  We investigate the influence of magnetic fields on the evolution of binary
neutron-star (BNS) merger remnants via three-dimensional (3D)
dynamical-spacetime general-relativistic (GR) magnetohydrodynamic (MHD)
simulations. We evolve a postmerger remnant with an initial poloidal magnetic
field, resolve the magnetoturbulence driven by shear flows, and include a
microphysical finite-temperature equation of state (EOS). A neutrino leakage
scheme that captures the overall energetics and lepton number exchange is also
included. We find that turbulence induced by the magnetorotational instability
(MRI) in the hypermassive neutron star (HMNS) amplifies magnetic field to
beyond magnetar-strength ($10^{15}\, \mathrm{G}$). The ultra-strong toroidal
field is able to launch a relativistic jet from the HMNS. We also find a
magnetized wind that ejects neutron-rich material with a rate of
$\dot{M}_{\mathrm{ej}} \simeq 1 \times10^{-1}\, \mathrm{M_{\odot}\, s^{-1}}$.
The total ejecta mass in our simulation is $5\times 10^{-3}\,
\mathrm{M_{\odot}}$. This makes the ejecta from the HMNS an important component
in BNS mergers and a promising source of $r$-process elements that can power a
kilonova. The jet from the HMNS reaches a terminal Lorentz factor of $\sim 5$
in our highest-resolution simulation. The formation of this jet is aided by
neutrino-cooling preventing the accretion disk from protruding into the polar
region. As neutrino pair-annihilation and radiative processes in the jet (which
were not included in the simulations) will boost the Lorentz factor in the jet
further, our simulations demonstrate that magnetars formed in BNS mergers are a
viable engine for short gamma-ray bursts (sGRBs).
