Magnetic Modeling of a Rotating Flux Concentrator System 

Designed to Mitigate Noise in “Large” Magnetic Sensors

by Gregory A. Fischer and Alan S. Edelstein

ARL-TR-5317 September 2010

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ARL-TR-5317 September 2010

Magnetic Modeling of a Rotating Flux Concentrator System 

Designed to Mitigate Noise in “Large” Magnetic Sensors

Gregory A. Fischer and Alan S. Edelstein

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Magnetic Modeling of a Rotating Flux Concentrator System Designed to Mitigate 

Noise in “Large” Magnetic Sensors

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6. AUTHOR(S)

Gregory A. Fischer and Alan S. Edelstein

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14. ABSTRACT

This report discusses the magnetic modeling results of a proof of concept system for 1/f noise mitigation in “large” sensors. 

The 1/f noise reduction is achieved by rotating flux concentrators that shift the operating frequency of the sensor to higher 

frequencies where 1/f noise is lower. The goal is to design systems with magnetic flux concentrators that maximize the 

enhancement of the field and the percentage modulation of the field but minimize size. These issues in execution and necessary 

tradeoffs in performance are discussed, and magnetic modeling is presented, showing a clear road map to increased 

performance from the viewpoint of field enhancement and modulation.

15. SUBJECT TERMS

Magnetic modeling, 1/f noise, magnetic sensors, flux concentrator

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Gregory A. Fischer

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iii

Contents

List of Figures iv

List of Tables v

Acknowledgments vi

Executive Summary vii

1. Introduction 1

2. Magnetic Modeling Details and Parameters 2

3. Rotating Flux Concentrator Designs 3

3.1 Magnetic Modeling Results for Design 1........................................................................3

3.2 Magnetic Modeling Results for Design 2........................................................................5

3.3 Magnetic Modeling Results for Design 3........................................................................7

4. Conclusion 10

5. References 11

Distribution List 12
iv 

List of Figures 

Figure 1.  Schematic of magnetoelectric sensor. The gray region consists of a piezoelectric 

material sandwiched between slabs of a magnetostrictive material. Sensitivity is already 

under 1 nT. .................................................................................................................................1

Figure 2. First concept of rotating flux concentrators. The red concentrators are stationary 

and the blue concentrators are free to rotate. The maximum magnetic field enhancement 

at the origin of the coordinate axis is achieved when (a) the concentrators are aligned and 

the minimum is achieved when (b) the outermost pair of concentrators have rotated 90°

from the position shown in (a). ..................................................................................................4

Figure 3. Schematic of design 1 showing various dimensions of interest. .....................................4

Figure 4. Plot of the magnetic field strength in the plane perpendicular to the x-y plane for 

the position producing a maximum value of enhancement at the origin. ..................................5

Figure 5. Rotating flux concentrator apparatus. ..............................................................................5

Figure 6. Model results showing the magnetic field lines for (a) the “shunt” and (b) the 

“concentration” orientation. The sensor position is indicated by the black dot. Permalloy 

shunts are shown in blue and the concentrators in red. Large arrows in (b) are the 

reference axis directions. ...........................................................................................................6

Figure 7. Modulation curve for design 2. .......................................................................................7

Figure 8. Magnetic field lines in a plane perpendicular to the concentrators for (a) the 

“concentration” orientation and (b) the “shunt” position. Sensor position is indicated by 

the black dot. Note the flux lines curling down through the sensor location in (b). .................7

Figure 9.  Design 3 of the rotating flux concentrator, showing all of the essential elements 

except for brackets to hold the permalloy rods in place and the non-ferrous air turbine 

designed to spin the disc. ...........................................................................................................8

Figure 10.  Comparison of the noise with a stationary disc and with the disc being rotated by 

an electric motor. ......................................................................................................................8

Figure 11. Dimensions of the beveled permalloy rod. ....................................................................9

Figure 12.  Magnetoelectric sensor position relative to the beveled rod and disc. The sensor 

is shown in yellow. ....................................................................................................................9

Figure 13. Model results showing the magnetic field lines for the (a) “concentration” and (b) 

“shunt” orientation. The sensor position is indicated by the yellow square. Permalloy 

strip and beveled rod are shown in blue while the flat-faced rod is shown in gray. The 

magnetic field strength is denoted by color and size of the arrows, with small and dark 

blue being low, and large and green being high. .....................................................................10
v

List of Tables

Table 1. Summary of enhancement factors and percentage modulation at the position of the 

sensor. ......................................................................................................................................10
vi

Acknowledgments

This work was supported by the Defense Advanced Research Projects Agency (DARPA) under 

the Heterostructural Uncooled Magnetic Sensor (HUMS) Program.
vii

Executive Summary

There are numerous applications that can benefit from small, inexpensive, low-power, lowfrequency sensors capable of detecting ultra-low magnetic fields not only within the military 

community but also in the areas of medical diagnostics, information technology, and commercial 

industry (1). Until recently, the detection of fields between 1 pT (10−8 Oe) and 0.1 nT (10−6 Oe) 

was dominated by relatively large, expensive, power-hungry sensors such as fluxgates, optically 

pumped magnetometers, and superconducting quantum interference devices (SQUIDs). 

