Resonant soft x-ray scattering experiments with photon energies near the O K and the Cu L3 edge on the system La1.8−xEu0.2SrxCuO4 for 0.1 ≤ x ≤ 0.15 are presented. A phase diagram for stripe-like charge ordering is obtained together with information on the structural transition into the low-temperature tetragonal phase. A clear dome for the charge ordering around x = 1 8 is detected well below the structural transition. This result is quite different from other systems in which static stripes are detected. There the charge order is determined by the structural transition appearing at the same temperature. Furthermore we present results for the coherence length and the incommensurability of the stripe order as a function of Sr concentration. Later on static stripe order was also detected in the compounds La 2−x Ba x CuO 4 (LBCO) [3][4][5] and La 1.8−x Eu 0.2 Sr x CuO 4 (LESCO). 6-8In all these systems it is believed that static stripe order is stabilized by a structural transition from a low temperature orthorhombic (LTO) to a low temperature tetragonal (LTT) phase in which the CuO 6 octahedra are tilted along the [110] HT T and [100] HT T directions of the high temperature tetragonal (HTT) phase, respectively. Generally, the stripe order is accompanied by a suppression of coherent superconductivity and the amount of this suppression is increasing with increasing tilt angle Φ in the LTT phase. 9The tilt angle increases with decreasing ionic radius of substitutes on the La sites due to a chemical pressure along the CuO 2 layers. In LESCO with the small Eu ions the antiferromagnetic stripe order almost completely replaces the superconducting phase for x < ∼ 0.2. This apparent anticorrelation between stripe order and superconductivity, however, was recently questioned by the interpretation of transport data in LBCO in terms of a layer decoupled stripe superconductor with no phase coherence perpendicular to the CuO 2 layers. 10So far complete phase diagrams for the structural, the charge, and the spin order in the systems LBCO, LNSCO, and LESCO were proposed in Ref. In this Brief Report we complete our previous resonant soft x-ray scattering (RSXS) studies on the stripe like charge order in LESCO. 8While there we have reported data only for doping concentrations x ≥ 1 8 , in the present contribution we present measurements on both sides of the concentration x = 1 8 . Furthermore we present more information on the correlation length and on the incommensurability wave vector as a function of doping concentration. Finally we show an extended phase diagram for the lattice and the charge order in LESCO.Traditionally, charge order was detected by measuring superstructure reflections with x-ray or neutron scattering. Both methods were used to study stripe-like charge order in LNSCO and LBCO. 2,11,17 In the case of LESCO, only hard x-ray scattering was successful. 18RSXS at the O K and Cu L edges is a particular sensitive method to detect charge order in doped cuprates. 5,8At the prepeak of the O K edge, the form factor ...

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We report combined soft and hard x-ray scattering studies of the electronic and lattice modulations associated with stripe order in La1.875Ba0.125CuO4 and La1.48Nd0.4Sr0.12CuO4. We find that the amplitude of both the electronic modulation of the hole density and the strain modulation of the lattice is significantly larger in La1.875Ba0.125CuO4 than in La1.48Nd0.4Sr0.12CuO4 and is also better correlated. The in-plane correlation lengths are isotropic in each case; for La1.875Ba0.125CuO4, ξ hole = 255±5Å whereas for La1.48Nd0.4Sr0.12CuO4, ξ hole = 111±7Å. We find that the modulations are temperature independent in La1.875Ba0.125CuO4 in the low temperature tetragonal phase. In contrast, in La1.48Nd0.4Sr0.12CuO4, the amplitude grows smoothly from zero, beginning 13 K below the LTT phase transition. We speculate that the reduced average tilt angle in La1.875Ba0.125CuO4 results in reduced charge localization and incoherent pinning, leading to the longer correlation length and enhanced periodic modulation amplitude.

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods. AbstractThis document provides supporting information to "Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction" regarding the implementation and numerical setting of the optimization methods as well as a visualization of the different optimization strategies.

The geometry of a Si3N4 lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing-wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing-wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.