Defects intentionally introduced into magnetic materials often have a profound effect on the physical properties. Specifically tailored neutron spectroscopic experiments can provide detailed information on both the local exchange interactions and the local distances between the magnetic atoms around the defects. This is demonstrated for manganese dimer excitations observed for the magnetically diluted three-, two- and one-dimensional compounds KMnxZn1-xF3, K2MnxZn1-xF4 and CsMnxMg1-xBr3, respectively, with x=0.10. The resulting local exchange interactions deviate up to 10% from the average, and the local Mn-Mn distances are found to vary stepwise with increasing internal chemical pressure due to the Mn/Zn or Mn/Mg substitution. Our analysis qualitatively supports the theoretically predicted decay of atomic displacements according to 1/r**2, 1/r and constant (for three-, two- and one-dimensional compounds, respectively) where r denotes the distance of the displaced atoms from the defect.