Dynamical properties of a three-dimensional diluted Heisenberg model

We study the magnetic excitation spectrum in three-dimensional diluted ferromagnetic nearest-neighbor systems down to the percolation threshold. The disorder effects resulting from the dilution are handled accurately within self-consistent local random phase approximation approach. The calculations are performed using relatively large systems containing typically $20000$ localized spins, a systematic average over many configurations of disorder is performed. We analyze in details the change in the magnon spectrum and magnon density of states as we increase the dilution. The zone of stability of the well-defined magnon modes is shown to shrink drastically as we approach the percolation threshold. We also calculate the spin stiffness which appears to vanish at the percolation threshold exactly. A comparison with available data, based on a different theoretical approach, is also provided. We hope that this study will motivate new experimental studies based on inelastic neutron-scattering measurements.

Figure 1

(Color online) Magnon density of states $\rho \left(\omega \right)$ as a function of the energy $\omega$ for different concentration of localized spins $x$. The energy axis ($x$ axis) is in $\omega /J$.

Figure 2

(Color online) Spectral function $A\left(\mathbf{q},\omega \right)$ as a function of the energy $\omega$ in the (1,0,0) direction for different values of $q_x$ with varying concentration of localized spins $\left(x\right)$. The energy axis ($x$ axis) is in $\omega /J$.

Figure 3

(Color online) Spectral function $\overline{A}\left(\mathbf{q},\omega \right)$ in the $\left(q,\omega \right)$ plane for different concentration of localized spins $\left(x\right)$. (The size of the simple cubic lattice is $L=32$.)

Figure 4

(Color online) Magnon energy $\omega \left(q\right)$ (in $\omega /J$) as a function of $q^2$ for different concentration of localized spins $\left(x\right)$. The size of the simple cubic lattice varies from $L=20$, 24, 28, and 32.

Figure 5

(Color online) Spin stiffness $D$ (in $D/J$) as a function of the concentration of the localized spins $\left(x\right)$. The diamonds represent the data from Ref. 35. The squares are calculated within SC-LRPA. The dashed line is the virtual crystal approximation value. ($x_c$ is the percolation threshold.)