  The merger of two neutron stars may give birth to a long-lived hypermassive
neutron star. If it harbours a strong magnetic field of magnetar strength, its
spin-down could explain several features of short gamma-ray burst afterglows.
The magnetorotational instability (MRI) has been proposed as a mechanism to
amplify the magnetic field to the required strength. Previous studies have,
however, neglected neutrinos, which may have an important impact on the MRI by
inducing a viscosity and drag. We investigate the impact of these neutrino
effects on the linear growth of the MRI by applying a local stability analysis
to snapshots of a neutron star merger simulation. We find that neutrinos have a
significant impact inside the hypermassive neutron star, but have at most a
marginal effect in the torus surrounding it. Inside the hypermassive neutron
star, the MRI grows in different regimes depending on the radius and on the
initial magnetic field strength. For magnetic fields weaker than
$10^{13}-10^{14}\,{\rm G}$, the growth rate of the MRI is significantly reduced
due to the presence of neutrinos. We conclude that neutrinos should be taken
into account when studying the growth of the MRI from realistic initial
magnetic fields. Current numerical simulations, which neglect neutrino
viscosity, are only consistent, i.e. in the adopted ideal regime, if they start
from artificially strong initial magnetic fields above $\sim10^{14}\,{\rm G}$.
One should be careful when extrapolating these results to lower initial
magnetic fields, where the MRI growth is strongly affected by neutrino
viscosity or drag.
