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Sensors and Materials, Vol. 31, No. 10 (2019) 3007–3022
MYU Tokyo
S & M 1988

Magnetic Scattering in Ni Wires Fabricated on Ferroelectric
LiNbO3 Substrate for Magnetic Sensor Application
Ryo Nakamura,1,3 Shunya Saegusa,1,3 Satoru Suzuki,1 Aiko Nakao,1
Yuichi Utsumi,1 Takuo Ohkochi,2,3 Masaki Oura,3 Yukako Takizawa,4Tsunemasa Saiki,4 Taekhyeon Lee,5 Kab-Jin Kim,5 Keisuke Yamada,6Takeshi Ogasawara,7 and Akinobu Yamaguchi1,3*
1

Laboratory of Advanced Science and Technology for Industry, University of Hyogo,
3-1-2 Kouto, Kamigori, Hyogo 678-1205, Japan
2
Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
3
RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan
4
Manufacturing Technology Department, Hyogo Prefectural Institute of Technology,
3-1-12 Yukihira, Suma, Kobe, Hyogo 654-0037, Japan
5
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
6
Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University,
1-1 Yanagido, Gifu City, Gifu 501-1193, Japan
7
Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology,
Tsukuba, Ibaraki 305-8565, Japan(Received June 28, 2019; accepted September 30, 2019)

Keywords: magnetoresistance, heterojunction, magnetic domain structure, spin-dependent scattering,
multiferroic functional materials

We investigated the magnetoresistive property of a micrometer-scale Ni wire with a uniaxial
magnetic anisotropy induced by the formation of a heterojunction between a Ni layer and asingle-crystal lithium niobate (LiNbO3) substrate. We revealed that the domain structure canbe controlled by adjusting the wire alignment and that its magnetoresistance (MR) is dependent
on the magnetic domain structure as well as the reversal process. The introduction of aheterojunction is a crucial method of controlling the magnetic domain structure owing to theadditional generation of the magnetic anisotropy. This control of the magnetic domain structure
is very useful for investigating the fundamental physical mechanism and producing artificial
multiferroic functional materials and devices. The relatively large MR response observed intransport measurements alludes to the possibility that the spin-dependent scattering mechanism
occurs in the domain and domain wall.

1.

Introduction

The control of the domain structure, domain wall propagation, and magnetization reversal
is at the heart of magnetism; exchange interaction, crystalline anisotropy, demagnetizing field
control due to shape, exchange bias, and magnetostriction work to direct the magnetization
along the respective preferred directions and maintain balance among them, resulting in themagnetic domain structure being formed to minimize the total energy of the system. In*

Corresponding author: e-mail: yamaguti@lasti.u-hyogo.ac.jp
https://doi.org/10.18494/SAM.2019.2494
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 31, No. 10 (2019)

