  The Tayler-Spruit dynamo is one of the most promising mechanisms proposed to
explain angular momentum transport during stellar evolution. Its development in
proto-neutron stars spun-up by supernova fallback has also been put forward as
a scenario to explain the formation of very magnetized neutron stars called
magnetars. Using three-dimensional direct numerical simulations, we model the
proto-neutron star interior as a stably stratified spherical Couette flow with
the outer sphere that rotates faster than the inner one. We report the
existence of two subcritical dynamo branches driven by the Tayler instability.
They differ by their equatorial symmetry (dipolar or hemispherical) and the
magnetic field scaling, which is in agreement with different theoretical
predictions (by Fuller and Spruit, respectively). The magnetic dipole of the
dipolar branch is found to reach intensities compatible with observational
constraints on magnetars.
