Engineering non trivial topological phases in materials, specially skyrmion-like arrangements, has been of great interest in the last decade due to its potential technological applications. In this work, we study a model of electrons coupled to a magnetic texture in the kagome lattice interacting with magnetic moments via Rashba spin orbit coupling in the large Hund interaction limit. We obtain the effective spin Hamiltonian and study the emergent low temperature phases under an external magnetic field using large scale Monte Carlo simulations. We show that strong geometric frustration, characteristic of the kagome lattice, and the competition between the effective exchange, antisymmetric and anisotropic couplings, gives rise to a large variety of non-trivial topological phases. On the one hand, for antiferromagnetic exchange coupling a pseudo-antiferromagnetic skyrmion crystal is stabilized for a broad range of parameters. As the exchange coupling gets smaller, chiral single-q and double-q phases emerge. On the other hand, in the ferromagnetic case, even though the competition of the different interactions produce a series of exotic textures, a remarkable parallel may be drawn with the pure ferromagnetic model with antisymmetric interactions. Finally, for the special case where the exchange coupling is completely suppressed, we show that, coming from a higher temperature cooperative paramagnet, an "umbrella-like" plaquette order with semiextensive degeneracy is induced by the external magnetic field.

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