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

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.


I. INTRODUCTION
Hydrides and hydrogen-rich compounds continue to attract considerable attention as the search for effective and "green energy" materials intensifies [1,2]. Recent theoretical [3], computational [4][5][6], and experimental [7,8] 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 a pressure (P) of approximately 150 GPa [9], is a prominent example of such metal-hydride (MH) systems.
A systematic analysis of computational results [10,11] suggests that two properties are particularly important for achieving high-T c superconductivity in metallic MH: (i) a significant contribution of hydrogen to the electronic density of states at the Fermi energy NðE F Þ and (ii) strong effects of hydrogen vibrations on the electronic structure of the material (i.e., electron-phonon coupling). Unfortunately, the lack of experimental methods that provide access to electronic states of hydrogen in MHs at such P prohibits 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 100 GPa using magnetic flux tailoring Lenz lenses [12][13][14]. NMR spectroscopy is widely recognized [15][16][17][18][19] for its sensitivity to small 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, enabling the detection of deviations from free-electron gas behavior or even electronic topological transitions of the Fermi surface and direct evidence of the Meissner-Ochsenfeld effect in the metal's superconducting state.
In density-functional-theory-based calculations, Peng et al. [20] demonstrate that in clathratelike metal hydrogen systems, such as LaH 10 or YH 10 , the nearest H-H distances should be ≤ 1.5 Å for the development of significant hydrogen-hydrogen interactions. In nonmagnetic fcc FeH, stable above 25 GPa [21], average H-H distances are in the range of 2.6-2.3 Å at 200 GPa [22], suggesting that P-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 a reference system for our NMR-based approach to the investigation of the electronic structure of hydrogen in metal hydrides.

