Elastic coupling and spin-driven nematicity in iron-based superconductors

Spin-driven nematic order that has been proposed for iron-based superconductors is generated by pronounced fluctuations of a striped density wave state. On the other hand it is a well known fact that the nematic order parameter couples bilinearly to the strain, which suppresses the fluctuations of the nematic order parameter itself and lowers the upper critical dimension, yielding mean-field behavior of the nematic degrees of freedom for d > 2. This is consistent with the measured Curie-Weiss behavior of the nematic susceptibility. Here we reconcile this apparent contradiction between pronounced magnetic fluctuations and mean-field behavior of the nematic degrees of freedom. We show, by developing phi(4) theory for the nematic degrees of freedom, that the coupling to elastic strain does not suppress the fluctuations that cause the nematic order in the first place (magnetic fluctuations), yet it does transform the Ising-nematic transition into a mean-field transition. In addition, we demonstrate that the mean-field behavior occurs in the entire temperature regime where a softening of the shear modulus is observed.