For a 'quick format' (or corruption) on any kind of disk, some free or cheap "undelete" software can recover most or all of the files, depending on what has happened after the format.
A curious thing about magnetic media is that if you go deep into the physical ferromagnetic layer, it's possible to determine both what is there now, and what was there before (as in you can in some cases see previous data that has actually been overwritten). A binary 1-was-0 is distinguishable from a 1-was-1, if you look closely enough.
This is not something you can do with a bit of freeware on your laptop, you need a clean room to disassemble the HD and extremely expensive equipment to read the platters and analyse the images. This is MI6 or Serious Organised Crime level stuff.
Modern file scrubbing software takes that into account and writes over the binary bits multiple times, hopefully thwarting any reliable analysis of the historic state of the bit.