On the angular anisotropy of the randomly averaged magnetic neutron scattering cross section of nanoparticles

Abstract

The magnetic small-angle neutron scattering (SANS) cross section of dilute ensembles of uniformly magnetized and randomly oriented Stoner–Wohlfarth particles is calculated using the Landau–Lifshitz equation. The focus of this study is on the angular anisotropy of the magnetic SANS signal as it can be seen on a two-dimensional position-sensitive detector. Depending on the symmetry of the magnetic anisotropy of the particles (e.g. uniaxial, cubic), an anisotropic magnetic SANS pattern may result, even in the remanent state or at the coercive field. The case of inhomogeneously magnetized particles and the effects of a particle-size distribution and interparticle correlations are also discussed.

Revealing Unusual Bandgap Shifts with Temperature and Bandgap Renormalization Effect in Phase‐Stabilized Metal Halide Perovskite Thin Films

“…To consider appropriate distortion modes in our systems, we first rule out the tilting of the rigid [PbI 6 ] 4− (or [SnI 6 ] 4− ) octahedra for the following reasons: 1) static tilting breaks the cubic symmetry, inconsistent with the observed PXRD results; 2) the activation of more dynamic tilting modes is associated with negative thermal lattice expansion and a positive gap pressure coefficient, [27] which are opposite in sign to those observed in our Pb-and PbSnperovskites.…”

“…Previous studies have explained the temperature effect on the perovskite's bandgap using the theory developed for conventional semiconductors, [10,11] which considers the thermal lattice expansion effect [12][13][14][15][16] and the electron-phonon coupling effect. [17][18][19][20] However, compared with conventional semiconductors, perovskites have soft and flexible structures [21][22][23] and can exhibit lattice distortions such as octahedral tilting [24][25][26][27] and the atom off-centering. [28][29][30][31][32][33] While both static distortions (the structure at equilibrium) at low temperatures [24,25,34,35] and dynamic lattice vibrations at high temperatures [21][22][23]36] have been shown to be essential for understanding the lattice dynamics in perovskites, their connection to the thermal evolution of the bandgap remains to be carefully examined.…”