Available online 8 June 2011.
Sensitive magnetometry has been established as a powerful technique for the characterization and testing of materials, with the most demanding applications relying on SQUID magnetometers operating at cryogenic temperatures. The recent development of compact, non-cryogenic atomic magnetometers with sub-femtotesla sensitivity and easy sample access has opened up a number of new possibilities. We give examples of sample thermal demagnetization measurements with sensitivity better than 10−9 emu/Hz½ up to 420 °C and of magnetic detection of water droplets on an aluminum surface. Recent research on magnetometry with laser-cooled atoms and color centers in diamond promises to extend the reach of atomic magnetic sensors to the micro- and nanoscale.
Measurement of the magnetic field is one of the most basic material characterization techniques, informing on both fundamental magnetic properties of the material and the nature of any defects or inclusions. A large number of methods are commonly used for magnetic material characterization. For example, Superconducting Quantum Interference Device (SQUID) based Magnetic Property Measurement Systems are fairly standard equipment in many laboratories. More specialized instruments include scanning SQUID1 and Hall probe2 microscopes. Here we review another magnetometry technique that is based on the spin precession of atoms. Recent progress in this field makes atomic magnetometry more suitable than SQUIDs for material characterization under some conditions. We give an example of a practical measurement system and briefly summarize new techniques that may result in even greater capabilities in the near future.
SQUID magnetometers have been recognized as the most advanced tool for magnetic characterization due to their high sensitivity and ability to operate in a large magnetic field. SQUID magnetometers with centimeter-sized pick-up coils can reach a sensitivity down to 1 fT/Hz½3. The pick-up coil can be easily arranged in a gradiometer configuration to reduce sensitivity to ambient field fluctuations. Furthermore, SQUIDs are differential sensors, so they naturally measure a change of the magnetic field when a sample is introduced into the system, even in the presence of a large constant magnetic field. These advantages of SQUIDs are balanced by some limitations. They require cryogenic cooling since the basic operating principles rely on the superconductivity of both the Josephson junctions in the SQUID and the pick-up coil flux transformer. High-Tc SQUIDs cooled with liquid nitrogen have become fairly common, but still suffer from one to two orders of magnitude loss in sensitivity compared with low-Tc SQUIDs, particularly at low frequencies4. The cryogenic requirements limit the temperature range of samples that can be studied with SQUIDs. Radiation shields are usually used to separate the sample from the sensor, but they introduce additional magnetic field noise due to Johnson currents5. The high sensitivity of SQUIDs to RF interference requires extensive shielding and presents challenges for their use outside of the laboratory.
Atomic magnetometers were initially introduced for monitoring the Earth's field6 and have become quite common for measurements of magnetic fields outside of the lab. They rely on accurate measurement of the Larmor spin precession frequency of electrons in a magnetic field.
Alkali-metal atoms (K, Rb, and Cs) with an unpaired valence electron are commonly used because of their high vapor pressure and convenient optical transitions, which can easily be accessed with diode lasers. The gyromagnetic ratio γ in alkali-metal atoms is modified from that of a free electron due to the hyperfine interaction with the nuclear spin and is generally on the order of 2π × 5 kHz/μT. Atomic magnetometers are sensitive to the total value of the magnetic field, unlike SQUIDs which measure a change in the magnetic field. Therefore it is easiest to operate an atomic magnetometer in a low field, typically below 1 mT, although it should be possible to push their operating range to the Tesla regime with microwave and high-bandwidth optical techniques.
The sensitivity of atomic magnetometers depends on the precision of the frequency measurements7. As with all spectroscopic measurements, there is a fundamental limit on the frequency uncertainty due to quantum fluctuations, which can be expressed by the following relationship
For many of the applications of atomic magnetometers, including material characterization, the active volume of the sensor is also an important parameter. A sample with a uniform magnetization M and a volume V creates a magnetic field on the order of B μ0M / 4π over a volume of order V outside the sample. Hence, an optimal size of the sensor is approximately equal to or slightly smaller than the sample size. The dual requirements of a small sensor volume and a large number of atoms naturally lead one to increase the density of atoms until collisions between them limit the coherence time. For hot atoms the collisional resonance linewidth can be written as
To circumvent this limitation we use the fact that spin relaxation due to spin-exchange collisions in alkali-metal atoms can be eliminated by operating in a very low magnetic field, which was first demonstrated in the 1970s10. The key requirement is that the Larmor frequency is much smaller than the rate of spin-exchange collisions, which is satisfied for fields on the order of 1 nT or less for typical alkali-metal density. In the absence of relaxation due to spin-exchange, the cross-section for spin relaxation that goes into eq. 3 can be as low as σ = 10−22 m2 for K atoms11. This results in fundamental sensitivity limit of less than 0.01 fT/Hz½ for a 1 cm3 sensor.
