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 unpolarized. 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 be detected by a measurement of the relaxation time $T_2$ in nuclear magnetic resonance.

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• Edge states
• Hall effect
• Landau levels
• Quantum Hall effect
• Two-dimensional electron system
• Mean field theory