Geometrical dependence of spin current absorption into a ferromagnetic nanodot
Tatsuya Nomura, Kohei Ohnishi, and Takashi Kimura
Citation: Journal of Applied Physics 120, 142121 (2016); doi: 10.1063/1.4961975
View online: http://dx.doi.org/10.1063/1.4961975
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JOURNAL OF APPLIED PHYSICS 120, 142121 (2016)

Geometrical dependence of spin current absorption into a ferromagnetic
nanodot
Tatsuya Nomura,1 Kohei Ohnishi,1,2 and Takashi Kimura1,2,a)
1

Department of Physics, Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan
Research Center for Quantum Nano-Spin Sciences, Kyushu University, 744 Motooka,
Fukuoka 819-0395, Japan
2(Received 29 April 2016; accepted 18 August 2016; published online 2 September 2016)
We have investigated the absorption property of the diffusive pure spin current due to aferromagnetic nanodot in a laterally configured ferromagnetic/nonmagnetic hybrid nanostructure.
The spin absorption in a nano-pillar-based lateral-spin-valve structure was confirmed to increase
with increasing the lateral dimension of the ferromagnetic dot. However, the absorption efficiency
was smaller than that in a conventional lateral spin valve based on nanowire junctions because thelarge effective cross section of the two dimensional nonmagnetic film reduces the spin absorption
selectivity. We also found that the absorption efficiency of the spin current is significantly
enhanced by using a thick ferromagnetic nanodot. This can be understood by taking into accountthe spin absorption through the side surface of the ferromagnetic dot quantitatively. Published by
AIP Publishing. [http://dx.doi.org/10.1063/1.4961975]

I. INTRODUCTION

Efficient manipulation of the spin current is a key ingredient for realizing next-generation spintronic devices with ultralow electric power consumption.1–4 Pure spin current has several advantages over the conventional spin-polarized current
because of the absence of the electric current.5–9 This leads tothe suppression of the extra heat dissipation due to Joule heating, leading to the improvement of the limitation of the maximum generating spin current.10 However, in general, the purespin current is created by electrical spin injection in a laterally
configured ferromagnetic (F)/nonmagnetic (N) metal hybrid
structure. Therefore, the maximum magnitude of the pure spincurrent is limited by the allowable current density at the injecting F/N junction. Since most of the lateral spin valves reported
so far based on ferromagnetic nanowires, which has relatively
high resistivity compared to the nonmagnetic wire, a large heatdissipation due to Joule heating is generated by flowing the current. As a result, the magnitude of the spin current is restrictedby the allowable maximum current density of the ferromagnetic
nanowire, typically 108 A/cm2 for the continuous current.11–16
To solve this issue, we have recently developed adifferent-type lateral spin valve, consisting of pillar-shaped ferromagnetic nanodots and a quasi-two-dimensional nonmagnetic film.17,18 We showed that the Joule heating from theferromagnetic injector is significantly suppressed in the nanopillar-based lateral spin valve because of the reduction of thevolume of the ferromagnetic element in the current probe andthe efficient heat sink effect of a two dimensional nonmagnetic
film. Moreover, because of its geometrical flexibility, one caneasily increase the number of the spin injectors, leading to themulti-terminal spin injection. As a result, the magnitude of thegenerated spin current is significantly enhanced. Minimum heat
This paper is part of the Special Topic “Cutting Edge Physics in Functional
Materials” published in J. Appl. Phys. 120, 14 (2016).
a)t-kimu@phys.kyushu-u.ac.jp.
0021-8979/2016/120(14)/142121/6/$30.00