The large improvement in sensitivity comes at the expense of the requirement that the sensor operates near absolute zero of the magnetic field in all directions. In practice, it is not hard to realize a magnetic field of less than 1 nT using multi-layer magnetic shields and coils inside the shields to zero out residual fields using the magnetometer itself as a 3-axis sensor12. Atomic magnetometers are particularly well suited for measurements of remanent ferromagnetism and other magnetic phenomena that do not require a bias field. Besides higher magnetic sensitivity, they can measure samples over a wide range of temperatures. Since the cell containing alkali metal is typically heated to 150 – 200 °C to achieve sufficient vapor density, it is particularly easy to make measurements with the sample at elevated temperatures. Room temperature measurements can also be easily performed with a minimum amount of thermal insulation.
An example of a high sensitivity atomic magnetometer for materials characterization recently built in our laboratory is shown in Fig. 1. Potassium atoms are contained in a 1 inch spherical glass cell at the center of the apparatus. The cell also contains several atmospheres of helium gas to slow the diffusion of atoms to the walls and 50 torr of N2 to radiationlessly quench the excited state of K atoms, preventing radiation trapping of optical pumping radiation. The cell is surrounded by a boron nitride oven, which is heated to about 200 °C by flowing AC currents at 20 kHz in a tightly twisted pair of high resistivity wires. The inner layer of the magnetic shield is made from a low-loss electrically insulating ferrite material to minimize the magnetic noise from thermal electrical currents13. A set of coils inside the shield allows control of all components of the magnetic field and first order gradients in order to cancel residual magnetic fields at the magnetometer or introduce a known bias field. The K atoms are optically pumped into a spin-polarized state by illumination with several milliwatts of circularly polarized laser light tuned to the D1 optical resonance (4S½→4P½). Changes in the polarization of the atoms due to the magnetic field are probed with a linearly polarized laser perpendicular to the pump. The probe laser beam is detuned from resonance so it is largely transmitted through the cell. The plane of the probe light polarization is rotated by the atoms due to the paramagnetic Faraday effect. For small magnetic fields, the polarization rotation angle is proportional to the magnetic field component perpendicular to both the pump and the probe lasers. The polarization of the transmitted probe light is monitored with a sensitive polarimeter and gives a continuous measurement of the magnetic field with a bandwidth given by the atomic spin-relaxation rate, typically in the range of 5 to 100 Hz. Because of slow diffusion of K atoms, different parts of the cell can be used as independent magnetometers. This allows additional cancellation of the magnetic noise generated by the shields14. In this apparatus the best magnetic field sensitivity of 0.16 fT/Hz½ has been obtained for magnetic field signals near 40 Hz15.
|Full-size image (36K) |
High-quality image (317K)
Schematic of an atomic magnetometer with sample access. The cell (a) containing K atoms and buffer gas is located at the center of the ferrite magnetic shield (g). It is heated in a boron-nitride oven (b) to 200 °C with access holes (d) for pump and probe lasers. The sample is introduced through a quartz tube that goes through the shield. The sample can be heated using an electrical oven (f) with diamond heat spreader bars. The sample is shielded from thermal radiation with a patterned gold coating (c). Magnetic coils and water cooling lines are held by G10 form (e). The distance between the centers of the sensor cell and the sample tube is 1 inch.
Reprinted with permission from15 ©American Institute of Physics.
The sample is introduced close to the sensor through a 12 mm ID quartz tube that goes through the length of the apparatus. The distance from the center of the sample tube to the center of the sensor cell is about 1 inch. The sample can be heated by electric heaters mounted on the tube or maintained near room temperature by a gentle flow of air through the tube. We use a single layer of radiation shielding, consisting of a gold coating patterned into 0.3 × 0.3 mm2 electrically isolated squares to reduce magnetic noise from Johnson currents16. The radiation transfer power can be much larger in our system than in a typical cryogenic environment, so we use a single-layer radiation shield instead of multi-layer cryogenic insulation. The sample is typically attached to a long rod and rotated at 5 – 10 Hz, thereby introducing a clear modulation of the signal at a frequency above 1/f noise and allowing simultaneous measurements of the two transverse components of the magnetization. Great care must be taken to minimize magnetic contamination of the sample holder. The best results are obtained using a quartz tube etched in acid with the sample held by suction using a vacuum pump attached to the other end of the tube with a rotary connection. We could not find a glue or cement that can hold the sample without introducing some magnetic contamination.
