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Abstract: The role of electron-electron interactions is analyzed for Rashba-like andspin-split systems within a tight-binding single-band Hubbard model withon-site and all nearest-neighbor matrix elements of the Coulomb interaction. ByRashba-like systems we refer to the Dresselhaus and Rashba spin-orbit coupledphases; spin-split systems have spin-up and spin-down Fermi surfaces shiftedrelative to each other. Both systems break parity but preserve time-reversalsymmetry. They belong to a class of symmetry-breaking ground states thatsatisfy: i electron crystal momentum is a good quantum number ii thesestates have no net magnetic moment and iii their distribution of `polarizedspin- in momentum space breaks the lattice symmetry. In this class, therelevant Coulomb matrix elements are found to be nearest-neighbor exchange $J$,pair-hopping $J-$ and nearest-neighbor repulsion $V$. These ground states lowertheir energy most effectively through $J$, hence we name them Class $J$ states.The competing effects of $V-J-$ on the direct and exchange energies determinethe relative stability of Class $J$ states. We show that the spin-split andRashba-like phases are the most favored ground states within Class $J$ becausethey have the minimum anisotropy in `polarized spin-. On a square lattice wefind that the spin-split phase is always favored for near-empty bands; above acritical filling, we predict a transition from the paramagnetic to theRashba-like phase at $ J {c1}$ and a second transition to the spin-split stateat $J {c2}>J {c1}$. An energetic comparison with ferromagnetism highlights theimportance of the role of $V$ in the stability of Class $J$ states. We discussthe relevance of our results to i the $\alpha$ and $\beta$ phases proposed byWu and Zhang in the Fermi Liquid formalism and ii experimental observationsof spin-orbit splitting in \emph{Au}111 surface states.



Author: A. Alexandradinata, J. E. Hirsch

Source: https://arxiv.org/







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