  We consider magnetic field screening and spontaneous magnetic fields in
$s+is$ and $s+id$ superconductors both analytically and numerically. We show
that in general, the linearized model couples the moduli of order parameters to
the magnetic modes. This causes magnetic field screening that does not follow
the standard exponential law and hence cannot be characterized by a single
length scale: the London penetration length.
  We also demonstrate that the resulting linear mixed modes, correctly predict
spontaneous fields and their orientation. We show that these mixed modes cause
external fields to decay non-monotonically in the bulk. This is observed as the
magnetic field twisting direction, up to an angle of $\pi/2$, as it decays in
the nonlinear model.
  Finally, we demonstrate that there are two non-degenerate domain wall
solutions for any given parameter set. These are distinguished by either
clockwise or anti-clockwise interpolation of the inter-component phase
difference, each producing a different solution for the other fields. However,
only domain wall solutions in $s+id$ systems exhibit magnetic field twisting.
