  Using series expansions and spin-wave theory we calculate the spin-stiffness
anisotropy $\rho_{sx}/\rho_{sy}$ in Heisenberg models on the square lattice
with anisotropic couplings $J_x,J_y$. We find that for the weakly anisotropic
spin-half model ($J_x\approx J_y$), $\rho_{sx}/\rho_{sy}$ deviates
substantially from the naive estimate $\rho_{sx}/\rho_{sy} \approx J_x/J_y$. We
argue that this deviation can be responsible for pinning the electronic liquid
crystal direction, a novel effect recently discovered in YBCO. For
completeness, we also study the spin-stiffness for arbitrary anisotropy
$J_x/J_y$ for spin-half and spin-one models. In the limit of $J_y/J_x\to 0$,
when the model reduces to weakly coupled chains, the two show dramatically
different behavior. In the spin-one model, the stiffness along the chains goes
to zero, implying the onset of Haldane-gap phase, whereas for spin-half the
stiffness along the chains increases monotonically from a value of $0.18 J_x$
for $J_y/J_x=1$ towards $0.25 J_x$ for $J_y/J_x\to 0$. Spin-wave theory is
extremely accurate for spin-one but breaks down for spin-half presumably due to
the onset of topological terms.
