Main

Increasing requirements of sensitivity and of spectral dispersion have driven the development of NMR magnets to higher and more homogeneous magnetic fields, which are obtained by immobile and expensive superconducting magnets. With the best field homogeneities available (ΔB/B∼10−9 over 1 cm3, where B is the magnetic field), ultrahigh-resolution carbon (13C) NMR spectra at 4.2 T with an instrumental broadening below 50 mHz have been realized2. For 1H high-field NMR spectroscopy (1–20 T), it is difficult to measure linewidths with an instrumental broadening below 100 mHz.

We define our ideal NMR spectrometer by two requirements: first, it should measure NMR spectra with high resolution and all relevant NMR parameters, such as the longitudinal (T1) and transverse (T2) relaxation times, the chemical shift and the dipolar and J-coupling, in a single scan; and second, the spectrometer should be robust, low cost and mobile. Low cost and mobile means that heavy electro or superconducting magnets as well as superconducting quantum interference devices (SQUIDs) should be avoided. Single-scan and high-resolution NMR implies that sufficiently high premagnetization of the spins and a very homogeneous magnetic field are required. Do we come closer to this ideal by performing NMR in low field or in the Earth’s magnetic field (2.5–7.5×10−5 T)? Important steps towards mobile chemical-shift-resolved low-field NMR in inhomogeneous fields have been shown4,5. The first NMR spectra in the Earth’s field were demonstrated by Packard and Varian6. NMR has been performed in the Earth’s field in order to measure the 1H–31P and 1H–14N J-coupling constants7,8. Self-diffusion and relaxation-time measurements9,10,11, proton magnetic resonance imaging11 (MRI), the detection of groundwater reservoirs12 (>1 m3) and the determination of water diffusion in the pores of the Antarctic shelf ice13 were achieved by Earth’s field NMR. Heteronuclear J-coupling constants have been measured with a spectral resolution of about 1 Hz in the micro- and nanotesla regime14,15,16 by using SQUID sensors17,18.

Two facts are important for the application of NMR in the Earth’s field. First, for most spin species, the chemical shift cannot be resolved. This is owing to the fact that the spectral lines are normally much broader than the line separation induced by chemical-shift differences. One exception is hyperpolarized xenon (129Xe), which allows Earth’s field Xe chemical-shift measurements in liquids with a precision comparable to that of superconducting magnets19. Second, only heteronuclear J-couplings can be measured in the Earth’s field, because the chemical-shift differences for a given nuclear-spin species (<0.1 Hz) are smaller than the typical values of the homonuclear J-coupling constants (∼0.5–200 Hz).

In this contribution, we report single-scan measurements of heteronuclear J-coupled resolved NMR spectra in the Earth’s magnetic field with an accuracy of a few millihertz. Very narrow lines are observed for 1H, 7Li and 19F nuclei in the liquid state. The origin of these narrow lines is that far enough away (>100 m) from buildings and steel constructions the Earth’s field is very homogeneous (ΔB/B<10−6) over a sample volume of 1 cm3. For nuclei with T1∼T2>3 s, the linewidth is well below 0.1 Hz, and the instrumental broadening of Earth’s field NMR is smaller than a few millihertz. In the case of thermally polarized samples with a volume of a few cm3, the signal-to-noise ratio (S/N) is smaller than 10−2 for coil-based Earth’s field NMR20. Therefore, the nuclear spins have to be premagnetized to a value of at least 10,000 times the Boltzmann magnetization at 5×10−5 T. Advanced hyperpolarization methods21,22,23,24,25,26,27 and the use of mobile electromagnets13 are successful premagnetization techniques, but the most simple mobile and robust tool is a cylindrical Halbach magnet28 with a typical field strength of 1–2 T inside the bore and a negligible field outside (see Fig. 1). The following liquid samples with a volume of 2 cm3 were investigated in the Earth’s field: benzene (C6H6), lithium chloride (7LiCl) dissolved in water, tetramethylsilane (TMS), silicone oil (Baysilone M10), octamethyl-cyclotetrasiloxane (CTS) and nonafluorohexene (NFH).

Figure 1: Setup of mobile ultrahigh-resolution Earth’s field NMR.
figure 1

The nuclear spins of a liquid sample are first prepolarized by using a Halbach magnet and then transported to the NMR probe of the spectrometer. After a 90∘ d.c. pulse excitation, the FID of the nuclear spins in the Earth’s magnetic field (∼5×10−5 T) is acquired and processed.

