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It is shown that an asymmetric spin-orbit interaction is appreciablyrenormalized by the effect of critical spin fluctuations. As an explicitexample, the Rashba-type interaction is predicted to be suppressed byanti-ferromagnetic critical fluctuations near the hot line (or point), leadingto a deformation of the Fermi surface near the hot line (or point) around whichthe band splitting is decreased, while ferromagnetic critical fluctuations areshown to enhance the Rashba-type interaction everywhere on the Fermi surface,leading to an increase in the band splitting. It is also found that themany-body mass renormalization, which diverges towards the magnetic quantumcritical point, is in the opposite sign for the two split bands by theRashba-type interaction. These predictions are observable by the de Haas-vanAlphen (dHvA) effect in principle.

Deformation of the Fermi Surface and Anomalous Mass Renormalization by Critical Spin Fluctuations through Asymmetric Spin-Orbit Interaction