Exact spin dynamics of the 1/r² supersymmetric t-J model in a magnetic field

The dynamical spin structure factor S^{zz}(Q,omega) in the small momentum region is derived analytically for the one-dimensional supersymmetric t-J model with 1/r^2 interaction. Strong spin-charge separation is found in the spin dynamics. The structure factor S^{zz}(Q,omega) with a given spin polarization does not depend on the electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S^{zz}(Q,omega). These results are derived via solution of the SU(2,1) Sutherland model in the strong coupling limit.