A collective, macroscopic signature to detect radiation friction in laser-plasma experiments is proposed. In the interaction of superintense circularly polarized laser pulses with high density targets, the effective dissipation due to radiative losses allows the absorption of electromagnetic angular momentum, which in turn leads to the generation of a quasistatic axial magnetic field. This peculiar inverse Faraday effect is investigated by analytical modeling and three-dimensional simulations, showing that multi-gigagauss magnetic fields may be generated at laser intensities $>10^{23}~mbox{W cm}^{-2}$.
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