Magnetometers with a high sensitivity at weak magnetic fields are desirable for a wide range of sensing applications. Devices that operate on the principle of extraordinary magnetoresistance (EMR) are appealing candidates because of their simplicity and ability to operate at room temperature but they suffer from low sensitivity when compared to state-of-the-art magnetometers such as superconducting quantum interference devices. Since the EMR phenomenon is principally a geometric effect, the shapes of the various parts of the device represent additional degrees-of-freedom which can be manipulated in order to modify the performance of the devices. While previous studies have mostly focused on the inner part of the sensor, in this work, we study the effect of systematically manipulating the shape of the outer boundary. We show that the maximum sensitivity of the device can be increased by 70% by placing a constriction between the voltage or current probes and by 300% if the shape of the boundary is shifted from circular to elliptical. We also show that a finite zero-field sensitivity can be obtained if the horizontal symmetry of the device is broken. These results demonstrate that the outer boundary can have a significant effect on device performance, a finding which paves the way for using shape optimization on the outer boundary for designing sensitive magnetometers.

1.
J.
Moussa
,
L. R.
Ram-Mohan
,
J.
Sullivan
,
T.
Zhou
,
D. R.
Hines
, and
S.
Solin
, “
Finite-element modeling of extraordinary magnetoresistance in thin film semiconductors with metallic inclusions
,”
Phys. Rev. B
64
,
184410
(
2001
).
2.
Introduction to Nanoscale Science and Technology, Magnetoresistive Devices and Materials, edited by S. Di Ventra, M. Evoy, and J. R. Heflin (Springer, Boston, MA, 2004).
3.
Magnetic Sensors and Devices: Technologies and Applications, Giant (GMR) and Tunnel (TMR) Magnetoresistance Sensors: From Phenomena to Applications, edited by L. A. Francis and K. Poletkin (CRC Press, 2017), pp. 35–65.
4.
S.
Solin
,
T.
Thio
,
D. R.
Hines
, and
J. J.
Heremans
, “
Enhanced room-temperature geometric magnetoresistance in inhomogeneous narrow-gap semiconductors
,”
Science
289
,
1530
1532
(
2000
).
5.
D.
Kleinman
and
A.
Schawlow
, “
Corbino disk
,”
J. Appl. Phys.
31
(
12
),
2176
2187
(
1960
).
6.
M.
Kamada
,
V.
Gall
,
J.
Sarkar
,
M.
Kumar
,
A.
Laitinen
,
I.
Gornyi
, and
P.
Hakonen
, “
Strong magnetoresistance in a graphene corbino disk at low magnetic fields
,”
Phys. Rev. B
104
,
115432
(
2021
).
7.
C. H.
Möller
,
O.
Kronenwerth
,
D.
Grundler
,
W.
Hansen
,
C.
Heyn
, and
D.
Heitmann
, “
Extraordinary magnetoresistance effect in a microstructured metal-semiconductor hybrid structure
,”
Appl. Phys. Lett.
20
, 3988–3990 (
2002
).
8.
Nano-Scale Materials: From Science to Technology, Design and Properties of a Scanning EMR Probe Microscope, edited by S.N. Sahu, R. K. Choudhury, and P. Jena (Nova Science Publishers, 2006).
9.
A. S.
Troup
,
D. G.
Hasko
,
J.
Wunderlich
, and
D. A.
Williams
, “
Magnetoresistance in silicon-based semiconductor-metal hybrid structures
,”
Appl. Phys. Lett.
89
,
022116
(
2006
).
10.
S.
Pisana
,
P. M.
Braganca
,
E. E.
Marinero
, and
B. A.
Gurney
, “
Tunable nanoscale graphene magnetometers
,”
Nano Lett.
10
,
341
346
(
2010
).
11.
J.
Lu
,
H.
Zhang
,
W.
Shi
,
Z.
Wang
,
Y.
Zheng
,
T.
Zhang
,
N.
Wang
,
Z.
Tang
, and
P.
Sheng
, “
Graphene magnetoresistance device in Van der Pauw geometry
,”
Nano Lett.
11
(
7
),
2973
2977
(
2011
).
12.
D. C.
Wu
,
Y. W.
Pan
,
J. S.
Wu
,
S. W.
Lin
, and
S. D.
Lin
, “
High-sensitivity two-terminal magnetoresistance devices using InGaAs/AlGaAs two-dimensional channel on GaAs substrate
,”
Appl. Phys. Lett.
108
,
172403
(
2016
).
13.
S.
El-Ahmar
,
W.
Koczorowski
,
A. A.
Poźniak
,
P.
