A. Resonant magnetoelectric cantilevers

The cantilever design allows for the excitation of the mechanical resonances using an external alternating magnetic field. Considering the first bending mode, the amplitude of the cantilever deflection reaches its maximum after a settling time

(3) $$\tau = {Q \mathord{\left/ {\vphantom {Q {\left( {\pi {f_{{\rm{res}}}}} \right)\quad ,}}} \right. \kern-\nulldelimiterspace} {\left( {\pi {f_{{\rm{res}}}}} \right)\quad ,}}$$

where Q and f _res denote quality factor and resonance frequency. Accordingly, mechanical stress in the piezoelectric is enhanced and Q enters the equation for the generated ME voltage:

(4) $${V_{{\rm{ME}}}}\left( {{f_{{\rm{res}}}}} \right) = {{Q{d^{\rm{m}}}_{11}k{e_{31}}} \mathord{\left/ {\vphantom {{Q{d^{\rm{m}}}_{11}k{e_{31}}} {({\varepsilon _0}{\varepsilon _{33}})z{H_{{\rm{AC}}}}}}} \right. \kern-\nulldelimiterspace} {({\varepsilon _0}{\varepsilon _{33}})z{H_{{\rm{AC}}}}}}\quad .$$

Figure 2(a) shows a measurement of V _ME as a function of f _AC for an exemplary Si cantilever with a ME functional layer stack Ta 15/FeCoSiB 2970/Ta 15/Pt 150/AlN 1600/Cr 5/Au 100 [thickness in nm]. The magnetic anisotropy of the FeCoSiB layer was aligned perpendicular to the long cantilever axis. H _AC and H _BIAS were applied along this cantilever axis. The enhancement of the ME voltage for a particular frequency f _AC is evident from the graph. At its maximum, V _ME amounts to about 1 V/Oe for 867 Hz, which is the first bending mode resonance frequency f _res of the millimeter sized cantilever. Out of resonance, the ME voltage is reduced by a factor of 1/Q ≈ 1/500. In Fig. 2(b) the absolute value of the ME coefficient is plotted as a function of the bias magnetic field H _Bias. During the measurement, f _AC was tuned to the resonance frequency. Since the piezomagnetic coefficient is magnetization dependent, the hysteretic behavior of the piezomagnetic phase transfers to the ME coefficient, which reaches its maximum |α_ME,max| = 6.9 kV/cm Oe at H _BIAS = ±2.4 Oe. These two features of ME behavior, enhancement by mechanical resonance and bias field dependence, are typical for ME cantilever sensors with a single magnetostrictive layer. As a result, resonance frequency and optimum bias magnetic field set the working point of such devices. Without operating them actively, i.e., by applying a magnetic modulation field or an electrical driving field, the sensor bandwidth is given by the width of the resonance curve.

FIG. 2.

ME properties of a cantilever sensor based on a single FeCoSiB layer and AlN as piezoelectric phase. (a) ME voltage versus f _AC for H _AC = 1 mOe. An optimum static field H _Bias = 2.4 Oe was applied for maximum ME response. (b) Absolute value of the ME coefficient versus H _Bias for H _AC = 1 mOe and f _AC tuned to f _res = 876 Hz. (c) ME voltage versus H _AC at the optimum working point (H _Bias = 2.4 Oe and f _AC = 876 Hz). Solid lines indicate linear fits of V _ME and the noise level. Their intersection determines the limit of detection (arrow). (b) and (c) are adapted from Ref. Reference Röbisch, Yarar, Urs, Teliban, Knöchel, McCord, Quandt and Meyners20.

For the optimum working point, the detection limit was determined [Fig. 2(c)]. Reducing H _AC continuously, first a linear decrease of the ME voltage output is observed over several orders of magnitude of alternating magnetic fields. Finally, the voltage noise floor covers the ME signal and the sensor output is not correlated to H _AC anymore. Linear fits of the ME signal and the noise floor are calculated. Their intersection appoints the LOD, at which the SNR equals 1. From the measurement it is derived that the detection limit is in the order of 1 pT/Hz^1/2, which is a representative result for this kind of resonant micromachined cantilever sensors. ^{Reference Röbisch, Yarar, Urs, Teliban, Knöchel, McCord, Quandt and Meyners20}

