Spin waves in fractals

Pascal Monceau (1, 2) , Jean-Claude Serge Lévy (3)

1 MSC - Matière et Systèmes Complexes
2 DPM - Département de Physique et Modélisation
3 MPQ (UMR_7162) - Laboratoire Matériaux et Phénomènes Quantiques

Spin wave frequencies and profiles of several Sierpinski Carpets taken at different iteration levels are calculated. Spin wave spectra of these fractals with short ranged ferromagnetic exchange are found to be singular continuous functions of the frequency with quite numerous steps and cliffs, i.e. energy gaps and degenerate modes, resulting in devil's staircase spectra. The study of connectivity reveals the existence of several different connectivity areas within each fractal. It marks mode localization and symmetry. Spin wave modes are found to be quite sensitive to fractal topology and connectivity as already observed about critical properties of fractals. The extension of the properties of magnetic excitations, first to random fractals, then to elastic waves as well as to electronic states in fractals is introduced. Applications to spin wave resonance in dilute magnetic semiconductors are discussed.

Mots clés: spin waves; fractals; singular continuous spectra; localization; fractal subdimensions

Domaines: Mécanique statistique [cond-mat.stat-mech]

Pascal Monceau, Jean-Claude Serge Lévy. Spin waves in fractals. Jean-Claude Serge Lévy. Nanostructures and their magnetic properties, Research Signpost, pp.227-256, 2009. ⟨hal-00521373⟩