II. EXPERIMENTAL METHODS
Two identical DACs of type BX90 [23] are prepared with two beveled diamond anvils with 100 μm culets. Rhenium gaskets are indented to about 15 μm thickness, and 40 μm holes are laser cut in the flat face of the preindentation to form the sample cavity. Using physical and chemical vapor deposition techniques, the anvils are covered by a 1 μmthick layer of copper, and the metallic rhenium gaskets are sputtered with a 500 nm-thick layer of Al 2 O 3 for electrical insulation. Subsequently, using a focused ion beam, three Lenz lenses (LLs) are cut out of the copper layers covering the diamond anvils: (i) along the anvil's pavilion, (ii) on the beveled area, and (iii) on the 100 μm culets [ Fig. 1(a)]. This procedure is necessary to avoid damage due to sharp edges from the 8°bevel and the culet rim when cupping under compression occurs. The nuclear magnetic resonators used in this study can be regarded as a generalization of the recently introduced double-stage Lenz lenses [14], enabling its use for single-beveled diamond anvils with culet sizes of ≤ 100 μm.
The cells are loaded by flooding the sample chamber with paraffin oil and then mixing fine iron powder of natural composition (Sigma-Aldrich, 4N purity) into it. Pressure in the sample chamber is estimated by the frequency shift of the first-order Raman peak of the diamond at its edge in the center of the sample cavity [ Fig. 1 [24,25].
The radio-frequency (rf) excitation coils are made using two identical 3 mm coils consisting of five turns of 150 μm Teflon-insulated copper wire. Each coil is fixed around the diamonds on the respective backing plates and connected to form a Helmholtz coil, ensuring optimal inductive coupling into the LL resonator structures. NMR measurements are conducted at a magnetic field of 1 T using a sweepable electron spin resonance magnet with a 50-mm magnet pole distance and a Techmac Redstone spectrometer for solidstate NMR applications. NMR measurements prior to cell loading do not exhibit any detectable hydrogen signals within typical experimental parameters, showing the absence of spurious hydrogen signals stemming from other parts of the NMR probe.
From rf nutation experiments, an optimal 90°pulse of 4 μs at an average pulse power of 40 W is established. This value does not change over the course of the experiment and is found to be valid for both DACs used. For measurements of spin-lattice relaxation rates, a saturation recovery pulse train consisting of 16 consecutive pulses is used. From the relation B 1 ¼ π=ð2γ n t π=2 Þ, with γ n the nuclear gyromagnetic ratio and t π=2 the π=2 pulse length, a B 1 field of 4.7 mT is deduced. Using the FEMM 4.2 package, the high-frequency B 1 field distribution across the 40 μm × 15 μm sample cavity is calculated using experimental parameters similar to the nutation experiments. An average B 1 field of 4.8 mT is found, in excellent agreement with the nutation experiments. The introduced LL resonators show the required sensitivity.
All resonance frequency shifts are referenced relative to the hydrogen signal of the paraffin hydrogen reservoir after laser heating. The values for the Knight shift ( Fig. 2) are higher by a factor of 6 than for other transition metal hydrides [26]. The choice of the reference material can, in principle, lead to an intrinsic overestimate as we deviate from the standard shift reference, tetramethylsilane (TMS) [27]. However, TMS does not induce the reaction to form FeH at a high P and temperature (T), to the best of our knowledge. The DACs are pressurized initially to about 30 GPa, into the stability field of nonmagnetic hcp Fe, and subsequently laser heated to 1200 K. X-ray diffraction (XRD) powder patterns taken at PETRA III (beam line P02) and ESRF (ID-15) show reflections from FeH and no residual Fe signal [ Fig. 1(c)], suggesting that iron has fully reacted with hydrogen from the paraffin reservoir. The most prominent diffraction peaks are those of fcc FeH previously identified [21,28]; a small amount of dhcp FeH x is also indexed.
As fcc FeH x is unstable at ambient conditions, the actual chemical composition cannot be measured directly using recovered samples. Narygina et al. [21] suggest that the hydrogenation factor x can be estimated by considering the volume expansion of the fcc unit cell in response to the dissolution of hydrogen on the octahedral interstitial lattice sites of fcc Fe by with V FeH x and V Fe the atomic volumes of iron hydride and fcc iron, respectively. ΔV H is the volume expansion due to hydrogenation. As the latter parameter is not well defined by other fcc-structured 3d transition metals at ambient conditions, the actual hydrogenation value x is estimated by comparing the recorded data with equations of state of FeH [21] and fcc iron [29]. Using this procedure, x ¼ 1.0ð1Þ in both DACs is found, close to stoichiometry. Further XRD measurements at 150 GPa suggest that fcc FeH remains stable with similar composition throughout the whole P range of this study. Prior to laser heating, 1 H-NMR spectra are recorded C n H 2nþ2 reservoir, a single NMR signal positioned at the Larmor frequency for hydrogens is observed. The center of gravity of the paraffin signal is found at 45.0737 MHz, corresponding to a polarizing magnetic field of B 0 ¼ 1.058 mT within the sample cavity. Small deviations of up to 10% in B 0 are found to originate from a slightly different positioning of the DACs within the region of the highest magnetic field of the electromagnet but can be neglected, since the hydrogen reservoir serves as an internal reference. The recorded spectra of paraffin at 32 (cell 1) and 29 GPa (cell 2) are found to be similar to earlier 1 H-NMR spectra of C n H 2nþ2 in terms of linewidths and relaxation rates [12]. After laser heating, an additional intense signal is found at lower frequencies at about −1200 ppm relative to the hydrogen reference [ Fig. 2(a)]. Comparing signal intensities from spectra recorded after full relaxation of both independent spin systems, we determine an intensity ratio of about 4∶7 of FeH to C n H 2nþ2 in cell 1 and 1∶5 in cell 2. These ratios are found to be constant at all P, suggesting that further reaction of hydrogen with the iron powder during cold compression cycles does not occur.

III. COMPUTATIONAL DETAILS
All ab initio calculations performed are based on the Kohn-Sham density functional theory and are performed with QUANTUM ESPRESSO [30,31] using the projector augmented wave approach [32]. We use the generalized gradient approximation by Perdew-Burke-Ernzerhof [33] to exchange and correlation with corresponding potential files; for Fe, we use a valence electron configuration that includes electronic states 3s and higher, applicable to extreme pressure [34].
Convergence tests for the electronic band structure and density of state calculations lead to reciprocal space sampling with a Monkhorst-Pack [35] k-point grid of 32 × 32 × 32 and a cutoff energy for the plane wave expansion of 120 Ry. In addition to the total electronic density of states, site and orbital projections are computed, with particular attention to the crystal field splitting of the 3d electronic states into the e g and t 2g orbitals.
In order to identify regions of charge localization, we use the electron localization function (ELF) [36] that quantifies the probability of finding two electrons in close proximity by the ratio of a computed charge density and its spatial derivative to the value of the homogeneous electron gas of the same density.

