High-damping alloys with the magnetomechanical damping mechanism, based on the Fe-Cr system, have been studied. It has been shown that the direct investigation of the magnetic domain structure in the bulk materials using the neutron refraction method allows one to obtain important quantitative information concermng the formation of the high-damping state. The dependence of the damping capacity on the average magnetic domain size was found to possess a sharp maximum, thus revealing a range of the optimal domain sizes. The results obtained are important for the development of the technology of high-damping materials.