  We develop a theory of the correlated magnetically ordered insulating state
at the edge of a two-dimensional topological insulator. We demonstrate that the
gapped spin-polarized state, induced by the application of the magnetic field
$B$, is naturally facilitated by electron interactions, which drive the
critical easy-plane ferromagnetic correlations in the helical liquid. As the
key manifestation, the gap $\De$ in the spectrum of collective excitations,
which carry both spin and charge, is enhanced and exhibits a scaling dependence
$\De \propto B^{1/(2-K)}$, controlled by the Luttinger liquid parameter $K$.
This scaling dependence could be probed through the activation behavior $G \sim
(e^2/h) \exp(- \De/T)$ of the longitudinal conductance of a Hall-bar device at
lower temperatures, providing a straightforward way to extract the parameter
$K$ experimentally. Our findings thus suggest that the signatures of the
interaction-driven quantum criticality of the helical liquid could be revealed
already in a standard Hall-bar measurement.
