  The origin of magnetic fields that permeate the blast waves of gamma-ray
bursts (GRBs) is a long-standing problem. The present paper argues that in four
GRBs revealing extended emission at >100 MeV, with follow-up in the radio,
optical and X-ray domains at later times, this magnetization can be described
as the partial decay of the micro-turbulence that is generated in the shock
precursor. Assuming that the bulk of the extended emission >100 MeV can be
interpreted as synchrotron emission of shock accelerated electrons, we model
the multi-wavelength light curves of GRB 090902B, GRB 090323, GRB 090328 and
GRB 110731A, using a simplified then a full synchrotron calculation with
power-law-decaying microturbulence \epsilon_B \propto t^{\alpha_t} (t denotes
the time since injection through the shock, in the comoving blast frame). We
find that these models point to a consistent value of the decay exponent -0.5 <
\alpha_t < -0.4.