Advances in magnetic tunnel junctions MgO barriers combined with concepts for mitigating the 

1/f noise present in these magnetoresistive devices open the possibility of using small, lowpower, high-sensitivity devices for the detection of weak, low frequency magnetic fields (2–4). 

Extending magnetic sensor sensitivity to the sub-picotesla range necessitates looking beyond just 

the limitations imposed by 1/f noise. It can be shown (5) that by increasing the volume of the 

sensor or the sensing element area from microns to 1 or 2 cm2

, an additional gain in sensitivity 

can be achieved. Magnetoresistive sensors are intrinsically small. In contrast to 

magnetoresistance sensors, magnetoelectric sensors are inherently larger sensors because their 

output signal increases with their length. Magnetoelectric sensing elements can be made in the 

appropriate size range such that, with the mitigation of 1/f noise, sub-picotesla sensitivity is 

possible.

This report presents magnetic modeling results of a proof of concept system for 1/f noise 

mitigation in “large” sensors. The 1/f noise reduction is achieved by rotating flux concentrators 

that shift the operating frequency of the sensor to higher frequencies where 1/f noise is lower. 

The goal is to design systems with magnetic flux concentrators that maximize the enhancement 

of the field and the percentage modulation of the field but minimize size. These issues in 

execution and necessary tradeoffs in performance are discussed, and magnetic modeling is 

presented, showing a clear road map to increased performance from the viewpoint of field 

enhancement and modulation. In order for the magnetoelectric sensor team to meet the metrics 

of the Defense Advanced Research Projects Agency (DARPA) Heterostructural Uncooled 

Magnetic Sensor (HUMS) Program, it is essential that a solution be found.
viii

INTENTIONALLY LEFT BLANK.
1

1. Introduction

Considerable progress has been made recently in magnetic sensors, including (1) the discovery 

(4, 6) that using MgO barriers in magnetic tunnel junctions leads to magnetoresistance values as 

large as several hundred percent and (2) the invention (7) of magnetoelectric sensors. 

Magnetoelectric sensors are composed of a piezoelectric material sandwiched between slabs of a 

magnetostrictive material. In a magnetic field the magnetostrictive material stresses the 

piezoelectric material which, in turn, generates a voltage. Thus, an output is generated without 

using any input power. These magnetoelectric sensors already have a sensitivity of less than

1 nT and they must have dimensions of several centimeters to maintain good sensitivity. 

The sensitivity of magnetic sensors is limited by the magnitude of their response to a magnetic 

field and their noise. Sensors with larger responses to a magnetic field also tend to have larger 

1/f noise. Figure 1 shows an example to 1/f noise in an electromechanical sensor. Because of the 

importance of 1/f noise, anisotropic magnetic sensors that only have magnetoresistance values of 

less than 3.5% are still widely used because their 1/f noise is small. The large 1/f noise in 

magnetic tunnel junctions with MgO barriers has limited their use at low frequencies. This led to 

research (8) on the micro-electromechanical system (MEMS) flux concentrator, a device that 

modulates the field and thus increases the modulation frequency to a region where 1/f noise is 

less important. The MEMS flux concentrator is a viable solution for solving the problem of 1/f

noise in small magnetic sensors. 

Figure 1. Schematic of magnetoelectric sensor. The gray region consists of a 

piezoelectric material sandwiched between slabs of a magnetostrictive 

material. Sensitivity is already under 1 nT.
2

Besides the 1/f noise term, there are other contributions to the noise. Both shot noise and thermal 

magnetic noise (5), which depend on the size of the sensor, are important. Thus, to achieve subpT sensitivities it is probably necessary to use larger sensors. These points make 

magnetoelectric sensing elements excellent candidates. Since the MEMS flux concentrator was 

designed to be used with small sensors, a different approach is needed to achieve sub-pT 

sensitivities with large magnetic sensors. We describe a new approach, based on using a rotating 

disk, which allows us to modulate the field for sensors occupying a volume of about 1 cubic cm. 