nanomagnetism and spintronics, this control of magnetism is of interest because they arestrongly associated with not only the fundamental magnetism but also magnetic device
applications. For example, nonvolatile magnetic random accesses memory and microwave
oscillators are expected to be developed as next-generation devices. In a confined artificial
magnet, a disciplined magnetic domain structure and magnetization switching properties can beachieved to some extent by nano/microfabrication.(1–8) In such an artificial magnet, lateral andvertical confinement often leads to special states, such as vortex(9–13) and antivortex domain
configurations,(14) which can be achieved using a strong magnetic shape anisotropy. The
exchange bias and magnetostriction also offer key techniques to control the magnetic domain
structure and its reversal characteristics.(15–22) The magnetization dynamics in these systems
have been studied by various techniques including time-resolved X-ray magnetic circulardichroism-photoemission electron microscopy (XMCD-PEEM),(23–25) Kerr microscopy,(26,27)
Brillouin light scattering (BLS),(28,29) and electrical detection techniques.(3,5,13,22,30–34)
Recently, attempts to fabricate artificial multiferroic materials with their functionalities
above room temperature have been focused on because the control of magnetic domain
structures and their magnetization dynamics using electric fields or strain that is electricallyinduced through the piezoelectric effect has the potential to decrease the power consumption ofdevices from the viewpoint of constituent materials.(35) One idea to create a novel multiferroic
material is given by introducing the concept of artificially fabricating a heterojunction composedof ferromagnetic and ferroelectric materials. In previous studies,(36,37) the piezoelectric effectwas demonstrated to modulate magnetic characteristics through the magnetoelastic effect ormagnetostriction. The competition between the shape magnetic anisotropy and the uniaxial
magnetic anisotropy induced by the heterojunction results in the formation of a specificmagnetic domain structure and the modulation of magnetization switching properties.(23,24)
For example, a stripe domain structure in a Ni wire whose longitudinal axis was perpendicular
to the X-axis of a lithium niobate (LiNbO3) substrate was spontaneously formed in the nearabsence of a magnetic field, whereas a single-domain state was formed in a Ni wire aligned
parallel to the X-axis direction of the LiNbO3 substrate. Thus, this finding may provide aclue to developing novel artificial multiferroic materials with their functionalities above room
temperature. Before the integration of artificial multiferroic materials, the magnetic properties
associated with the heterojunction should be unveiled to take advantage of the development ofapplications such as domain wall logic and magnetic sensors.
The heterojunction leads to a specific spin texture through the formation of domain walls ina stripe domain structure. Recently, the Dzyaloshinskii–Moriya interaction (DMI)(38,39) at theinterface has attracted much attention because it facilitates the stabilization of homochiral Néel
domain walls.(40) Thus, a domain wall is not only a unique object but also plays a significant
role in magnetization reversal and scattering properties. Here, we investigated the fundamental
properties of the domains and domain walls formed in the Ni wire fabricated on the singlecrystal lithium niobate (LiNbO3) Y-cut 128° substrate. In particular, we present a physicalinterpretation of the magnetoresistance (MR) of Ni wires with the stripe domain structure. The
role of the physical origin of the MR in the interpretation of our experiments is discussed indetail.

Sensors and Materials, Vol. 31, No. 10 (2019)

2.

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Materials and Methods

Ni micrometer-scale wires of 30 nm thickness were fabricated on a Y-cut 128° LiNbO3
substrate by an electron-beam lithography and lift-off process with magnetron sputtering. Afterthe formation of Ni wires, the wires were coated with a resist for electrode formation and baked
at 100 ℃ for 3 min using a hot plate in air ambient. Separately from the microfabrication,
25-nm-thick Ni continuous films deposited on SiO2/Si and Y-cut 128° LiNbO3 substrates wereprepared to evaluate their magnetization characteristics using a vibrating sample magnetometer(VSM: VSM-C7-10A, Toei Industry Co., Ltd., Tokyo). Figures 1(a)–1(c) show the magnetization
curves of the Ni films deposited on various substrates, namely, (a) SiO2/Si, (b) LiNbO3 asdeposited, and (c) LiNbO3 baked at 100 ℃ for 3 min using a hot plate, respectively, to confirm
whether that the baking treatment contributes to magnetism. As shown in Fig. 1(a), themagnetization curves are almost independent of the magnetic field direction. In contrast to
Fig. 1(a), the magnetization curves in Figs. 1(b) and 1(c) depend on the magnetic field direction,
enabling us to adequately recognize the existence of easy and hard magnetization axes. These

(a)

(b)

(c)
Fig. 1. (Color online) Magnetization hysteresis loops measured using vibrating magnetometer with 25-nm-thickNi film deposited on (a) SiO2/Si and (b) and (c) Y-cut 128° LiNbO3 substrates. All the Ni films were covered witha 1-nm-thick Au capping layer to prevent oxidization. Only sample (c) was baked at 100 ℃ by using a hot plate in
air ambient. The magnetic fields are applied parallel and perpendicular to the orientation flat (OF) direction of the
LiNbO3 substrate.

