Pressure induced Hydrogen-Hydrogen interaction in metallic FeH revealed by NMR

TL;DR

This study uses NMR to reveal pressure-induced hydrogen-hydrogen interactions in FeH up to 200 GPa, challenging previous assumptions about their occurrence only at extremely high pressures and suggesting new pathways for high-temperature superconductor discovery.

Contribution

First experimental NMR evidence of pressure-induced H-H interactions in FeH at accessible pressures, supported by ab-initio calculations showing electronic structure changes.

Findings

H-H interactions occur between 64 and 110 GPa

Formation of an intercalating electron density sublattice

Enhanced hydrogen contribution to electronic density of states

Abstract

Knowledge of the behavior of hydrogen in metal hydrides is the key for understanding their electronic properties. So far, no experimental methods exist to access these properties beyond 100 GPa, where high-Tc superconductivity emerges. Here, we present an 1H-NMR study of cubic FeH up to 200GPa. We observe a distinct deviation from the ideal metallic behavior between 64 and 110 GPa that suggests pressure-induced H-H interactions. Accompanying ab-initio calculations support this interpretation, as they reveal the formation of an intercalating sublattice of electron density, which enhances the hydrogen contribution to the electronic density of states at the Fermi level. This study shows that pressure induced H-H interactions can occur in metal hydrides at much lower compression and larger H-H distances than previously thought and stimulates an alternative pathway in the search for novel high-temperature superconductors.

Full text

Hydrides and hydrogen-rich compounds attract considerable attention as the search for effective and ”green energy” materials intensifies Mohtadi and Orimo (2016); Zhang et al. (2017). Recent theoretical Gor’kov and Kresin (2016), computational Zurek et al. (2009); Jarlborg and Bianconi (2016); Bianconi and Jarlborg (2015) and experimental Drozdov et al. (2015a); Somayazulu et al. (2019) results indicate that hydrides may hold the key to a deep understanding of high-temperature superconductivity and the synthesis of compounds exhibiting high critical temperatures ($T_{c}$). Sulphur hydride, $H_{3}S$, with a $T_{c}$ of 200 K at pressures of about 1.5 Mbar Drozdov et al. (2015b) is a prominent example of such metal hydride (MH) systems.

A systematic analysis of computational results Semenok et al. (2018a, b) suggests that two properties are particularly important for achieving high-Tc superconductivity in metallic MH: (1) significant contribution of hydrogen to the electronic density of states at the Fermi energy (EF), and (2) strong effects of hydrogen vibrations on the electronic structure of the material (i.e. electron-phonon coupling). Unfortunately, the lack of experimental methods in high pressure research able to access the electronic states of hydrogen in MHs at extreme pressures has prohibited a direct confirmation of this hypothesis.

Recent developments in our group led to the implementation of Nuclear Magnetic Resonance (NMR) spectroscopy in diamond anvil cells (DACs) at pressures approaching the megabar regime using magnetic flux tailoring Lenz lenses Meier et al. (2017, 2018a, 2018b). NMR spectroscopy is widely recognized Carter et al. (1977); Baek et al. (2009); Fujiwara et al. (2003); Meier (2018) for its sensitivity to fine electronic effects. In particular, Knight shift measurements provide a well-established technique to investigate the density of states of conduction electrons at the Fermi energy, $N(E_{F})$, enabling detection of deviations from free electron gas behavior or even electronic topological transitions of the Fermi surface and providing direct evidence of the Meissner-Ochsenfeld effect in the metal’s superconducting state.

In density functional theory (DFT) based calculations Peng et al. Peng et al. (2017) demonstrated that in clathrate-like metal hydrogen systems, such as LaH${}_{1}0$ or YH${}_{1}0$, nearest H-H distances should be $\leq$ 1.5 Åfor the development of significant hydrogen-hydrogen interactions. In non-magnetic fcc FeH, stable above 25 GPa Narygina et al. (2011), average proton-proton distances are in the range of 2.6 - 2.3 Å  at 200 GPa Pépin et al. (2014), suggesting that pressure induced H-H correlations are unlikely. As the synthesis of fcc FeH in a DAC is well established and the crystal structure well defined, hydrogenation and composition of FeH samples can be closely controlled. Therefore, fcc iron monohydride can be regarded as an ideal archetypal test or reference system for the investigation of the electronic structure of hydrogen in metal hydrides.