Two examples of sample measurements are shown in [Fig. 2] and [Fig. 3]. Fig. 2 shows measurements of the remanent magnetization of an ancient dolomite rock as a function of temperature. Such thermal demagnetization measurements are very common in paleomagnetic studies17, but in the past could only be performed with a high sensitivity by repeatedly transferring the sample between a SQUID magnetometer and a magnetically-shielded furnace. The ability to simultaneously heat the sample to as high as 500 °C and measure its magnetization with a sensitivity below 10−9 emu/Hz½ is unique to atomic magnetometers. Atomic magnetometers for the measurement of remanent magnetization in paleomagnetic applications are starting to be commercially developed18.
|Full-size image (24K) |
High-quality image (177K)
Measurements of the remanent magnetization of a weakly magnetized dolomite sample as a function of temperature. The sample is continuously rotated while the temperature is slowly increased. The inset shows the spectrum of the magnetometer signal at the highest temperature. The peak at 8 Hz and its harmonics are due to the magnetic field from the sample. Analysis of the signal phase allows independent measurements of the two magnetization components that are orthogonal to the rotation axis. The magnetic moment sensitivity of the magnetometer is below 10−9 emu even at the highest sample temperature.
Reprinted with permission from15. ©American Institute of Physics.
|Full-size image (21K) |
High-quality image (124K)
Measurement of magnetic signals from the aluminum surface interaction with water. A small water droplet is placed on an aluminum sample which is then continuously rotated at 7 Hz. The inset shows the relative placement of the sample and alkali-metal cell. The plot shows the magnitude of the magnetic signal at the rotation frequency. At 60 seconds the water droplet evaporates, with the signal dropping to a small residual value due to magnetic contamination of the sample.
Fig. 3 shows the magnetic signals that are generated by surface interactions between aluminum and water. Magnetic signatures of corrosion have previously been studied using SQUID magnetometers19. We have made a few preliminary measurements of this effect using the atomic magnetometer. For this application the sample was held near room temperature by gently blowing air through the access tube. In addition to magnetic signals from corrosive chemicals, such as HCl and NaOH, we have also observed electrochemical magnetic signals using deionized water that are an order of magnitude smaller. We observe a magnetic field that quickly disappears as the water droplet evaporates. The field can be caused by ionic currents due to chemical reaction or possibly due to thermal currents generated by a temperature difference between the evaporating water and aluminum20. No signal is observed if the aluminum surface is coated with a thin polymer coating before the application of the water droplets. The ability to detect weak magnetic signals from the interaction between water and aluminum would be interesting for many non-destructive testing applications, such as the detection of hidden corrosion21.
So far we have focused on atomic magnetic field detectors on the centimeter scale, which is a convenient size for measurements on bulk samples. However, in many materials applications one desires to perform magnetic field scans on a much smaller scale. New atomic magnetometers are currently being developed from the millimeter to nanometer scales and may soon become available for materials characterization applications.
The scaling of hot-vapor alkali-metal magnetometers to smaller dimensions is not particularly favorable. To limit the spin relaxation of atoms on cell walls one has to increase the pressure of the buffer gas to slow down the diffusion of atoms. More frequent collisions of alkali-metal atoms with the buffer gas then result in an additional spin relaxation that broadens the magnetic resonance. One can partly compensate for this loss in sensitivity by increasing the density of the alkali-metal atoms in the cell. However, the spin-relaxation cross-sections quickly increase with temperature22 so the higher temperatures required also lead to increased resonance broadening. Currently the most sensitive millimeter sized sensors are being developed at NIST23 and a sensitivity of 5 fT/Hz½ has been achieved. Such sensors have been used, for example, for magnetorelaxometry measurements of magnetic nanoparticles24. Another approach that may be promising is the use of anti-relaxation coatings, typically made from long hydrocarbon chains, which largely prevent relaxation of alkali-metal atoms on cell walls. Recent studies of alkene coatings show that they allow up to 106 collisions of Rb atoms with cell walls before spin relaxation25. Such coatings may help to scale down the dimensions of the sensor, although so far they have been shown to operate only at relatively low temperatures.
To improve atomic magnetometer spatial resolution to the sub-millimeter size likely requires a different approach. Measurement with laser-cooled and trapped atoms is a natural technique for this length scale, since cold atomic clouds trapped at a focus of a laser beam or held in a microchip magnetic trap typically have dimensions of 10 – 100 μm. Long spin coherence times have been achieved in optical26 and magnetic traps27, but the number of trapped atoms is typically much smaller than used in vapor cells. The overall sensitivity of cold atom sensors is already quite competitive with SQUID magnetic microscopes. Two different approaches are currently being explored in this active area of research. In one approach the frequency of Larmor spin precession of atoms is measured with a probe laser28, just as in hot atom magnetometers. In another approach, one simply measures the density of the atomic cloud in a shallow trap. The extra energy from interaction of the atomic magnetic moment with the magnetic field ΔE = −μ · B leads to a perturbation of the atomic density that can be directly imaged with a laser29. Atoms with a large magnetic moment, such as Dy, have a larger magnetic interaction energy than alkali-metal atoms and may further increase the sensitivity of such sensors30. One of the challenges of using cold trapped atoms for sample studies is the requirement that they operate in ultra-high-vacuum (UHV); typically 10−10 – 10−11 Torr, since any collision with background gas will eject the atoms from the trap. Therefore all samples would have to be introduced through a load-lock system compatible with a UHV environment or placed behind a very thin vacuum window.
