Influence of structural short-range order on the phase diagram of diluted anisotropic Heisenberg ferromagnet

The diluted anisotropic Heisenberg ferromagnet is considered in the pair approximation. The structural short-range-order, described by the Warren-Cowley parameter, is taken into account. In the presence of interaction anisotropy, the influence of dilution and structural correlations on the phase diagrams is studied. In particular, for the model in question the critical concentrations and Curie temperatures are calculated for exemplary two-dimensional and three-dimensional lattices.

Figure 1

The critical concentration as a function of Warren-Cowley parameter for nearest neighbors, (a) for 2D honeycomb lattice and (b) for 3D fcc lattice. The bold solid line encloses the physically allowed range of variables. The dashed line (H) is for isotropic Heisenberg case whereas the dashed-dotted one (I) is for anisotropic case.

Figure 2

The critical temperature for honeycomb lattice as dependent on the concentration of magnetic atoms, (a) for pure Ising model and (b) for interaction anisotropy $J^{\prime }/J=0.9$. Various values of Warren-Cowley parameter were adopted.

Figure 3

The critical temperature for fcc lattice as dependent on the concentration of magnetic atoms, (a) for pure Ising model and (b) for isotropic Heisenberg model. Various values of Warren-Cowley parameter were adopted.

Figure 4

The critical temperature as a function of concentration of magnetic atoms for various interaction anisotropies, (a) for honeycomb lattice with $\alpha =0.5$ and (b) for fcc lattice with $\alpha =-0.25$.

Figure 5

The critical temperature as dependent on interaction anisotropy for various values of Warren-Cowley parameter, (a) for honeycomb lattice with $p=2/3$ and (b) for fcc lattice with $p=1/3$.

Figure 6

The critical temperature as dependent on the interaction anisotropy, presented in (a) linear scale and (b) logarithmic scale, in the vicinity of the critical effective coordination number $z_{\text{eff}}=4$ (for which the solid line was plotted).