Density of states and magnetic susceptibilities on the octagonal tiling

We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two sites are equivalent in a quasiperiodic tiling. We present the site-dependent magnetic susceptibility of electrons on this tiling, which also has six characteristic dependences. We show the existence of a non-local spin susceptibility, which decays with the square of the distance between sites and is the quasiperiodic version of Ruderman-Kittel oscillations. These results are obtained for a tight-binding Hamiltonian with pure hopping.Finally, we investigate the formation of local magnetic moments when electron-electron interactions are included.Comment: 8 pages, LaTeX, figures on reques

Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry

In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a structure having pentagonal loops. Such five-fold loops can be expected to occur naturally in quasicrystals, as seen for example in a number of experimental studies of surfaces of icosahedral alloys. Our model considers classical vector spins placed on vertices of a subtiling of the two dimensional Penrose tiling, and interacting with nearest neighbors via antiferromagnetic bonds. We give a set of recursion relations for this system, which consists of an infinite set of embedded clusters with sizes that increase as a power of the golden mean. The magnetic ground states of this fractal system are studied analytically, and by Monte Carlo simulation.Comment: 7 pages, 7 figures, contribution to ICQ11 (Sapporo, Japan 2010) conference proceeding