  In this paper, we discuss a possibility to improve constraints on
spin-dependent short-range interactions in the range of 1 - 200 micrometer
significantly. For such interactions, our constraints are without competition
at the moment. They were obtained through the observation of gravitationally
bound states of ultracold neutrons. We are going to improve these constraints
by about three orders of magnitude in a dedicated experiment with polarized
neutrons using the next-generation spectrometer GRANIT.