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Sensors and Materials, Vol. 31, No. 10 (2019)

results indicate that the uniaxial magnetic anisotropy in the Ni films deposited on the LiNbO3
substrate can be simultaneously induced.
By taking advantage of the uniaxial magnetic anisotropy induced from the substrate, we
controlled the magnetic domain structure and magnetization reversal properties. Next, wemeasured the wire width dependence of the MR. Figure 2(a) shows a typical schematic of
the MR measurement setup and system consisting of Ni wires and electrodes for the MR
measurement. A Ni wire is placed in the aperture between the conductive strip lines of thecoplanar waveguide (CPW) consisting of Cr (5 nm)/Au (80 nm). The wires prepared between
the CPW strip lines are w = 700 nm, 1 μm, 2 μm, 3 μm, and 5 μm in width and 100 μm in
length as shown in Fig. 2. Furthermore, we investigated the wire width dependence of the MR.
The ground-signal-ground (GSG)-type microwave probe is connected to the CPW electrode,and the MR is measured by the lock-in detection technique. The external magnetic field is
additionally applied in the substrate at tilting angles of θ = 0 and 90° from the longitudinal
axis of the wire aligned perpendicular and parallel to the orientation flat (OF) direction of the
LiNbO3 substrate. The OF direction is parallel to the X-axis direction of the LiNbO3 substrate.

(a)

(b)

(c)

Fig. 2. (Color online) (a) Schematic of the MR measurement setup. The Ni wire is placed in the aperture between
the conductive strip lines of the CPW consisting of Cr/Au. The GSG-type microwave probe is connected to the
CPW and the MR is measured by the lock-in amplifier detection technique. The electrode gap is 30 µm. Typical
XMCD-PEEM images of the Ni wires aligned (b) perpendicular and (c) parallel to the OF direction.

Sensors and Materials, Vol. 31, No. 10 (2019)

3011

In this study, we prepared the systems in which the Ni wires were allocated perpendicular andparallel to the OF direction. We also focused on the basic magnetic response with respect tothe field applied parallel or perpendicular to the Ni wire. All these experimental measurements
were performed at room temperature.

3.

Results and Discussion

In our previous study using XMCD-PEEM at the BL17SU and BL25SU beamlines
of SPring-8,(23–25) the stripe domain and single-domain structures can be formed in the
micrometer-scale Ni wires aligned perpendicular and parallel to the OF direction of the LiNbO3
substrate, respectively. Figures 2(b) and 2(c) show the typical XMCD-PEEM images of stripe
domain and single-domain structures in the Ni wires aligned perpendicular and parallel to
the OF direction of the LiNbO3 substrate, respectively. The length of the Ni wire is 30 μm.
To investigate the magnetization reversal process, we measured the MR. Figure 3 shows the
typical resistivity measurement results of the 700-nm-wide Ni wire when the magnetic fields
were applied parallel and perpendicular to the longitudinal axis of the wire. Here, the Ni wire
was directed perpendicular to the OF direction. In the MR measurements using the CPW
electrode connected to the GSG probe, it is difficult to completely remove artifact effects
associated with the contact resistance because of quasi four-probe measurement using the lockin detection and prober system. Therefore, the absolute value of resistivity is not completely
correct. In this study, we evaluated the MR ratio in the following. Figure 4 shows the MR
ratio measurement results as a function of an external magnetic field applied parallel andperpendicular to the Ni wires with widths of 700 nm, 2 μm, and 5 μm in plane. Here, the MR
ratio is defined as MR ratio (%) = [R(H) − R(H0)] / R(H0) × 100, where R(H) and R(H0) denote

Fig. 3. (Color online) Resistivity of Ni wire aligned perpendicular to the uniaxial magnetic anisotropy inducedby the heterojunction as a function of magnetic field applied parallel or perpendicular to the wire. The width of thewire is 700 nm.

