  The triangular-lattice Heisenberg antiferromagnet (HAF) is known to carry
topological Z_2 vortex excitations which form a gas at finite temperatures.
Here we show that the spin-orbit interaction, introduced via a Kitaev term in
the exchange Hamiltonian, condenses these vortices into a triangular $Z_2$
vortex crystal at zero temperature. The cores of the Z_2 vortices show abrupt,
soliton-like magnetization modulations and arise by a special intertwining of
three honeycomb superstructures of ferromagnetic domains, one for each of the
three sublattices of the 120-degree state of the pure HAF. This is a new
example of a nucleation transition, analogous to the spontaneous formation of
magnetic domains, Abrikosov vortices in type-II syperconductors, blue phases in
cholesteric liquid crystals, and skyrmions in chiral helimagnets. As the
mechanism relies on the interplay of geometric frustration and spin-orbital
anisotropies, such vortex mesophases can materialize as a ground-state property
in spin-orbit coupled correlated systems with nearly hexagonal topology, as in
triangular or strongly frustrated honeycomb iridates.
