  In this paper, we investigate the convergence rates of inviscid limits for
the free-boundary problems of the incompressible magnetohydrodynamics (MHD)
with or without surface tension in $\mathbb{R}^3$, where the magnetic field is
identically constant on the surface and outside of the domain. First, we
establish the vorticity, the normal derivatives and the regularity structure of
the solutions, and develop a priori co-norm estimates including time
derivatives by the vorticity system. Second, we obtain two independent
sufficient conditions for the existence of strong vorticity layers: (I) the
limit of the difference between the initial MHD vorticity of velocity or
magnetic field and that of the ideal MHD equations is nonzero. (II) The cross
product of tangential projection on the free surface of the ideal MHD strain
tensor of velocity or magnetic field with the normal vector of the free surface
is nonzero. Otherwise, the vorticity layer is weak. Third, we prove high order
convergence rates of tangential derivatives and the first order normal
derivative in standard Sobolev space, where the convergence rates depend on the
ideal MHD boundary value.
