  The release of spin-down energy by a magnetar is a promising scenario to
power several classes of extreme explosive transients. However, it lacks a firm
basis because magnetar formation still represents a theoretical challenge.
Using the first three-dimensional simulations of a convective dynamo based on a
protoneutron star interior model, we demonstrate that the required dipolar
magnetic field can be consistently generated for sufficiently fast rotation
rates. The dynamo instability saturates in the magnetostrophic regime with the
magnetic energy exceeding the kinetic energy by a factor of up to 10. Our
results are compatible with the observational constraints on galactic magnetar
field strength and provide strong theoretical support for millisecond
protomagnetar models of gamma-ray burst and superluminous supernova central
engines.
