# High Sensitivity Planar Hall Effect Magnetic Field Gradiometer for Measurements in Millimeter Scale Environments

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## Abstract

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## 1. Introduction

## 2. Experimental Techniques

## 3. Equivalent Magnetic Noise Characterizations

## 4. Equivalent Gradient Magnetic Noise

## 5. Summary

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**left**) Schematics of EPHEG geometry (not to scale). The orange regions are gold electrical contact pads. The long and short axes of the ellipse are labeled as a and b, respectively. The sensor is excited between I${}_{x1}$ and I${}_{x2}$, and the transverse signal is measured across any of the parallel 9 voltage pairs (marked from 1 to 9). ${b}_{n}$ is the distance between voltage pairs n. (

**right**) Photograph of a sensor on a dime as a size reference.

**Figure 2.**Plot showing the variation of EMN with the position of the voltage pairs for 50, 10, 1, and 0.1 Hz frequencies and for the highest excitation current of ∼130 mA.

**Figure 3.**Frequency– dependence of EGMN of 4 voltage pairs 1–9, 2–8, 3–7 and 4–6. Data and fit according to Equation (8) are shown only for the 1-9 voltage pairs. For clarity, only the fit is shown for remaining pairs.

**Figure 4.**The variation of the magnetic field from a current-carrying wire with a distance from the wire (measured outside the magnetic shield) with an EPHEG along with the calculated magnetic field. The standard deviation of 10 measurements is presented as the error at each point. The inset depicts the schematics of the measurement setup. The current-carrying wire is in the z-direction perpendicular to the plane of the figure.

**Figure 5.**The magnetic field from a wire carrying 0.2 mA and 0.4 mA measured at a distance of ∼40 mm using five voltage pairs. The error bar shown for each data point represents the standard deviation of 20 measurements.

**Table 1.**Typical values of ${R}_{y}$, ${H}_{eff}$, ${S}_{y}$ (for ${I}_{x}$ = ∼130 mA (peak)), $\Delta $R, and ${b}_{n}$ for different parallel voltage-pairs of EPHEG.

V-pair | ${\mathit{R}}_{\mathit{y}}$ | ${\mathit{H}}_{\mathbf{eff}}$ | ${\mathit{S}}_{\mathit{y}}$ | $\mathbf{\Delta}$R | ${\mathit{b}}_{\mathit{n}}$ |
---|---|---|---|---|---|

No: | ($\mathbf{\Omega}$) | (Oe) | (V/T) | ($\mathbf{\Omega}$) | (m) |

1 | 10.05 | 5.68 | 17.83 | 0.0778 | 4.200 × 10${}^{-4}$ |

2 | 11.14 | 5.44 | 22.43 | 0.0938 | 5.866 × 10${}^{-4}$ |

3 | 11.53 | 5.43 | 23.06 | 0.0964 | 6.837 × 10${}^{-4}$ |

4 | 11.57 | 5.35 | 23.62 | 0.0973 | 7.365 × 10${}^{-4}$ |

5 | 11.79 | 5.35 | 23.68 | 0.0975 | 7.533 × 10${}^{-4}$ |

6 | 11.61 | 5.43 | 23.39 | 0.0974 | 7.365 × 10${}^{-4}$ |

7 | 11.49 | 5.46 | 23.02 | 0.0966 | 6.837 × 10${}^{-4}$ |

8 | 11.07 | 5.52 | 22.70 | 0.0966 | 5.866 × 10${}^{-4}$ |

9 | 10.12 | 5.66 | 18.01 | 0.0781 | 4.200 × 10${}^{-4}$ |

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**MDPI and ACS Style**

Nhalil, H.; Schultz, M.; Amrusi, S.; Grosz, A.; Klein, L.
High Sensitivity Planar Hall Effect Magnetic Field Gradiometer for Measurements in Millimeter Scale Environments. *Micromachines* **2022**, *13*, 1898.
https://doi.org/10.3390/mi13111898

**AMA Style**

Nhalil H, Schultz M, Amrusi S, Grosz A, Klein L.
High Sensitivity Planar Hall Effect Magnetic Field Gradiometer for Measurements in Millimeter Scale Environments. *Micromachines*. 2022; 13(11):1898.
https://doi.org/10.3390/mi13111898

**Chicago/Turabian Style**

Nhalil, Hariharan, Moty Schultz, Shai Amrusi, Asaf Grosz, and Lior Klein.
2022. "High Sensitivity Planar Hall Effect Magnetic Field Gradiometer for Measurements in Millimeter Scale Environments" *Micromachines* 13, no. 11: 1898.
https://doi.org/10.3390/mi13111898