Utilization of vibrating structures for sensing purposes holds the potential risk of cross-sensitivity to environmental noise sources such as acoustic waves and structure-born sound. These types of noise can lead to mechanical vibrations of the sensing unit. In case of a ME cantilever sensor, such vibrations are transferred to the sensor output via piezoelectricity and interfere with the ME signal. Special designs for noise rejection in laminated ME sensors have been proposed based on the fundamental observation that the ME signal should occur in one oscillatory mode, whereas noise actuation should be restricted to another mode. ^{Reference Xing, Zhai, Li and Viehland21} A structural design concept fulfilling this requirement, could be a ME laminate, which enables a mechanically symmetrical response to an applied magnetic field and only asymmetrical responses to vibrational noise. Following this general route, it has been proposed to make use of a tuning fork-like assembly of two ME sensors as it is depicted in Fig. 3(a). ^{Reference Salzer, Jahns, Piorra, Teliban, Reermann, Höft, Quandt and Knöchel14} The two sensors have an asymmetric layer stack with the piezoelectric and magnetostrictive phases on opposite cantilever sides. Since the sensors are placed opposing each other, a magnetic field causes an upward deflection of one of the cantilevers, whereas the other cantilever will bend downwards. In this sense, an applied alternating magnetic field generates a mechanically mirror symmetrical response of the sensor pair. Due to the deflections the piezoelectric layers on both cantilevers are either under compressive or tensile stress simultaneously, i.e., the ME signals are in phase. By contrast, vibrational interference predominantly produces cantilever deflections in the same direction. Hence, vibrational interference leads to voltage outputs of the upper and lower cantilevers being opposite in phase. During a measurement, the sum signals can serve as a measure of the applied magnetic field, whereas the difference contains information about interfering disturbances. Overall, the tuning fork like assembly results in a magnetic sensor structure that is more robust against acoustic waves and structure-borne noise. A prerequisite for the construction is that the constituent cantilever sensors match in their mechanical and magnetoelectric properties. This emphasizes the need for sensor fabrication based on micromachining on wafer level, because it provides high reproducibility of all physical properties.

FIG. 3.

(a) Tuning fork-like assembly of two ME cantilever sensors. The inset shows details of the layer stack configuration. (b) ME voltage versus H _AC using the in phase signals of both ME cantilevers with and without application of wideband noise. (c) displays the corresponding measurements of a single cantilever sensor. Adapted from Ref. Reference Salzer, Jahns, Piorra, Teliban, Reermann, Höft, Quandt and Knöchel14.

Figure 3(b) displays a measurement of the detection limit for two ME cantilever sensors combined to a tuning fork as described in more detail in Ref. Reference Salzer, Jahns, Piorra, Teliban, Reermann, Höft, Quandt and Knöchel14. The sensors with ID electrodes consist of the layers Ta 5 nm/FeCoSiB 4 µm/Si 300 µm/ZrO₂ 300 nm/PZT 2 µm/Cr 5 nm/Au 100 nm. The first bending mode oscillation occurs at a frequency f _res = 958 Hz. In Fig. 3(c) the LOD determination of an identically constructed single sensor is shown. In absence of any artificially induced disturbing influences, its LOD is about 5 pT/(Hz)^1/2 (blue crosses). By superimposing additional wideband noise using a piezoelectric loudspeaker, the voltage noise level increases by almost two orders of magnitude and the detection limit is worsened by the same amount (red dots). In contrast to that, the noise level of the assembled sensors increases by a factor of only 4, if the external noise source is operated. This shows that the tuning fork-like assembly is by far less sensitive to acoustic noise. Additionally, the LOD ≈ 500 fT/(Hz)^1/2 is significantly better than the detection limit of the individual sensors. This is an indication that shielding against acoustic interference and air-born sound of the measurement set-up is not perfect. As a result, the effect of the noise cancellation property of the tuning fork is already detectable without operating the loudspeaker.

