  In the present work, we have studied the spectrum of the primordial
gravitational waves due to magnetic instability in the presence of neutrino
asymmetry. The magnetic instability generates a helical magnetic field on a
large scale. The anisotropic stress generated by the magnetic field shown to be
a source of primordial gravitational waves (GWs) at the time of matter-neutrino
decoupling. We expect that the theoretically predicted GWs by this mechanism
may be detected by Square Kilometer Array (SKA) or pulsar time array (PTA)
observations. We also compare our findings with the results obtained by the
earlier work where the effect of magnetic instability was not considered.
