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We present a detailed derivation of a model to study effects ofself-gravitation from semi-classical gravity, described by theSchr\"odinger-Newton equation, employing spin superposition states ininhomogeneous magnetic fields, as proposed recently for experiments searchingfor gravity induced entanglement. Approximations for the experimentallyrelevant limits are discussed. Results suggest that spin interferometry couldprovide a more accessible route towards an experimental test of quantum aspectsof gravity than both previous proposals to test semi-classical gravity and theobservation of gravitational spin entanglement.

Dephasing and inhibition of spin interference from semi-classical self-gravitation