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Sensors and Materials, Vol. 31, No. 10 (2019)

Fig. 4. (Color online) MR ratio as a function of the strength of the external magnetic field, Hext, applied paralleland perpendicular to the longitudinal axis of the Ni wires with widths of (a, b) 700 nm, (c, d) 2 µm, and (e, f) 5 µm.
The electric current I flows along the wires. The Ni wires are aligned parallel and perpendicular to the uniaxial
magnetic anisotropic field HA. There are four combinations for the MR ratio measurements: [1] I  H ext & I ⊥ H A , [2]I ⊥ H ext & I ⊥ H A, [3] I ⊥ H ext & I  H A , and [4] I  H ext & I  H A .

the MRs at the applied magnetic fields of H and H0 , respectively. Here, H0 = 0. The red andblack lines correspond to the MR ratio curves measured when the magnetic fields were applied
parallel and perpendicular to the Ni wire, respectively. As is well known, when the magnetic
field exceeded the coercive force, the MR was observed to be almost independent of the appliedSensors and Materials, Vol. 31, No. 10 (2019)

3013

magnetic field except the forcing effect. Below the coercive force, the MR varies with (cosθ)2,where θ is the angle between the magnetization and the electric current. The MR behaviors
are well known as the anisotropic MR (AMR) effect. The increase and decrease in MR ratio
correspond to the increase in magnetization component directed parallel and perpendicular to
the electric current I, respectively. Therefore, when the magnetic field (Hext) is applied parallelto the Ni wire aligned perpendicular to the OF direction of the LiNbO3 substrate (X-axis of
LiNbO3 crystal) in Fig. 4(a) (corresponding to the red MR curve, I  H ext & I ⊥ H A), the MR
ratio is minimum near zero magnetic field, indicating that stripe domain structures are formed.
Here, HA is the uniaxial magnetic anisotropy induced by the heterojunction and directed along
the OF direction. The MR ratio is maximum in the near absence of a magnetic field when themagnetic field was applied perpendicular to the Ni wire, as shown in Fig. 4(a) (corresponding
to the black MR curve, I ⊥ H ext & I ⊥ H A). In this case, when the magnetization is saturated
by a strong external magnetic field and directed to the external magnetic field perpendicular to
the wire, the MR is low. With decreasing external magnetic field, the stripe domain is formed,
and the magnetization component parallel to the electric current increases, resulting in theincrease in MR. In the near absence of the external magnetic field, the stripe domain structureis expected to be spontaneously formed by the competition between the magnetic shapeanisotropy and the magnetic anisotropy induced by the heterojunction in the Ni wire aligned
perpendicular to the X-axis of the LiNbO3 substrate. In contrast, when the Ni wire was aligned
parallel to the OF direction, the MR ratio behaviors shown in Fig. 4(b) are very different fromthe results shown in Fig. 4(a). This difference is attributed to the fact that the single-domain
structure is formed in the Ni wire aligned parallel to the OF direction of the substrate. The MR
ratio behaviors shown in Fig. 4(b) can be understood using the typical magnetization reversal
model with rotation magnetization and domain wall displacement.
To understand the magnetization reversal properties of the stripe domain and single-domain
structures, micromagnetic simulation is performed.(41) Here, we analyzed a 30-nm-thick Ni
wire with unit cells (size: 8 × 8 × 30 nm3). To clarify the magnetic basic behaviors of thesystem with the competition between the shape magnetic anisotropy and the uniaxial magnetic
anisotropy induced by the heterojunction, the calculation model of 5 μm length and 1 μm width
is systematically used to shorten the time for the calculation by understanding the physics. The
material parameters of Ni, namely, the saturation magnetization Ms of 0.6 T and the exchange
stiffness constant A of 0.5 × 10−11 J/m, are adopted in this study. We assumed that the magnetic
anisotropy derived from the heterojunction between the Ni wire and the LiNbO3 substrate was
Ku = 5.7 kJ/m3. We set the Gilbert damping constant α = 0.01, 0.1, and 1. The basic physicalmechanism and magnetic properties in the system can be semiquantitatively evaluated, althoughdiffering in detail.
We calculated the four alignments corresponding to the experimental MR measurementalignments. Figures 5(a) and 5(b) show the magnetization reversal processes of the stripe
domain structure formed at zero magnetic field in the Ni wire aligned perpendicular to theuniaxial magnetic anisotropy when the external magnetic fields are swept parallel (case [1]) andperpendicular (case [2]) to the longitudinal axis of the Ni wire, respectively. The magnetic fielddependences of magnetization components are also shown. These results can quantitatively

