Spin-driven nematic instability of the multiorbital Hubbard model: Application to iron-based superconductors

Nematic order resulting from the partial melting of density waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems - the multiorbital Hubbard model - displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard random phase approximation (RPA) method. Here, by including fluctuations beyond RPA in the multiorbital Hubbard model, we derive its nematic susceptibility and contrast it with its ferro-orbital order susceptibility, showing that its leading instability is the spin-driven nematic phase. Our results also demonstrate the primary role played by the dxy orbital in driving the nematic transition and reveal that high-energy magnetic fluctuations are essential to stabilize nematic order in the absence of magnetic order.