  Hartman effect for spin waves tunnelling through a barrier in a thin magnetic
film is considered theoretically. The barrier is assumed to be created by a
locally increased magnetic anisotropy field. The considerations are focused on
a nanoscale system operating in the exchange-dominated regime. We derive the
formula for group delay $\tau_{gr}$ of spin wave package and show that
$\tau_{gr}$ saturates with increasing barrier width, which is a signature of
the Hartman effect predicted earlier for photonic and electronic systems. In
our calculations we consider the general boundary exchange conditions which
take into account different strength of exchange coupling between the barrier
and its surrounding. As a system suitable for experimental observation of the
Hartman effect we propose a CoFeB layer with perpendicular magnetic anisotropy
induced by a MgO overlayer.
