  Bond-dependent magnetic interactions can generate exotic phases such as
Kitaev spin-liquid states. Experimentally determining the values of
bond-dependent interactions is a challenging but crucial problem. Here, I show
that each symmetry-allowed nearest-neighbor interaction on triangular and
honeycomb lattices has a distinct signature in paramagnetic neutron-diffraction
data, and that such data contain sufficient information to determine the spin
Hamiltonian unambiguously via unconstrained fits. Moreover, I show that
bond-dependent interactions can often be extracted from powder-averaged data.
These results facilitate experimental determination of spin Hamiltonians for
materials that do not show conventional magnetic ordering.