dissipation under the spin injection in the nano-pillar-based lateral spin valve has been confirmed in the experiment about the
spin injection into a superconductor.19 We clearly demonstrated that the spin current was insulated at the Nb surface
after the superconducting transition by using the extended
nano-pillar-based lateral spin valve. It should be noted thatsuch a spin current insulation has never been observed in thesimilar experiment using the nanowire-based lateral spin valve
because of the reduction of the superconducting gap under the
spin injection.20,21 For realizing the efficient manipulation of
the pure spin current, it is important not only to generate thespin current but also to absorb the spin current into the anotherferromagnet.22–26 However, the spin absorption efficiency in
nano-pillar based lateral spin valves has not yet been evaluated.
Since the large effective cross section for a two dimensional
nonmagnetic film decreases the effective spin resistance of thenonmagnetic channel, the spin absorption efficiency may
decrease. In the present study, we experimentally evaluate thespin current absorption efficiency in the nano-pillar-based lateral spin valve. In addition, we also explore the better structure
for realizing the efficient spin absorption.
II. NANOPILLAR-BASED LATERAL SPIN VALVE

We have fabricated a nano-pillar-based lateral spin valve
consisting of five ferromagnetic nanodots formed on a uniform nonmagnetic film. First, 200-nm-thick Cu and 20-nmthick Permalloy (Py) films were deposited by electron-beam
evaporation on a thermally oxidized Si substrate at the basepressure of 4  109 Torr. Subsequently, electron-beamlithography was performed to form the elliptical-shaped resist
masks. The Ar ion milling process has been performed tomake the Py nano-pillar structures, followed by the SiO2 sputtering. After making the contact holes in the SiO2 insulating
layer, the top Cu electrodes were formed by the conventional
lift-off process. Thus, the array of the ferromagnetic nanodots
was formed on the two-dimensional uniform nonmagnetic Cu

120, 142121-1

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Nomura, Ohnishi, and Kimura

J. Appl. Phys. 120, 142121 (2016)

FIG. 1. Scanning electron microscopy
image of the fabricated nano-pillarbased lateral spin valve with the multispin injectors together with a schematic illustration for the fabricated lateral spin valve. The top and bottom
electrodes are electrically connected
via the Py nanopillars, and otherregions are separated by a 100-nmthick SiO2 insulating layer.

film, as schematically shown in Fig. 1. Here, the desired lateral dimensions for the Py1, Py2, Py3, and Py 4, which werediagonally located on the Cu film, are approximately
120 nm  180 nm. The desired dimension of the middle Py
dot (Py5) is 120 nm  350 nm, respectively. All the measurements in this study have been performed at 77 K. Here, theresistivity for the Py is 24 lX cm at 77 K and that for Cu is
1.6 lX cm at 77 K.
First, we evaluated the spin injection and detection efficiency for each dot by measuring the nonlocal spin valve

DRS ¼

signals, which is a barometer for the lateral spin transports,
with various probe configurations. Here, we fixed the voltage
probe to the middle dot (Py5). The spin injection was performed from one of the diagonally located dots (Py1, Py2,
Py3, or Py4). Since the Py5 is located at the shortest distancefrom each ferromagnetic dot, we only consider the spin
injector and detector (Py5) by neglecting the influence of theadditional ferromagnetic dots. In this case, we can adapt thefollowing basic equation for the nonlocal spin signal DRS
commonly used in a conventional lateral spin valve:27

P2 RFI RFD RN:
ðRN ðRFI þ RFD Þ þ 2RFI RFD Þðcoshðd=kN Þ þ sinhðd=kN ÞÞ þ R2N sinhðd=kÞ

(1)

Here, DRS corresponds to the overall change of the nonlocal
voltage divided by the excitation current. P is the spin polarization for the injector or detector. d is the center-center distance
between the injector and detector. kN is the spin diffusion
length for the nonmagnetic channel, in this case Cu. RFI, RFD,

and RN are the spin resistances for the injector, detector, andnonmagnetic channel. The spin resistance is defined by 2qk/
(S(1  P2)), where q and S are, respectively, the electricalresistivity and the effective cross section for the spin current.28
Figure 2 shows the spin valve signals for four different
configurations. The nonlocal spin signals exhibit clear
spin-valve effects corresponding to either parallel (high) or
antiparallel (low) state. Here, the negative and positive resistance changes correspond to the magnetization reversals forthe spin injector and the detector, respectively. Although thedesired distance between the injector and detector is fixed to
be 650 nm in all configurations, the magnitudes of the spinsignals are distributed from 0.57 mX to 0.70 mX. This difference may be due to the distributions of the lateral dimensions

FIG. 2. Nonlocal spin valve signals by using the Py5 detector with various
spin injectors measured at 77 K. The inset shows a schematic illustration of
the probe configuration and the obtained spin signal.

