# Far-Field Spatial Response of Off-Diagonal GMI Wire Magnetometers. Application to Magnetic Field Sources Sensing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Magnetometer

#### 2.1. GMI Sensor

#### 2.2. Magnetometer Characteristics

## 3. Setup

#### 3.1. Three-Dimensional Helmholtz Coil System

#### 3.2. The Rotating Magnetic Field

#### 3.3. The Sensed Magnetic Field

## 4. Discussion

#### Far-Field Pattern

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ripka, P. Review of fluxgate sensors. Sens. Actuators A
**1992**, 33, 29–141. [Google Scholar] [CrossRef] - Mohri, K.; Uchiyama, T.; Panina, L.V.; Yamamoto, M.; Bushida, K. Recent Advances of Amorphous Wire CMOS IC Magneto-Impedance Sensors: Innovative High-Performance Micromagnetic Sensor Chip. J. Sens.
**2015**, 2015, 718069. [Google Scholar] [CrossRef] - Murata, N.; Karo, H.; Sasada, I. Fundamental mode orthogonal fluxgate magnetometer applicable for measurements of DC and low-frequency magnetic fields. IEEE Sens. J.
**2018**, 99, 2705–2712. [Google Scholar] [CrossRef] - Knobel, M.; Vázquez, M.; Kraus, L. Giant magnetoimpedance. In Handbook of Magnetic Materials; Buschow, K.H.J., Ed.; Elsevier: Amsterdam, The Netherlands, 2003; Volume 15, pp. 497–563. [Google Scholar]
- Fodil, K.; Denoual, M.; Dolabdjian, C. Experimental and Analytical Investigation of a new 2D Magnetic Magnetic Imaging Method using magnetic nanoparticules. IEEE Trans. Magn.
**2016**, 52, 6500109. [Google Scholar] [CrossRef] - Clem, T.R.; Kelis, G.J.; Lathrop, J.D.; Overway, D.J.; Wynn, W.M. Superconducting Magnetic Gradiometers for Mobile Applications with an Emphasis on Ordnance Detection. In SQUID Sensor: Fundamentals, Fabrication and Applications; Weinstock, H., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; Volume 329. [Google Scholar] [CrossRef]
- Sheinker, A.; Frumkis, L.; Ginzburg, B.; Salomonski, N.; Kaplan, B.-Z. Magnetic Anomaly Detection Using a Three-Axis Magnetometer. IEEE Trans. Magn.
**2009**, 45, 160–167. [Google Scholar] [CrossRef] - Zhao, Y.; Zhang, J.H.; Li, J.H.; Liu, S.; Miao, P.X.; Shi, Y.C.; Zhao, E.M. A brief review of magnetic anomaly detection. Meas. Sci. Technol.
**2021**, 32, 042002. [Google Scholar] [CrossRef] - Dolabdjian, C.; Cordier, C. Analysis by systemic approach of magnetic dipole source location performances by using an IoT software gradiometer head. IEEE Sens. J.
**2022**, 22, 7709–7716. [Google Scholar] [CrossRef] - Dufay, B.; Saez, S.; Dolabdjian, C.P.; Yelon, A.; Menard, D. Characterization of an optimized off-diagonal GMI-based magnetometer. IEEE Sens. J.
**2013**, 13, 379–388. [Google Scholar] [CrossRef] - Esper, A.; Dufay, B.; Saez, S.; Dolabdjian, C. Theoretical and Experimental Investigation of Temperature-Compensated Off-Diagonal GMI Magnetometer and Its Long-Term Stability. IEEE Sens. J.
**2020**, 20, 9046–9055. [Google Scholar] [CrossRef]

**Figure 1.**View of (

**a**) the GMI sensor mount with its pick coil and (

**b**) its conditioning electronic boards.

**Figure 2.**View of the three-axis Helmholtz coil system. In its center, the homogenous induced magnetic field covers a volume of around 25 × 25 × 25 cm

^{3}. The system is controlled with a desktop, which manages each field axis in terms of shape, frequency, and amplitude, independently.

**Figure 3.**(

**a**) Normalized ideal far-field pattern (blue curve) compared to the non-ideal far-field pattern response (red curve) having ${k}_{yx}={k}_{zx}=0.2.$ (

**b**) The orange curve shows the difference between both.

**Figure 4.**(

**a**) Normalized ideal ${T}_{x}\left(\theta \right)$ 2D dependence (blue curve) compared to a non-ideal ${T}_{x}\left(\theta \right)$ dependence (orange curve). (

**b**) For two identical magnetometers placed orthogonally, the blue and orange curves give a circular response in the ideal case $(\left|T\left(\theta \right)\right|=1$) and a distorted response in a non-ideal case $\left({T}_{x}\left(\theta \right)=0.5{T}_{{x}_{0}}\left\{1+Cos\left(2\theta \right),{k}_{1}Sin\left(2\theta \right)\right\}Sign\left(cos\left(\theta \right)\right)\right)$, respectively.

**Figure 6.**Experimental three-axis fluxgate directional far-field patterns (or angular sensitivity dependence) versus an applied rotating magnetic field having an amplitude, ${B}_{0}$, of 10 µT. Notice that the curve is normalized in amplitude by ${B}_{0}$. Blue, red and green curves highlight the projection of the magnetic sensor response in each plane (z, y), (x, y) and (z, y), respectively.

**Figure 7.**Experimental GMI directional far-field patterns or angular dependence of their sensitivity versus an applied rotating magnetic field having an amplitude of 10 µT. Notice that the curve is normalized in amplitude by ${B}_{0}$. Blue, red and green curves highlight the projection of the magnetic sensor response in each plane (z, y), (x, y) and (z, y), respectively.

**Figure 8.**

**Experimental**GMI magnetometer error associated to the far-field pattern given in Figure 7. Blue, red and green dots highlight the projection of the magnetic sensor errors in each plane (z, y), (x, y) and (z, y), respectively.

Characteristics | Units | |
---|---|---|

Sensitivity | 54,000 | V/T |

White noise level | 15 | pT/√Hz |

Bandwidth | 30,000 | Hz |

1/f noise corner | 5 | Hz |

Dynamic range | ±60 | µT |

Long-term stability | >5 | nT/h |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gasnier, J.; Dolabdjian, C.
Far-Field Spatial Response of Off-Diagonal GMI Wire Magnetometers. Application to Magnetic Field Sources Sensing. *Magnetism* **2024**, *4*, 47-53.
https://doi.org/10.3390/magnetism4010004

**AMA Style**

Gasnier J, Dolabdjian C.
Far-Field Spatial Response of Off-Diagonal GMI Wire Magnetometers. Application to Magnetic Field Sources Sensing. *Magnetism*. 2024; 4(1):47-53.
https://doi.org/10.3390/magnetism4010004

**Chicago/Turabian Style**

Gasnier, Julien, and Christophe Dolabdjian.
2024. "Far-Field Spatial Response of Off-Diagonal GMI Wire Magnetometers. Application to Magnetic Field Sources Sensing" *Magnetism* 4, no. 1: 47-53.
https://doi.org/10.3390/magnetism4010004