Kuświk
,
M.
Przychodnia
,
J.
Dembowiak
, and
W.
Strupiński
, “
Planar configuration of extraordinary magnetoresistance for 2D-material-based magnetic field sensors
,”
Sens. Actuators, A
296
,
249
253
(
2019
).
14.
L.
Wang
,
I.
Meric
,
P. Y.
Huang
,
Q.
Gao
,
Y.
Gao
,
H.
Tran
,
T.
Taniguchi
,
K.
Wantabe
,
L. M.
Campos
,
D. A.
Muller
,
G.
Juo
,
P.
Kim
,
J.
Hone
,
K. L.
Shepard
, and
C. R.
Dean
, “
One-dimensional electrical contact to a two-dimensional material
,”
Science
342
,
614
617
(
2013
).
15.
C. R.
Dean
,
A. F.
Young
,
I.
Meric
,
C.
Lee
,
L.
Wang
,
S.
Sorgenfrei
,
K.
Watanabe
,
T.
Taniguchi
,
P.
Kim
,
K. L.
Shepard
, and
J.
Hone
, “
Boron nitride substrates for high-quality graphene electronics
,”
Nat. Nanotechnol.
5
,
722
726
(
2010
).
16.
B.
Zhou
,
K.
Watanabe
,
T.
Taniguchi
, and
E. A.
Henriksen
, “
Extraordinary magnetoresistance in encapsulated monolayer graphene devices
,”
Appl. Phys. Lett.
216
,
053102
(
2020
).
17.
T.
Huang
,
L.
Ye
,
K.
Song
, and
F.
Deng
, “
Planar structure optimization of extraordinary magnetoresistance in semiconductor–metal hybrids
,”
J. Supercond. Novel Magn.
27
,
2059
2066
(
2014
).
18.
T.
Hewett
and
F. V.
Kusmartsev
, “
Geometrically enhanced extraordinary magnetoresistance in semiconductor-metal hybrids
,”
Phys. Rev. B Condens. Matter Mater. Phys.
82
(
21
),
212404
(
2010
).
19.
Z.
Moktadir
and
H.
Mizuta
, “
Magnetoresistance in inhomogeneous graphene/metal hybrids
,”
J. Appl. Phys.
113
(
8
),
083907
(
2013
).
20.
R.
Erlandsen
, “Enhancing the extraordinary magnetoresistance by variations in geometry and material properties,” Ph.D. thesis (Technical University of Denmark, 2022).
21.
T.
Zhou
,
S.
Solin
, and
D. R.
Hines
, “
Extraordinary magnetoresistance of a semiconductor-metal composite van der Pauw disk
,”
J. Magn. Magn. Mater.
00
,
226
230
(
2001
).
22.
J.
Sun
and
J.
Kosel
, “
Finite element analysis on the influence of contact resistivity in an extraordinary magnetoresistance magnetic field micro sensor
,”
J. Supercond. Novel Magn.
25
(
8
),
2749
2752
(
2012a
).
23.
T.
Zhou
,
D. R.
Hines
, and
S.
Solin
, “
Extraordinary magnetoresistance in externally shunted van der Pauw plates
,”
Appl. Phys. Lett.
78
(
5
),
667
669
(
2001
).
24.
R.
Erlandsen
,
R.
Bjørk
,
L.
Kornblum
,
N.
Pryds
, and
D. V.
Christensen
, “
Symmetry breaking in magnetoresistive devices
,”
Phys. Rev. B
106
(
1
),
014408
(
2022
).
25.
J.
Sun
and
J.
Kosel
, “Finite-element modelling and analysis of Hall effect and extraordinary magnetoresistance effect,” in
Finite Element Analysis—New Trends and Developments
(InTech Open, 2012b).
26.
T.
Désiré Pomar
,
R.
Erlandsen
,
B.
Zhou
,
L.
Iliushyn
,
R.
Bjørk
, and
D. V.
Christensen
, “Extraordinary magnetometry—A review on extraordinary magnetoresistance,” arXiv (2022).
27.
S.
Solin
and
T.
Zhou
, “Extraordinary magnetoresistance of an off-center van der Pauw disk,” in Extended Abstracts of the 2001 International Conference on Solid State Devices and Materials (The Japan Society of Applied Physics, 2001), p. 1.
28.
M.
Holz
,
O.
Kronenwerth
, and
D.
Grundler
, “
Enhanced sensitivity due to current redistribution in the Hall effect of semiconductor-metal hybrid structures
,”
Appl. Phys. Lett.
86
(
7
),
072513
(
2005
).
You do not currently have access to this content.