1. Introduction

The first report on the ME magnetic field sensor was made at the International Conference, MEIPIC-4 in 2001 ^[1][10]. The sensor was a disk or plate based on a bulk composite of the composition of iron-yttrium garnet–zirconate–lead titanate (PZT) and a layered structure based on nickel-zinc ferrite—PZT. The maximum sensor sensitivity was of 0.06 mV/Oe.

Further, of note are the results of the group of Prof. D. Viehland, who significantly advanced theour knowledge of ME magnetic field sensors and their capabilities ^{[2][3][4][5][6][7][8][9][10]}[11,12,13,14,15,16,17,18,19]. In ^[2][11], Dong et al. showed that L-T mode in the structure Terfenol-PMN-PT has extremely high magnetic field sensitivity: at room temperature, an output ME voltage with a good linear response to magnetic field H ac was found over the range of 10 −11 < H ac < 10 −3 T. Then, a number of articles was published in which the authors of this group applied new ideas: the use of push–pull ^[3][12] and bimorph structures ^[4][13] to increase a ME effect and sensitivity by reducing the vibrational and thermal noises ^[5][14], and the transition to higher signal processing frequencies ^[6][7][15,16], which made it possible to significantly increase the sensitivity of sensors and achieve a pico-Tesla sensitivity of a sensor at room temperature ^[8][9][10][17,18,19]. These innovations made it possible to improve the parameters and obtain high values of the sensitivity and noise characteristics of sensors both in the low-frequency region and in the field of electromechanical resonance (EMR). The sensitivity limit was about 20 pT/Hz 1/2 or 2 × 10 −16 C/Hz 1/2 at 1 Hz, and about 2 fT/Hz 1/2 at 78 kHz in the EMR range ^[8][17]. Extremely low values of the equivalent magnetic noise of 6.2 pT/Hz 1/2 at a frequency of 1 Hz were obtained on a heterostructure consisting of a PMN-PT bimorph doped with 1% Mn and longitudinally magnetized Metglas layers. As the frequency increased to 10 Hz, the equivalent magnetic noise significantly decreased and amounted to <1 nT/Hz 1/2 ^[10][11][3,19]. A sharp jump in the number of articles on ME magnetic field sensors was noted after the publication of a number of works in which a sensitivity of 1–10 pT was achieved at room temperature ^{[12][13][14][15][16]}[4,5,6,7,9].

As known, most of the studies of ME magnetic field sensors were carried out on the basis of such components as piezoelectric PZT, PMN-PT, lithium niobate and magnetic Terfenol, and Metglas in the linear ME effect mode. At the same time, it should be noted that in recent years, original works have appeared in which new approaches were used and high characteristics of sensors were obtained. In particular, the magnetostrictive component was replaced by a NdFeB magnet ^[17][20], then a miniature and highly sensitive MEMS structure ^[18][19][21,22], and NEMS and nanoresonator ^[20][21][22][23,24,25] for biomedicine were proposed, and a nonlinear regime and new components such as piezoelectric AlN and soft magnetic Ni ^[23][24][25][26,27,28] were used. In addition, new possibilities for developing sensors on the basis of the ΔE—effect have been discussed ^[26][27][29,30]. In this article, we look at these options in more detail.

Analysis of the characteristics of ME magnetic field sensors shows that in a number of parameters they are superior to the commonly used Hall and magnetoresistive sensors and have great prospects for application in technics and biomedicine. With this in mind, this articlentry aims to review the current state of the art of ME magnetic field sensors. The article is organized as follows. The second section provides information about the principle of operation and topology of ME sensors developed on the basis of the structures Terfenol-PZT/PMN-PT, Metglas-PZT/PMN-PT, Metglas-Lithium Niobate, and other original structures with the best characteristics. Special attention is paid to promising ME sensors presented in recent years. The third section compares the features and discusses how they can be improved. Finally, some concluding remarks close the article.

2. Main Section

As already noted, this part of the article will provide information on the ME magnetic field sensors based on Terfenol –PZT/PMN-PT, Metglas PZT/PMN –PT, Metglas –Lithium Niobate, and other original structures, on which high characteristics were obtained.

As a result of recent research on sensors based on ME composites, it has become clear that they have enormous potential for detecting weak magnetic fields. Applying the lock-in amplifier method, Dong et al. showed the possibility of detecting a magnetic field of the order of 10 −12 T at a frequency of f > 1 Hz. The magnetic field sensor based on ME composites is a small passive device that operates at room temperature and has a sensitivity at low frequencies in the picotesla range. The main task of the studies carried out by various scientific groups is to obtain the maximum ME voltage coefficient, increase the sensitivity, and obtain the minimum noise of the ME magnetic field sensor.

Figure 18 a shows the output voltage signal of the ME flexible Metglas/PZT structure under the action of AC magnetic field at a frequency of 1018 Hz and under bias field 4.5 Oe. The ME output voltage signal demonstrated linear response to AC magnetic field. The change of ME voltage could not be observed if the amplitude of AC magnetic field was smaller than 100 nT. Hence, the limit of detection (LoD) of the ME sensor was only 200 nT. As it is shown in Figure 8 b, the output voltage of ME flexible sensor vs. AC magnetic field at resonant frequency under optimal bias field 4.5 Oe was measured. The obtained magnetic field sensitivity of the AC magnetic field 0.2 nT at resonance frequency was much more than that at 1018 Hz. The authors consider that the main advantage of the proposed flexible structure is that it is prospective for applications in biomedicine.

Results demonstrate the potential of ME bidomain LN structures to be used in the creation of supersensitive magnetic field sensors for biomedicine.