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Figure 2a, b shows two examples of experimental single-scan free induction decays (FIDs). Long T2-relaxation times are observed for the 1H signal of deoxygenated benzene (T2=9.4±0.1 s, see Fig. 2a) and for the 7Li+ quadrupolar nuclei dissolved in deoxygenated water (T2=18.7±0.9 s, see Fig. 2b). The signal-to-noise ratio for one single scan is 100 for the 1H spectrum and about 3 for the 7Li spectrum. A lorentzian fit of the 1H spectrum allows the determination of the 1H-Larmor frequency in the Earth’s field with an accuracy of 3×10−5 Hz. This corresponds to an accuracy of 1 pT for the absolute value of the local Earth’s magnetic field. This might be useful for geophysical applications29. In Fig. 2b, the concentration of the 7Li+ ions in water was 5.4×1021 cm−3 (7Li : nuclear spin I=3/2, natural abundance 92.6%). We found that the 7Li linewidth and the T2-relaxation time are extremely sensitive to the temperature and to the 7Li+ ion concentration. Figure 2c shows that the 7Li T2-relaxation time decreases linearly with the 7Li+ ion concentration and increases with increasing temperature of the solvent. A maximum value of T2=31 s is observed for T=70 ∘C and for low 7Li+ concentration.

Figure 2: Single-scan 1H and 7Li NMR signals measured in the Earth’s field.
figure 2

a, 1H FID of 2 cm3 deoxygenated benzene (left) and the corresponding Fourier-transformed spectrum (right). The linewidth w is 0.034 Hz full-width at half-maximum. Note the absolute scale of the frequency axis of the spectrum, showing a 1H-Larmor frequency of 2,060.22020±3×10−5 Hz. b, Single-scan FID of the 7Li+ ion in solution at T=70 ∘C and the corresponding spectrum (right). The 7Li-Larmor frequency is 800.4967±4×10−4 Hz and the linewidth is 0.017±2×10−3 Hz full-width at half-maximum. c, T2-relaxation time of 7Li+ ions in water as a function of the 7Li+ concentration. The squares (triangles) correspond to a sample temperature of 20 ∘C (70 ∘C). The solid lines are guides for the eye.

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The results of Fig. 2c can be explained as follows. The T2-relaxation time of the 7Li+ ion in water is dominated by the quadrupolar and by the 1H–7Li dipole–dipole relaxation mechanisms30. In the short-correlation limit (2πνLiτc≪1, where νLi is the 7Li Larmor frequency and τc is the correlation time), both relaxation rates depend linearly on τc, which grows with increasing viscosity of the LiCl solution. The viscosity is higher at low temperatures and at high 7Li+ concentration. Note that, for liquids in the Earth’s field, the short-correlation limit is valid because τc≪10−6 s even for a saturated and viscous LiCl solution. Owing to the large dynamic range of the T2-relaxation time in low field, NMR and MRI measurements of 7Li+ ions may be important for medical applications and for materials science. For example, MRI could be used for brain-function mapping owing to the change of the 7Li+ T2-relaxation time in the ion channels of the neurons.

The narrow 1H lines observed in the Earth’s field allow accurate measurement of the heteronuclear J-coupling constants of molecules. The J-coupling constant is a measure of the strength of the electron-mediated indirect nuclear spin–spin coupling3. To compare the resolution of high-field NMR with Earth’s field NMR, Fig. 3a shows a 1H–29Si J-coupled 1H spectrum of TMS, which has been measured with a well-shimmed superconducting high-field magnet at 9.4 T. Although using a good shimming of ∼3 p.p.b., the 1H–29Si J-coupled doublet with a coupling constant of J=6.6±0.1 Hz can be barely seen in Fig. 3a. The dominant line of the protons (width ∼1 Hz) bound to 28Si and to 30Si (I=0, natural abundance 95.3%) masks the small doublet of the protons coupled to the 29Si (I=1/2, natural abundance 4.7%). Figure 3b (black spectrum) shows a proton spectrum of TMS, but measured with a single scan in the Earth’s magnetic field. Compared with Fig. 3a, the TMS spectrum is better resolved by a factor of twenty, and the 1H–29Si J-coupling constant of 6.620±0.002 Hz can be determined with high accuracy.