An essential part of designing the device was understanding the behavior of the magnetic field 

lines both for enhancing the field at the position of the sensor as well as maximizing modulation 

of the field. These needs motivated the work on macro-magnetic modeling described in this 

report.

2. Magnetic Modeling Details and Parameters

We performed magnetic modeling using a commercial finite element code program called 

Maxwell 3D, from ANSYS. Maxwell 3D is capable of analyzing AC magnetic, DC magnetic, 

and electrostatic field problems. The 3D DC magnetic portion of the software computes static 

magnetic fields where the source originates from a DC current or voltage, permanent magnets, or 

externally applied magnetic fields. It can directly compute the magnetic field (H) and current 

distribution (J), and derive the magnetic flux density (B) from the H field. In addition, it can 

automatically calculate force, torque, inductances, and saturation in devices containing linear, 

nonlinear, and anisotropic materials. The post-processor portion of the software can provide 

plots of flux lines, B and H fields, energy densities, and saturation. The modeling process 

consists of drawing the objects of interest, assigning properties (coercivity, permeability, etc.) to 

the objects, assigning boundaries or sources, seeding the objects and creating a mesh, and then 

processing the now defined problem.

Each model investigated involved the same fundamental sequence of steps. The first step in the 

analysis of the flux concentrator was to draw the model. Drawing the model consists of drawing 

three dimensional objects and either joining them together or subtracting them from each other. 

This allows one to create complex objects. A sufficiently large region around the flux 

concentrators and the sensing region were defined as a background. The flux concentrators were

drawn as solid pieces and assigned the material properties of permalloy (NiFe), with a 

permeability of 5000 as that is a value readily achieved in this material. The material properties 

assigned to this background are those of a vacuum, with a relative permeability of 1. The 

modeling is macro-magnetic in nature, as it does not take into account domain structure but does 

incorporate demagnetization factors. The initial mesh is created by the program, but one can 

create regions in which the initial mesh is denser so as to force more tetrahedrons into regions 

where one has a greater interest in the solutions without significantly increasing solution time. 
3

Mesh refinement is also handled by the program as part of an iterative process in which energy 

error and percentage decrease to a predetermined figure. All nonmagnetic structural material 

was ignored. The magnetic material of the sensor was also ignored as the thicknesses of the 

various layers are small enough to have only a small influence on the surrounding flux 

environment. 

We are interested in the magnetic field strength and flux line behavior at the position the sensor 

would occupy. Two main quantities of interest to us are the enhancement factor and the

percentage modulation. The enhancement factor is defined as HS/Happl, where HS and Happl

denote the magnetic field strength at the position of the sensor and the applied magnetic field 

strength, respectively. For the rotating flux concentrator design, there are two main positions to 

consider: (1) the position in which the magnetic field is at a maximum value at the sensor 

location and (2) the position that achieves a minimum in field strength, or shunts the field away, 

at the sensor position. Periodic motion between these two positions at a high frequency 

modulates the field, thus achieving the desired shift of the operating frequency of the sensor to 

higher frequencies where 1/f noise is lower. We then define the percentage field modulation at 

the position of the sensor as

EH(max)/ EH(min) * 100 (1)

where EH(max) and EH(min) are the enhancement factors at the maximum and minimum 

magnetic field strength positions, respectively. Section 3 discusses the designs we have 

modeled.

3. Rotating Flux Concentrator Designs

Due to the size of the sensor (figure 1), we decided that the best way to modulate the field was 

via rotation. The first design to be discussed was modeled but never constructed. Designs 2 and 

3 were both modeled and constructed.

3.1 Magnetic Modeling Results for Design 1

This design is essentially a compound flux concentrator system. There are two pairs of 

concentric flux concentrators in close proximity to each other. As shown in figure 2, the inner 

most pair of concentrators is stationary while the outermost pair rotates around the common 

center axis. The sensor position would be at the origin of the shown coordinate axis. The 

parameters that were varied for this design were (1) the permalloy thickness of the concentrators

and (2) the length of the rotating concentrators. The air gap between the innermost pair of 

concentrators, the region which would contain the sensor, was set to 1.5 mm and the air gap 

between the stationary and rotating concentrators was set to 0.1 mm (figure 3). An initial model 
4

indicated that a deposition of a thin layer of permalloy, 0.25 microns, would only result in a 

maximum enhancement value of 1.2. Subsequent models used a permalloy thickness of 0.2 mm. 

Figure 2. First concept of rotating flux concentrators. The red concentrators are stationary and the blue 

concentrators are free to rotate. The maximum magnetic field enhancement at the origin of the 

coordinate axis is achieved when (a) the concentrators are aligned and the minimum is achieved when 

(b) the outermost pair of concentrators have rotated 90° from the position shown in (a).

