Berlin 2008 – scientific programme

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MA: Fachverband Magnetismus

MA 18: Poster I : Bio Magn. (1-2); Mag.Imgaging (3-9); Magn. Semiconductors (10-16); Half Metals & Oxides (17-20); Coupl.Phenomena (21-27); Magn. Mat. (28-41); Micro & Nanostr. Magn. Materials (42-61); Micro Magn. (62-64); Surface Magnetism (65-70); Transport Phenomena (71-85)

MA 18.45: Poster

Tuesday, February 26, 2008, 15:15–18:30, Poster E

Analytic formulae for multipole moments of general ellipsoids, elliptic cylinders and prisms — •Nikolai Mikuszeit, Matthias Schult, Elena Vedmedenko, and Roland Wiesendanger — Institute of Applied Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany

The multipole moments of different homogeneously polarised/charged geometries are calculated analytically. The general shapes include important limits: spheroid and sphere, cylinder or disc, and cube. It is shown that all multipole moments can be expressed as polynomials. The polynomial functions depend on the particle shape and the aspect ratios. Even the solutions for the general ellipsoid, where hypergeometric functions appear, can be expanded in finite polynomials of the semi-axes [1]. The calculations are valid up to every order of the multipole expansion. Some results are extended to symmetric two-/multidomain states.

The results allow to calculate potentials as well as interaction energies within the framework of multipole expansion. It is therefore easy to consider important higher order interactions—corrections to dipole-dipole energies—in systems of interacting particles, where the interparticle distance is of the order of the particle size [2].

[1] M. Schult, N. Mikuszeit, E. Y. Vedmedenko, and R. Wiesendanger, 2007, J. Phys. A, accepted

[2] E. Y. Vedmedenko, N. Mikuszeit, H. P. Oepen, and R. Wiesendanger, 2005, Phys. Rev. Lett. 95, 207202