Revealing the role of lattice distortions in the hydrogen-induced metal-insulator transition of SmNiO3

The discovery of hydrogen-induced electronic phase transitions in strongly correlated materials such as rare-earth nickelates has opened up a new paradigm in regulating materials’ properties for both fundamental study and technological applications. However, the microscopic understanding of how protons and electrons behave in the phase transition is lacking, mainly due to the difficulty in the characterization of the hydrogen doping level. Here, we demonstrate the quantification and trajectory of hydrogen in strain-regulated SmNiO3 by using nuclear reaction analysis. Introducing 2.4% of elastic strain in SmNiO3 reduces the incorporated hydrogen concentration from ~1021 cm−3 to ~1020 cm−3. Unexpectedly, despite a lower hydrogen concentration, a more significant modification in resistivity is observed for tensile-strained SmNiO3, substantially different from the previous understanding. We argue that this transition is explained by an intermediate metastable state occurring in the transient diffusion process of hydrogen, despite the absence of hydrogen at the post-transition stage.


Supplementary Methods
Thin SmNiO3 thin films were grown on SrTiO3 (001), LaAlO3 (001) and (La,Sr)(Al,Ta)O3 (001) single crystal substrates by pulsed laser deposition (PLD) by using ceramic targets with nominal compositions of SmNiO3. The 248 nm laser at a constant ablation fluence of around 1.8 J.cm 2 was used to ablate the target material at an oxygen pressure of around 20 Pa within a vacuum chamber with the repetition frequency of 10 Hz. During the deposition, the substrates were heated to 650 °C, and the deposition thickness of the films were around 200 nm. High-angle annular dark-field (HAADF) and annular bright-field (ABF) scanning transmission electron m microscopy (STEM) experimental techniques were carried out on JEM-ARM 200F TEM operated at 200 kV with a cold field emission gun and aberration correctors for both probe-forming and imaging lenses. The crystal structures were characterized by X-ray diffraction (XRD) and reciprocal space mapping (RSM). The diffraction patterns of [114] reciprocal space vectors from the film and substrate were projected at [110] and [001], representing the in-plane and cross-plane reciprocal space vector (Q// and Q  ), respectively. The RSM result from [114] diffraction pattern demonstrates the in-plane lock between film and substrate in the other in-plane direction of [100]. The resistance of as-grown thin films was measured in vacuum by using a commercialized CTA-system within the temperature range from 300 K-550 K.
To hydrogenate as-grown SmNiO3 thin films, the patterns of platinum electrode (round shape and with diameter of 50 μm, see scheme S1) were deposited on the surface of the film material. The samples were annealed in 1% H2/He gas at 300 °C for 15-60 minutes, followed by the same exposure time in the air before NRA. The dehydrogenation was performed by annealing the samples in oxygen at 300 °C for 30 minutes.
The oxygen composition of the thin film was measured by Rutherford Back Scattering (RBS) by using a 2 MeV 4 He beam and a silicon PIN diode detector at θ = 168°. The collected RBS data were simulated using the RUMP software. The uncertainty for as-measured composition is within 5%. The nuclear reaction analysis (NRA) measurement was performed in the Micro Analysis Laboratory, Tandem accelerator (MALT) at The University of Tokyo. Owing to the resonant nature of the nuclear reaction, only the 15 N 2+ ions with kinetic energies (EK) of 6.385 MeV can resonant with the hydrogen element and yield detectable gamma-ray yield. Otherwise, at an EK level of MeV range that much higher than the ones associated to the outer or inner shells of electrons, the kinetic loss is mainly related to the elastic scatterings by the atoms at a constant rate per penetration depth. Taking the present SmNiO3 as an example, the constant of proportionality is the reciprocal of the energy loss cross section (3.1945 keV nm -1 ) that can be considered as a constant (within 1 %) for thin films. The energy loss cross section (3.1945 keV nm -1 ) of SmNiO3 is derived based on supplementary ref. [20] and [1]. In brief, the stopping power (S) for the compound SmNiO3 can be calculated by using the Bragg`s Rule, which is the composition-weighed average of elemental stopping powers for Sm, Ni and O: SSmNiO3=  [20]: For a specific penetration depth of the ion beam, the spatial resolution of the measured profile is limited by the width of the energy distribution of the ions, and the width of the energy distribution is the full width at half maximum (FWHM) of this distribution. The total FWHM (ГT) includes the contribution associate with the width of the resonance itself (ГL)，the energy spread of the incoming ion beam (ГB), the Doppler broadening (ГD), the energy straggling (ГS), and the interface inhomogeneity (ГI) . It can be written as [1,20]: The cross section resonance of the nuclear reaction has the Lorentzian line shape of a Breit-Wigner dispersion function, where ER (6.385MeV), σR, and ΓL(1.8 keV) denote the resonance energy, the maximum, and the spectral width of the cross section, respectively The incident ion beam energy distribution (as delivered by the accelerator) can usually be treated approximately by a Gaussian function with a width parameter δB (standard deviation), as shown below [2] ] 2 The experimentally accessible beam energy spread, ГB, is the FWHM of this distribution, as show below: where the 15 N 2+ ion beam at an energy of 6.385 MeV was monochromatized with an energy analyzer of the double-focused magnetic-sector type with an energy dispersion of 2540 mm. Both entrance and exit slit widths of the energy analyzer were carefully measured and set to 3.0 mm.
The spatial confinement of the hydrogen atoms inside their chemical bond potentials causes an inevitable uncertainty of their momentum according to the Heisenberg relation, and the wave function of the resulting zero-point vibration is Gaussian in momentum space (assuming a harmonic oscillator model for the nuclear motion). Although the zero-point vibrational energy of the H nuclei is small (some tens of meV) compared to the nuclear reaction energy ER, the resulting Doppler shift of the 15 N 2+ -H collision energy translates into a sizeable Gaussian broadening D(E), as shown below [3] ) 2 The Doppler broadening ГD is the FWHM of this distribution, as shown below: where the parameter, δD, is the width parameter of the Doppler-broadening distribution.
Straggling, an energy fluctuation caused by multiple weak scattering interactions of the ion with the target electrons, simultaneously broadens this energy distribution, as shown in Supplementary Eq. 8. Due to the stochastic nature of the straggling process the energy broadening function is Gaussian and its width parameter increases in proportion to the square root of the ion trajectory length in the analyzed material. Straggling becomes the dominant limitation of the depth resolution from probing depths (z) beyond several nanometer, the precise value depending on the stopping power and straggling cross section of the projectile in the target. is equal to 1.8973 keV. The energy loss cross section or stopping powers for is for the compound (e.g., SmNiO3, SiO2) can be estimated in a first approximation, the so-called Bragg`s Rule, as the stoichiometry weighed average of the respective elemental stopping powers [4,20].
The straggling length, ГS, is the FWHM of this distribution is shown as, where the Δh corresponds to the penetrated thickness of 15 N ions. It is also worth noticing that the pronounced hydrogen concentration minima and maxima close to the surface is attributed to the effects of the resonant nuclear reaction analysis (NRA) instrumental function [20], rather than simply associated to the surface hydrogen concentration. The resonance in the near surface differs from the situation of the bulk, and the near surface peak is resulted from the convolution of the Lorentzian resonance of the 1 H( 15 N,αγ) 12 C nuclear reaction at 6.385 MeV 2 with the incident ion beam energy distribution (as delivered by the accelerator) 3 and the Doppler broadening effect induced by the zeropoint vibration of the hydrogen atoms against the sample surface 4 and the straggling of the incident ion projectiles inside the sample [5]. The resonant NRA instrumental function is in shape of Voigt profile and the main limitation for the near-surface depth resolution [20], and therefore results in the pronounced concentration minima and maxima close to the surface of the samples.

