  Approximately 1/4-1/2 of short duration Gamma-Ray Bursts are followed by
variable X-ray emission lasting ~ 100 s with a fluence comparable or exceeding
that of the initial burst itself. The long duration and significant energy of
this `extended emission'(EE) poses a major challenge to the standard binary
neutron star merger model. metzger08 recently proposed that the EE is powered
by the spin-down of a strongly magnetized neutron star. However, the effects of
surrounding material on the magnetar outflow have not yet been considered. Here
we present time-dependent axisymmetric relativistic magnetohydrodynamic
simulations of the interaction of the relativistic proto-magnetar wind with a
surrounding 10^-1 10^-3 M_\odot envelope, which represents material ejected
during the merger; the supernova following AIC; or via outflows from the
accretion disk. The collision between the relativistic magnetar wind and the
expanding ejecta produces a magnetized nebula inside the ejecta. A strong
toroidal magnetic field builds up in the nebula, which drives a bipolar jet out
through the ejecta, similar to the magnetar model developed in the case of long
duration GRBs. We quantify the `break-out' time and opening angle of the jet
theta_j as a function of the wind energy flux dot{E} and ejecta mass M_ej. We
show that dot{E} and theta_j are inversely correlated, such that the
beaming-corrected (isotropic) luminosity of the jet is primarily a function of
M_ej. Both variability arguments, and the lower limit on the power of magnetar
outflows capable of producing bright emission, suggest that the true opening
angle of the magnetar jet must be relatively large. The model thus predicts a
class of events for which the EE is observable with no associated short GRB.
These may appear as long-duration GRBs or X-Ray Flashes, which may be detected
by future all-sky X-ray survey missions.
