  Coupling of the spin and orbital degrees of freedom on the surface of a
strong three-dimensional insulator, on the one hand, and textured magnetic
configuration in an adjacent ferromagnetic film, on the other, is studied using
a combination of transport and thermodynamic considerations. Expressing
exchange coupling between the localized magnetic moments and Dirac electrons in
terms of the electrons' out-of-plane orbital and spin magnetizations, we relate
the thermodynamic properties of a general ferromagnetic spin texture to the
physics in the zeroth Landau level. Persistent currents carried by Dirac
electrons endow the magnetic texture with a Dzyaloshinski-Moriya interaction,
which exhibits a universal scaling form as a function of electron temperature,
chemical potential, and the time-reversal symmetry breaking gap. In addition,
the orbital motion of electrons establishes a direct magnetoelectric coupling
between the unscreened electric field and local magnetic order, which furnishes
complex long-ranged interactions within the magnetic film.