3. Discussion

One of the most important characteristics of an ME magnetic field sensor is its equivalent magnetic noise dependence on frequency. The magnitude of the sensor equivalent magnetic noise almost completely determines the main characteristic of the magnetic field sensor—the minimum measurable value of the magnetic field.

Comparison of the data in this table shows that in the low-frequency region, the most sensitive of the presented ME magnetic field sensors are those described in ^{[28][29][30][31][32]}[46,47,48,49,62], and in resonance mode is a sensor based on bidomain LN y +140°/Metglas 2826 MB ^[33][60] and the sensor described in ^[34][50]. In practice, the most important characteristic of ME magnetic field sensors is the equivalent magnetic noise. Reducing the equivalent magnetic noise allows for the sensitivity of such sensors to be increased. Moreover, for alternating magnetic field sensors, the frequency range in which they can measure the magnetic field is of great importance. In some cases, it is necessary to measure the amplitude of a very low frequency alternating magnetic field. For example, for the use of ME magnetic field sensors in magnetoencephalography, the frequency band in which these sensors are sufficiently sensitive should be from 10 mHz to 1 kHz ^[35][63]. In this case, the main of studies of ME sensors of an alternating magnetic field were carried out in the frequency range from 1 Hz to 1 kHz ^[9][10][18,19]. To study such low frequencies from 10 mHz to 1 Hz, researchers should use more suitable ME structures ^[36][41]. Moreover, for these purposes, the noise of the amplifier must be reduced. To do this, one can use high-rated feedback resistors. However, making resistors with such large resistances with very small tolerances is very difficult. To increase the sensitivity of ME magnetic field sensors, a decrease in external noise is of great importance. One of the best opportunities for this is a gradiometry. In this method, several ME magnetic field sensors are combined in such a way that the signals of individual sensors are subtracted from each other in the total signal. This leads to the fact that the coherent external noise is compensated ^[37][64]. Gradiometer systems successfully combat coherent external noise but do little to combat the internal inconsistent noise of individual sensors. Moreover, the usefulness of the gradiometer method is reduced with serious differences between the individual ME sensors of the magnetic field of the system, especially when it comes to phase characteristics. Therefore, it is clear that for the successful application of the gradiometer method in ME magnetic field sensors, it is necessary to reduce the equivalent magnetic noise and the phase shift of the ME sensors that make up the system.

Important and promising types of ME magnetic field sensors are ME sensors based on the delta-E effect, that is, a change in elastic properties caused by a magnetic field. The delta-E effect ^[38][65] manifests itself in the relationship between deformation and magnetostriction, which leads to a magnetoelastic change in the direction of magnetization in unsaturated magnetic materials. The addition of magnetostrictive deformation to elastic deformation leads to a clear decrease in elastic moduli, the dependence on the magnetic field of which is used to measure the magnetic field.

The current operating modes are based on the detection of resonant detuning, induced by a magnetic field, in electromechanical bulk ^[20][23] and cantilever resonators ^[19][22]. Electrical sensing as well as mechanical excitation is achieved through the piezoelectric layer. The operating points are determined by the mechanical resonance frequency of the system f r and the magnetic operating point, which is selected near the maximum change in the electromechanical resonance frequency as a function of the magnetic field. In this case, the magnetic field is converted into a frequency shift of the resonance. By simultaneously working with several mechanical modes and detecting them ^[39][66], the sensitivity of sensors based on the delta-E effect can be increased. An alternative approach is based on the dispersion of the magnetic field of the propagating phase shift of acoustic surface shear waves in the delay line sensor ^[40][67]. In general, delta-E sensors offer high performance broadband sensors suitable for detecting magnetic signals from heart and brain.

4. Conclusions

In conclusion, let peopleus discuss the possible applications of ME sensors of the magnetic field and the problems that should be solved in the future. First of all, these are measurements of weak magnetic fields in various technical applications, such as in the search for iron ore deposits or in control systems during the movement of large magnetic masses, i.e., in cases where high magnetic sensitivity and mobility in control are required. The next important area of application is biomedicine, for which, in addition to the above-mentioned requirements, the following are also necessary: small dimensions of the sensor and its operation in a wide low-frequency range from 10 MHz to 1 kHz. In ^[22][25], data are given for the first successful application of a thin-film ME sensor in the bending mode in biomedicine for magnetoencelographic measurements. Taking into account the requirements for the frequency range and dimensions, ME swensors should be considered ME sensors based on the delta-E effect to be more promising for biomagnetic measurements. In ^[19][26][41][22,29,68], such sensors with high sensitivity and micro-design are described, which can find wide application in biomedicine.

At the same time, for a wider application of ME magnetic field sensors, it is necessary, first, to increase the magnetic sensitivity and bring it to a level exceeding 700 fT /Hz 1/2 , in order to replace optically pumped atomic magnetometers ^[42][69] and giant magnetoimpedance sensors [70]. As ^[43]follows from the analysis of the data in Table 3 , such parameters can be achieved in the near future.

The second problem of ME sensors is the need to reduce the level of external noise. The use for this purpose of a system of two sensors or a gradiometer ^[37][64] made it possible, as a result of antiphase addition of individual noise signals, to sharply reduce the level of external noise and ensure the operation of the sensor at room temperature without additional shielding.

As a result, it can be noted that ME magnetic field sensors can provide passive operation at room temperature without additional shielding and are most effective for measuring weak magnetic fields in the low-frequency range. With their high magnetic sensitivity and low noise level at micro- and nano-sizes, the sensors are especially promising for use in biomedicine.