For an NMR study of FeH under pressure, an FeH sample was synthesized in a DAC at about 32 GPa through a direct reaction between iron and paraffin upon laser heating of their mixture at 1200 K. The DAC preparation, the synthesis, and experimental procedure are described in detail in the Supplementary Materials. Fig. 1a shows typical proton spectra prior to and after the sample synthesis (at about 32 GPa and 35 GPa, respectively) and after compression to 190 and 202 GPa. Before laser heating only a single NMR signal is observed, originating from the paraffin proton reservoir which has been characterized in earlier experiments Meier et al. (2017). After the sample synthesis, an additional 1H-NMR signal appears at about -1200 ppm relative to the paraffin proton reservoir (Fig. 1a; Fig. S1). If this tremendous shift is due to an onset of hydrogen Knight shift ($K_{H}$) Knight (1949) in the metallic state, nuclear relaxation, as described by Heitler and Teller Heitler and Teller (1936), must occur as well. We find, indeed, that spin-lattice relaxation rates ($R_{1}$) increase by more than one order of magnitude from $\approx$ 1 Hz in the proton reservoir to $\approx$ 40 Hz in the spin system associated with the additional signal (Fig. 1a; Fig. S2). Combining shift and relaxation rates, the Korringa ratio Korringa (1950), $K_{H}^{2}TR_{1}^{-1}$ (where $K_{H}$, $R_{1}$ and $T$ denote the hydrogen Knight shift, the spin-lattice relaxation rate and the sample temperature, respectively; see Supplementary Materials for more information), should yield values intermediate to those for pure 57Fe metal ($\approx$ 250 $\mu$sK) and Fermi-gas like value of the proton site ($\approx$ 0.3 $\mu$sK). The value of the Korringa ratio recorded directly after sample synthesis was found to be $\approx$ 10 $\mu$sK, half-way in magnitude between these two values (Fig. 1b). Therefore, the appearance of the additional signal can be attributed to the formation of metallic FeH in the DAC. Similar proton NMR spectra of other metal hydride systems, synthesized at ambient conditions, confirm this conclusion Goring et al. (1981); Goren et al. (1986). Figure 1b also shows the pressure evolution of the Korringa ratio which should be volume independent in metallic systems Meier et al. (2015). However, a distinct pressure dependence is observed between 30 and 202 GPa. To investigate this phenomenon, we focused on the analysis of the volume dependence of the hydrogen Knight shift $K_{H}$.

As $K_{H}$ scales with the density of states of d-electrons at the Fermi energy, $N_{d}(E_{F})$, in transition metal hydrides (see Supplementary Materials for details), a volume dependence with a scaling exponent of $\alpha=2/3$ for the free electron gas can be expected. Figure 2a shows a double logarithmic power plot of the relative volumes, using the equation of state (EOS) from Narygina et al. Narygina et al. (2011), against relative changes in the Knight shift. Three distinct regions can be identified: 1) up to 64 GPa, the exponent closely follows a Fermi-gas electronic behavior; 2) a deviation from metallic scaling exponents occurs between 64 GPa and 110 GPa and 3) the re-occurrence of free electron gas behavior from 110 GPa to highest pressures. After compression and data collection up to 202 GPa, one of the DAC experiments was decompressed to $\approx$ 100 GPa and subsequently to 33 GPa (red arrows in Fig. 2a). NMR spectra collected on decompression agree with those obtained during compression, showing that the observed effect is fully reversible. As X-ray diffraction data do not show any sign of a structural phase transition (see Fig. S3a and Pépin et al. (2014); Thompson et al. (2018)), the origin of this observation should be linked to changes in the electronic environment of the protons in FeH.

To explore this hypothesis, we applied Kohn-Sham DFT using Quantum Espresso Giannozzi et al. (2009) (see Supplementary Materials for computational details). Both electronic band structure and density of states (Fig. S4) do not indicate any discontinuities such as van-Hove singularities Volovik (2017) close to $E_{F}$. Therefore topological transitions of the Fermi surface Lifshitz (1960), which would influence both spin shift and relaxation rates, can be excluded. Values of the total density of states at $E_{F}$, $N_{total}(E_{F})$, as well as its projection on the $3d~{}t2g$ and $eg$ states, $N_{t2g}(E_{F})$ and $N_{eg}(E_{F})$, respectively, from the calculations are included in Fig. 2a (dashed lines). The volume dependence of $N_{t2g}(E_{F})$ closely follows the NMR spin shifts to 64 GPa. Above this pressure, experimental data points and $N_{t2g}(E_{F})$ diverge beyond experimental errors.

