  The dominant mechanism for generating free-floating planets has so far
remained elusive. One suggested mechanism is that planets are ejected from
planetary systems due to planet-planet interactions. However, instability
around a single star requires a very compactly spaced planetary system. We find
that around binary star systems instability can occur even with widely
separated planets that are on tilted orbits relative to the binary orbit due to
combined effects of planet-binary and planet-planet interactions, especially if
the binary is on an eccentric orbit. We investigate the orbital stability of
planetary systems with various planet masses and architectures. We find that
the stability of the system depends upon the mass of the highest mass planet.
The order of the planets in the system does not significantly affect stability
but, generally, the most massive planet remains stable and the lower mass
planets are ejected. The minimum planet mass required to trigger the
instability is about that of Neptune for a circular orbit binary and a
super-Earth of about $10$ Earth masses for highly eccentric binaries. Hence, we
suggest that planet formation around misaligned binaries can be an efficient
formation mechanism for free-floating planets. While most observed
free-floating planets are giant planets, we predict that there should be more
low-mass free floating planets that are as yet unobserved than higher mass
planets.
