Spin Correlations in Iron

Abstract

Measurements of diffuse magnetic neutron scattering from an iron single crystal show that there is strong ferromagnetic short-range order above the Curie temperature. The associated small-angle scattering is spherically symmetric and decreases smoothly in reciprocal space, indicating that there is no systematic orientation relationship between spin clusters. Correlation coefficients, defined as ${\ensuremath{\gamma}}_{r}=\frac{{(\mathbf{S}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}^{\ensuremath{'}})}_{r}}{S(S+1)}$ where S and S\ensuremath{'} are spin vectors with spin quantum number $S$ separated by the vector r, were obtained from a quasielastic analysis of the data. The correlation coefficients follow the relationship ${\ensuremath{\gamma}}_{r}=A \mathrm{exp}(\ensuremath{-}\frac{r}{\ensuremath{\delta}})$ at short correlation distances. Beyond 15 \AA{} the Van Hove relationship, ${\ensuremath{\gamma}}_{r}=(\frac{B}{r})\mathrm{exp}(\ensuremath{-}\ensuremath{\kappa}r)$, is followed. The quantities $\ensuremath{\delta}$ and $\frac{1}{\ensuremath{\kappa}}$ are correlation ranges, and the factors $A$ and $B$ are related to the strength of the correlation. The first-neighbor spin coupling energy was calculated from nearest-neighbor correlation coefficients and magnetic specific-heat data. The resultant exchange energy, ${J}_{1}=0.012$ eV, and this is in good agreement with recent calculations for a Heisenberg ferromagnet above the Curie temperature. Observations of small-angle scattering show that the spin disorder persists well below the Curie temperature. Measurements were made of the total diffuse magnetic scattering in the vicinity of the Curie temperature, and these data also demonstrate the gradual and continuous onset of spin disorder as the temperature is raised toward the critical point.