Extremely Low-Frequency Spectroscopy in Low-Field Nuclear Magnetic Resonance

We demonstrate a new phenomenon in nuclear magnetic resonance spectroscopy, in which nuclear spin transitions are induced by radio frequency irradiation at extremely low frequencies (of the order of a few Hz). Slow Rabi oscillations are observed between spin states of different exchange symmetry. These “forbidden” transitions are rendered weakly allowed by differential electronic shielding effects on the radio frequency field. We generate coherence between the singlet and triplet states of ${}^{15}\mathrm{N}$-labeled nitrous oxide in solution, and estimate the scalar coupling between the two ${}^{15}\mathrm{N}$ nuclei with a precision of a few mHz.

Figure 1

Equipment used to perform ELF NMR experiments.

Figure 2

Experimental timing sequences. (a) Magnetic fields, involving transport of the sample from the high magnetic field $B_{\mathrm{high}}$ to the low magnetic field $B_{\mathrm{low}}$, and back again. The transport time is ${\tau }_{\mathrm{tr}}$. (b) Radio frequency fields, resonant with the ${}^{15}\mathrm{N}$ nuclei in $B_{\mathrm{high}}$. The pulse flip angles and rf phases are given in degrees. The time spent in $B_{\mathrm{low}}$ is ${\tau }_{\mathrm{LF}}$. (c) ELF pulse sequence for observing singlet-triplet nutation. After a time ${\tau }_{\mathrm{TE}}$ to allow triplet equilibration, a resonant ELF pulse is applied of duration ${\tau }_{\mathrm{ELF}}$. (d) ELF pulse sequence for observing the precession of singlet-triplet coherence. Two ELF pulses, with the same phase, are separated by a variable evolution interval ${\tau }_{\mathrm{ev}}$. The ELF sequences are executed in parallel with sequences (a) and (b). The timing sequences are not to scale: the low-field pulses are about 4 orders of magnitude longer than the high-field ones.

Figure 3

Experimental peak amplitudes plotted against the timing intervals of ELF pulse experiments. (a) Singlet-triplet nutation experiment, varying the duration ${\tau }_{\mathrm{ELF}}$ of the ELF pulse in Fig. 2c. (b) Singlet-triplet coherence evolution experiment, varying the duration ${\tau }_{\mathrm{ev}}$ of the evolution interval in Fig. 2d, with the two ELF pulse durations fixed to ${\tau }_{\mathrm{ELF}}=2.15\mathrm{s}$. Black circles and white boxes refer to the amplitudes of the two components of the high-field doublet in the ${}^{15}\mathrm{N}_2\mathrm{O}$ spectrum. The solid lines are best fits to exponentially decaying cosine functions with an added offset from zero. Experiments were performed on a sample of ${}^{15}\mathrm{N}_2\mathrm{O}$ dissolved in locally produced Calabrian olive oil using the following timings: ${\tau }_1=198\mu \mathrm{s}$, ${\tau }_2=99\mu \mathrm{s}$, ${\tau }_{\mathrm{tr}}=10\mathrm{s}$, and ${\tau }_{\mathrm{TE}}=60\mathrm{s}$. The ELF irradiation frequency was ${\omega }_{\mathrm{ELF}}/2\pi =8.693\mathrm{Hz}$ in all cases.