Fig. 1. Schematic representation of Lee–Goldburg decoupling pulse experiments in DACs. By irradiating the sample with a long and weak off-resonant pulse, the precessing spin system is forced to relax in the magic angle Θ ≈ 54.7° (see the text for details), effectively averaging out dominant nonsecular spin interactions. The resulting free induction decay in the rotating frame (FIDRF) will be subject only to those spin interactions that are linear in the nuclear Zeeman interaction perturbation (e.g., isotropic chemical, paramagnetic, or Knight shifts).

Fig. 2. High-pressure NMR resonator setup for high-frequency applications. (a) To drive the Lenz lens resonators, a pair of single-loop coils made from PCB-plated copper is used. To match the resonators’ small inductance (≈1 nH) to the desired resonance, a surface-mount device capacitor (≈10 nF) is placed in series with each coil. (b) In the closed DAC assembly, a Helmholtz coil arrangement drives the Lenz lens resonators.

Fig. 3. Comparison of LG decoupling using standard coils and in DACs. (a) ¹⁹F-free induction decays in the laboratory frame (FID) and in the rotating frame (FIDRF), sampled as described in the text, of a single crystal of CaF₂ obtained from a 150 pl (500 µm diameter, 750 µm height)-sized solenoidal coil. (b) The corresponding coherence diagram (red dots are data points and the purple lines are guides to the eye) clearly shows a rapid dephasing of the FIDRF within ∼100 µs. (c) ¹H FID and FIDRF of a single crystal of dense magnesium silicate phase D from a Lenz-lens-based resonator design as described in the text. (d) The corresponding coherence diagram shows a slow dephasing of the real and imaginary parts of the FIDRF, corresponding to a stretching factor of about two orders of magnitude. The resulting Fourier transform NMR signal (not shown) has a FWHM linewidth of 0.12 ppm.

Fig. 4. ¹⁴N-LG-NMR spectra of molecular nitrogen up to 85 GPa. (a) The quintuplet state of molecular nitrogen ¹⁴N₂ possesses a nuclear molecular spin I = 2, leading to significantly broadened spectra of about 2 MHz (≈10⁵ ppm). The full spectrum is a sum of spin echoes (orange) acquired at variable frequency offsets. The blue spectrum is a broadened envelope of all subspectra. (b) Application of LG decoupling allowed the resolution of isotropic chemical shifts of molecular nitrogen at ultrahigh densities with an accuracy of ∼10 ppm.

Fig. 5. High-resolution 2D-LG-NMR on ferromagnetic (Al_0.3, Fe_0.7)OOH. (a) Local atomic structure of the hydrogen bond ensembles in (Al_0.3, Fe_0.7)OOH. As both Al³⁺ and Fe³⁺ cations are statistically distributed, several hydrogen bond environments are likely to appear in the ¹H-NMR spectra. (b) 2D-¹H LG-NMR spectrum at 15.7 GPa. The hydrogen-bonded species Qⁱ (i = 1, …, 6) appear at different paramagnetic shift values in the indirect LG projection dimension. Using the probability distribution of these species according to the stoichiometry of the sample (c), signal assignment via intensity ratios was possible.

Fig. 6. 2D-¹H-LG-NMR spectra of dense magnesium silicate phase D (Mg_0.88, Fe_0.12) · (Si_0.9, Al_0.1)₂O₆H₂. (a) The spectra have linewidths in the LG projection dimension of less than 1 ppm, allowing the observation of the high-spin to low–spin transition of the ferric Fe³⁺ ions resulting in a partial collapse of the paramagnetic shift interaction with the hydrogen nuclei. (b) Resonance shift ω − ω₀ at pressures between 70 GPa and ambient conditions. Under the influence of strong paramagnetic interactions in the high-spin state below 40 GPa, the ¹H-NMR signals of phase D are shifted by 30 ppm downfield (higher ppm values). The electron spin crossover to a low-spin configuration leads to a pronounced reduction in the paramagnetic shift at higher pressures.

Fig. 7. High-resolution ¹H-NMR spectrum of yttrium hydrides synthesized at 45 GPa and 2500 K. The spectrum of YH₂ appears at 0 ppm and is not shown. In addition to synthesized YH₃, the formation of at least one other hydride of slightly higher hydrogen content than YH₃ or of ternary compounds with incorporation of carbon can be observed.