I recall reading article in a popular science magazine about hypothetical negative mass with exactly these properties. It was about 25 years ago and the magazine was Russian language. Unfortunately, I can't recall its name now.
Oh, thanks to the power of the internet search, I found a scan of that article: http://epizodsspace.airbase.ru/bibl/tm/1990/10/otrits-massa.... The journal is "Техника-молодежи" (a Soviet style name that I am incapable of translating to English) and the article is from 1990. And that article refers to a publication by Robert Forward in a journal with a name like Aerospace Technology or Aerospace Engineering. But I fo…
Anyone interested in the implications of negative mass should probably check out Timemaster, a sci-fi novel by Forward. Negative mass can hypothetically do some interesting things. Things such as allowing lightspeed travel by matching negative mass to positive mass in equal amounts, leaving a non-photon object with rest mass = 0, or producing energy by accelerating negative mass to high velocities.
Unfortunately, Forward is much better as an idea guy than he is as an author. The scene where the hero travels back in time and has a threesome with himself and his wife is a bit awkward...