Critical Fields in Ferromagnetic Thin Films: Identification of Four Regimes

We are interested in critical fields for ferromagnetic elements: At which strength of the external field does a branch of stationary magnetizations become unstable, and what is the unstable mode? We consider samples which are infinite in the direction of the external field and have a rectangular cross-section, of much smaller thickness than width, as an idealization of a thin film element. For this geometry Aharoni [Phys. Stat. Sol. 16, 3-42 (1966)] claims that there are only three different regimes: The unstable mode is either of coherent rotation type, of buckling type, or of curling type. We discover a large fourth parameter regime with an unstable mode displaying an oscillation in the infinite direction. We prove the existence of exactly four regimes by rigorously analyzing the scaling of the Rayleigh quotient of the Hessian of the energy functional. The parameters are the film width, the film thickness, and the exchange length.     

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Electrostatic calculation of the substituent effect: an efficient test on isolated molecules

The energy of a disubstituted molecule has often been approximated by simple electrostatic formulas that represent the substituents as poles or dipoles. Herein, we test this approach on a new model system that is more direct and more efficient than testing on acid-base properties. The energies of 27 1,4-derivatives of bicyclo[2.2.2]octane were calculated within the framework of the density functional theory at the B3LYP/6-311+G(d,p) level; interaction of the two substituents was evaluated in terms of isodesmic homodesmotic reactions. This interaction energy, checked previously on some experimental gas-phase acidities, was considered to be accurate and served as reference to test the electrostatic approximation. This approximation works well in the qualitative sense as far as the sign and the order of magnitude are concerned: beginning with the strongest interaction between two poles, a weaker interaction between pole and dipole, and the weakest between two dipoles. However, all the electrostatic calculations yield energies that are too small, particularly for weak interaction, and this fundamental defect is not remedied by some possible improvements. In particular, variation of the effective permittivity would require a physically impossible value less than unity. The explanation must lie in a more complex distribution of electron density than anticipated in the electrostatic model. It also follows that possible conclusions about the transmission of substituent effects "through space" have little validity.