Figure 3: Precision measurements of 1H–29Si J-couplings for different silicon compounds.
figure 3

a, 1H-reference spectrum of TMS measured at the 1H Larmor frequency νH=400 MHz with a superconducting magnet shimmed to a few p.p.b. (with kind permission of R. Hoffman of the Department of Organic Chemistry, The Hebrew University of Jerusalem). The original p.p.m. scale was rescaled to the frequency scale. b, Single-scan 1H Earth’s field NMR spectra of TMS (black), silicone oil M10 (red) and CTS (blue). All three spectra show different values of the 1H–29Si J-coupling constants. The amplitude of the central peak (which corresponds to 95.3% of the protons without a J-coupling) is normalized to 1. c, Statistics over eight scans of all measured 1H–29Si J-coupling constants. The squares correspond to TMS, the circles to silicone oil and the triangles to CTS. The fluctuations mainly arise from the imperfect phasing of the spectrum. The error bars indicate the standard deviation of the mean J-value (solid lines).

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The J-coupling is very sensitive to the structure and type of the chemical bonds. For example, the 1H–29Si J-coupling depends on the number of oxygen atoms bound to the 29Si atom. This is demonstrated in Fig. 3b (blue spectrum), where a single-scan 1H spectrum of CTS is displayed. The chemical structure of the CTS ring is shown on the upper right of Fig. 3b. One single 1H–29Si J-coupling constant with J=7.470±0.005 Hz is observed. This value is significantly different from the J-coupling constant of TMS (6.620 Hz), because in the CTS ring two oxygens are bound to the 29Si, which modify the energy of the molecular orbitals of the SiMe2 group (where Me refers to the methyl group). This CTS ring is an important educt in the ring-opening polymerization to long-chained silicone oil molecules (polydimethylsiloxane).

The 1H–29Si J-coupling constants can also be measured for long macromolecular chains. In Fig. 3b (red spectrum) the Earth’s field 1H spectrum of silicone oil (Baysilone M10) is shown, which consists of macromolecules with an average chain length of n=16, with 14 –[O– SiMe2 ]– repeat units, and two terminal –O– SiMe3 groups (see Fig. 3b upper left). The spectrum points out two distinct 1H–29Si J-coupling constants, one with J=7.420±0.005 Hz corresponding to the –[O–SiMe2 ]– group and another with J=6.78±0.01 Hz corresponding to the terminal –O–SiMe3 groups. The peak integral below one J-coupled line is proportional to the total number of methyl groups. In our case, the ratio of the peak integrals between the large and the small J-coupled lines is about 2.7. Obviously, the silicone oil has more –O– SiMe3 groups than expected. For a linear molecular chain with an average total chain length of n=16, the expected peak-integral ratio would be 28/6=4.66. This means that the silicone oil consists of branched molecules, and there are more than two –O– SiMe3 groups per molecule. An overview of all measured 1H–29Si J-coupling constants for TMS, silicone oil and CTS is given in Fig. 3c. For each molecule, eight single-scan measurements have been performed in order to estimate the statistical errors of the measured J-coupling constants. Note that the two J-coupling constants J=7.47 Hz for CTS and J=7.42 Hz for the silicone oil belong to the same chemical group –[O–SiMe2 ]–, but they differ by 0.05 Hz. The O–Si–O bonding angle of the CTS ring must be slightly distorted and thus it differs from that in the silicone oil. The ability to discriminate between the molecular structure of the CTS ring and the silicone oil opens the possibility for the mobile online characterization of a polymerization reaction.

The splitting due to the 1H–19F J-coupling in trifluoroethanol has been detected at ∼1 μT using SQUID NMR17,18, and the linewidths of the 1H and 19F resonances were about 1 Hz. Figure 4 shows a complicated case, the 19F spectrum of NFH. In the Earth’s field, the NFH molecule is characterized by eight heteronuclear 1H–19F J-coupling constants. Homonuclear 19F–19F J-couplings are not observable. Therefore, the spectrum is a superposition of four triplets and four doublets. In the weak-coupling limit (J≪|νH−νF|=121.7 Hz, where νH and νF are the 1H and 19F Larmor frequencies, respectively), each observed triplet and doublet can be assigned to a J-coupling constant JF–Ha and JF–Hb, respectively. The largest value is 3JF–Hb=3.58 Hz (doublet d3), where proton Hb is coupled over three bonds to the two 19F spins of a CF2 group. The smallest value is 7JF–Ha=0.19 Hz (triplet t7), where the two protons Ha are coupled over seven bonds to the three 19F spins of the CF3 group. The J-coupling values over four, five and six bonds have been assigned by arguing that the coupling constant decreases monotonically with increasing number of bonds, and that a double bond results in a larger J-coupling constant than a single bond. The simulation (the red line in Fig. 4) of the 19F spectrum of NFH obtained by a superposition of four triplets and four doublets reflects the basic features of the measured spectrum.

