The Dirac equation gives electrons in magnetic materials an intrinsic Berry curvature of 1/(2m^2c^2) at zero momentum that the Schrödinger-Pauli theory cannot reproduce without spin-orbit coupling.
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Time inversion symmetry in the Dirac and Schr\"odinger-Pauli theories
The Dirac equation gives electrons in magnetic materials an intrinsic Berry curvature of 1/(2m^2c^2) at zero momentum that the Schrödinger-Pauli theory cannot reproduce without spin-orbit coupling.