Antiferromagnetic Resonance in the Quadratic-Layer Antiferromagnets ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$

Antiferromagnetic resonance has been observed in the quadratic-layer antiferromagnets ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ ($T_N=42.1\mathrm{}$K) and ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$ ($T_N=38.4\mathrm{}$K) at a frequency of 24 GHz as a function of the temperature from 1.5 up to 38 and 34 K, respectively, with the static magnetic field parallel to the $c$ axis. To reduce these data to zero-field magnon energy gaps, the frequency renormalization method of Oguchi including a static magnetic field was used. The resulting equations in frequencies and spin-wave occupation numbers were solved self-consistently. The gaps as a function of the temperature appear to scale approximately with the magnetization. By extrapolation, the gaps at $T=0\mathrm{}$K were found to be 7.40±0.05 K for ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$, and 7.28±0.05 K for ${\mathrm{Rb}}_2$Mn${\mathrm{F}}_4$. The antiferromagnetic-resonance linewidths increase steadily in approaching $T_N$.