In the internal shock model for gamma-ray bursts (GRBs), the synchrotron spectrum from the fast cooling electrons in a homogeneous downstream magnetic field (MF) is too soft to produce the low-energy slope of GRB spectra. However the magnetic field m
ay decay downstream with distance from the shock front. Here we show that the synchrotron spectrum becomes harder if electrons undergo synchrotron and inverse-Compton cooling in a decaying MF. To reconcile this with the typical GRB spectrum with low energy slope $ u F_ upropto u$, it is required that the postshock MF decay time is comparable to the cooling time of the bulk electrons (corresponding to a MF decaying length typically of $sim10^5$ skin depths); that the inverse-Compton cooling should dominate synchrotron cooling after the MF decay time; and/or that the MF decays with comoving time roughly as $Bpropto t^{-1.5}$. An internal shock synchrotron model with a decaying MF can account for the majority of GRBs with low energy slopes not harder than $ u^{4/3}$.