As summarized above, the magnetic field detection by a ME sensor is based on a conversion of magnetoelastic energy to piezoelectric energy. Thus, the LOD is expected to be dependent on the volume V of the respective magnetostrictive and piezoelectric phases. The noise spectral density has been theoretically analyzed for laminated ME composites without substrate in Ref. Reference Zhuang, Cordier, Saez, Sing, Dolabdjian, Gao, Li and Viehland22. For such kind of sensors the noise spectral density is found to scale with 1/V ^1/2. As a result, the reduction of size should degrade the achievable LOD of miniaturized ME sensors. In Fig. 2 the functionally active layers have a size of 0.18 mm³ and the sensor’s LOD is about 1 pT/(Hz)^1/2. In resonance almost the same LOD = 2 pT/(Hz)^1/2 has been recorded for a FeCoBSi and AlN based ME sensor with a significantly reduced V = 0.007 mm³. ^{Reference Zabel, Kirchhof, Yarar, Meyners, Quandt and Faupel18} Apparently, for the sensors discussed here, the experimentally observed LODs are influenced by nonlinear magnetic effects, which do not simply scale with the volume. For example, a reduction in sensor size involves a change of the exhibited magnetic domain configurations of the magnetostrictive phase, which translates into a complex size dependency of the piezomagnetic coefficient.

B. Magnetoelectric composites with exchange biased magnetostrictors

A well-known disadvantage of most ME heterostructures comprising only one magnetostrictive layer is that a bias magnetic field has to be applied to enhance the ME response to an alternating magnetic field [see Sec. III. A, Fig. 2(b)]. This is caused by the piezomagnetic coefficient usually being almost zero at zero bias field. Hence, an external magnetic field source is needed to provide the optimum H _Bias. The integration of such a magnetic field source inevitably complicates the construction of closely arranged sensor arrays and vector field magnetometers, because of the required space, cross-talk, and potentially added magnetic noise. Therefore, several concepts were investigated with the aim to integrate an internal magnetic field source into a self-biasing ME heterostructure. A straightforward concept utilizes additional magnetic layers with magnetic anisotropy and coercivity being larger than the accordant properties of the magnetostrictive phase. ^{Reference Li, Zhiguang, Wang, Li and Viehland23–Reference Tadahiko and Isao25} Here, the permanent moment of the hard magnetic layer creates the desired bias magnetic field. A second approach to self-biased ME structures is based on the use of magnetostrictive phases with a pronounced hysteretic behavior and high remanence magnetization. ^{Reference Zhang, Li, Wen, He, Yang, Wang, Yang and Lu26} It was demonstrated that such magnetostrictors can be realized by fabricating compositionally stepped ferromagnetic layers. ^{Reference Mandal, Sreenivasulu, Petrov and Srinivasan27,Reference Laletin, Sreenivasulu, Petrov, Garg, Kulkarni, Venkataramani and Srinivasan28} A unique strategy was presented in Ref. Reference Onuta, Wang, Long and Takeuchi9 which describes the exploitation of the field-dependent resonant frequency in a hysteretic magnetostrictive material. Alternatively, the use of mechanical stress by means of the inverse magnetostriction effect can enhance the ME effect under zero magnetic bias. ^{Reference Jing and Fang29} Successful application of this concept demands precise control of the stress state within the constituent layers. This impedes the transfer to miniaturized thin film ME sensors. The other aforementioned approaches have in common that additional magnetic stray fields are generated or a magnetic history dependent sensor performance is expected. The thin film approach to ME heterostructures favors the incorporation of exchange biased magnetostrictive layers. ^{Reference Lage, Kirchhof, Hrkac, Kienle, Jahns, Knöchel, Quandt and Meyners5} Strength and direction of exchange coupling can be controlled and the use of multilayer systems is possible with the benefit of an increase in the magnetostrictively active volume.

The magnetostrictive strain of exchange biased FeCo layers as a function of an external magnetic field H _Bias is presented by Fig. 4. The investigated multilayers consisted of 40 repetitions of the layer sequence Ta 7/Cu 3/Mn₇₀Ir₃₀ 7/Fe₅₀Co₅₀ 20 [thickness in nm]. The unidirectional anisotropy introduced by the exchange coupling between MnIr and FeCo was established for various angles φ = 36°, 66°, and 90° (φ denotes the angle between H _EB and the long cantilever axis, see inset of Fig. 4). For φ = 90°, magnetic anisotropy and unidirectional anisotropy are perpendicular to H _Bias. As a result, a symmetrical magnetostriction curve is recorded. The λ(H _Bias)-behavior resembles that of a single magnetostrictive material with a magnetic anisotropy aligned in y-direction. The piezomagnetic coefficient, i.e., the derivative of the magnetostriction vanishes at H _Bias = 0. With increasing inclination of the unidirectional anisotropy (decreasing φ), the asymmetry of the magnetostriction curves becomes more pronounced and minimum strain is measured at increasing absolute values of H _Bias. The tilted orientation of the unidirectional anisotropy causes a deviation of the FeCo magnetization from the y-direction for zero magnetic field. Consequently, the derivative of the magnetization dependent magnetostriction is nonzero. For this particular multilayer, a maximum piezomagnetic coefficient d ^m = 0.46 ppm/Oe is observed for φ ≈ 66° and H _Bias = 0. Further investigation of the ME response as a function of the angle γ between H _AC and H _EB (γ = 0° in Fig. 4) revealed a more general property. ^{Reference Jahns, Piorra, Lage, Kirchhof, Meyners, Gugat, Krantz, Gerken, Knöchel and Quandt31} Under zero bias field condition, the response is at its maximum for φ = 45°, when the condition γ = 90° is satisfied. Using this finding, vector field sensors can be fabricated. ^{Reference Lage, Woltering, Quandt and Meyners32}

