Magnetoelastic Quantum Fluctuations and Phase Transitions in the Iron Superconductors

We examine the relevance of magnetoelastic coupling to describe the complex magnetic and structural behavior of the different classes of the iron superconductors. We model the system as a two-dimensional metal whose magnetic excitations interact with the distortions of the underlying square lattice. Going beyond the mean field, we find that quantum fluctuation effects can explain two unusual features of these materials that have attracted considerable attention: first, why iron telluride orders magnetically at a non-nesting wave vector $(\pi /2,\pi /2)$ and not at the nesting wave vector $(\pi ,0)$ as in the iron arsenides, even though the nominal band structures of both these systems are similar, and second, why the $(\pi ,0)$ magnetic transition in the iron arsenides is often preceded by an orthorhombic structural transition. These are robust properties of the model, independent of microscopic details, and they emphasize the importance of the magnetoelastic interaction.

Figure 1

Magnetoelastic coupling [Eq. (1)] describing scattering of paramagnons (straight line) (a) with phonons (wavy line) at finite $\mathbf{k}$ and (b) with orthorhombic distortion (dashed line) at the $\mathbf{k}\to 0$ limit. The associated matrix elements $g_{\alpha }(\mathbf{k},\mathbf{q})$ and $h(\mathbf{q})$ are defined in Eqs. (2, 3), respectively.

Figure 2

Magnetoelastic coupling induced quantum fluctuations producing (a) static paramagnon self-energy ${\Pi }_2(\mathbf{q})$ due to scattering with phonons and (b) correction to the orthorhombic elastic constant $C_0$ due to paramagnons.

Figure 3

(a) Paramagnon self-energy ${\Pi }_2(\mathbf{q})$ along the high symmetry directions of the Brillouin zone for increasing values of magnetoelastic coupling ${\lambda }_0=1,\dots ,5$ (bottom to top) in units of $10\mathrm{meV}/\AA$. It is always peaked at $(\pi /2,\pi /2)$. (b) The corresponding renormalized paramagnon dispersions ${\chi }^{-1}(\mathbf{q})={\Pi }_0(\mathbf{q})-{\Pi }_2(\mathbf{q})$ (second-from-top to bottom curves, respectively) and the bare dispersion ${\Pi }_0(\mathbf{q})$ (topmost curve, shifted up by 0.2 meV for clarity). At large enough ${\lambda }_0$ (bottommost) the global minima changes to $(\pi /2,\pi /2)$ (dashed arrow) from the nesting-driven $(\pi ,0)$ wave vector (solid arrow).