Structural changes at the semiconductor-insulator phase transition in the single layered La0.5Sr1.5MnO4 perovskite

The semiconductor-insulator phase transition of the single-layer manganite La0.5Sr1.5MnO4 has been studied by means of high resolution synchrotron x-ray powder diffraction and resonant x-ray scattering at the Mn K edge. We conclude that a concomitant structural transition from tetragonal I4/mmm to orthorhombic Cmcm phases drives this electronic transition. A detailed symmetry-mode analysis reveals that condensation of three soft modes -Delta_2(B2u), X1+(B2u) and X1+(A)- acting on the oxygen atoms accounts for the structural transformation. The Delta_2 mode leads to a pseudo Jahn-Teller distortion (in the orthorhombic bc-plane only) on one Mn site (Mn1) whereas the two X1+ modes produce an overall contraction of the other Mn site (Mn2) and expansion of the Mn1 one. The X1+ modes are responsible for the tetragonal superlattice (1/2,1/2,0)-type reflections in agreement with a checkerboard ordering of two different Mn sites. A strong enhancement of the scattered intensity has been observed for these superlattice reflections close to the Mn K edge, which could be ascribed to some degree of charge disproportion between the two Mn sites of about 0.15 electrons. We also found that the local geometrical anisotropy of the Mn1 atoms and its ordering originated by the condensed Delta_2 mode alone perfectly explains the resonant scattering of forbidden (1/4,1/4,0)-type reflections without invoking any orbital ordering.Comment: 3 tables and 10 figures; accepted in Phys. Rev.

Recognising Multidimensional Euclidean Preferences

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d-Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferencesand the behaviour of other metrics, and survey a variety of related work.Comment: 17 page

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

Interplay of atomic displacements in the quantum magnet (CuCl)LaNb2O7

We report on the crystal structure of the quantum magnet (CuCl)LaNb2O7 that was controversially described with respect to its structural organization and magnetic behavior. Using high-resolution synchrotron powder x-ray diffraction, electron diffraction, transmission electron microscopy, and band structure calculations, we solve the room-temperature structure of this compound [alpha-(CuCl)LaNb2O7] and find two high-temperature polymorphs. The gamma-(CuCl)LaNb2O7 phase, stable above 640K, is tetragonal with a(sub) = 3.889 A, c(sub) = 11.738 A, and the space group P4/mmm. In the gamma-(CuCl)LaNb2O7 structure, the Cu and Cl atoms are randomly displaced from the special positions along the {100} directions. The beta-phase [a(sub) x 2a(sub) x c(sub), space group Pbmm] and the alpha-phase [2a(sub) x 2a(sub) x c(sub), space group Pbam] are stable between 640 K and 500 K and below 500 K, respectively. The structural changes at 500 K and 640 K are identified as order-disorder phase transitions. The displacement of the Cl atoms is frozen upon the gamma --> beta transformation, while a cooperative tilting of the NbO6 octahedra in the alpha-phase further eliminates the disorder of the Cu atoms. The low-temperature alpha-(CuCl)LaNb2O7 structure thus combines the two types of the atomic displacements that interfere due to the bonding between the Cu atoms and the apical oxygens of the NbO6 octahedra. The precise structural information resolves the controversy between the previous computation-based models and provides the long-sought input for understanding the magnetic properties of (CuCl)LaNb2O7.Comment: 12 pages, 10 figures, 5 tables; crystallographic information (cif files) include