The diverse physical properties and interrelationship between various ground states offer a rich physics to explore in 122 $A$TM$_2$As$_2$ ($A = $Ca, Sr, Ba and TM = 3d transition metals). This thesis discusses three examples of the 122 $A$TM$_2$As$_2$ compounds, TM = Fe, Co and Mn, where the focus is to understand their diverse magnetic properties and interplay between the magnetism and electronic properties including superconductivity. Therefore, the spin dynamics (spin fluctuations) of these compounds were studied using inelastic neutron scattering technique.

CaFe$_2$As$_2$ and the derived compounds are the first system discussed in this work. In this com- pound, correlation between the magnetism and superconductivity was studied. CaFe$_2$As$_2$ belongs to the 122 $A$Fe$_2$As$_2$ family of high–Tc iron-based superconductors, where previous studies suggest that the overdamped spin dynamics are necessary for superconductivity. The CaFe$_2$As$_2$ compound has some unique features compared to other members of $A$Fe$_2$As$_2$ compounds, therefore presents a different scenario to study this relationship. A study performed using the inelastic neutron scattering on various Co substituted CaFe$_2$As$_2$ compounds are discussed. The results verify the link between the overdamped spin dynamics and superconductivity. In addition, the results also indicate that some peculiar features are present in the spin fluctuations of Ca(Fe$_{1−x}$Co$_x$)$_2$As$_2$ compounds. These peculiar features seem to be consistent with the unique magnetostructural properties of Ca(Fe$_{1−x}$Co$_x$)$_2$As$_2$ compounds.

Another compound discussed in this thesis is CaCo$_{1.86}$As$_2$, which is in the collapsed tetragonal phase and exhibits magnetic ground state, unlike its $A$Fe$_2$As$_2$ counterparts. Inelastic neutron scattering measurements performed on this compound revealed extremely anisotropic spin fluctuations along the two directions of the reciprocal space. The result suggests that the CaCo$_{1.86}$As$_2$ is a unique example of highly–frustrated square–lattice system.

The final compound discussed is the K substituted BaMn$_2$As$_2$, i.e. Ba$_{1−x}$K$_x$Mn$_2$As$_2$ compounds. K substitution (hole doping) in BaMn$_2$As$_2$ changes the insulating ground state of the parent BaMn$_2$As$_2$ compound to the metallic state. Previous measurements of these compounds indicate that the hole doping induces itinerant ferromagnetism that coexists with the local moment antiferromagnetism of the parent BaMn$_2$As$_2$ compound. To further understand the effects of hole doping on magnetism, inelastic neutron scattering measurements were performed on Ba$_{1−x}$K$_x$Mn$_2$As$_2$ compounds with x = 0, 0.125 and 0.25. The results suggest minor changes in the spin fluctuations with the hole doping, i.e. minor changes up to hole carrier concentrations of 12.5% per Mn ion (i.e. x = 0.25). This is consistent with the idea that the charge transport and antiferromagnetism are decoupled in the Ba$_{1−x}$K$_x$Mn$_2$As$_2$ compounds, i.e. the doped holes have small effects on the antiferromagnetism.