Ultralow magnetic fields elicit unexplained spin dynamics in water

Placed in an external magnetic field, nuclear spins respond by dancing a two-step: They wobble, or precess, about the field axis, and polarize in the field direction. At room-temperature in a 100-µT field—comparable to that of an ordinary bar magnet—it takes water’s spin-1⁄2 hydrogen nuclei about 10 seconds to relax, or achieve equilibrium polarization. In a 10-µT field, the spins relax in roughly 3⁄4 the time.

The difference has to do with the protons’ precession rate, or Larmor frequency, which is proportional to magnetic field intensity. As the Larmor frequency decreases, slower mechanisms can contribute to the relaxation process. At 100 µT, a proton’s Larmor frequency is about 4 kHz, and spin relaxation is facilitated mostly by thermal fluctuations. At 10 µT the lower Larmor frequency of about 400 Hz allows proton exchange between H₃O⁺ and H₂O and between H₂O and OH⁻ to help usher the system to equilibrium. The increase in the relaxation rate occurs around Larmor frequencies near 700 Hz (17 µT), roughly the same frequency with which protons hop between the various water complexes.

Aided by a superconducting quantum interference device (SQUID), low-field nuclear magnetic resonance experts at the National Metrology Institute in Berlin have now discovered yet another jump in water’s spin-relaxation rate. ¹ Led by Stefan Hartwig and Martin Burghoff, the team stumbled across the jump while probing relaxation at the ultralow Larmor frequencies produced by nanotesla fields, previously uncharted territory for NMR experiments.

A slow precession

As sketched in figure 1, the Berlin group subjected a water sample to a succession of three static magnetic fields. To start, they generated a polarization field B_p in the vertical direction. That field, a few millitesla in intensity, induces a spin polarization of about ten parts per billion in the water sample—about a thousand times weaker than in conventional NMR, but still too strong to reveal new spin dynamics.

Next, they switched off B_p and switched on a much weaker, coaligned evolution field B_e. Incorporating a feedback control scheme to counter field induction, they could achieve that switch in less than a millisecond. In B_e, the precession of water’s protons slows down, and the sample’s magnetization begins to decay exponentially. Charting that decay over time gives what’s known as the longitudinal relaxation rate R₁.

But the magnetic field generated by the faintly polarized water is minute, as small as a few picotesla. To accurately measure it, the researchers switched off B_e after some time τ and switched on the horizontally oriented detection field B_d. At that instant, water’s upward-pointing magnetization vector M begins to precess about the detection field, which causes the vertical component of its magnetic field, detected by a nearby SQUID magnetometer, to oscillate and decay. From that decay, the researchers could extract a reliable estimate of M at the moment B_e was turned off. By measuring M(τ) for τ varying from 1 to 15 seconds and then successively repeating the procedure for B_e extending to less than 1 µT, the researchers pieced together R₁ values for Larmor frequencies as low as a few hertz.

The weakest fields the team probed were less than 1/500 the strength of Earth’s geomagnetic field. At those intensities, even tiny fluctuations due to ambient RF waves would have foiled the experiment had the team not availed itself of the institute’s state-of-the-art magnetically shielded room.

“They must have been extremely meticulous measurements,” says Michelle Espy of Los Alamos National Laboratory, whose group also does ultralow-field NMR experiments. “At microtesla and below, magnetization from things that ordinarily are negligible can suddenly swamp what you’re trying to measure.”

A mystery mechanism

The Berlin team’s low-field measurements weren’t merely an exercise; they also revealed surprising physics. Apart from the expected rise due to proton exchange reactions, the measured R₁ values, shown in red in figure 2, also display an unexplained uptick as the Larmor frequency drops below 100 Hz.

Follow-up experiments suggest the rate increase has to do with coupling between H⁺ nuclei and spin-5⁄2 ¹⁷O nuclei. But as to the exact mechanism, Hartwig concedes, “We don’t have a good explanation. Right now, we’re hoping other theorists can offer some ideas.”

Also sure to keep theorists busy are the team’s measurements of water’s transverse relaxation rate R₂, at which precessing nuclear spins decohere. The researchers obtained those measurements with the same experimental setup, except they bypassed the evolution field and switched directly from B_p to B_d. The resulting oscillations in M_y have a Fourier peak corresponding to the Larmor frequency at B_d. The width of that peak gives R₂.

The measured R₂ values, shown in blue in figure 2, exceed theoretical predictions and thus again implicate an as-yet-unknown relaxation mechanism. In a win for theory, however, the long-held principle that R₁ and R₂ should converge as the Larmor frequency approaches zero appears to hold true.

More surprises in store?

The usefulness of ultralow-field NMR extends beyond creating challenging theoretical puzzles. For example, experiments have hinted that healthy and cancerous tissues can be distinguished by their longitudinal relaxation times—a strategy known as T₁ contrasting—but only in microtesla fields and lower. Hartwig is not alone in suspecting that the same may be true of other materials; Espy, for one, hopes to use T₁ contrasting as a noninvasive way to identify explosive materials.

But as Espy puts it, for all the potential applications, “there’s also real science to be discovered at low fields. We’ve thought for a long time that ultra-low-field NMR might reveal interesting molecular dynamics, but now the Berlin team has actually shown it—surprising things really do happen down there.”