We show that an effective gravitational field naturally emerges in quantum materials with long-wavelength spin (or pseudospin) textures. When the itinerant electrons' spin strongly couples to the background spin texture, it effectively behaves as a spinless particle in a curved space, with the curvature arising from quantum corrections to the electron's spin orientation. The emergent curved space gives rise to the electron lensing effect, an analog of the gravitational lensing. The lensing effect can appear in systems without (emergent) magnetic fields, such as those with coplanar spin textures. Our work shows that “gravitational” phenomena generically appear in quantum systems due to nonadiabaticity.

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• Fluids & classical fields in curved spacetime
• Geometric & topological phases
• Spin texture
• Spintronics
• Adiabatic approximation