FIG. 4.

Magnetostriction λ as a function of an externally applied magnetic field H _Bias. The values for λ were calculated from the measured magnetoelastic coupling coefficient according to λ = −b(1 + ν_f)(1/E _f). ^{Reference Kolkholm30} Here, ν_f = 0.3 and E _f = 230 GPa denote the effective Poisson ratio and Young modulus of the FeCo layer system. Every 70th data point is represented by a symbol. The inset specifies the sample set-up including the definition of angle φ. Adapted from Ref. Reference Lage, Kirchhof, Hrkac, Kienle, Jahns, Knöchel, Quandt and Meyners5.

The concept of exchange biased magnetostrictors can be transferred to multilayers based on the amorphous FeCoSiB alloy. The best LOD at zero bias magnetic field achieved so far equals LOD = 10 pT/(Hz)^1/2 at mechanical resonance. The properties of sensors discussed up to this point are summarized in Table II.

TABLE II.

Limit of detection for thin film magnetoelectric cantilever sensors operated in mechanical resonance.

C. Frequency conversion technique

In the preceding sections, it was demonstrated that Si bulk micromachined ME heterostructures based on a thin film approach for the functional phases have the potential to detect alternating magnetic fields as small as a few pT. Especially, a tuning fork-like assembly of ME cantilevers is a promising candidate for magnetic field sensor applications. However, exploiting the resonant properties of the cantilever structures results in narrow bandwidth sensors with maximum sensitivity around the mechanical resonance frequency, which is typically in the order of several hundred Hz up to several kHz. On the other hand, many applications such as biomedical ones require high sensitivity and low LOD for frequencies down to a few Hz. Advanced medical applications such as magnetoencephalography and magnetocardiography require highly sensitive DC magnetometers, so far making the utilization of SQUIDs inevitable. In the recent past, considerable progress has been made in enhancing the sensitivity of ME sensors to low frequency and DC magnetic fields. Using a ME nanoelectromechanical resonator, a limit of detection of DC magnetic fields of about 300 pT has been demonstrated. ^{Reference Nan, Hui, Rinaldi and Sun2} High sensitivity to DC magnetic fields has also been reported for a ME microcantilever. ^{Reference Lee, Kim, Yoo, Han, Chun, Kim, Kim, Hwang, Kim, Jo, Kim, Song and Lee4} Such a microcantilever incorporates magnetostrictive Terfenol-D and PZT and is driven off-resonance through a 60 Hz AC magnetic field. An alternative route to high magnetic field sensitivity at low frequency is the frequency conversion technique. This technique is based on applying either magnetic or electric excitation fields. ^{Reference Jahns, Greve, Woltermann, Quandt and Knöchel15,Reference Zhuang, Sing, Dolabdjian, Wang, Finkel, Li and Viehland33–Reference Hayes, Salzer, Reermann, Yarar, Röbisch, Piorra, Meyners, Höft, Knöchel, Schmidt and Quandt35}