Another technique currently being explored for sensitive magnetometry uses nitrogen-vacancy (NV) color centers in diamond31. This crystal defect, consisting of a nitrogen substitution next to a carbon vacancy with overall negative charge, is paramagnetic and has very favorable optical and coherence properties. The level diagram of the color center is shown in Fig. 4. The ground state has electron spin S = 1 with a splitting between mS = 0 and mS = ±1 states of 2.8 GHz due to magnetic spin-spin interactions with the applied field. In the presence of a magnetic field the mS = ±1 states are further split by the electron magnetic moment interaction. The color center can be optically excited using a laser at a convenient green wavelength, such as 532 nm, and decays back by emitting florescence at 637 nm. However, the fluorescence properties of mS = 0 and mS = ±1 states are different. Whereas color centers excited from the mS = 0 state are quickly cycled back to the mS = 0 state, those excited from the mS = ±1 states have a significant probability of decaying to a metastable singlet state, where they remain for 200 – 500 ns32 before decaying back to the mS = 0 state. Thus, the initial rate of 637 nm fluorescence depends on the spin state of the color center, whereas after a sufficiently long time all color centers are optically pumped into the mS = 0. The spin coherence of the ground state is also surprisingly long for a solid state system, reaching T2 = 2 ms for specially prepared diamond samples depleted in 13C isotope33. Microwaves are used to measure the frequency of the magnetic field-dependent ΔmS = ±1 transitions to determine the magnetic field. A bias field of several mT is applied parallel to the crystal axis of the NV center to split the ΔmS = ±1 transitions, so that they can be resolved individually with microwave spectroscopy. Furthermore, because of local magnetic field fluctuations usually caused by the natural abundance of 13C nuclear spins, the highest sensitivity is realized for AC magnetic fields at a frequency of 1 to 100 kHz which are applied synchronously with a microwave spin-echo sequence34. Since the signal is measured by simply detecting the intensity of the fluorescence, a CCD camera can be used to directly image the distribution of the magnetic fields35. So far single NV color centers have reached magnetic field sensitivity of 4 nT/Hz33 whereas continuous magnetic field mapping can be realized with 20 nT/Hz½ sensitivity and 250 nm resolution36, close to the sensitivity of LHe-cooled SQUIDs on this length scale. The main advantage of diamond color centers is their ability to operate under ambient conditions and over a wide range of temperatures, without the need for UHV. One of the first examples of such measurements is the detection of the Meissner effect in a high-Tc superconductor with a diamond magnetometer37.
|Full-size image (25K) |
High-quality image (84K)
Energy levels of NV− color centers in diamond. The ground state of the color center has electron spin S = 1. Optical excitation of the m = 0 state at 532 nm brings the color center back to the m = 0 state by emission of a 637 nm photon. Following optical excitation of the m = ± 1 states the color center has a 30 % probability of decaying into a metastable singlet state, resulting in a reduction of the fluorescence signal. This spin-dependent difference of the optical scattering properties allows simple optical preparation and detection of the electron spin. Microwave transitions between m = 0 and m = ± 1 states are used to measure the magnetic field energy shift, μB.
In conclusion, atomic magnetometers have been undergoing rapid development over the last few years. Some of the first atomic sensors suitable for material characterization will soon start to enter the commercial market. They can achieve higher magnetic field sensitivities than SQUID magnetometers and can easily make measurements on samples heated well above room temperature. However, unlike SQUIDs, atomic magnetometers are absolute field sensors and do not easily allow application of large bias fields, in fact, they achieve the highest sensitivity at zero magnetic field. Presently the most sensitive atomic sensors operate on a centimeter length scale. However, active research is ongoing in laser-cooled atom magnetometers and color centers in diamond that should be able to achieve impressive sensitivities on the micron and nanometer scale. Such magnetometers may eventually replace SQUID, Hall, and magnetic force resonance microscopy (MFRM) probes in a variety of magnetic microscopy applications. At the same time, absence of cryogenics should allow atomic magnetic sensors to gain wider acceptance in industrial and geophysical applications.
7 D. Budker and M. Romalis, Nature Phys 3 (2007), p. 227.