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 nonmonotonically 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 nondegenerate domain wall solutions for any given parameter set. These are distinguished by either clockwise or anticlockwise interpolation of the intercomponent phase difference, each producing a different solution for the other fields. However, only domain wall solutions ins + id systems exhibit magnetic field twisting.