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In order to explain the variance of the solar rotation law during theactivity minima and maxima, the angular momentum transport by rotatingmagnetoconvection is simulated in a convective box penetrated by an inclinedazimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses {and} the Lorentz force of the large-scale magnetic background field are thebasic transporters of angular momentum. Without rotation, the sign of themagnetic stresses naturally depends on the signs of the field components aspositive (negative) $B_\theta B_\phi$ transport the angular momentum poleward(equatorward). For fast enough rotation, however, the turbulence-originatedReynolds stresses start to dominate the transport of the angular momentum flux.The simulations show that positive ratios of the two meridional magnetic fieldcomponents to the azimuthal field reduce the inward radial as well as theequatorward latitudinal transport,%by the rotating magnetoconvection whichresult from hydrodynamic calculations. Only for $B_\theta B_\phi>0$ (generatedby solar-type rotation laws with an accelerated equator) does themagnetic-influenced rotation at the solar surface prove to be flatter than thenonmagnetic profile together with the observed slight spin-down of the equator.The latter phenomenon does not appear for antisolar rotation with polar vortexas well as for rotation laws with prevailing radial shear.

Angular momentum transport by magnetoconvection and the magnetic modulation of the solar differential rotation