Critical Magnetic Neutron Scattering from Ferrous Fluoride

A detailed investigation of the static and dynamic correlations in the nearly ideal uniaxial anisotropic antiferromagnet Fe${\mathrm{F}}_2$ has been carried out using quasielastic and inelastic neutron scattering. The scattering from transverse and longitudinal fluctuations can be determined separately in this compound, and the measurements test recent scaling theory and model calculations for anisotropic antiferromagnets. The transverse fluctuations are only weakly dependent on temperature, the inverse transverse correlation length ${\kappa }_{\perp }=(0.145\mathrm{}\pm 0.040)$ ${\mathrm{\AA }}^{-1\mathrm{}}$ at $T_N$, and the transverse relaxation rate ${\Gamma }_{\perp }(q=0, T_N)=(1.5\mathrm{}\pm 0.4)$ meV. The inverse longitudinal correlation length ${\kappa }_{\parallel }\mathrm{}\left(T\right)\mathrm{}$ and the staggered longitudinal susceptibility ${\kappa }_{\parallel }(q=0, T)$ are described above $T_N$ by the critical exponents $\nu =0.67\mathrm{}\pm 0.04$ and $\gamma =1.38\mathrm{}\pm 0.08$, respectively. Below $T_N$ these remain unchanged within the experimental error. The longitudinal relaxation rates are three to five times smaller than those found in the weakly anisotropic Mn${\mathrm{F}}_2$. They obey a homogeneous scaling relation in ($q, {\kappa }_{\parallel }$) of degree close to 2, as predicted by scaling theory. The scaling function $\Omega \left(\frac{q}{{\kappa }_{\parallel }}\right)=\frac{{\Gamma }_{\parallel }(q, {\kappa }_{\parallel })}{{\kappa }_{\parallel }^2}$ bears a close resemblance to that found for Mn${\mathrm{F}}_2$.