Geometrical optimization of a local ballistic magnetic sensor
Yuhsuke Kanda, Tatsuya Nomura, Takashi Kimura, and Masahiro Hara
Citation: Applied Physics Letters 104, 142408 (2014); doi: 10.1063/1.4871002
View online: http://dx.doi.org/10.1063/1.4871002
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/14?ver=pdfcov
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APPLIED PHYSICS LETTERS 104, 142408 (2014)

Geometrical optimization of a local ballistic magnetic sensor
Yuhsuke Kanda,1 Tatsuya Nomura,2 Takashi Kimura,2,3 and Masahiro Hara1
1Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555,
Japan
2
Advanced Electronics Research Division, INAMORI Frontier Research Center, Kyushu University,744 Motooka, Fukuoka 819-0395, Japan
3Department of Physics, Kyushu University, 6-10-1 Hakozaki, Fukuoka 812-8581, Japan(Received 13 February 2014; accepted 30 March 2014; published online 9 April 2014)
We have developed a highly sensitive local magnetic sensor by using a ballistic transport property
in a two-dimensional conductor. A semiclassical simulation reveals that the sensitivity increases
when the geometry of the sensor and the spatial distribution of the local field are optimized. We
have also experimentally demonstrated a clear observation of a magnetization process in apermalloy dot whose size is much smaller than the size of an optimized ballistic magnetic sensor
C 2014 AIP Publishing LLC.
fabricated from a GaAs/AlGaAs two-dimensional electron gas. V[http://dx.doi.org/10.1063/1.4871002]

Various types of magnetic nanoparticles are utilized not
only in magnetic devices but also in medical diagnoses.1–3
There are different types of biosensors for magnetic label
detection: giant magnetoresistance (GMR) sensor,1 Hall sensor,4 anisotropic magnetoresistance (AMR) ring sensor,5spin-valve sensor,6 and magnetoimpedance (MI) sensor.7 A
further miniaturization of the nanomagnets demands a highly
sensitive local magnetic sensor for detecting a small amountof the magnetization. It is well known that a micro/nanosuperconducting quantum interference device (SQUID) sensitively detects a magnetic flux from an individual magnetic
nanoparticle.8–10 However, the SQUID sensors operate only
below the critical temperature of the superconductor, which
restricts fundamental analyses and applications in a wide
range of temperatures including a room temperature. A sensitive detection based on anomalous Hall effect (AHE)
reveals a magnetic behavior in a single nanodot with diameter range of several tens of nm.11,12 Although a current flow
inside the single ferromagnet is necessary for observing theAHE signal, typical nanoparticles are covered with insulating molecules for avoiding aggregations.13 Hence, the AHE
technique is applicable only for conductive magnetic nanoparticles with good electric contacts to the sensor.
As an alternative approach for the sensitive detection ofa small magnet, we are focusing on the ballistic transports in
two-dimensional electron systems. Ballistic trajectories ofelectrons in the sensor are deflected by the normal component of the local stray field from the magnet. The ballistic
character effectively appears not in a Hall resistance but in abend resistance. A contribution of the parallel component of
the magnetic field is negligibly small so that we can detect aslight change in the magnetization under an external in-planemagnetic field. In fact, the magnetization reversal process ofsubmicron-sized patterned ferromagnets were precisely
investigated from ballistic bend resistance measurements
using a micro-Hall cross in GaAs/AlGaAs two-dimensional
electron gas (2DEG) systems.14–17 We have also reported
that the ballistic response with respect to an uniform magnetic field can be effectively tuned by changing the geometryof the sensor in recent.18 In this Letter, we will report an0003-6951/2014/104(14)/142408/4/$30.00

