the force that pushes the magnets sideways must be due to the interactions of field lines perpendicular to the direction of attraction. One possibility is,
where at the ends of the magnets, the domains reversed and the field lines on one side run parallel to the end surface. The interactions of these field lines push the the magnets sideways. The diagram on the right shows a more definitive way to make such magnets. These are,
electromagnetic version of the same, where strong parallel field lines at the end of the them create a strong push side-way in a stater-rotor configuration.
Just thinking out loud.