Supplementary
Supplementary Figure 5. The absolute values of R0, RH for the films with different strain. It can be seen that before the hydrogenation process, the most tensile strained SNO/STO shows a larger resistance, compared to SNO/LSAT and SNO/LAO. Upon hydrogenation, the difference in resistance was further enhanced. For example, more than 5 orders enhancement in the resistance was observed for SNO/STO, while the increase in resistance for SNO/LSAT is around 4 orders and for SNO/LAO is less than 4 orders. It has been pointed out by previous investigations that an accurate quantitative curve fitting of the Ni XPS spectra is nearly not possible, owning to the presence of satellite peaks (sitting 6 eV higher than 2p2/3) originating form interatomic, non-local electronic coupling and screening effects in Ni 2+ and Ni 3+ compounds [6][7][8]. To demonstrate the more effective reduction in valance state of Ni for SNO/STO as compared to SNO/LAO upon hydrogenation, we utilize the main peak position corresponding to the Ni 3+ (high valance: HV), Ni 2+ (middle valance: MV) and Ni 0 (low valance: LV) for the numerical curve fitting, despite their overlapping with the satellite peaks.

Supplementary Discussions
We have performed first-principles calculations using spin-polarized density functional theory (DFT) based Vienna Ab initio Simulation Package [9]. The electron-ion interaction was described using projector augmented wave (PAW) method [ [16]. Next, we derive the Hi diffusivity from the probability of the Hi defect. Based on the transition state theory, 18 the transition rate for an interstitial defect jumping to one of its neighboring sites is given by Supplementary Eq. 10: where ν 0 is the attempt frequency, ∆ is the free energy difference between the transition state and the initial state, B is Boltzmann's constant and T is the absolute temperature. Here we approximate the ∆ by energy barrier between the transition state and the initial state at zero temperature. We note that the contribution from vibrational energy term to the free energy difference is ignored in our current study due to the high computational cost required for the evaluation of the vibrational frequencies of the system in the saddle configuration [19]. With this approximation, we find that at room temperature