IV. KNIGHT SHIFT IN IRON HYDRIDE
As both stable iron hydride phases, fcc and dhcp, are thought to be metallic [37,38], the influence of hyperfine interaction of conduction electrons with the nuclei must be taken into account to explain the NMR signal. For transition metal hydrides, the magnetic susceptibility (χ) can be written as a sum of several contributions, stemming from spin interactions with s-or d-conduction electrons, the orbital paramagnetic, and the diamagnetic contribution of the ion cores, respectively. Therefore, the electron-nuclear hyperfine interaction, described in terms of the Knight shift K tot and the spin-lattice relaxation rate R 1 [39,40], are caused by various mechanisms [41]: and where A is Avogadro's constant and μ B the Bohr magneton. For a free-electron Fermi gas, we can substitute χ ðs;dÞ ¼ 2μ 0 μ 2 B N ðs;dÞ ðE F Þ in Eq. (2), leading to a reduced representation of the Knight shift: Equation (4) demonstrates that various mechanisms producing hyperfine fields at the hydrogen site need to be taken into account. However, as the 1s electronic states of hydrogen and the 4s states of iron typically lie far below and above the Fermi energy, respectively, it seems reasonable to assume their contribution to K tot to be negligible to first approximation in FeH.
The effect of orbital motion of 3d electrons on the hydrogen Knight shift (K H ) is expected to be virtually nonexistent, as such an interaction would dominate Eq. (4) and lead to positive values of K H which are not observed in other MH systems measured at ambient conditions [41][42][43][44]. Also, considering the good correlation between K H and N t 2g ðE F Þ (discussed in greater detail below), an influence of spin orbit coupling on the 1 H-NMR spectra can be ruled out (Fig. 3). Therefore, both Eqs. (3) and (4) are reduced to their d-electron core polarization contribution, with a Korringa-type [45] relation given by For cubic lattices, the reduction factor q can be described by q ¼ 1 3 f 2 þ 1 2 ð1 − fÞ 2 , where f is the fractional character of t 2g orbitals at the Fermi surface [47,48], determining the deviation from the free-electron value given by S ¼ ½ℏ=ð4πk B Þðγ e =γ n Þ 2 [15], with γ e the gyromagnetic ratio of the electron.
In general, the Korringa-ratio constitutes an indicator for metallicity of a given material [15] using the volume independence of Eq. (5). As the Korringa ratio depends on only physical constants, values for the free-electron gas behavior for every metallic system can be readily estimated. For FeH, two different limiting scenarios can be identified: (i) pure 57 Fe metal with K 2 T=R 1 ¼ 250.11 μsK and (ii) electronic Fermi-gas-like behavior of metallic hydrogen with a value of 0.263 μsK. The Korringa ratio for the binary system consisting of Fe and H can be anticipated to lie in between these extreme values.

