Neutron scattering study of magnetic ordering in the double-layer antiferromagnetK3Mn2F7

Elastic and quasielastic scattering of neutrons from the double-layer Heisenberg antiferromagnet with weak anisotropy ${\mathrm{K}}_3$ ${\mathrm{Mn}}_2$ ${\mathrm{F}}_7$ has been employed to study the magnetic structure, the variation with temperature of the sublattice magnetization, the generalized susceptibility, and the spin-spin correlation length. At $T_N=58.3\mathrm{}\pm 0.2$ K ${\mathrm{K}}_3$ ${\mathrm{Mn}}_2$ ${\mathrm{F}}_7$ exhibits a second-order phase transition to antiferromagnetic order with the spins aligned along the tetragonal axis. In the low-temperature region, the sublattice magnetization excellently follows a previous renormalized spin-wave result up to $\sim \frac{T_N}{2}$. Near $T_N$, the critical exponent for the order parameter is $\beta =0.154\mathrm{}\pm 0.006$. As is the case in single-layer structures, neutron scattering from spin-spin correlations above $T_N$ occurs along ridges in reciprocal space, with the noticeable difference that in the double-layer structure these ridges are modulated in intensity due to interference of the paired layers separated by $\delta =4.18\mathrm{}\pm 0.07$ Å, while at 4 K $a=4.181\mathrm{}\pm 0.003$ Å and $c=21.55\mathrm{}\pm 0.02$ Å. From the development of the ridge profile, the critical exponents for the generalized susceptibility $\chi \left(\overrightarrow{\mathrm{q}}\right)$ and inverse correlation length are found to be $\gamma =1.9\mathrm{}\pm 0.3$ and $\nu =1.1\mathrm{}\pm 0.2$, and from these, with $\nu (2-\eta )=\gamma$, $\eta =0.20\mathrm{}\pm 0.05$ for the deviation from the Ornstein-Zernike $\chi \left(\overrightarrow{\mathrm{q}}\right)$. The critical exponents are essentially equal to those in comparable single-layer systems, such as ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$, while they do not differ substantially from the exact two-dimensional Ising results. In addition, in ${\mathrm{K}}_3$ ${\mathrm{Mn}}_2$ ${\mathrm{F}}_7$ spin-spin correlation near