FIG. 3. (a) Nonlocal spin valve signal by using the Py1 injector and Py4
detector. (b) Nonlocal spin valve signal by using the Py1 injector and Py3
detector. Here, Py 5 is placed at the middle between Py1 and Py3.

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142121-3

Nomura, Ohnishi, and Kimura

FIG. 4. Schematic illustrations for two different spin diffusion models: (a)model A and (b) model B. (c) Schematic illustrations for the representative
probe configurations A, B, and C.

for the Py injectors and detectors, leading to the dispersionof the spin resistances for the injector and detector. Indeed,
we can confirm from the SEM image that the Py3 has a relatively small lateral dimension compared to other Py dots.
We also mention that the effective distance between theinjector and detector has a small difference, leading to the
distribution of the spin signal. Therefore, we believe that the
distribution in the spin signals is not by the material parameters such as uniformity and interface condition but by the dispersion of the geometrical parameters in the device.
In the above analysis, we neglected the influence of theother ferromagnetic dots on the spin current distribution.
However, the obtained spin signal was smaller than the previously reported device with a similar lateral dimension.17 Thisis because the spin current distribution is affected by other ferromagnetic dots. To clarify the influence of the multi spin
injectors and analyze the spin absorption efficiency due to thePy5, we evaluate the nonlocal spin valve signal with various
probe configurations. Here, we compare the nonlocal spin
valve signals between two configurations. One is the nonlocal
spin valve measurement using Py1 and Py4 and the other one
is that using Py 1 and Py 3. Here, it should be noted that in thelatter configuration, a middle ferromagnetic dot (Py5) islocated in between Py1 and Py4. Therefore, we expect thatthe significant reduction of the spin signal is expected becauseof the spin current absorption effect into Py5. As in Fig. 3(a),the obtained spin signal using Py1 and Py4 is 0.37 mX, whichis smaller than the value expected from the previous nanopillar lateral spin valve.17 Moreover, as in Fig. 3(b), we obtain
0.26 mX, which is comparable to the spin signal in Fig. 3(a)J. Appl. Phys. 120, 142121 (2016)

although a spin absorber is located at the center of the injector
and detector. These results imply that the spin current absorption exists in both configurations.
To survey the probe-configuration dependence of thespin signal, we propose two different models based on the
one dimensional spin diffusion model.29 In the first model(model A), we consider the spin absorption effect only in thespin current diffusion along the diagonal direction, as conceptually shown in Fig. 4(a). Here, we neglect the influenceof the middle spin absorber on the spin diffusion to Py2 andPy3. In this case, by using qPy kPy =qCu kCu ¼ 0:2, which isapproximately equal to the ratio of the spin resistance for the
ferromagnetic dot to that for the nonmagnetic Cu film,27 wecan calculate the spin signals DRAS ; DRBS , and DRCS for theconfigurations A, B, and C shown in Fig. 4(c). From the calculation, we obtained the following relationship of the spinsignals:
DRBS ¼ 1:41DRAS ;DRCS ¼ 0:25DRAS :Although the second relationship is reasonable, the first relationship is quite far from the experimental result, indicating
invalid situation of the proposed model. To improve these
discrepancies, we proposed another model (model B), in
which we consider the spin absorption effect due to the middle Py dot for all branches. By using the same values ofqPy kPy =qCu kCu as in model A, we obtain the following relationship for the spin signals:
DRBS ¼ 0:65DRAS ;DRCS ¼ 0:32DRAS :These values show reasonable consistency with the experimental results, indicating that the middle ferromagnetic dot
acts as a good spin absorber even in the nanopillar-based lateral spin valve because of its large lateral dimension of the
Py dot. However, because of the small spin resistance of thequasi-two-dimensional Cu film, the absorption efficiency issmaller than the conventional lateral spin valve.30
III. SPIN CURRENT ABSORPTION THROUGH SIDESURFACE

