Spin-glass state in nanoparticulate (La0.7Sr0.3MnO3)(1-x) (BaTiO3)(x) solid solutions: Experimental and density-functional studies

We report the transition from robust ferromagnetism to a spin- glass state in nanoparticulate La0.7Sr0.3MnO3 through solid solution with BaTiO3. The field- and temperature-dependent magnetization and the frequency-dependent ac magnetic susceptibility measurements strongly indicate the existence of a spin- glass state in the system, which is further confirmed from memory effect measurements. The breaking of long-range ordering into short-range magnetic domains is further investigated using density-functional calculations. We show that Ti ions remain magnetically inactive due to insufficient electron leakage from La0.7Sr0.3MnO3 to the otherwise unoccupied Ti-d states. This results in the absence of a Mn-Ti-Mn spin exchange interaction and hence the breaking of the long-range ordering. Total-energy calculations suggest that the segregation of nonmagnetic Ti ions leads to the formation of short-range ferromagnetic Mn domains.

Benchmark analytical solutions from beams with shared eigenpair

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.