Structure and magnetism of self-organized Ge(1-x)Mn(x) nano-columns

We report on the structural and magnetic properties of thin Ge(1-x)Mn(x)films grown by molecular beam epitaxy (MBE) on Ge(001) substrates at temperatures (Tg) ranging from 80deg C to 200deg C, with average Mn contents between 1 % and 11 %. Their crystalline structure, morphology and composition have been investigated by transmission electron microscopy (TEM), electron energy loss spectroscopy and x-ray diffraction. In the whole range of growth temperatures and Mn concentrations, we observed the formation of manganese rich nanostructures embedded in a nearly pure germanium matrix. Growth temperature mostly determines the structural properties of Mn-rich nanostructures. For low growth temperatures (below 120deg C), we evidenced a two-dimensional spinodal decomposition resulting in the formation of vertical one-dimensional nanostructures (nanocolumns). Moreover we show in this paper the influence of growth parameters (Tg and Mn content) on this decomposition i.e. on nanocolumns size and density. For temperatures higher than 180deg C, we observed the formation of Ge3Mn5 clusters. For intermediate growth temperatures nanocolumns and nanoclusters coexist. Combining high resolution TEM and superconducting quantum interference device magnetometry, we could evidence at least four different magnetic phases in Ge(1-x)Mn(x) films: (i) paramagnetic diluted Mn atoms in the germanium matrix, (ii) superparamagnetic and ferromagnetic low-Tc nanocolumns (120 K 400 K) and (iv) Ge3Mn5 clusters.Comment: 10 pages 2 colonnes revTex formatte

Exchange bias in GeMn nanocolumns: the role of surface oxidation

We report on the exchange biasing of self-assembled ferromagnetic GeMn nanocolumns by GeMn-oxide caps. The x-ray absorption spectroscopy analysis of this surface oxide shows a multiplet fine structure that is typical of the Mn2+ valence state in MnO. A magnetization hysteresis shift |HE|~100 Oe and a coercivity enhancement of about 70 Oe have been obtained upon cooling (300-5 K) in a magnetic field as low as 0.25 T. This exchange bias is attributed to the interface coupling between the ferromagnetic nanocolumns and the antiferromagnetic MnO-like caps. The effect enhancement is achieved by depositing a MnO layer on the GeMn nanocolumns.Comment: 7 pages, 5 figure

Strain and correlation of self-organized Ge_(1-x)Mn_x nanocolumns embedded in Ge (001)

We report on the structural properties of Ge_(1-x)Mn_x layers grown by molecular beam epitaxy. In these layers, nanocolumns with a high Mn content are embedded in an almost-pure Ge matrix. We have used grazing-incidence X-ray scattering, atomic force and transmission electron microscopy to study the structural properties of the columns. We demonstrate how the elastic deformation of the matrix (as calculated using atomistic simulations) around the columns, as well as the average inter-column distance can account for the shape of the diffusion around Bragg peaks.Comment: 9 pages, 7 figure

Tournaments and Even Graphs are Equinumerous

A graph is called \emph{odd} if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and \emph{even} otherwise. Pontus von Br\"omssen (n\'e Andersson) showed that the existence of such an automorphism is independent of the orientation, and considered the question of counting pairwise non-isomorphic even graphs. Based on computational evidence, he made the rather surprising conjecture that the number of pairwise non-isomorphic \emph{even graphs} on $n$ vertices is equal to the number of pairwise non-isomorphic \emph{tournaments} on $n$ vertices. We prove this conjecture using a counting argument with several applications of the Cauchy-Frobenius Theorem

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

Load-Balancing for Parallel Delaunay Triangulations

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Comment: Short version submitted to EuroPar 201

Quantitative magneto-optical investigation of superconductor/ferromagnet hybrid structures

We present a detailed quantitative magneto-optical imaging study of several superconductor/ferromagnet hybrid structures, including Nb deposited on top of thermomagnetically patterned NdFeB, and permalloy/niobium with erasable and tailored magnetic landscapes imprinted in the permalloy layer. The magneto-optical imaging data is complemented with and compared to scanning Hall probe microscopy measurements. Comprehensive protocols have been developed for calibrating, testing, and converting Faraday rotation data to magnetic field maps. Applied to the acquired data, they reveal the comparatively weaker magnetic response of the superconductor from the background of larger fields and field gradients generated by the magnetic layer.Comment: 21 pages, including 2 pages of supplementary materia