Here we have established neutron spin echo (NSE) optics by observing spin precession through magnetic Fabry-Perot films of [Permalloy45(Fe_(55)Ni_(45))(abbreviated as PA)-Ge]~n-PA with n=10 including the tunneling region, through multilayer film of (PA-Ti)~n with n=15 at the Bragg condition, as well as through helical magnetic crystal of holmium at the Bragg conditions using a forward scattering (transmission) neutron spin echo interferometer in KURRI and JAERI. The number of Larmor precession through these materials gives a phase shift between the trapped arrow up spin wave function of neutron due to the magnetic potential wells and the arrow down spin wave function traveling through non reflecting magnetic layers as a function of the incident angle. These extra spin precessions through multilayer magnetic films are well reproduced by the simulation between the phase difference of arrow up and arrow down spin wave function by solving Schrodinger equation based on one dimensional multi-well potentials. While the observed spin precessions of O-wave through helical magnetic crystal of holmium or ferromagnetic crystal of permalloy at Bragg condition seems proportional to the rocking curve intensity of the magnetic Bragg reflection and different from the predicted one through a magnetic perfect crystal. These results indicate that the multiple Bragg reflection of arrow up spin neutron causes the extra-phase shift while that of the arrow down spin merely path through the crystal without Bragg reflection.
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