Origin of doping-induced suppression and reemergence of magnetism in ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$

We investigate the evolution of magnetic properties as a function of hydrogen doping in the iron-based superconductor ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ using dynamical mean-field theory combined with density-functional theory. We find that two independent consequences of doping, namely the increase of the electron occupation and the structural modification, have the opposite effects on the strength of electron correlation and magnetism, resulting in the minimum of the calculated magnetic moment around the intermediate doping level as a function of $x$. Our result provides a natural explanation for the recent, puzzling experimental discovery of two separated antiferromagnetic phases at low and high doping limits. Furthermore, the increase of the orbital occupation and correlation strength with doping results in reduced orbital polarization of $d_{xz/yz}$ orbitals and an enhanced role of the $d_{xy}$ orbital in the magnetism at high doping levels, and their possible implications on the superconductivity are discussed in line with the essential role of the magnetism.

Figure 1

(a) Schematic phase diagram of ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ for the hydrogen concentration $x$ and temperature. AFM1 and AFM2 denote the first and second AFM phases, while SC1 and SC2 represent the first and second superconducting phases, respectively. Note that the bond length between Fe and As atoms increases with $x$. (b) Local magnetic moment and magnetic susceptibility ${\chi }_{\text{local}}(\omega =0)$ in the AFM phase as a function of $x$, which exhibit minima around $x=0.3$. (c) Mass enhancement $1/Z$ is calculated as a function of $x$ with three different treatments of doping in the PM phase: both electron addition and structural change are included (filled squares), but only structural change is allowed while no extra electron is added (empty circles), and an extra electron is added with $x$ while fixing the structure to that of the $x=0$ case (filled circles). (d) Local magnetic susceptibility as a function of $x$ in the AFM phase for three different treatments for doping analogous to (c). For the structure-only case, we use the number of extra electrons fixed to that for the $x=0.6$ case.

Figure 2

FS for (a)–(c) $x=0$, (d)–(f) $x=0.3$, and (g)–(i) $x=0.5$ calculated on the $k_z=0$ plane of the PM phase. Top rows are plots of $A$($k,\omega =0$) from the DFT+DMFT calculations, middle rows denote their Fe $d$ orbital characters, while bottom rows are from the usual DFT calculations. Each orbital character is represented by the depth of the assigned color as well as the thickness of the Fermi surface line.

Figure 3

The spectral function projected onto the Fe $d_{xy}$ orbital of an Fe atom, $A_{xy}\left(\omega \right)$, with majority- and minority-spin channels displayed in positive and negative axes, respectively, in the AFM phase. (a) From $x=0$ to 0.3, the magnetic moment decreases with decreasing exchange splitting. (b) From $x=0.4$ to 0.6, the magnetic moment increases. The inset depicts $A_{xy}\left(\omega \right)$ by the black line for a majority-spin channel of $x=0.6$. The shoulder structure around $-1$ eV indicated by a black arrow is correlated with the peak structure in $\mathrm{Im}{\mathrm{\Sigma }}_{xy}\left(\omega \right)$ shown by the red line at a slightly higher energy location, as indicated by a red arrow.

Figure 4

The spectral function in the two spin channels in the AFM phase, projected onto $d_{xz}, d_{yz}$, and $d_{xy}$ orbitals in a Fe atom, for (a) $x=0$ and (b) $x=0.5$. The orbital order that corresponds to the difference between $xz$ and $yz$ components is suppressed at $x=0.5$ compared with $x=0$.

Figure 5

The dynamic spin structure factor $S(\mathbf{q},\omega )$ in the PM state for (a) $x=0$, (b) $x=0.3$, and (c) $x=0.5$ is plotted along the high-symmetry path ($H,K,L=\pi$) in the first Brillouin zone of the single-iron unit cell, where ($H,K)=(\pi ,0$) is the AFM ordering vector. (d) Total $S(\mathbf{q},\omega )$ is plotted as a function of $\omega$ for different $x$ at the fixed momentum $q=(\pi +\delta ,0)$, which is slightly off the AFM ordering vector at which the spin susceptibility diverges below the AFM transition temperature. Here we take $\delta =-0.0625\pi$. The orbital decomposed $S(\mathbf{q},\omega )$ is displayed also at $q=(\pi +\delta ,0)$ for (e) $x=0$, (f) $x=0.3$, and (g) $x=0.5$.