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Sensors and Materials, Vol. 31, No. 10 (2019)

(a)

(b)

Fig. 5. (Color online) Schematic illustrations of the micromagnetic simulation setup in the cases (a) [1]I  H ext & I ⊥ H A and (b) [2] I ⊥ H ext & I ⊥ H A. A uniaxial magnetic anisotropic field, HA, is induced along the
OF direction. The OF direction is parallel to the X-axis of the LiNbO3 substrate. The calculated magnetization
distributions at magnetic fields of 0.8, 4, 8, 16, 24, 32, 40, and 80 kA/m are shown. The rainbow color indicatesthe in-plane component of magnetization. The summed perpendicular magnetization component mx is shown as afunction of the applied magnetic field under the assumed damping constants of α = 0.01, 0.1, and 1.

explain the MR behaviors. In a similar way, Figs. 6(a) and 6(b) show the simulation results
obtained when the Ni wire is aligned parallel to the uniaxial magnetic anisotropy (cases [4] and [3]).
As a result, all the demonstrated micromagnetic simulation results are in qualitatively good
agreement with the experimental results.
As described in our previous studies,(23,24) the comparison of MRs shown in Fig. 4 reveals
that each saturation field is almost independent of the wire width. We reconfirm that theuniaxial magnetic anisotropy is derived from the heterojunction. Next, we examine whether

Sensors and Materials, Vol. 31, No. 10 (2019)

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(a)

(b)

Fig. 6. (Color online) Schematic illustrations of the micromagnetic simulation setup in the cases (a) [4]I  H ext & I  H A and (b) [3] I ⊥ H ext & I  H A. A uniaxial magnetic anisotropic field, HA, is induced along the
OF direction. The OF direction is parallel to the X-axis of the LiNbO3 substrate. The calculated magnetization
distributions at magnetic fields of 0.8, 4, 8, 16, 24, 32, 40, and 80 kA/m are shown. The rainbow color indicates thein-plane component of magnetization. The summed perpendicular magnetization component δmy/Ms is shown as afunction of the applied magnetic field under the assumed damping constants of α = 0.01, 0.1, and 1.

the MR ratio is dependent on the wire width. Here, we define the difference in MR ratio, ΔMR
ratio, as ΔMR ratio (%) = [|MR(HR) − MR(HSAT)|], where MR(HR) is the MR obtained at themagnetic field HR. In typical cases, MR(HR) is maximum or minimum in the near absenceof the magnetic field HR, while MR(HSAT) becomes constant in the case of application of a
sufficient magnetic field HSAT enough to saturate the magnetization. The value is strongly
dependent on the angle between the magnetization and the electric current I. This MRchange is basically derived from the AMR effect. Here, MR(H0) is defined as the MR in theabsence of a magnetic field, H0 ~ 0 kA/m. The estimated ΔMR ratios (%) of the 4 cases are
as follows: [case 1: ΔMR1] I  H ext & I ⊥ H A, [case 2: ΔMR2] I ⊥ H ext & I ⊥ H A, [case3: ΔMR3] I  H ext & I  H A, and [case 4: ΔMR4] I ⊥ H ext & I  H A, where I is the electric
current flowing in the Ni wire. Hext and HA are respectively the external magnetic field andthe uniaxial magnetic anisotropy field, which is induced parallel to the X-axis of the LiNbO3
substrate. Moreover, we define ‘Total ∆MR ( ⊥ H A )’ and ‘Total ∆MR (  H A )’ as the maximum
differences in MR ratio obtained by subtracting the MR ratios at which the magnetization
is directed parallel and perpendicular to the electric current I, respectively. Here, ‘Total

