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Theoretical evidence of the Berry-phase mechanism in anomalous Hall transport: First-principles studies of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi><mml:msub><mml:mi mathvariant="normal">Cr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Se</mml:mi><mml:mrow><mml:mn>4</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">Br</mml:mi><mml…
To justify the origin of the anomalous Hall effect (AHE), it is highly desirable to have the system parameters tuned continuously. By quantitative calculations, we show that the doping-dependent sign reversal in $\mathrm{Cu}{\mathrm{Cr}}_{2}{\mathrm{Se}}_{4\ensuremath{-}x}{\mathrm{Br}}_{x}$, observed but not understood, is nothing but direct evidence for the Berry-phase mechanism of the AHE. Systematic …