  We derive a new microscopic spin Hamiltonian for Rashba-coupled double
exchange metals. The Hamiltonian consists of anisotropic interactions of the
Dzyaloshinskii-Moriya (DM) and Kitaev form, in addition to the standard
isotropic term. We validate the spin Hamiltonian by comparing results with
those on the exact spin-fermion model, and present its phase diagram using
large scale Monte Carlo simulations. In addition to ferromagnetic, planar
spiral and flux states, the model hosts skyrmion crystal and classical
spin-liquid states characterized, respectively, by multiple peaks and a diffuse
ring pattern in the spin structure factor. The filamentary domain wall
structures in the spin-liquid state are in remarkable agreement with
experimental data on thin films of MnSi-type B20 metals and transition metals
and their alloys.
