Microscopic magnetic Hamiltonian for exotic spin textures in metals

We derive and study a microscopic spin Hamiltonian on a lattice for Rashba-coupled double exchange metals. The Hamiltonian consists of anisotropic interactions of the Dzyaloshinskii-Moriya and pseudodipolar 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.