Paramagnetic iron spin dynamics simulations

The contradiction\footnotemark[2]\footnotetext[2]{J. W. Lynn, Phys. Rev. B {\bf 11}, 2624 (1975).}\footnotemark[3]\footnotetext[3]{G. Shirane, O. Steinsvoll, Y. J. Uemura and J. Wicksted, J. Appl. Phys. {\bf 55}, 1887 (1984).}\footnotemark[4]\footnotetext[4]{H. A. Mook and J. W. Lynn, J. Appl. Phys. {\bf 57}, 3006 (1985).} about paramagnetic BCC iron spin dynamics is investigated using a classical Heisenberg model with four shells of interacting neighbors and exchange parameters derived from electronic structure calculations. For $T\geq T_c$ (up to at least $1.2T_c$), the spin dynamics simulated dynamic structure factor $S(\vec{q},E)$\footnotemark[5]\footnotetext[5]{Shan-Ho Tsai, Alex Bunker and D. P. Landau, Phys. Rev. B {\bf 61}, 333 (2000).}, with $\vec{q}$ fixed, has two symmetric peaks and a third peak at zero energy. Fitting results show that the symmetric peaks are due to spin-waves. The dispersion curves soften in energy with increasing temperatures and generally lie lower than those of the experiments\footnotemark[2], but both sets have the same qualitative features and suggest that spin wave excitations persist above $T_c$.