  We show that spinor fields nonminimally coupled to gravity can grow
spontaneously in the presence of matter. We name this phenomenon spontaneous
spinorization after the spontaneous scalarization scenario in scalar-tensor
theories. Underlying reason for the growth of the spinor is an instability
similar to the tachyon of spontaneous scalarization. We first present the
structure of a tachyonic Dirac equation, and incorporate it into the matter
coupling in gravity. This causes the zero-spinor solution to be unstable and
leads to spontaneous growth. We investigate the behavior of the resulting
theory for a spherically symmetric neutron star that has grown a spinor cloud.
Spontaneous spinorization has the potential to lead to order-of-unity
deviations from general relativity in strong fields in a similar manner to its
close relative spontaneous scalarization. This makes the theory especially
relevant to gravitational wave science and neutron star astrophysics.