V. RESULTS AND DISCUSSION
At approximately 30 GPa and before laser heating, only a single NMR signal is observed [ Fig. 2(a)], originating from the paraffin hydrogen reservoir which has been characterized in earlier experiments [12]. After FeH synthesis at 1200 K, an additional 1 H-NMR signal appears at about −1200 ppm relative to the paraffin hydrogen reservoir (Fig. 2). If this huge shift is due to the occurrence of K H in the metallic state [39], nuclear relaxation, as described by Heitler and Teller [49], must occur as well. We observe, indeed, that, in response to FeH synthesis, the spin-lattice relaxation rates (R 1 ) increase by more than one order of magnitude from approximately 1 Hz in the hydrogen reservoir to approximately 20 Hz in the spin system associated with the additional signal [ Fig. 2(b)].
Combining shift and relaxation rates, the Korringa ratio [Eq.  Fig. 3(c)]. The value of the Korringa ratio recorded directly after sample synthesis is found to be approximately 10 μsK, halfway in magnitude between these two values [ Fig. 2(c)]. Therefore, the appearance of the additional signal can be attributed to the formation of metallic FeH in the DAC. Similar 1 H-NMR spectra of other metal-hydride systems, synthesized at ambient conditions, confirm this Black arrows denote respective pressures points; red arrows show data recorded under decompression. (b) Evolution of N H−1s ðE F Þ. Indicated pressure markers are related to the experimental data points from (a). (c) Volume dependence of N total ðE F Þ, N t 2g ðE F Þ, and N e g ðE F Þ for fcc Fe over a similar compression range.
conclusion [41,50]. Figure 2(c) also shows the pressure evolution of the Korringa ratio which should be volume independent in metallic systems [Eq. (5)]. However, a distinct P dependence is observed between 30 and 202 GPa. To investigate this phenomenon, we focus on the analysis of the volume dependence of K H . Figure 3 shows a double logarithmic power plot of the relative volumes, using the equation of state from Narygina et al. [21], against relative changes in the Knight shift. Three distinct regions can be identified: (i) Up to 64 GPa, the exponent of the Knight shift ratio closely follows a Fermi-gas electronic behavior with ∝ V 2=3 , (ii) a deviation from metallic scaling exponents occurs between 64 and 110 GPa, and (iii) the reoccurrence of free-electron gas behavior from 110 GPa to highest P. After compression and data collection up to 202 GPa, one of the DAC experiments is decompressed to approximately 100 GPa and subsequently to 33 GPa [red arrows in Fig. 3(a)]. 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 [22,28], the origin of this observation should be linked to changes in the electronic environment of the hydrogens in FeH.
The computed electronic band structure (Fig. 4) and density of states do not indicate any discontinuities close to E F , such as van Hove singularities [51]. Therefore, topological transitions of the Fermi surface [52], which would influence both spin shift and relaxation rates, can be excluded. Values of the total density of states at E F , N total ðE F Þ, as well as its projection on the 3d − t 2g and e g states, N t 2g ðE F Þ and N e g ðE F Þ, respectively, from the calculations are included in Fig. 3(a). The volume dependence of N t 2g ðE F Þ closely follows the NMR spin shifts to 64 GPa. Above this P, experimental data points and N t 2g ðE F Þ 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 [Eq. (4)]. At ambient conditions, the latter interaction can be regarded as negligible due to the density of states at E F being almost zero for the hydrogen 1s electron, N H−1s ðE F Þ [ Fig. 3(b)]. The contribution of N H−1s ðE F Þ to the total density of states begins to increase around 64 GPa and continuously rises with P, up to 202 GPa, the highest P considered. This effect can qualitatively explain the observed offset between experimental data and calculated density of state values. Figure 3(c) shows the respective volume dependence of the density of states at E F of the 3d electrons for fcc-Fe over the same compression range as the FeH data. The P-dependent effects observed on the density of states of the 3d − t 2g orbitals in fcc FeH [ Fig. 3(a)] are not present in fcc Fe. This difference allows us to conclude that they are caused by the presence of hydrogen atoms. Both the scaling anomaly in N t 2g ðE F Þ and the continuous increase in N H−1s ðE F Þ with compression suggest a shift of conduction electron density between iron and hydrogen atoms in FeH.
In order to elucidate this possibility, we map the ELF in three different crystal planes [(1 0 0), (1 1 0), and (1 1 2)] at compressions between V=V 0 ¼ 1.0 and V=V 0 ¼ 0.61 (21 steps) and consider the correlations between the evolution of the ELF maps and the data shown in Fig. 3 (Movie S1 in Supplemental Material [53]); Fig. 5 presents the ELF maps for V=V 0 ¼ 0.9 and V=V 0 ¼ 0.69, corresponding to approximately 30 and approximately 200 GPa, respectively.
At V=V 0 ¼ 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 H-H bonds are bridged as well. Strikingly, the deviation from free-electron gas behavior 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 ðE F Þ also correlates qualitatively with both the formation and connection of these areas.

VI. CONCLUSIONS
Combining experimental observations from NMR measurements and ab initio computational results, we propose the following qualitative explanation for the high-P evolution of FeH: With increasing P, the electron density from partially uncompensated 3d − t 2g Fe orbitals in FeH is pushed towards the hydrogen electron clouds. The successive addition of charges leads to the formation of an intercalating free-electron sublattice of connected hydrogen atoms, exhibiting a continuous enhancement of the electronic density of states of hydrogen at E F . Our data suggest that this effect can be observed by NMR when average H-H distances become smaller than approximately 2.5 Å, which is significantly larger than expected based on previous computational work.
This result suggests that P-induced interactions between hydrogen and the transition metal atoms as well as between H atoms themselves can occur and influence electronic properties of metal hydrides at much lower P than previously anticipated. The experimental findings, supported by ab initio calculations, suggest that other candidates for phonon-mediated high-T c superconductivity may be found far off the proclaimed "lability belt," including the rare-earth sodalite-clathrate superhydrides [54].
The data supporting the findings of this study are available from the corresponding author upon reasonable request.

ACKNOWLEDGMENTS
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 E FIG. 5. Electron localization function maps in three major crystal planes at a compression of V=V 0 ¼ 0.9 and 0.69, corresponding to 30 and 200 GPa, respectively (for further compression points, see Movie S1 in Supplemental Material [53]). Brown spheres represent iron atoms, white spheres hydrogen. Green areas (ELF ∼ 0.5) correspond to Fermi-gas-like regions of free electrons.