The hydrogen Knight shift is the sum of interactions due to core polarization of uncompensated d-orbitals and contact interaction of s-electrons with the nuclei (see equation (3) in the Supplementary Materials). At ambient conditions, the latter interaction can be regarded negligible due to the density of states at $E_{F}$ being almost zero for the hydrogen 1s-electron, $N_{H-1s}(E_{F})$, (Fig. 2b). The contribution of $N_{H-1s}(E_{F})$ to the total DOS begins to increase around 64 GPa and continuously rises up to 200 GPa. This effect qualitatively explains the observed offset between experimental data and calculated DOS values.

Figure 2c shows the respective volume dependence of the density of states at $E_{F}$ of the 3d electrons for fcc-Fe over the same compressional range as the FeH data. The pressure dependent effects observed on the DOS of the 3d-t2g orbitals in fcc FeH, seen in Fig. 2a, are not present in fcc Fe. That allows us to conclude that they are caused by the presence of hydrogen atoms. Both the scaling anomaly in $N_{t2g}(E_{F})$ and the continuous increase in $N_{H-1s}(E_{F})$ with compression suggest a shift of conduction electron density between iron and hydrogen atoms in FeH.

In order to elucidate this possibility, electron localization function (ELF) maps have been computed. Fig. 3 shows the ELF maps in three different crystal planes at compressions of $V/V_{0}$=0.9 and $V/V_{0}$=0.69 corresponding to about 30 and 200 GPa. At $V/V_{0}$=0.9, electron clouds associated with Fe and H atoms are localized, evidencing the ionic character of FeH. Regions exhibiting Fermi-gas electronic behavior, i.e. ELF values of 0.5, start to develop and spread at $V/V_{0}~{}<$ 0.88, which are particularly pronounced in the (110) and (112) planes. These regions of increased electron density connect at $V/V_{0}~{}<$ 0.78, corresponding to pressures of 80-90 GPa, forming an interconnecting network with respect to the hydrogen nuclei. At $V/V_{0}~{}<$ 0.73, the nearest neighbor hydrogen-hydrogen bonds are bridged as well. An animation of the results (Movie S1) shows the correlation between the different ELF maps and the data shown in Fig. 2. Strikingly, the deviation from free electron gas behavior observed for $V/V_{0}~{}=$0.88 coincides with the increase of electron density in the interstitial regions of FeH. The reemergence of Fermi-gas behavior above 110 GPa corresponds to the connection of these areas of enhanced electron density. The pronounced increase in $N_{H-1s}(E_{F})$ also correlates qualitatively with both the formation and connection of these areas. Combining experimental observations and computational results, we propose the following qualitative explanation of the high-pressure behavior of FeH: With increasing pressure, in FeH electron density from partially uncompensated 3d-t2g Fe orbitals is pushed towards the hydrogen electron clouds. The successive addition of charges leads to the formation of an intercalating free-electron sub-lattice of connected hydrogen atoms, exhibiting a continuous enhancement of the electronic density of states from the hydrogen at $E_{F}$. Our data suggest that this effect can be observed by NMR when average H-H distances become smaller than $\approx$ 2.5 Å which is significantly larger than expected based on previous computational work [12]. In this study of hydrogen in iron monohydride FeH we have shown that pressure induced interactions between hydrogen atoms and the transition metal atoms as well as between H-atoms themselves can occur and influence electronic properties of metal hydrides at much lower pressures than previously anticipated. The experimental findings, supported by ab-initio calculations, suggest that other candidates for phonon-mediated high temperature super-conductivity may be found far off the proclaimed ”lability belt”, including the rare-earth sodalite-clathrate super-hydrides Heil et al. (2019).

I Acknowledgements

We thank Nobuyoshi Miyajima and Katharina Marquardt for help with the FIB milling. We also thank Caterina Melai, Serena Dominijanni and Catherine McCammon for help with XRD measurements.

II Funding

N.D. and L.D. thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG, projects DU 954-11/1, DU-393/13-1, and DU-393/9-2) and the Federal Ministry of Education and Research, Germany (BMBF, grant no. 5K16WC1) for financial support. S.P., and F.T. were financed by the German Research Foundation (DFG projects PE 2334/1-1, FOR 2440).

III Author Contributions

T.M. and L.D. designed the experiment. T.M., S.K. and S.P. prepared the DACs and NMR resonators. S.K. performed focused ion beam cutting as well as structure refinement after laser heating. L.D. performed the sample synthesis in the DACs. S.C. and T.F. as well as S.D. and C.M. performed XRD measurements at DESY and ESRF, respectively. F.T. and G.S.N. performed the calculations and analyzed the results. T.M., F.T., G.S.N., N.D. and L.D. performed the data analysis and wrote the manuscript.

IV Competing Interests

The authors declare that they have no competing interests.

V Data availability

The data supporting the findings of this study are available from the corresponding author upon reasonable request.