Magnetometry - Techniques, Recent Developments, Applications

Magnetometry broadly refers to measuring magnetic fields and is a topic that is hard to cover in its generality. The fields to be measured could be constant or variable (for example, oscillating or pulsed), and, depending on the application, can range in magnitude from femtotesla (fT) to hundreds of tesla. Sometimes, one is interested in the overall magnitude of the field, and sometimes, a projection of the field on certain directions is of interest. Scalar and vector magnetometers, respectively, are used for these two types of measurement. Obviously, completely different methods are needed to cover the broad multidimensional range of parameters required by applications. In this short article, we present a glimpse of some of the magnetometric techniques related to the author’s interests.

Among the most widespread magnetometers typically used to measure magnetic fields with magnitudes from tens of microtesla to about a tesla are solid-state devices such as Hall probes and fluxgate sensors (many practical magnetic sensors are discussed in Ref. 1). Another rapidly developing solid-state magnetometry technology is based on the effect of anisotropic magnetoresistance. If one can cool the sensor to cryogenic temperatures, the highest sensitivity is afforded by superconducting quantum-interferometer devices (SQUID, discussed in detail in Ref. 2).

While SQUID magnetometers have held the reputation of the most sensitive magnetic sensors for many years, in the last decade, despite continuous developments in the SQUID technology, they have been increasingly challenged by optical atomic magnetometers (Fig. 1), which have been reviewed in Ref. 3. In such a magnetometer, polarized light transfers its polarization to atomic (typically, alkali-metal or helium) spins; the spins evolve under the influence of the magnetic field to be measured; and, finally, the state of the spins is read out using a “probe” light beam by measuring its intensity and/or state of polarization after the interaction with the atoms. A magnetometer based on this general principle has recently demonstrated a record sensitivity on the order of 0.1 fT with a measurement time on the order of a second⁴.

A fundamental limit for the sensitivity of a spin-precession (and, in fact, perhaps of any spin-based magnetometer) is given by the quantum mechanical spin-projection noise as;

In this expression, known among practitioners by the name “Equation One,” ħ is the Planck’s constant, g stands for the gyromagnetic ratio, μ is the Bohr magneton (so that gμ is, up to a numerical factor, the magnetic moment associated with one spin), N is the number of spins involved in the measurement, t is the spin-relaxation time, and T is the total measurement time, assumed here to be longer than t. Thus, given particular kinds of spins (atoms), the figure-of-merit for a magnetometer is (Nt)^1/2, so that optimization and design of new magnetometer schemes often revolve around finding ways to simultaneously increase the number of spins and their relaxation time. In fact, the record setting magnetometer of Ref. 4 is based on the ingenious spin-exchange relaxation free (SERF) technique that eliminates a dominant source of relaxation, allowing operation at atomic densities several orders of magnitude higher than in more traditional magnetometers, without significantly compromising the relaxation time.

Traditional applications of atomic magnetometers are in measuring the geomagnetic field and its anomalies (such as, for example, due to the presence of magnetic ores or a friendly submarine deep under the surface where other methods of detection are difficult). In recent years, many other applications have sprung up; including measuring biomagnetic fields produced by a beating heart, active brain, and possibly even a plant⁵, although the latter remains a subject of an ongoing search. Atomic magnetometers are also becoming useful tools for the study of nominally nonmagnetic materials, as well as for petrology, the science of rocks⁴. In the past, atomic magnetometers have been launched on spacecraft, and it is likely that the new generation of magnetometers will also be used for exploring magnetic fields in space, from those produced by planets in the solar system to the ones in the outer space beyond its limits. On the other end of the spectrum of applications of atomic magnetometers is laboratory (and eventually, perhaps also field) measurements of the feeble fields produced by polarized nuclei, for instance, detection of nuclear magnetic resonance (NMR). Recent developments of microfabricated millimeter-scale vapor cells have facilitated the application of atomic SERF magnetometers to NMR detection onboard a microfluidic chip⁶, as well as conducting NMR experiment completely without magnets⁷.