Figure 3. Schematic of design 1 showing various dimensions of interest.

With the permalloy thickness now held constant, we ran the first model with the length of the 

stationary magnetic flux concentrators set to 7.4 mm. The maximum field enhancement 

achieved for this model was 2.15. In an effort to increase this enhancement value, we next 

increased the length of the rotating concentrators to 17.4 mm. As we see in figure 4, the aligned 

flux concentrators do a good job of focusing the magnetic flux lines at the origin of the 

coordinate axis and the maximum enhancement value was determined to be 3.46. However, 

knowing that (1) the air gap was already smaller than the electromagnetic sensor we would 

eventually use, (2) it would be difficult to run electrical leads to a sensor at the center of rotation, 

and (3) the 0.1 mm gap between the inner and outer flux concentrators is a challenge given the 

high speed of rotation that would required of the inner concentrators, we decided to alter the 

design.
5

Figure 4. Plot of the magnetic field strength in the plane perpendicular to the x-y plane for the position 

producing a maximum value of enhancement at the origin.

3.2 Magnetic Modeling Results for Design 2

The initial design is shown in figure 5. The sensor is positioned about 1 mm above and centered 

on the edge of the rotating disc. The rotation is driven by an electrical motor and the rotation 

rate is monitored by using a photo cell and holes in the disc. Thin pieces (0.25 mm thick) of 

sheet permalloy on the disc act either as flux concentrators or as flux shunts that shield the sensor 

from the magnetic flux.

Figure 5. Rotating flux concentrator apparatus.
6

The results of modeling the flux concentrator apparatus are shown for two orientations in figure 

6. Extracting the data from the models to determine the enhancement factors lead to a startling 

result. The enhancement factor for the “shunt” position (figure 6b) is 1.02 and, for the 

“concentrating” position (figure 6a), it is 0.45. While this leads to a modulation percentage of 

about 225%, it was clear the design was not influencing the flux lines as we had envisioned. 

Figure 6. Model results showing the magnetic field lines for (a) the “shunt” and (b) the “concentration” orientation. 

The sensor position is indicated by the black dot. Permalloy shunts are shown in blue and the 

concentrators in red. Large arrows in (b) are the reference axis directions.

Plotting the enhancement factors for several orientations of the disc produces a modulation curve 

and serves to illustrate that the shunt position actually maximizes the field strength at the 

position of the sensor as the disc rotates (figure 7). We had initially believed that the permalloy 

shields below the sensor would pull the magnetic field away from the sensor location and allow 

the field lines to circulate around the center of the disc while the concentrators would provide 

more of a direct line path for flux lines, thus enhancing the field at the position of the sensor. 

Figure 6 supports this line of reasoning; however, if we look at the magnetic flux lines out of the 

plane of the rotating disc (figure 8), we see that because the permalloy shields extend all the way 

out to the edge, the magnetic flux lines curl down into the shields through the sensor position. 

This results in the magnetic field strength actually being higher at the sensor location in the shunt 

position.
7

Figure 7. Modulation curve for design 2.

Figure 8. Magnetic field lines in a plane perpendicular to the concentrators for (a) the “concentration” orientation 

and (b) the “shunt” position. Sensor position is indicated by the black dot. Note the flux lines curling 

down through the sensor location in (b).

3.3 Magnetic Modeling Results for Design 3

While the modulation percentage of our second design was adequate, the enhancement factor for 

concentrating the field at the position of the sensor needed to be higher. The new design we 

considered is shown in figure 9. The permalloy shunts and concentrators have been replaced 

with a single strip of permalloy, 0.25 mm thick and 40 mm wide, running across the diameter of 

the disc and cut to conform to the curvature of the disc’s edge. Additionally, two permalloy rods 

have been added to the apparatus. These rods were heat treated to maximize their magnetic 

permeability after they had been cut and machined. This new design also uses a non-ferrous air 
8

turbine to spin the disc. This was done because the electric motor of design 2 was raising the 

noise floor, creating extra peaks, and broadening other peaks in the frequency domain 

(figure 10). 

Figure 9. Design 3 of the rotating flux concentrator, showing all of the essential elements 

except for brackets to hold the permalloy rods in place and the non-ferrous air 

turbine designed to spin the disc.

