Impact of dynamic orbital correlations on magnetic excitations in the normal state of iron-based superconductors

We show here that orbital degrees of freedom produce a distinct signature in the magnetic excitation spectrum of iron-based superconductors above the magnetic ordering temperature. Because $d_{xz}$ and $d_{yz}$ orbitals are strongly connected with Fermi surface topology, the nature of magnetic excitations can be modified significantly due to the presence of either static or fluctuating orbital correlations. Within a five-orbital itinerant model, we show that static orbital order generally leads to an enhancement of commensurate magnetic excitations even when the original Fermi surface lacks nesting at $(\pi ,0)$ or $(0,\pi )$. When long-range orbital order is absent, Gaussian fluctuations beyond the standard random-phase approximation capture the effects of fluctuating orbital correlations on the magnetic excitations. We find that commensurate magnetic excitations can also be enhanced if the orbital correlations are strong. Our results offer a natural explanation for the incommensurate-to-commensurate transformation observed in a recent neutron scattering measurement (Xu et al., arXiv:1201.4404), and we propose that this unusual transformation is an important signature to distinguish orbital from spin physics in the normal state of pnictides. Implications for the magnetic and superconducting states are discussed.

Figure 1

The imaginary part of the spin susceptibility is plotted along $\vec{q}=(\pi ,q_y)$ for (a) $\phi =0$, (b) $\phi =30$ meV, (c) $\phi =60$ meV, and (d) Gaussian fluctuations with ${\lambda }^2=60$ meV. In this figure, the chemical potential $\mu$ is set to be 0 in the tight-binding model proposed in Ref. 18, corresponding to an electron doping of about $5\%$.

Figure 2

The imaginary part of the spin susceptibility is plotted for a doping level of about $9\%$ for (a) $\phi =0$, (b) $\phi =10$ meV, (c) $\phi =20$ meV, and (d) Gaussian fluctuations with ${\lambda }^2=30$ meV.

Figure 3

Inelastic neutron scattering measurement (data from Xu et al.[20]) of Fe${}_{1-x}$Ni${}_x$Te${}_{0.5}$Se${}_{0.5}$ with $x=0.04$ along the transverse direction to $Q_{\text{AFM}}$ for (a) the high-temperature normal state ($T>T_{\text{fluc}}$) and (b) the superconducting state ($T<T_c$). An incommensurate-to-commensurate transformation is observed as the sample is cooled down.

Figure 4

Demonstration of the evolution of the imaginary part of the spin susceptibility along $\vec{q}=(\pi ,q_y)$ as the temperature is lowered from high temperature. The parameters in the tight-binding model are the same as in Fig. 1, and a broadening in the $\vec{q}$ space of $q_0=0.1\pi$ is introduced with the form of $\mathrm{Im}{\chi }^B(\vec{q},\omega )={\sum }_{{\vec{q}}^{\prime }}{e}^{-{(\vec{q}-{\vec{q}}^{\prime })}^2/q_0^2}\mathrm{Im}\chi ({\vec{q}}^{\prime },\omega )/{\sum }_{{\vec{q}}^{\prime }}{e}^{-{(\vec{q}-{\vec{q}}^{\prime })}^2/q_0^2}$ for ease of comparison with the experimental data in Fig. 3. For $T>T_{\text{fluc}}$, orbital fluctuations do not affect the magnetic excitations. In this case, $H_{\text{OO}}$ is completely turned off. For $T_{\text{fluc}}>T>T_s$, the system does not have long-range orbital order but rather has fluctuating orbital correlations, which can be described at the Gaussian level (in the plot, ${\lambda }^2=30$ meV is used). For $T<T_s$, an orbital order is formed and the magnetic excitation is commensurate. The orbital order parameter in the plot is $\phi =20$ meV.