Before concluding this brief tour of magnetometers big and small, let us mention one more example of each that seem particularly exciting. On the small side, the last three or so years (at the time of writing) have seen the emergence of magnetic sensors based on nitrogen-vacancy (NV) color centers in diamond (a particular type of impurity that gives diamonds their fascinating colors) that promise and are already beginning to deliver an unprecedented combination of sensitivity and spatial resolution⁸. Going back to Eq. (1), this is due to the fact that one can pack a lot of these “artificial atoms” (paramagnetic NV centers) in a small volume, while maintaining very long spin relaxation times, at least by the standards of solid-state systems. Even single NV centers can be used for magnetometry providing a way to measure magnetic and even nuclear spins with atomic-scale resolution. Recently, researchers have conducted magnetometric experiments with NV centers in nanodiamond crystals imbedded into living and dividing (!) cells⁹. On the large scale, and returning to alkali-metal-vapor magnetometers, experiments are being mounted, where instead of alkali atoms contained in vapor cells, sodium atoms in the mesosphere are used, which are located in a »10 km thick layer approximately 100 km above the surface of the earth¹⁰. The sodium atoms are deposited into the atmosphere by meteorites and can be excited by shining lasers from the ground, forming artificial laser guide stars (LGS). Magnetometers based on the LGS technology will complement and have important advantages over surface-based magnetic measurements on the one hand, and aircraft or satellite-based measurements on the other.

Finally, let us mention that an in-depth discussion of magnetometers and their applications will be given in a book tentatively titled Optical Magnetometry edited by D. Budker, D. F. Jackson Kimball, and M. V. Romalis, scheduled for publication by Cambridge University Press towards the end of 2011.

Figure 1. A schematic of a possible configuration of an all-optical atomic magnetometer. [From D. Budker,  Nature 422, 574 (2003).]

References and Further Reading

1. Pavel Ripka, Magnetic Sensors and Magnetometers, ISBN: 1580530575
2. John Clarke and Alex I. Braginski (eds.), The SQUID Handbook. Volume I: Fundamentals and Technology of SQUIDs and SQUID Systems; Volume II: Applications of SQUIDs and SQUID Systems
3. D. Budker and M. V. Romalis, Optical Magnetometry, Nature Physics 3, 227 - 234 (2007); physics/0611246
4. Dang, H. B., Maloof, A. C. & Romalis, M. V., Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer, Applied Physics Letters 97, 151110-3 (2010)
5. Eric Corsini, Victor Acosta, Nicolas Baddour, James Higbie, Brian Lester, Paul Licht, Brian Patton, Mark Prouty, and Dmitry Budker, Search for plant biomagnetism with a sensitive atomic magnetometer, J. Appl. Phys. 109, 074701 (2011)
6. M.P. Ledbetter, C.W. Crawford, A. Pines, D.E. Wemmer, S. Knappe, J. Kitching, and D. Budker, Optical detection of NMR J-spectra at zero magnetic field, Journal of Magnetic Resonance 199 (2009) 25–29; arXiv:0901.4069
7. Thomas Theis, Paul Ganssle, Gwendal Kervern, Svenja Knappe, John Kitching, Micah Ledbetter, Dmitry Budker, Alex Pines, Parahydrogen enhanced zero-field nuclear magnetic resonance; To appear in Nature Physics, arxiv:1102.5378
8. J.M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, M. D. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nature Physics 4, 810 - 816 (01 Oct 2008), doi: 10.1038/nphys1075
9. L. McGuiness et. al. Nature Nanotechnology (in press)
10. J. M. Higbie, S. M. Rochester, B. Patton, R. Holzlöhner, D. Bonaccini Calia, D. Budker, Magnetometry with Mesospheric Sodium, PNAS 10.1073/pnas.1013641108 (2011) (arXiv:0912.4310)