Raising the bar

Today, scientists investigate many technological frontiers with the help of magnetometers, which have important uses in industrial, biomedical, oceanographic, and space applications. Magnetometers are routinely used in the law-enforcement arena for the detection of metallic weapons such as handguns. During the Galileo Orbiter mission of the 1990s, a fluxgate magnetometer was used to map the structure and dynamics of Jupiter's magnetosphere.

The recent trend has been toward smaller magnetometers that minimize power consumption while still retaining sensitivity comparable to devices such as fluxgate and vapor magnetic-field sensors.^1,2 Optical detection in combination with micro- electro-mechanical-systems (MEMS) technology offers a method for achieving these goals.

One such MEMS-based device that has been shown to possess nanotesla sensitivity and a large dynamic range is the recently developed Lorentz-force xylophone bar magnetometer, which uses an interferometric device to measure displacement of the bar related to the magnetic field.^3-5

shifting the bar

Figure 1. The active element of a magnetometer is a conductive bar with support arms at the nodes of its fundamental mode of mechanical vibration. The Lorentz force F is proportional to the product of the magnetic field B and the amplitude of the current, I_ac, through the bar.

The active magnetometer element is a conductive xylophone bar supported at the nodes of its fundamental mode of mechanical vibration (see figure 1). Under typical operating conditions, an alternating sinusoidal current is supplied to the bar at a frequency that matches its fundamental resonance frequency. An external magnetic field generates a Lorentz force F via the coupling of the bar current and the external magnetic field, according to

F = l_barIBsinθ    (1)

where l_bar is the bar length, I is the alternating drive current, B is the magnitude of the magnetic field, and θ is the angle between I and B. The Lorentz force in turn generates an orthogonal displacement of the xylophone bar, d_o, which alternates at the frequency of the driving current, f, and is expressed by

  (2)

where f_o is the fundamental resonance frequency of the bar, Q is the resonance quality factor, and d_dc is the midpoint deflection at constant current. The latter parameter is proportional to the product of the cube of the bar length and the magnitude of the Lorentz force. In other words, the magnetic force, which is directed orthogonal to the bar surface, will cause the bar to vibrate at the frequency of the driving current with an amplitude that is linearly proportional to the drive current, magnetic field, and the mechanical quality factor of the resonator. High-field sensitivity is achieved by placing a position-sensitive detector 20 cm from the xylophone bar surface and detecting the small directional change in the reflected intensity.

For the copper-beryllium (CuBe) bar, nanotesla to microtesla magnetic fields produce a displacement at resonance that is on the order of 1 to 10 Å (see frontis).^5,6 In our initial investigations, an optically monitored deflection transducer incorporating a high-Q CuBe xylophone bar demonstrated nanotesla field sensitivity.

The initial magnetometer studies used an optical beam deflection transduction scheme, which monitored xylophone bar displacements via variations in the reflected angle of an optical probe. We detected angular variations in the reflected probe beam with a photodiode bi-cell, which provided nanotesla sensitivity when the xylophone bar-to-detector distance was on the order of 30 cm.

An interferometric displacement sensor, which detects optical path length differences rather than angular beam displacements, improved sensitivity by a factor of four relative to the optical deflection approach.⁷ Perhaps more important for MEMS-based devices, the interferometric approach can realize significantly smaller sensor packages than systems based on optical deflection technology.

The interferometer design used in our experiments is a path-stabilized Michelson system with a predicted displacement sensitivity on the order of 10^-4 Å-Hz^-1/2 using conventional laboratory instrumentation (see figure 2).⁸ The present design allows simultaneous monitoring of two orthogonal xylophone bars, which provides vectorial information regarding an external magnetic field.

The interferometer light source is a dc-driven gallium arsenide (GaAs) diode laser generating about 5 mW at 675 nm. The laser output passes through a beamsplitter that transmits 50% of the incident beam to each of the xylophone bars. Upon reflection from each bar, the optical beams are recombined at the beamsplitter and directed toward a photodiode/preamplifier detector package.

As part of the protocol for path stabilization in the interferometer, one xylophone bar is mounted onto a piezoelectric stage and position-modulated at a fixed frequency (f_ref = 1 kHz, Δ = ± 5 nm). The amplitude and frequency of the current source to the respective xylophone bar determines the characteristics of the magnetic-field-induced displacement.

The output of the photodetector is monitored by three independent lock-in amplifiers that analyze the signal at the frequency of the two current supplies and at the second harmonic (2f_ref ) of the piezoelectric modulation frequency. The 2f_ref component facilitates active stabilization of the optical path length difference between the two arms of the interferometer.

Feedback electronics provide a control voltage to the piezoelectric stage that minimizes the amplitude of 2f_ref, ensuring that the position of the first xylophone bar relative to the position of the second xylophone bar is "locked" to a path length difference of λ/4.⁷ Under room-temperature stabilization conditions, the optical path length difference between the two arms of the interferometer can be maintained at a value of λ/4 (approximately 1680 Å) to within an accuracy of approximately 0.6 X 10^-4 Å. This stabilization approach is similar to an electromechanical/optical network that is predicted to have a detectable displacement limit of about 10^-5 Å-Hz^-1/2.

The interferometer-based magnetometer can sense small field variations that are superimposed on a large magnetic field background (see figure 3). In this plot, one of the xylophone bars is subjected to a 20 nT magnetic field modulation, while immersed in the approximately 10 µT dc background level of Earth's magnetic field. In performing this measurement, the current supply to the bar was fixed at the fundamental resonance frequency, which assured maximum sensitivity in the sensor response. The ability to sense magnetic fields below 5 nT in our laboratory was compromised by environmental noise issues. The determination of the ultimate sensitivity of this interferometric system will require investigation in a magnetically isolated environment.

The Michelson design also can be used to provide vectorial information on the external magnetic field if the two independent xylophone bars are orthogonal, for example, where the dependence of the dual xylophone bar magnetometer on field direction is interrogated with a 100 nT magnetic field. The variation in the response of each bar is a direct consequence of the Lorentz force relation shown in Eq. 1, where the coupling between bar current and magnetic field is dependent on the angle between the two vectors. In performing this measurement, the resonance frequency of the two bars must be well-separated so as to minimize coupling effects in the interferometer detection electronics. The magnetic field sensitivity of the two bars is markedly different, which is a result of the different Q value for each respective xylophone.

A variety of applications are being developed with this simple magnetometer platform. For example, the coupling between the drive current and magnetic field indicates that the xylophone bar can be used as a high-efficiency mixer for the detection of ac magnetic fields. The high Q factor of the xylophone bar allows the magnetometer to be used as a narrow-band spectrum analyzer for nonsinusoidal magnetic fields.⁵ We also are pursuing nonmagnetic-field sensing applications, which rely on the ability of an adsorbed species to induce changes in the resonance frequency of the xylophone bar. Such a process could be quite useful for small, high-sensitivity chemical and biological sensing applications. oe

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