work we show that Germanium semiconductor beads behave as optically induced oscillators when subjected to a highly focused laser beam. Such unusual motion is due to the competition between the usual optical forces [1-3] and the radiometric force related to thermal effects, which pushes the beads from the focal region [4]. We characterize the behavior of the Germanium beads in detail and propose a model accounting for the related forces, in good agreement with the experimental data. The well defined direction of oscillations can be manipulated by the polarization of the light beam. Such kind of system can potentially revolutionize the field of optical manipulation, contributing to the design of single molecule machines and the application of oscillatory forces in macromolecules and other soft matter systems., Comment: 6 pages and 4 figures

This article shows that the spin-to-charge current conversion in single-layer graphene (SLG) by means of the inverse Rashba-Edelstein effect (IREE) is made possible with the integration of this remarkable 2D-material with the unique ferrimagnetic insulator yttrium iron garnet (YIG = $Y_{3}Fe_{5}O_{12}$) as well as with the ferromagnetic metal permalloy (Py = $Ni_{81}Sb_{19}$). By means of X-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD) techniques, we show that the carbon atoms of the SLG acquires an induced magnetic moment due to the proximity effect with the magnetic layer. The spin currents are generated in the magnetic layer by spin pumping from microwave driven ferromagnetic resonance and are detected by a dc voltage along the graphene layer, at room temperature. The spin-to-charge current conversion, occurring at the graphene layer, is explained by the extrinsic spin-orbit interaction (SOI) induced by the proximity effect with the ferromagnetic layer. The results obtained for the SLG/YIG and SLG/Py systems confirm very similar values for the IREE parameter, which are larger than the values reported in previous studies for SLG. We also report systematic investigations of the electronic and magnetic properties of the SLG/YIG by means of scanning tunneling microscopy (STM)., Comment: Main text: 12 pages and 6 figures, Supplemental Material: 4 pages and 4 figures