  We study the ground state of a system with an interface between $\nu=4$ and
$\nu=3$ in the quantum Hall regime. Far from the interface, for a range of
interaction strengths, the $\nu=3$ region is fully polarized but $\nu=4$ region
is locally a singlet. Upon varying the strength of the interactions and the
width of the interface, the system chooses one of two distinct edge/interface
phases. In phase A, stabilized for wide interfaces, spin is a good quantum
number, and there are no gapless long-wavelength spin fluctuations. In phase B,
stabilized for narrow interfaces, spin symmetry is spontaneously broken at the
Hartree-Fock level. Going beyond Hartree-Fock, we argue that phase B is
distinguished by the emergence of gapless long-wavelength spin excitations
bound to the interface, which can, in principle, be detected by a measurement
of the relaxation time $T_2$ in nuclear magnetic resonance.