Figure 4: Experimental and simulated 19F Earth’s field NMR spectra of NFH.
figure 4

The NFH structure is shown in the upper right corner. Each proton species, labelled as Ha and Hb, is J-coupled to the 19F nuclei of three CF2 groups and one CF3 group. The spectrum is a superposition of four doublets (d3–d6, where, for example, d3 stands for a doublet with three bonds between 19F and 1H b) and four triplets (t4–t7) with eight corresponding 1H–19F J-coupling constants, as indicated by the arrows. The J-coupling constants are plotted on the right. The black (red) line represents the experimental (simulated) NFH spectrum. For the experimental spectrum, nine scans have been averaged in order to improve the signal-to-noise ratio. The parameters for the simulation are the eight J-coupling constants, and the linewidths (0.16–0.40 Hz) are extracted from the NFH spectrum. The integrated intensity of each multiplet spectrum is chosen to be proportional to the number of fluorine atoms of the corresponding chemical group (CF2 and CF3).

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We have shown that the molecular structure can be explored by single-scan ultrahigh-resolution NMR in the Earth’s field. In future, the potential of low-field NMR could be further improved by combining the methods of multidimensional NMR1 with advanced mobile hyperpolarization technologies (spin-exchange optical pumping, SEOP21,22,23,24; para-hydrogen-induced polarization transfer, PHIP25,26; and spin-polarization-induced nuclear Overhauser effect, SPINOE27). In low magnetic fields, these techniques will allow time-resolved NMR measurements of rare spins such as 6Li, 13C and 29Si, and the separation of their corresponding spin interactions with high precision. Many applications of mobile low-field NMR in medicine and materials science are likely. This includes the NMR and MRI of hyperpolarized 6Li+ and 7Li+ migrating through ion channels or membranes, the measurement of biomagnetic fields, the detection of tiny changes of the Earth’s field in geologically active regions, the characterization of mineral oil in well logging, and the online detection of chemical reactions.

Methods

Sample preparation

An NMR glass tube (20 mm outer diameter) equipped with a valve was filled with 2 cm3 of the liquid sample. All samples were deoxygenated by several freezing and thawing cycles under high-vacuum conditions. Finally, the samples were flushed with 4He gas at a few bars’ pressure, and the valve closed.

NMR setup

The Halbach permanent magnet28 with a bore of 50 mm was composed of eight magnetized FeNd segments, which were combined in a cylinder with an outer diameter of 130 mm and a height of 150 mm. The field strength in the centre was about 1 T. The weak stray field outside the magnet typically broadens a proton NMR line at 1 m distance to about 0.1 Hz. This broadening was avoided by increasing the distance between the Halbach magnet and the NMR probe to several metres. The probe had two components: a cylindrical receiver coil (with a few thousand windings of copper wire) and a saddle coil for the spin excitation. The 90∘ pulse was produced by the saddle coil in terms of a d.c. magnetic field of strength B1=1.8×10−4 T for a duration of 50–150 μs. The direction of the B1 field was orthogonal to the direction of the Earth’s magnetic field vector. The probe was 60 cm away from the preamplifier, which had a voltage noise of <2 nV Hz1/2. A 20-mm-thick aluminium cylinder provided a shielding from ambient electromagnetic noise. The signal after preamplification was processed by a home-made lock-in amplifier, which operated at a reference frequency close to the Larmor frequency of the spins. Typically, the detection bandwidth was 20 Hz. The whole receiver electronics had a noise contribution that was smaller than the Johnson noise of the receiver coil (∼10 nV). Therefore, our NMR setup was operating close to the Johnson noise limit.

Measurement

Nuclear spins with a longitudinal relaxation time T1>1 s were premagnetized with a 1 T Halbach magnet (Fig. 1), and then carried within 1–2 s to the coil of the Earth’s field NMR spectrometer. There, transverse magnetization was generated by a 90∘ d.c. magnetic field pulse with the saddle coil; the subsequent FID was picked up by the NMR receiver coil, amplified and processed.