Abstract
The present paper reports on the detailed studies concerning the neutron spin interference visibility observed after transmitting through multilayer magnetic resonators in a spin echo condition with very cold neutrons from a high flux reactor. The observed visibility of the interference between upward and downward spin components perpendicular to the Larmor precession plane of the neutron spin are compared with the numerical simulations in the plane wave theory and also in the Schrödinger wave-packet model. The comparison revealed the instructive characteristic features of obvious additional visibility decrease observed in the interference between the tunnelling and refractive transmissions of each spin components in a single as well as a couple of multilayer magnetic resonators.