Magnon-fracton crossover in quenched random site-diluted ferromagnets

Abstract

The strong departure from the Bloch ${T}^{3/2}$ law behavior of magnetization in dilute amorphous ${(T}_{p}{\mathrm{Ni}}_{1\ensuremath{-}p}{)}_{80}{\mathrm{B}}_{16}{\mathrm{Si}}_{4}$ $(T=\mathrm{Fe},\mathrm{Co})$ alloys is shown to be a manifestation of the crossover from hydrodynamic to critical spin wave dynamics induced by the diverging correlation length near percolation threshold. An appropriate choice of the density of states for magnetic excitations on self-similar (fractal) percolation network permits an accurate determination of the magnon-to-fracton crossover line in the magnetic phase diagram of quenched random site-diluted ferromagnets. By unambiguously demonstrating that the fracton dimensionality ${d}_{f}\ensuremath{\simeq}4/3$ and the conductivity percolation critical exponent ${\ensuremath{\sigma}}_{p}<2,$ the present results vindicate the Alexander-Orbach conjecture and the Golden inequality for percolating network with Euclidean dimension $d=3.$