Magneto-structural coupling and harmonic lattice dynamics in CaFe${}_2$As${}_2$ probed by M\"ossbauer spectroscopy

In this paper we present detailed M"ossbauer spectroscopy study of structural and magnetic properties of the undoped parent compound CaFe${}_2$As${}_2$ single crystal. By fitting the temperature dependence of the hyperfine magnetic field we show that the magneto-structural phase transition is clearly first-order in nature and we also deduced the compressibility of our sample to be $1.67\times {10}^{-2}GP{a}^{-1}$. Within the Landau’s theory of phase transition, we further argue that the observed phase transition may stem from the strong magneto-structural coupling effect. Temperature dependence of the Lamb-M"ossbauer factor show that the paramagnetic phase and the antiferromagnetic phase exhibit similar lattice dynamics in high frequency modes with very close Debye temperatures, ${\mathrm{\Theta }}_D\sim$270,K.