Spin excitations in K$_{0.84}$Fe$_{1.99}$Se$_2$ superconductor as studied by M\"ossbauer spectroscopy

M\"ossbauer spectroscopy was used to probe the site specific information of the $K_{0.84}Fe_{1.99}Se_2$ superconductor. Possibility of coexistence of superconductivity and magnetism is discussed. A spin excitation gap, $\Delta E \approx$5\,meV, is observed by analyzing the temperature dependence of the hyperfine magnetic field (HMF) at the iron site within the spin wave theory. Using a simple model suggested in the literature, the temperature dependence of the HMF is well reproduced, suggesting that, below room temperature, the iron-selenide superconductors can be regarded as ferromagnetically coupled spin blocks that interact with each other antiferromagnetically to form the observed checkerboard-like magnetic structure.