Spin-Driven Nematic Instability in Realistic Microscopic Models: Application to Iron-Based Superconductors

Electronic nematicity due to the partial melting of density waves is a prevalent phenomenon in the field of high temperature superconductivity. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven order cannot be captured by the standard RPA method. By including fluctuations beyond RPA, we derive the orbitally-resolved nematic susceptibility of a generic multi-orbital Hubbard model, thus putting it on equal footing with other electronic susceptibilities of weakly and moderately interacting systems. Application to iron-based superconductors reveals that the $d_{xy}$--orbital plays a primary role in promoting a nematic transition preempting the magnetic transition. It furthermore demonstrates the importance of high-energy magnetic fluctuations in stabilizing nematic order in the absence of magnetic order. Finally, we show that the RPA ferro-orbital susceptibility shows no divergence on its own, providing strong evidence for a magnetic mechanism for nematicity.