  Spin-wave instability for parallel pumping is studied theoretically. The
spin-wave instability threshold is calculated in ferromagnetic thin films under
oblique field which has an oblique angle to the film plane. The butterfly curve
of the threshold usually has a cusp at a certain value of the static external
field. While the static field value of the cusp point varies as the oblique
angle changes, the general properties of the butterfly curve show little
noteworthy change. For very thin films, however, multiple cusps of the
butterfly curve can appear due to different standing spin-wave modes, which
indicate a novel feature for thin films under oblique field.
