A heat pump system includes a magneto-caloric material disposed within a chamber of a regenerator housing. A back iron extends between an outer magnet and an inner magnet in order to provide a flux path between the outer and inner magnets. At least a portion of the back iron extends between the outer and inner magnets along the radial direction and is not positioned coplanar with the inner and outer magnets in a plane that is perpendicular to the axial direction. A related refrigerator appliance is also provided.