Entanglement is a remarkable peculiarity in quantum mechanics. It occurs in quantum systems that consist of space-like separated parts, or in systems whose observables belong to disjoint Hilbert spaces. The latter is the case in single-neutron systems. Entangled states are renowned for exhibiting non-classical correlations between observables of individual sub-systems. In a perfect Si-crystal interferometer experiment entanglement between three degrees of freedom in a single-neutron system is created. The prepared entanglement of spin, path and energy is induced by interaction with an oscillating magnetic field. The generated Greenberger-Horne-Zeilinger (GHZ) state is analyzed with an inequality derived by Mermin, yielding a value M = 2.558(4) 2, which exhibits a clear violation of the classical assumption. In addition observation of a GHZ entanglement, consisting of spin, momentum and total energy, in a neutron polarimetric experiment is presented. Here the advantages of neutron polarimetry, such as high contrast or insensitivity to ambient disturbances, are utilized resulting in final value of M = 3.936(2) 2.