  We report the results of a new search for long range spin-dependent
interactions using a Rb -$^{21}$Ne atomic comagnetometer and a rotatable
electron spin source based on a SmCo$_{5}$ magnet with an iron flux return. By
looking for signal correlations with the orientation of the spin source we set
new constrains on the product of the pseudoscalar electron and neutron
couplings $g^e_p g^n_p/\hbar c<1.7\times10^{-14}$ and on the product of their
axial couplings $g^e_A g^n_A/\hbar c<5\times10^{-42}$ to a new particle with a
mass of less than about $1~\mu$eV. Our measurements improve by about 2 orders
of magnitude previous constraints on such spin-dependent interactions.
