What is the thick, dashed, magenta line on a sectional chart?
The Atlanta sectional near KANB, KASN, and KPLR gives a hint:

FOR REASONS OF NATIONAL SECURITY
PILOTS ARE REQUESTED TO AVOID FLIGHT
AT AND BELOW 5000’ AGL IN THIS AREA

It is called a National Security Area, which FAA’s training ALC-42: Airspace, Special Use Airspace and TFRs describes as follows.

National Security Areas
National Security Areas consist of airspace of defined vertical and lateral dimensions established at locations where there is a requirement for increased security and safety of ground facilities. Pilots are requested to voluntarily avoid flying through the depicted NSA. When it is necessary to provide a greater level of security and safety, flight in NSAs may be temporarily prohibited by regulation under the provisions of 14 CFR Section 99.7. Regulatory prohibitions will be issued by System Operations, System Operations Airspace and AIM Office, Airspace and Rules, and disseminated via NOTAM. Inquiries about NSAs Inquiries should be directed to Airspace and Rules.
Example — National Security Area near Pueblo, Co. and request to avoid flight at and below 3000’ AGL.


Wikipedia gives a brief description.

In United States aviation, a National Security Area is a designated airspace through which flight is discouraged for reasons of national security.
Flight through NSAs is not prohibited and no special advance clearance or authorization need be obtained to enter them. However, pilots of aircraft are strongly encouraged to either stay clear of NSAs or obtain prior authorization to pass through them in order to reassure the controlling agency that no threat to national security exists.
NSAs are a compromise between normal airspace and restricted or prohibited airspace. NSAs can be temporarily converted into restricted airspace by NOTAMs.
On VFR sectional charts, NSAs are delimited by a heavy dashed magenta border and a special notation.