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Sensors and Materials, Vol. 31, No. 10 (2019)∆MR ( ⊥ H A ) ’ and ‘Total ∆MR (  H A ) ’ are obtained when the uniaxial magnetic anisotropy is
directed perpendicular and parallel to the longitudinal axis of the Ni wire, respectively. ‘Total∆MR (  H A ) ’ is nearly equal to ΔMR4. The evaluated values of ΔMR and Total ΔMR aresummarized in Fig. 7. In all the cases, the ΔMR ratios tend to saturate after increasing with thewire width. We found a clear anisotropic behavior: the ΔMR ratio is strongly dependent on the
direction of the uniaxial magnetic anisotropy induced by the heterojunction. This is attributed
to the fact that the resistance change is significantly affected by the domain structure andscattering process.
In particular, note that the magnetization component differences shown in Figs. 5(a), 5(b),and 6(b) are the same. The AMR differences in the cases of Figs. 5(a), 5(b), and 6(b) are
expected to be the same; however, the experimental results are not consistent with the behaviors
anticipated from the micromagnetic simulation results. These results indicate that the spindependent scattering derived from the stripe domain structure and domain walls contribute to
the MR behaviors shown in Figs. 3 and 4. Therefore, the study on the heterojunction between
ferromagnetic and ferroelectric materials provides clues to understanding the fundamental
physics induced by the interface and controlling the magnetic domain structure, pinning,
switching, and anisotropy, resulting in the modulation of the electric and magnetic responses ofthe devices.
Next, we reconsider the MR ratio change. The MR, R(H) = ρ(H)L/S, where ρ(H), L, andS are the resistivity when the external magnetic field H is applied, length, and cross-sectional
area of the wire, respectively. Therefore, the MR ratio should be independent of the wiredimensions. The relationship is given by MR ratio (%) = [ρ(H) − ρ(H0)] / ρ(H0) × 100%. The

Fig. 7. (Color online) Wire width dependence of MR ratio differences, ΔMR ratio. [ΔMR1] I  H ext & I ⊥ H A, [ΔMR2]
I ⊥ H ext & I ⊥ H A, [ΔMR3] I  H ext & I  H A , and [ΔMR4] I ⊥ H ext & I  H A , where I is the electric current flowing
in the Ni wire. ‘Total ∆MR ( ⊥ H A ) ’ and ‘Total ∆MR (  H A ) ’ as the maximum differences in MR ratio obtainedby subtracting MR ratios at which the magnetization is directed parallel and perpendicular to the electric current,
respectively.

Sensors and Materials, Vol. 31, No. 10 (2019)3017

ΔMR ratio (%), which is defined as the difference between the maximum and minimum MR
ratios, should also be independent of the wire dimensions. In fact, as shown in Fig. 7, theΔMR ratio (%) increases with the wire width in all the cases. Before discussing this behavior,
we observe that the ΔMR ratio (%) of the case [ΔMR4] seems to saturate as the wire width
increases. The AMR of the single-domain state is expected to contribute to the saturation
value. To simplify the observed phenomena, we assume that the stripe domain structure
consists of series-connected single domains and domain walls as shown in Fig. 8. Then, we
n × ∆MR 4 + ( n − 1) × RDW ~ n × ( ∆MR 4 + RDW ), where n is thedefine that the ∆MR ratio ( % ) =number of single domains directed perpendicular to the longitudinal axis of the wire and R DW isthe resistance derived from the domain wall. This approximation is the series resistance circuit
model. In addition, we approximate that R DW is sufficiently smaller than ΔMR4. As a result,here, we approximately calculate n as n~ΔMR ratio (%) / ΔMR4.
In this study, we also assume that the MR ratio is independent of the direction of the uniaxial
magnetic anisotropy from the heterojunction for simplicity. We should consider that the stripe
domain structures and their resistivities obtained at the remaining state do not completely matchin the absence of the magnetic field as shown in Figs. 4 and 5. On the basis of the prerequisite,
we estimate the number of domains n by dividing ‘Total ∆MR ( ⊥ H A )’, ΔMR1, and ΔMR2 by
ΔMR4 as shown in Fig. 9.
In our previous studies,(23,24) the domain widths estimated using the XCMD-PEEM images
are well known to be in good agreement with those calculated by the micromagnetic simulation.
This result indicates that the domain width is almost proportional to the wire width and that thedomain size is about 75% of the wire width.(23,24) In this study, the electrode gap L is 30 μm,
and the domain size can be estimated. Then, the number of domains in the remaining state canbe evaluated as n ~ L / (0.75w). The fitting curve is drawn as the red solid line in Fig. 9. The

Fig. 8. (Color online) Schematic image of the coordinate system in the Ni wire. The domain structures of 0.5and 2.0-µm wide Ni wires were calculated by micromagnetic simulation.