During magnetic frequency conversion, a sinusoidal magnetic modulation field H _mod is applied to the sensor. The sensor is driven along its magnetostriction curve (see Fig. 4, φ = 90° case), leading to a modulation of the piezomagnetic coefficient and sensor sensitivity periodic in time. Due to the nonlinearity of the magnetostriction, the sensor acts as a frequency mixing component. If an alternating magnetic field is also present, the sensor voltage output will contain new frequency components such as f _± = f _mod ± f _AC. By adjusting f _mod so that either the sum frequency or difference frequency matches the resonance frequency, resonant enhancement of the ME voltage output is achieved. Thus, the frequency conversion technique increases the sensitivity to alternating magnetic fields having frequencies other than f _res. Moreover, sweeping f _mod can be used to broaden the effective bandwidth for periodic signals. In Table III LODs are compared for ME cantilevers exposed to magnetic signals with frequencies either matching the resonance frequencies or adjusted to 10 Hz. The magnetostrictive phase is a single 3 µm thick FeCoSiB layer or an exchange biased multilayer. Using the single magnetostrictive layer type sensor, the minimum detectable magnetic field equals 800 pT/(Hz)^1/2 for a 10 Hz signal. Thus, the LOD is increased by a factor of 800 compared to that for a resonant alternating magnetic field. Such a large increase cannot be solely explained by losses due to signal conversion into other frequencies than f _res. Thus, additional effects are present worsening the LOD for low frequency fields. A major difference exists between the resonant operation and the frequency conversion method in the presence of the modulation field, which is several orders of magnitude larger than the alternating magnetic field to be measured. Noise measurements confirmed that the noise voltage density increases when H _mod is applied. ^{Reference Röbisch, Yarar, Urs, Teliban, Knöchel, McCord, Quandt and Meyners20} This suggests that contributions related to the periodic magnetization reversal of the magnetostrictive layer add to the total noise level, thereby worsening the achievable LOD. This explanation is reinforced by the observation of the performance of exchange biased magnetostrictive type sensors (Table III). Since these sensors were fabricated for frequency conversion, the exchange bias direction was established by field cooling with an angle φ = 90°. In resonance, the LOD = 10 pT/(Hz)^1/2 is one order of magnitude larger as for the single layer magnetostrictive type. This is attributed to the three times lower total magnetostrictive thickness and the additional unidirectional anisotropy contribution changing the magnetic response characteristics. Increasing the number of repetitions of layer sequences from 5 to 20 improves the LOD for resonant magnetic fields significantly. By contrast, the LOD at 10 Hz reveals a reverse thickness dependency. The best limit of detection [180 pT/(Hz)^1/2] for the low frequency field is discovered for sensors having only 5 layer repetitions. At such a low total layer thickness, the additional uniaxial anisotropy imposed by the exchange coupling changes the magnetization reversal, which is accompanied by a lower level of the magnetic noise. ^{Reference Röbisch, Yarar, Urs, Teliban, Knöchel, McCord, Quandt and Meyners20} Upscaling of the total magnetostrictive volume gives rise to an increased demagnetizing field effect, leading to the formation of magnetic domains in the exchange biased layers. Accordingly, domain wall nucleation, movement, and annihilation cause magnetic noise again. In addition, domain wall induced effects can lead to a reduction of the ME response. ^{Reference Urs, Teliban, Piorra, Knöchel, Quandt and McCord36}

TABLE III.

Limit of detection at selected signal frequencies for thin film magnetoelectric cantilever sensors.

D. Magnetoelectric cantilever sensors for the detection of magnetic fields in medicine

Recently, a first demonstration of ME sensors in a biomedical application succeeded. A bulk laminated ME composite was effectively utilized as susceptometer for a quantitative measurement of iron concentration in liver phantoms. ^{Reference Xi, Qian, Lu, Mei, Rupprecht, Yang and Zhang37} The diagram in Fig. 5 compares typical signal amplitudes in challenging biomedical applications such as magnetocardiography (MCG), magnetoencephalography (MEG), and deep brain stimulation (DBS) ³⁸ to the LODs reported here. In general, MCG and MEG signals measured by SQUID based magnetometers are four to six orders of magnitude smaller than the environmental magnetic noise. In MCG, the signal amplitudes stemming from the beating heart range from 1 pT to roughly 100 pT in a frequency range between fractions of Hz and 100 Hz. Recording of brain signals is even more challenging as the signal amplitudes can be as small as 10 fT. The α-rhythm, one of the strongest brain signals, generates magnetic fields in the order of 10 pT at maximum. Compared to heart signals, the frequency range of brain activity is broader and frequencies up to about 1 kHz can be present.

FIG. 5.