approach for achieving higher sensitivity of the ballistic
magnetometry for a nanomagnet by optimizing the sensor
structure.
A schematic drawing of a 2DEG sensor with a permalloy (Py) dot, the target of the field detection in the present
study, is shown in Fig. 1(a). The depth of the 2DEG planefrom the surface in the magnetic sensor is 65 nm. In a twodimensional conductor, the resistance dominantly depends
on the magnetic field perpendicular to the conductive plane.
When the permalloy dot is fully magnetized in the long axis
(the þx direction), stray fields from the both edges penetrate
into the 2DEG plane as shown in Fig. 1(b). The estimatednormal component of the stray field profile in the 2DEG
plane is shown in Fig. 1(c). The amplitude of the magneticFIG. 1. (a) Geometry of the ballistic magnetic sensor with a Py dot. A bend
resistance measured by the current-voltage configurations is sensitive to thelocal stray field from the Py dot. (b) Field profile of the stray field from thePy dot magnetized in the þx direction. (c) Spatial distribution of the normalcomponent of the stray field in plane of the 2DEG. The peak amplitude ofthe local field is about 30 mT.

104, 142408-1

C 2014 AIP Publishing LLC
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Kanda et al.

Appl. Phys. Lett. 104, 142408 (2014)

flux from the each edge is about 8.5  10–16 Wb which issmaller than the flux quantum.
The transport properties in our 4-terminal mesoscopic
conductor have been evaluated by numerical calculations
based on the Landauer-B€uttiker formula19
XhIi ¼ ðNi  Tii Þli 
Tij lj :2e
j6¼i

resistance for shifting the position of the ferromagnet asshown in Fig. 3(a). The signal strongly depends on the position of the ferromagnet, which results from the ballistictransport property. The highest sensitivity is achieved when
the ferromagnet is placed at the center of the type II sensor.

(1)Here, Ii, Ni, and lj are the current in lead i, the numberof modes in lead i, and the chemical potential of lead j,respectively. Tij describes the transmission probability of anelectron injected from lead j to lead i.
We calculate the bend resistance R14,23 with the probe
configuration shown in Fig. 1(a). From the terminal conditions
I ¼ I1 ¼ I4; I2 ¼ I3 ¼ 0 for the bend-resistance measurement,
the bend resistance RB can be calculated as follows:
RB ¼ R14;23 ¼l2  l3
h T34 T21  T31 T24
¼ 2;
eI
D
2e(2)

where D is a factor independent of the current and voltage
configuration.
In the simulation, we consider a 2DEG cross with 90
corners for simplicity. The electron density ne and the Fermi
wavelength kF in our sensor are assumed to be 3.8  1015/m2
and 41 nm, respectively. The channel width in lead i isdefined as Wi ¼ Ni kF =2. Electrons are injected from eachprobe like a billiard ball with an angular distributionPðaÞ ¼ cos a=2. Classical trajectories of electrons are modified by the estimated stray field from the Py dot. We thencalculated transmission probabilities by counting number of
the transmitted electrons into each probe.20
The calculated bend resistance depends on the geometryof the 2DEG cross. We consider the following three cases:(I) N1 ¼ N2 ¼ N3 ¼ N4 ¼ N, (II) N1 ¼ N3 ¼ N, N2 ¼ N4 ¼ 90,and (III) N1 ¼ N3 ¼ 90, N2 ¼ N4 ¼ N. Here, N is a variable parameter between 20 and 90 in the simulation. The Py dot
magnetized in the þx or the –x direction is placed at the center of the sensor. Figure 2(a) shows the bend resistance as afunction of channel number N in the type I. The bend resistance has a negative value, which is characteristic in ballistic
conductors.21 The absolute value of the resistance without
the stray field from the Py dot jRB ð0Þj is proportional to theinverse of the channel number. The difference in the bend resistance between the positive magnetization RB (þ) and thenegative magnetization RB (–) is enhanced in smaller 2DEGcross. Figure 2(b) shows the bend resistance as a function ofchannel number N in the type II. The size-dependence of RB(0) is relatively small comparing with the type I. The
decrease of N1 ¼ N3 value while keeping N2 ¼ N4 constantleads to a significant difference between the positive and thenegative magnetization DR ¼ RB ðþÞ  RB ðÞ. By contrast,
the decrease of N2 ¼ N4 value (type III) leads to a muchsmaller difference. Figure 2(d) shows the relative sensitivityof the bend signal defined as DR=jRB ð0Þj for the three cases.
The type II is appropriate for a sensitive detection of strayfields from the tiny magnet.
In the above simulation, the target is placed at the centerof the sensor. We also calculated the change in the bend