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Fig. 9.

(Color online) Wire width dependence of MR ratio differences, ΔMR ratio.

trend agrees with the experimental results. However, as the width decreases, the disagreement
becomes larger. This result indicates that either the numerator is small or the denominator
ΔMR4 is large. ΔMR4 is the total AMR difference from the single-domain state. Therefore, theconsequence is to assume that the numerator is small. The result is attributable to the domain
structure formation and its resistivity property. The domain structure can be formed using thecompetition between the magnetic shape anisotropy KS and the uniaxial magnetic anisotropy
KU directed perpendicular to KS as schematically shown in Fig. 8. KU is basically fixed when
the interface or heterojunction is formed, whereas KS is dependent on the wire shape. As thewire width becomes smaller, KS becomes larger and the magnetization tends to align along
the major axis of the wire owing to the strong shape anisotropy, resulting in an unstable 180°
domain structure and magnetization that tends to tilt, as shown in Fig. 8, because the projection
component of the magnetic anisotropy in the minor axis direction of the wire is the origin of
domain structure formation. Consequently, the MR ratio difference decreases with decreasing
wire width as shown in Fig. 7. The result is one of the causes of the data fitting discrepancy
seen in the narrow areas in Fig. 9. The other reason is that the domain wall width is notconsidered in the fitting curve, and the number of domains is estimated to be large, yielding thediscrepancy.
In the discussion, we reconsider the contribution of the domain wall resistance. As shownin Fig. 4, the difference between the MR behaviors of the cases [1] I  H ext & I ⊥ H A and[2] I ⊥ H ext in the presence of the stripe domain structure is clearly seen. The difference
increases with the wire width. To explain the giant MR (GMR) effect, Valet and Fert described
the transport properties of current perpendicular to the plane (CPP) multilayers by startingwith a Boltzmann equation.(42) They took the spin diffusion length into account and also
included both volume and interface spin-dependent scattering. Their model is very helpful forunderstanding the physical process in the CPP-GMR effect. The theoretical and experimental

Sensors and Materials, Vol. 31, No. 10 (2019)3019

reports demonstrate that the MR is inversely proportional to the ferromagnetic layer thickness.
However, the description cannot be applied as it is suitable in the GMR effect because thecorresponding ferromagnetic layer thickness and domain length in this study are much larger
than the assumed spin relaxation length. Thus, the relatively large MR response observed intransport measurements alludes to the possibility that the spin-dependent scattering mechanism
in domains and domain walls occurs.(40,43–48) The heterojunction structure composed offerromagnetic and ferroelectric layers provides a crucial key to investigating the fundamental
physical mechanism and producing artificial multiferroic functional materials and devices.
According to the theory of Levy and Zhang,(44) the domain wall resistivity arises from the
mixture of resistivities in two spin channels. Here, β is defined as β = ρ0↑ / ρ0↓ , where ρ0↑ andρ0↓ denote the spin-up and spin-down channels, respectively. For current-in-wall (CIW) andcurrent-perpendicular-to-wall (CPW) geometries, each resistivity ratio is described by thefollowing formula:
∆ρCIP

ρ0

2

ξ 2 ( β − 1)
,
=
5
β

2
∆ρCPW ξ 2 ( β − 1)  10 β 
=
3 +
,
ρ0
5
β 
β + 1 (1)(2)

where ξ = π  2 k F / 4mJ δ DW , with , kF, m, and J being the Planck constant divided by 2π, theFermi wave velocity, the electron mass, and exchange splitting, respectively. The domain wall
width δDW is given byA,Kδ DW = π(3)where A and K are the exchange stiffness constant and magnetic anisotropy energy, respectively.
∆ρCPW

