Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.Comment: 21 pages, 10 figures, version 2: added two paragaph

On the homomorphism order of labeled posets

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.Comment: 14 page

Nanoscale mechanics of antiferromagnetic domain walls

Antiferromagnets offer remarkable promise for future spintronics devices, where antiferromagnetic order is exploited to encode information. The control and understanding of antiferromagnetic domain walls (DWs) - the interfaces between domains with differing order parameter orientations - is a key ingredient for advancing such antiferromagnetic spintronics technologies. However, studies of the intrinsic mechanics of individual antiferromagnetic DWs remain elusive since they require sufficiently pure materials and suitable experimental approaches to address DWs on the nanoscale. Here we nucleate isolated, 180{\deg} DWs in a single-crystal of Cr$_2$O$_3$, a prototypical collinear magnetoelectric antiferromagnet, and study their interaction with topographic features fabricated on the sample. We demonstrate DW manipulation through the resulting, engineered energy landscape and show that the observed interaction is governed by the DW's elastic properties. Our results advance the understanding of DW mechanics in antiferromagnets and suggest a novel, topographically defined memory architecture based on antiferromagnetic DWs.Comment: 3 pages, 3 figures plus Supplementary Material. Questions and comments are welcom

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.Comment: The free academic research software, CFinder, used for the publication is available at the website of the publication: http://angel.elte.hu/clusterin

Nanomagnetism of magnetoelectric granular thin-film antiferromagnets

Antiferromagnets have recently emerged as attractive platforms for spintronics applications, offering fundamentally new functionalities compared to their ferromagnetic counterparts. While nanoscale thin film materials are key to the development of future antiferromagnetic spintronics technologies, experimental tools to explore such films on the nanoscale are still sparse. Here, we offer a solution to this technological bottleneck, by addressing the ubiquitous surface magnetisation of magnetoelectic antiferromagnets in a granular thin film sample on the nanoscale using single-spin magnetometry in combination with spin-sensitive transport experiments. Specifically, we quantitatively image the evolution of individual nanoscale antiferromagnetic domains in 200-nm thin-films of Cr$_2$O$_3$ in real space and across the paramagnet-to-antiferromagnet phase transition. These experiments allow us to discern key properties of the Cr$_2$O$_3$ thin film, including the mechanism of domain formation and the strength of exchange coupling between individual grains comprising the film. Our work offers novel insights into Cr$_2$O$_3$'s magnetic ordering mechanism and establishes single spin magnetometry as a novel, widely applicable tool for nanoscale addressing of antiferromagnetic thin films.Comment: 22 pages, 7 figure

Nanomagnetism of Magnetoelectric Granular Thin-Film Antiferromagnets

Antiferromagnets have recently emerged as attractive platforms for spintronics applications, offering fundamentally new functionalities compared with their ferromagnetic counterparts. Whereas nanoscale thin-film materials are key to the development of future antiferromagnetic spintronic technologies, existing experimental tools tend to suffer from low resolution or expensive and complex equipment requirements. We offer a simple, high-resolution alternative by addressing the ubiquitous surface magnetization of magnetoelectric antiferromagnets in a granular thin-film sample on the nanoscale using single-spin magnetometry in combination with spin-sensitive transport experiments. Specifically, we quantitatively image the evolution of individual nanoscale antiferromagnetic domains in 200 nm thin films of Cr 2 O 3 in real space and across the paramagnet-to-antiferromagnet phase transition, finding an average domain size of 230 nm, several times larger than the average grain size in the film. These experiments allow us to discern key properties of the Cr 2 O 3 thin film, including the boundary magnetic moment density, the variation of critical temperature throughout the film, the mechanism of domain formation, and the strength of exchange coupling between individual grains comprising the film. Our work offers novel insights into the magnetic ordering mechanism of Cr 2 O 3 and firmly establishes single-spin magnetometry as a versatile and widely applicable tool for addressing antiferromagnetic thin films on the nanoscale. © 2019 American Chemical Society

Flexomagnetism and vertically graded Néel temperature of antiferromagnetic Cr2O3 thin films

Antiferromagnetic insulators are a prospective materials platform for magnonics, spin superfluidity, THz spintronics, and non-volatile data storage. A magnetomechanical coupling in antiferromagnets offers vast advantages in the control and manipulation of the primary order parameter yet remains largely unexplored. Here, we discover a new member in the family of flexoeffects in thin films of Cr2O3. We demonstrate that a gradient of mechanical strain can impact the magnetic phase transition resulting in the distribution of the Néel temperature along the thickness of a 50-nm-thick film. The inhomogeneous reduction of the antiferromagnetic order parameter induces a flexomagnetic coefficient of about 15 μB nm−2. The antiferromagnetic ordering in the inhomogeneously strained films can persist up to 100 °C, rendering Cr2O3 relevant for industrial electronics applications. Strain gradient in Cr2O3 thin films enables fundamental research on magnetomechanics and thermodynamics of antiferromagnetic solitons, spin waves and artificial spin ice systems in magnetic materials with continuously graded parameters

Spin transport and spin torque in antiferromagnetic devices

Ferromagnets are key materials for sensing and memory applications. In contrast, antiferromagnets which represent the more common form of magnetically ordered materials, have found less practical application beyond their use for establishing reference magnetic orientations via exchange bias. This might change in the future due to the recent progress in materials research and discoveries of antiferromagnetic spintronic phenomena suitable for device applications. Experimental demonstration of the electrical switching and detection of the Néel order open a route towards memory devices based on antiferromagnets. Apart from the radiation and magnetic-field hardness, memory cells fabricated from antiferromagnets can be inherently multilevel, which could be used for neuromorphic computing. Switching speeds attainable in antiferromagnets far exceed those of ferromagnetic and semiconductor memory technologies. Here we review the recent progress in electronic spin-transport and spin-torque phenomena in antiferromagnets that are dominantly of the relativistic quantum mechanical origin. We discuss their utility in pure antiferromagnetic or hybrid ferromagnetic/antiferromagnetic memory devices