We study the formation of dark matter clumps in the radiation era from the instability of a low-mass scalar-field component, in the non-relativistic regime.
We consider two scenarios: a tachyonic instability, associated with smooth potentials such as polynomials, and a parametric resonance, associated with axion monodromy, where a subdominant cosine potential corrects a mass term. 
We find that whereas for the tachyonic scenario the core density of the clumps is set by the characteristic scale of the potential,  for the axion monodromy, the core density scales with the soliton mass and radius.
Because of finite-size effects, these scenarios are not constrained by microlensing observations.
The scalar-field mass can range from $10^{-26}$ GeV to 10 GeV and the dark matter clumps from the size of atoms
to that of galactic molecular clouds.