In order to increase the spin absorption efficiency, thespin resistance for the spin absorber should be much smaller
than the spin resistance for the nonmagnetic channel. Since
the spin resistance is inversely proportional to the cross section, increasing the effective cross section is one of the ways
for improving the absorption efficiency.28 By increasing thelateral dimension of the F dot or F/N junction size, one canreduce the spin resistance for the spin absorber.24 Indeed, in

FIG. 5. Schematic illustration for the
spin absorption measurement together
with the cross-sectional SEM image ofthe 100-nm-thick Py nanowire.

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142121-4

Nomura, Ohnishi, and Kimura

J. Appl. Phys. 120, 142121 (2016)

FIG. 6. Spin absorption effect in a conventional lateral spin valve. Nonlocal
spin valve signal (a) without and (b) with the 100-nm-thick Py dot. (c)Reduction of the spin valve signal as a function of the dot thickness. The
inset of (c) is the reduction of the spin valve signal as a function of the effective junction size of the spin absorber.

the experiment of Sec. II, we showed that the spin current
was effectively absorbed into the ferromagnetic dot with alarge lateral dimension. However, increasing the lateraldimension does not improve the density of the spin current
and is not suitable for nano-sized spin devices from the view
point of the device integration. To improve the absorption
efficiency, we focus on the spin absorption from the side surface, which is another way for increasing the effective crosssection for the spin current.
To investigate the spin current absorption from the sidesurface, we have fabricated the lateral spin valves with middle ferromagnetic dots with different dot thicknesses, as
schematically shown in Fig. 5. Here, we have prepared 20-,40-, and 100-nm-thick ferromagnetic middle dots. We
believe that the side surface of the thick ferromagnetic dot
was cleaned by the conventional Ar ion milling because of
the forward tapered cross section of the ferromagnetic dot asshown in Fig. 5(b). In addition, the deposition rate of the Cu
was 0.5 nm/s to obtain a better surface covering around the
Py dot.
The absorption efficiency for each device has been evaluated by comparing the spin signal to that without the middle
absorber. Figures 6(a) and 6(b) show the typical results ofthe spin current absorption. We have clearly observed thesignificant reduction of the spin signal. Moreover, as can beseen in Fig. 6(c), it was confirmed that the reduction of thespin signal increases by increasing the dot thickness. Thisimplies that the side surface of the middle ferromagnet acts
as an efficient spin absorber.24,25 To clarify the influence ofthe spin absorption from the side surface, we replot the ratioof the spin signal as a function of the effective cross sectionin the inset of Fig. 6(c). Here, the effective cross section is
the sum of the top surface and two side surface areas. A large
reduction of the spin signal was observed at S  0.02 lm2.
To understand this behavior, we may have to take into
account the influence of the geometrical disorder, which may
induce the additional spin-flip scattering, when the thicknessof the middle ferromagnetic dot increases. However, since
the influence of the geometrical scattering also increases
with increasing the thickness, we cannot distinguish the origin of the reduction.
To exclude the influence of the geometrically induced
scattering, we have developed a modified lateral spin valve
consisting of a T-shaped Cu channel shown in Fig. 7. Here,the spin absorber is placed under the branch of the Cu channel. Therefore, the spin current diffusing into the Py detector
is not affected by the geometrical disorder of the spin
absorber. Here, we have fabricated the modified lateral spin
valves with the different dot thicknesses, 10, 30, 60, 80, and
100 nm. The spin absorption efficiency is evaluated from thecomparison of the spin signal with and without the ferromagnetic dot.
Figures 8(a) and 8(b) show the spin signals with andwithout the ferromagnetic absorber, respectively. Here, thespin signal without the absorber is slightly smaller than thatin Fig. 6(a), indicating that the influence of the additional Cu
branch is small in the spin diffusion in the Cu channel.
However, we have clearly observed the reduction of the spinsignal in Fig. 8(b) by putting the Py dot in the branchbecause of the spin absorption effect. Moreover, as shown in
Fig. 8(c), the spin signal monotonically decreases by increasing the dot thickness. This is a strong evidence that the purespin current is efficiently absorbed from the side surface ofthe ferromagnetic dot similarly to the top surface.
Here, we analyze the spin absorption efficiency in themodified lateral spin valve. Based on the one dimensional
spin diffusion model, the spin signal DRS with the middle
absorber can be approximately calculated as follows:27,28