FIG. 2. Simulated bend resistance as a function of variable channel number
N. (a) Type I: N ¼ N1 ¼ N2 ¼ N3 ¼ N4. (b) Type II: N ¼ N1 ¼ N3
 N2 ¼ N4 ¼ 90. (c) Type III: N ¼ N2 ¼ N4  N1 ¼ N3 ¼ 90. (d) Relative
sensitivity of the sensor as a function of channel number N for the threecases.

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142408-3

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Appl. Phys. Lett. 104, 142408 (2014)

FIG. 5. Bend resistance R14,23 as a function of in-plane magnetic field. Aclear hysteresis curve was observed in the magnetization reversal process.

FIG. 3. (a) Schematic illustration of the position of the Py dot. The center ofthe Py dot (xc, yc) shifts from the origin. 2D mapping of the relative sensitivity of the ballistic sensor depending on the center of the Py dot for (b) type I,(c) type II, and (d) type III.

In order to demonstrate the high sensitivity in the type II
sensor, we fabricated a sensor using a GaAs/AlGaAs 2DEGsystem. The density and mobility of the 2DEG before processing at 5 K were 3.8  1015/m2 and 68 m2/V s, respectively. The depth of the 2DEG plane from the surface is65 nm. The type II structure 0.6 lm  1.8 lm was fabricatedby means of Ar plasma etching. A scanning electron microscopy (SEM) image of the sample is shown in Fig. 4. The
electron mean free path of the 2DEG is 6.9 lm at 5 K, whichis larger than the size of the cross. A Py dot with thickness of
30 nm, width of 100 nm, and length of 200 nm is placed atthe center of the sensor. The total magnetic moment of thePy dot is estimated to be 5  1013 emu. 4-terminal resistance measurements were carried out using a low-frequency
ac technique at 5 K.

We measured a bend resistance R14,23 as a function of
in-plane magnetic field. We precisely aligned the magnetic
field in the 2DEG plane so that the change in the resistanceoriginates only from a stray magnetic field from the ferromagnet. As shown in Fig. 5, the change in the bend resistance reveals the magnetization reversal of the Py dot. The
ballistic transport character in the optimized sensor enables
us to detect a ferromagnet which is much smaller than thelateral size of the sensor. The observed two distinct resistance changes both in the forward and backward fieldsweeps implies that the magnetization reversal process proceeds through the nucleation and annihilation of the magnetic vortex.22 Micromagnetic simulation using OOMMF23
also supports that the Py dot with the same sample dimension favorably forms the vortex structure compared with thesingle domain structure. The relative sensitivity DR=jRB ð0Þj
is 0.13 in the experiment, which is smaller than the simulated value 0.36. The simulation overestimates the sensitivity since we assumes 90 corners of the junction andneglects any boundary and impurity scattering in thesensor.
In summary, we study a strategy for developing a highly
sensitive ballistic magnetic sensor. A magnetization processof a Py dot was clearly observed in an optimized 2DEG sensor with two narrow terminals and two wide terminals when
the Py dot was placed at the center of the sensor.
This work was supported by JSPS KAKENHI Grant
Nos. 25870548 and 25220605.
1

FIG. 4. SEM image of the fabricated sensor with a Py dot put on the center.
The widths of the two terminal (1,3) is narrower than those of the other twoterminals (2,4).

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