  Zero- to ultra-low-field nuclear magnetic resonance (ZULF NMR) provides a new
regime for the measurement of nuclear spin-spin interactions free from effects
of large magnetic fields, such as truncation of terms that do not commute with
the Zeeman Hamiltonian. One such interaction, the magnetic dipole-dipole
coupling, is a valuable source of spatial information in NMR, though many terms
are unobservable in high-field NMR, and the coupling averages to zero under
isotropic molecular tumbling. Under partial alignment, this information is
retained in the form of so-called residual dipolar couplings. We report zero-
to ultra-low-field NMR measurements of residual dipolar couplings in
acetonitrile-2-$^{13}$C aligned in stretched polyvinyl acetate gels. This
represents the first investigation of dipolar couplings as a perturbation on
the indirect spin-spin $J$-coupling in the absence of an applied magnetic
field. As a consequence of working at zero magnetic field, we observe terms of
the dipole-dipole coupling Hamiltonian that are invisible in conventional
high-field NMR. This technique expands the capabilities of zero- to
ultra-low-field NMR and has potential applications in precision measurement of
subtle physical interactions, chemical analysis, and characterization of local
mesoscale structure in materials.