Figure 10. Comparison of the noise with a stationary disc and 

with the disc being rotated by an electric motor.
9

We ran several models to ascertain the optimum combination of sensor height above the disc as 

well as air gap size between the permalloy rods and the disc. Here we present the magnetic 

modeling results for the optimized design parameters. For this design, the sensor is centered on, 

and 2 mm above, the edge of the disc. The permalloy rod on the side away from the sensor is 

3 mm away from, and centered on, the edge the disc, and the beveled permalloy rod near the 

sensor is 6 mm away from, and centered on, the edge of the disc. Figure 11 shows the 

dimensions of the beveled disc and figure 12 shows the sensor position relative to the rod. The 

enhancement factor for the “concentrating” position (figure 13a) is 8.36 and, for the “shunting 

position” position (figure 13b), it is 2.67. This leads to a modulation percentage of about 313% 

at the position of the sensor.

Figure 11. Dimensions of the beveled permalloy rod.

Figure 12. Magnetoelectric sensor position relative to the beveled rod and disc. The sensor is shown in 

yellow.
10

Examination of figure 13 indicates that in the “concentration” position field lines are being 

focused through the sensor position toward the permalloy strip. In the shunt position, the 

magnetic field lines are less focused and are curling away from the sensor position. While the 

enhancement factor is higher in the shunt position for this design than in design 2, the maximum 

enhancement is now 8× higher, thus providing a greater degree of field enhancement as well as 

increasing the modulation at the sensor location.

Figure 13. Model results showing the magnetic field lines for the (a) “concentration” and (b) “shunt” orientation. 

The sensor position is indicated by the yellow square. Permalloy strip and beveled rod are shown in 

blue while the flat-faced rod is shown in gray. The magnetic field strength is denoted by color and size 

of the arrows, with small and dark blue being low, and large and green being high.

4. Conclusion

We have shown how magnetic modeling helped to design a device that mitigates 1/f noise in 

large magnetic field sensors. The results are summarized in table 1. Focusing on the key design 

elements of air gaps, sensor position, and the arrangement of pieces of permalloy to serve as flux 

concentrators and shunts, we were able to create a design, which, when used with 

magnetoelectric sensors, should yield both a field enhancement and modulation sufficient to 

achieve less than 1 pT/Hz1/2 at 1 Hz detectivity.

Table 1. Summary of enhancement factors and percentage 

modulation at the position of the sensor.

EH(max) EH(min) Percentage Modulation

Design 1 3.46 n/a n/a

Design 2 1.02 0.45 225

Design 3 8.36 2.67 313
11

5. References

1. Lenz, J.; Edelstein, A. Magnetic Sensors and Their Applications. IEEE Sensors June 2006, 

6, 631–49.

2. Edelstein, A. S.; Burnette, J.; Fischer, G. A.; Cheng, S. F.; Egelhoff, W. F., Jr.; Pong, 

P.W.T.; McMichael, R. D. Advances in Magnetometry Through Miniaturization. J. Vac. 

Sci. Technol. A July 2008, 26, 757–62.

3. Guedes, A.; Patil, S. B.; Wisniowski, P.; Chu, V.; Conde, J. P.; Freitas, P. P. Hybrid 

Magnetic Tunnel Junction-MEMS High Frequency Field Modulator for 1/f Noise 

Suppression. IEEE Trans. Magn. November 2008, 44, 2554–7.

4. Parkin, S.S.P.; Kaiser, C.; Panchula, A.; Rice, P. M.; Hughs, B.; Samant M.; Yang, S. Giant 

Tunneling Magnetoresistance at Room Temperature with MgO (110) Tunnel Barriers. Nat. 

Mater. December 2004, 3, 862–7.

5. Egelhoff, W. F., Jr.; Pong, P.W.T.; Unguris, J.; McMichael, R. D.; Nowak, E. R.; Edelstein, 

A. S.; Burnette, J. E. Fisher, G. A. Critical Challenges for picoTesla Magnetic-tunneljunction Sensors. Sens. Actuators A October 2009, 155, 217–25.

6. Butler, W. H.; Zhang, X.-G.; Schulthess, T. C.; MacLaren, J. M. Spin-dependent Tunneling 

Conductance of Fe|MgO|Fe Sandwiches. Phys. Rev B 2001, 63, 054416/1–12.

7. Das, J.; Li, M.; Kalarickal, S. S.; Altmannshofer, S.; Buchanan, K. S.; Li, J. F.; Viehland, D. 

Control of Magnetic and Electric Responses with Electric and Magnetic Fields in 

Magnetoelectric Heterostructures. Appl. Phys. Lett. 2010, 96, 222508.

8. Edelstein, A. S.; Burnette, J. E.; Fischer, G. A.; Olver, K.; Eglehoff, Wm.; Nowak, E.;

Cheng, Shu-Fan. Validation of the Microelectromechanical System Flux Concentrator 

Concept for Minimizing the Effect of 1/f Noise. J. Appl. Phys. 2009, 105, 07E720, 2009.
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