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We introduce a notion of sectional regularity for a homogeneous ideal I, which measures the regularity of its general sections with respect to linear spaces of various dimensions. It is related to axial constants defined as the intercepts on the coordinate axes of the set of exponents of monomials in the reverse lexicographic generic initial ideal of I. We show the equivalence of these notions and several other homological and ideal-theoretic invariants. We also establish that these equivalent invariants grow linearly for the family of powers of a given ideal. 

Disorder‐induced inhomogeneity in blue‐fluorescent‐based organic light‐emitting diodes (OLEDs) based on mixtures of host and guest molecules is studied using magneto‐electroluminescence, MEL(B), response based on the so called “Δgmechanism”, where Δgis the difference in the Landég‐factor of electrons and holes. The disorder in the organic active layer is manifested by a unique non‐Lorentzian MEL(B) response that is analyzed using a distribution of spin lifetimes for the injected electron–hole pairs that is determined by a dispersive parameter, α (<1). The carriers’ inhomogeneous response also influences the free carrier absorption spectrum, which shows characteristic properties described by a dispersive parameter β (<1). From the measured MEL(B) response at various injection conditions it is found that α is robust at increasing current density showing that the inhomogeneity is governed by intrinsic disorder in the device active layer. Also the obtained increase in α at low temperature indicates that the organic layer becomes more ordered, where longer‐lived electron–hole spin pairs are formed.

 

We have investigated spin related processes in fullerene C 60 devices using several experimental techniques, which include magnetic field effect of photocurrent and electroluminescence in C 60 -based diodes; spin polarized carrier injection in C 60 -based spin-valves; and pure spin current generation in NiFe/C 60 /Pt trilayer devices. We found that the ‘curvature-related spin orbit coupling’ in C 60 plays a dominant role in the obtained spin-related phenomena. The measured magneto-photocurrent and magneto-electroluminescence responses in C 60 diodes are dominated by the difference in the g -values of hole and electron polarons in the fullerene molecules. We also obtained giant magneto-resistance of ∼10% at 10 K in C 60 spin-valve devices, where spin polarized holes are injected into the C 60 interlayer. In addition, using the technique of spin-pumping in NiFe/C 60 /Pt trilayer devices with various C 60 interlayer thicknesses we determined the spin diffusion length in C 60 films to be 13 ± 2 nm at room temperature. 

The isotope effect is studied in the magneto‐electroluminescence (MEL) and pulsed electrically detected magnetic resonance of organic light‐emitting diodes based on thermally activated delayed fluorescence (TADF) from donor–acceptor exciplexes that are either protonated (H) or deuterated (D). It is found that at ambient temperature, the exchange of H to D has no effect on the spin‐dependent current and MEL responses in the devices. However, at cryogenic temperatures, where the reverse intersystem crossing (RISC) from triplet to singlet exciplex diminishes, a pronounced isotope effect is observed. These results show that the RISC process is not governed by the hyperfine interaction as thought previously, but proceeds through spin‐mixing in the triplet exciplex. The observations are corroborated by electrically detected transient spin nutation experiments that show relatively long dephasing time at ambient temperature, and interpreted in the context of a model that involves exchange and hyperfine interactions in the spin triplet exciplex. These findings deepen the understanding of the RISC process in TADF materials.