ρ0

∝

1

δ DW

∝K

(4)

We note that the resistivity ratio described in Eqs. (1)−(3) is inversely proportional to δDW
and proportional to the magnetic anisotropy. This means that the resistivity ratio is inversely
proportional to δDW or is proportional to K in the presence of domain walls. In our system,
the whole magnetic anisotropy of the system is composed of KS and KU induced by theheterojunction. Considering the stripe domain formation case, since the magnetic anisotropic
directions are orthogonal, we should consider the total effective magnetic anisotropy K forthe domain wall stability, which is determined by the balance between the shape magnetic
and uniaxial magnetic anisotropies induced by the heterojunction. The projection component

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Table 1
Relationships among w, KS , KU, K, and δDW.
Wire width, w
narrow
→
wide
large
→
small
KS
constant→
constant
KU
K
small
→
large
large
→
small
δDW

K of the total magnetic anisotropy KU + KS to the minor axis of the wire is the origin of theformed stripe domain structure. As shown in Fig. 8, the projection component is KU. Here,KU is uniformly applied along the X-direction of the LiNbO3 substrate, that is, KU is constant.
In this study, the length and thickness of the Ni wires are fixed. The wire width w plays asignificant role in varying KS. As w increases, KS decreases.(49) Then, K increases with w. The
relationships associated with w, KS, KU, K, and δDW are shown in Table 1.
As shown in Fig. 8, we found that the domain wall width decreases with increasing wire
width. The MR ratio difference behavior, which increases with the wire width, between cases[1] and [2] in Fig. 4 suggests that the domain wall resistance might contribute the MR ratio
difference.

5.

Conclusions

The relatively large MR responses of Ni wires fabricated on single-crystal lithium niobate
LiNbO3 are measured at room temperature. In particular, we found that the MR characteristics
are significantly dependent on the wire alignment and direction of an external magnetic field.
The MR behaviors originate from the internal domain structure. The stripe domain or singledomain structure can be formed by controlling the wire alignment to the X-axis of LiNbO3.
The competition between the magnetic shape anisotropy and the uniaxial magnetic anisotropy
derived from the heterojunction plays a significant role in controlling the domain structure.
The heterojunction between the Ni layer and the LiNbO3 substrate can induce the uniaxial
magnetic anisotropy directed parallel to the X-axis of the LiNbO3 substrate, while the uniaxial
magnetic anisotropy is not induced in the Ni layer deposited on the SiO2/Si substrate. The
heterojunction between the Ni layer and the LiNbO3 substrate enables the formation of the
stripe domain structure in Ni wires with various widths. The difference in MR ratio increases
with the wire width. The width dependence of the MR ratio difference with the formation of
the stripe domain structure can be qualitatively explained using the series resistor circuit model.
The discrepancy between the fitting and experimental data is considered to be the possible
contribution of the domain wall resistance. This issue might be controversial for further study.
Our multiferroic system with the heterojunction might provide a clue to investigating theessential domain wall resistivity. Finally, this investigation demonstrated that the MR could beenhanced by the formation of a stripe domain. This significant increase in MR ratio sheds lighton developing sensor applications using an artificial multiferroic system.

Sensors and Materials, Vol. 31, No. 10 (2019)3021

Acknowledgments
We thank Professor M. Shima of Gifu University for the measurement of magnetization
hysteresis loops by VSM at Gifu University, Japan. This work was supported in part by JSPS
Grants-in-Aid for Scientific Research B (No. 17H02755), JSPS Grants-in-Aid for Scientific
Research C (No. 19K03757), JSPS Grants-in-Aid for Young Scientists A (No. 17H04795), andthe Iketani Science and Technology Foundation. The experiments at the BL25SU and BL17SU
beamlines of SPring-8 were performed with the approval and support of the Japan Synchrotron
Radiation Research Institute (JASRI, Proposal Nos. 2013B1735, 2014B1398, 2016A1252, and2016B1305).

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