2

RSAbs

;


DRS 
RSCu RSCu ð1  coshðd=kCu ÞÞ þ 2 RSPy þ RSAbs sinhðd=kCu Þ

where RSPy ; RSCu , and RSAbs are the spin resistances for Py, Cu,
and the middle spin absorber, respectively. P is the spin polarization for the Py. d is the distance between the injector anddetector. It should be noted that in this kind of lateral spin

PRSPy

(2)

valve based on the metallic wires, RSCu is much larger than
RSAbs and RSF . Since the spin absorber is placed in the Cu
branch at a small distance from the intersection, we neglect
the spin relaxation in the Cu branch. In order to consider the

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142121-5

Nomura, Ohnishi, and Kimura

J. Appl. Phys. 120, 142121 (2016)

FIG. 7. Scanning electron microscopy
image of the modified lateral spin
valve together with the schematic illustration of the fabricated device.

FIG. 8. Spin absorption effects in a
modified lateral spin valve. Nonlocal
spin valve signal (a) without and (b)with the 100-nm-thick Py dot. (c)Reduction of spin valve signal as aneffective junction size of the Py-dot.

influence of the absorber thickness, we assume that the effective cross section for the spin resistance is given by
Stop þ 2Sside , where Sside is wCutdot, as schematically shown in
the inset of Fig. 8(c). Using the above assumption, we tried toreproduce the reduction of the spin signal observed in Fig. 8.
The fitted curve roughly reproduces the experimental results.
However, the reduction rate significantly increases at
t > 80 nm. The reason for this deviation is unclear at the
moment but further reduction from the theoretical calculated
value indicates that the side surface is an efficient current
absorber for the diffusive spin current. It should also be mentioned that the expanded one-dimensional spin resistor model
may be useful for more quantitative understanding.25,31
IV. CONCLUSION

We have investigated the spin absorption properties in
nano-pillar-based and nanowire-based multi-terminal lateralspin valves. Although the spin absorption efficiency in the
nano-pillar-type device was smaller than that in the conventional wire-type device, the absorption rate in the nano-pillar
device was increased by increasing the junction size similarly in the conventional devices. However, the spin absorber
had to have a large lateral dimension in order to maintain thelarge spin absorption efficiency. To obtain a large spin
absorption efficiency with a small lateral dimension, we
proposed the spin absorption effect from the side surfaces ofa thick ferromagnetic dot. In order to evaluate the spin

absorption efficiency through the side surface properly, a
modified lateral spin valve with a T-shaped nonmagnetic
wire has been proposed. We clearly demonstrated that the
spin absorption from the side surface was consistently
enhanced by increasing the junction area of the side surface.
ACKNOWLEDGMENTS

This work was partially supported by Grant-in-Aid for
Scientific Research on Innovative Area, “Nano Spin
Conversion Science” (26103002), that for Challenging
Exploratory Research (26630162) and that for Scientific
Research (S) (25220605).
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