Quantum dynamics of hydrogen in the iron-based superconductor ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{D}}_{0.1}$ measured with inelastic neutron spectroscopy

Inelastic neutron scattering was performed for an iron-based superconductor ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{D}}_{0.1}$, where most of D (deuterium) replaces oxygen, while a tiny amount goes into the interstitial sites. By first-principles calculation, we characterize the interstitial sites for D (and for H slightly mixed) with four equivalent potential minima. Below the superconducting transition temperature $T_{\mathrm{c}}=26\mathrm{K}$, excitations emerge in the range 5–15 meV, while they are absent in the reference system ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{F}}_{0.1}$. The strong excitations at 14.5 and 11.1 meV broaden rapidly around 15 and 20 K, respectively, where each energy becomes comparable to twice the superconducting gap. The strong excitations are ascribed to a quantum rattling, or a band motion of hydrogen, which arises only if the number of potential minima is larger than two.

Figure 1

Color plots of $S_{\mathrm{A}}(Q,\hslash \omega )$ with $\text{A}=\text{D}$, F, and $\text{D}-\text{F}$ at 6 K (a), (c), (e), and 41 K (b), (d), (f). The incident neutron energy is $E_{\mathrm{i}}=17.5\mathrm{meV}$. (a), (b) $S_{\mathrm{D}}$ from ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{D}}_{0.1}$; (c), (d) $S_{\mathrm{F}}$ from ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{F}}_{0.1}$; (e), (f) the difference map $S_{\text{D}-\text{F}}$. U, M, and L in (e) signify the upper, middle, and lower modes, respectively.

Figure 2

Scattering intensities with incident neutron energy $E_{\mathrm{i}}=17.5\mathrm{meV}$ at (a) 6 K and (b) 23.5 K for $Q_0=2.15\pm 0.15{\AA }^{-1}$. The indigo solid line represents the sum of all components, the blue dashed line the U component, the red dashed line the M component, and the green dashed-dotted line the tail of the L component which works as a baseline for M and U components. Also shown are the temperature dependence of (c) the linewidth $\hslash {\mathrm{\Gamma }}_{\alpha }$ with $\alpha =\mathrm{U}$, M and (d) the peak position $\hslash {\omega }_{\alpha }$ for the U and M modes. The blue and magenta solid lines are the results on fitting the U and M peaks, respectively. The green solid line shows the temperature dependence of the BCS gap function $2\mathrm{\Delta }\left(T\right)$. The arrows indicate the temperature $T_{\alpha }$ corresponding to the midpoint of $\hslash {\mathrm{\Gamma }}_{\alpha }\left(T\right)$ as fitted by the sigmoid function.

Figure 3

(a) Crystal structure of ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{D}}_{0.1}$ with the interstitial site ${\mathrm{H}}_{\mathrm{int}}$. (b) Contour map of $\mathrm{\Delta }E$ in units of eV on the $xy$ plane at $z=0.425$. The four potential minima marked by the crosses are located at $(0.11,0.11,0.425)$ and the equivalent positions. The fourfold rotational axis runs along the line $(0.25,0.25,z)$. The coordinates are described by the crystallographic units.

Figure 4

(a) The line profiles of $\mathrm{\Delta }E$ through the minima A-B-C-D-A on $z=0.425$. The tunneling distance $d$ and the potential barrier $V_{\mathrm{b}}$ between the minima are indicated. The blue dashed line represents the ground state in the single harmonic potential at $\frac{1}{2}\hslash {\omega }_0$, while the orange dashed line represents the first excited state at $\frac{3}{2}\hslash {\omega }_0$. (b) The blue line shows the spectrum of the tunneling splitting, while the orange line shows that of the highly anharmonic phonons described as quantum rattling. (c) Schematic picture of hydrogen wave functions. ${\mathrm{\Psi }}_{\mathrm{g}}$ stems from the ground state of the harmonic oscillator with $n=0$, while ${\mathrm{\Psi }}_{\mathrm{e}}$ stems from $n=1$. The wave functions at neighboring sites have either the same phase ($k=0$), or opposite phase ($k=\pi /d$).