Amplitude and frequency range of MCG, MEG, and DBS signals in time domain. ^{Reference Sternickel and Braginski39–Reference Wikswo41} Detection limits of magnetoelectric cantilever sensors based on single magnetostrictive layers (exchange biased magnetostrictive multilayers) are represented by black circles (red asterisks). The LOD of the tuning fork-like assembly is indicated by a blue triangle. The direct measurement of the 10 Hz signals was conducted using an integration time equal to 3 s.

A comparison of the displayed data must take into account that the signal amplitudes of the biomagnetic applications specify signals in time domain. Accordingly, recording of MCG and MEG signals requires detection limits being roughly one order of magnitude lower than the respective amplitudes. On the other hand, the sensor to signal source separation must be considered. Especially for signal sources located close to the surface of the human body, the smaller separation achievable with miniaturized uncooled sensors can lead to a significant enhancement of signal amplitudes by more than one order of magnitude at the sensor location. This has been demonstrated by means of magneto-impedance sensors and miniaturized optically pumped atomic magnetometers, which were successfully applied to magnetoencephalographic and magnetocardiographic measurements. ^{Reference Wang, Tajima, Song, Hamada, Cai and Uchiyama42–Reference Alem, Sander, Mhaskar, LeBlanc, Eswaran, Steinhoff, Okada, Kitching, Trahms and Knappe45} From Fig. 5 it becomes evident that frequency conversion applied to ME heterostructures is a promising candidate for gaining access to the low frequency biomagnetic signals, too. At 10 Hz, the LOD = 180 pT/(Hz)^1/2 of ME sensors with exchange biased magnetostrictive multilayers is only a small factor above the upper MCG signal limit. From the data in Table III and the discussion in Sec. III. C, it can be concluded that further improvements are possible. If a rise of the effective in plane demagnetization field can be avoided, increasing the total magnetostrictive layer thickness will push the detection limit further downwards.

The detection limit of resonant ME cantilever sensors reaches the upper frequency limit of MEG signals. A reduction of the resonance frequency can be simply achieved by changing the sensor design. However, it is not considered to be a sufficient measure for enabling the detection of MEG signals with lower frequencies due to an increase of the 1/f dependent noise level. In fact, resonant ME sensors are envisaged for the application in deep brain stimulation. DBS is an established therapy for Parkinson’s disease. ^{Reference Schuepbach, Rau, Knudsen, Volkmann, Krack, Timmermann, Hälbig, Hesekamp, Navarro, Meier, Falk, Mehdorn, Paschen, Maarouf, Barbe, Fink, Kupsch, Gruber, Schneider, Seigneuret, Kistner, Chaynes, Ory-Magne, Brefel Courbon, Vesper, Schnitzler, Wojtecki, Houeto, Bataille, Maltête, Damier, Raoul, Sixel-Doering, Hellwig, Gharabaghi, Krüger, Pinsker, Amtage, Régis, Witjas, Thobois, Mertens, Kloss, Hartmann, Oertel, Post, Speelman, Agid, Schade-Brittinger and Deuschl46,Reference Deuschl and Agid47} Small electrodes are implanted in intracerebral nuclei for the electrical stimulation with the aim to influence brain circuits. For example, DBS of the thalamus can efficiently reduce tremor. Such a desired clinical effect depends on the electrode position and the stimulated current distribution in the brain of patients with their individual anatomy. Clinical applicability and understanding of DBS would benefit from an uncomplicated measurement technique identifying the area of the brain that is stimulated. Since the electrodes are operated at a fixed frequency ranging from 85 Hz to 185 Hz, ³⁸ a direct measurement of higher harmonics appears to be feasible by resonant ME cantilever sensors with single layer magnetostrictors or a tuning fork-like assembly of cantilever sensors. First test measurements using a head phantom and a ME sensor scanning the flux density distribution generated by a DBS electrode are shown in Fig. 6. During this first trial, the electrode was supplied with DBS pulses with a larger amplitude than the pulses applied in clinical practice. The pulse frequency was 160 Hz and its fifth harmonic was recorded.

FIG. 6.

(a) Photograph of a pneumatic scanner with head phantom and inserted DBS electrode. The ME sensor is surrounded by a copper coil to supply a static bias field. During scanner operation the sensor is moved around the phantom on a cylindrical surface. The phantom is a glass head filled with saline solution. The solution’s conductivity matches that of a human brain. (b) Plot of the magnetic flux distribution (radial component) surrounding the head phantom, recorded by the ME sensor while operating the DBS electrode.