Spin-textured neutron beams with orbital angular momentum

We present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a "cork-screw"phase singularity eiℓφ about the propagation axis where ℓ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle.