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# Effect of Magnetic Co–CoO Particles on the Carrier Transport in Monolayer Graphene

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ISSN 1063-7834, Physics of the Solid State, 2020, Vol. 62, No. 2, pp. 368–377. © Pleiades Publishing, Ltd., 2020.
Russian Text © The Author(s), 2020, published in Fizika Tverdogo Tela, 2020, Vol. 62, No. 2, pp. 316–325.
Effect of Magnetic Co–CoO Particles on the Carrier Transport
in Monolayer Graphene
J. A. Fedotovaa, A. A. Kharchankaa, *, A. K. Fedotova, M. V. Chichkovb, M. D. Malinkovichb,
A. O. Konakovc, S. A. Vorobyovac, J. V. Kasiuka, U. E. Gumiennika, M. Kulad,
M. Mitura-Nowake, A. A. Maximenkoe, J. Przewoźnik f, and Cz. Kapusta f
a Institute for Nuclear Problems, Belarusian State University, Minsk, Belarus
b National University of Science and Technology “MISiS,” Moscow, Russia
c Research Institute for Physical Chemical Problems, Belarusian State University, Minsk, Belarus
d Franciszek Górski Institute of Plant Physiology, Polish Academy of Sciences, Krakow, Poland
e Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland
f Department of Solid State Physics, Faculty of Physics and Applied Computer Science, AGH University of Science and
Technology, Krakow, Poland
*e-mail: XaaTM@mail.ru
Received September 17, 2019; revised September 17, 2019; accepted September 24, 2019
Abstract—Electrodeposition of cobalt on monolayer graphene synthesized by chemical vapor deposition pro-
duces Co–CoO/graphene composite structures, which is accompanied by increases in the electrical resis-
tance and magnetoresistance. We show that the observed magnetoresistance effect is caused by two compet-
ing contributions: negative (NMR) and positive (PMR) magnetoresistance. In weak magnetic fields, the
NMR is described by quantum localization correction to the Drude model of conductivity in graphene. The
enhancement of PMR observed in strong magnetic fields is related to the Lorentz mechanism in Co–CoO
particles.
Keywords: graphene, cobalt, cobalt oxide, carrier transport
DOI: 10.1134/S1063783420020134
1. INTRODUCTION
Fabrication and studying of magnetic and magne-
toresistive graphene-based composite structures is a
highly relevant problem, because it opens new per-
spectives for their use in magnetic tunneling transi-
tions, spin valves and filters, magnetoresistive memory
devices, and other spintronic elements [1–3]. These
kinds of structures can be successfully fabricated by
depositing particles or layers of various ferromagnetic
materials (e.g., Co and Ni) onto graphene [2, 4]. We
note that investigation of specific characteristic of
deposition and agglomeration of metallic particles
deposited on graphene is one of the issues related to its
prospective use in electronic devices since requires to
overcome the difficulty of making low-resistance
ohmic contacts to the graphene surface.
To date, there have been relatively few experimen-
tal and theoretical studies on the magnetic and galva-
nomagnetic properties of structures composed of a
ferromagnetic metal and graphene such as Co
nanoparticles or isolated Co islands deposited on
graphene synthesized by chemical vapor deposition
(CVD) [1, 4, 5]. Using X-ray photoelectron spectros-
copy and magnetic measurements, these studies
showed that the deposited cobalt particles were mark-
edly oxidized at the surface and often represented a
structure of the Co core–CoO shell type. Neverthe-
less, electrochemical deposition produces good (bar-
rier-free) ohmic electrical contacts, as was confirmed
in [5]. Among different mechanisms of low-tempera-
ture carrier transport and magnetotransport in pure
graphene, the interference mechanism is typically
used within the theory of quantum corrections to the
Drude model of conductivity subject to the condition
of weak localization [6–8]. Another conductivity
mechanism frequently used in this respect is the vari-
able-range hopping model within the Mott model [9],
Efros–Shklovsky [10] model (the case of zero mag-
netic field), and Mikoshiba [11] and Altshuler–
Aronov–Khmelnitsky [6] models for carrier transport
in a nonzero magnetic field. For composite metal–
graphene structures with a metal shunting, we cannot
eliminate the presence of the extraordinary magneto-
resistance effect observed in high transversal magnetic
fields [12].
With electrochemical deposition, nucleation of
metal nanoparticles was shown to take place specifi-
GRAPHENES
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
EFFECT OF MAGNETIC Co–CoO PARTICLES ON THE CARRIER TRANSPORT 369
cally in regions with morphological alterations,
including those caused by residual copper fragments
that formed after transferring a graphene sample onto
a Si/SiO2 substrate [13].
The findings of previous studies thus suggest that
the situation at the metal/graphene interface and
defectiveness of the initially obtained graphene play a
key role in determining the carrier transport and mag-
netotransport characteristics of composite
metal/graphene structures, especially at low tempera-
tures.
The aim of this work is to investigate the interrela-
tion between the electric and magnetic properties of
composite structures consisting of a ferromagnetic
metal and graphene that are fabricated by electro-
chemical deposition of cobalt nanoparticles onto
monolayer CVD graphene, since this will enable us to
identify the effects that cobalt islands have on carrier
transport in zero and nonzero external magnetic fields.
2. EXPERIMENTAL TECHNIQUES
AND SAMPLE PREPARATION
Graphene was synthesized on copper foil by CVD
using a PlanarTech G2 unit. Acetylene was used as a
carbon precursor, and hydrogen was fed into the reac-
tor alongside acetylene for dilution; the ratio of gas-
eous components was C2H2 : H2 = 1 : 4. The process
was carried out at 1040°C at a pressure of 6 Torr. Syn-
thesized graphene was transferred using polymethyl-
methacrylate (PMMA). For this, a 4% solution of the
polymer in anisole was applied on a copper
foil/graphene sample inside a spin coating system that
was operated at a rate of 1500 rpm. The resulting sam-
ple was baked in an oven at a temperature of 150°C.
Copper foils were subsequently etched in an aqueous
ferric chloride solution. The resulting PMMA film was
rinsed twice with deionized water and placed on a sub-
strate. The film was dried, while in the spin coater, at
a rate of 3000 rpm, then heated at a temperature of
120 °C in order to remove folds. The PMMA layer was
dissolved away in acetone.
Cobalt nanoparticles were deposited onto
graphene from a solution containing 1.25 g/L CoSO4 ·
6H2O and 0.064 g/L NaCl using a PI-50-1.1 potentio-
stat coupled to a PR-8 programming unit. Depositions
were performed in the pulse reverse mode, a con-
trolled-current technique, at a cathodic current den-
sity of 2.5 mA/cm2 (pulse duration, 5 s) and anodic
current density of 1.25 mA/cm2 (pulse duration, 2 s);
the total deposition time was 30 s.
Raman spectroscopy was carried out on a Nicolet
Almega XR Raman microscopy system equipped with
Omnic 8 software (Thermo Fisher Scientific, USA).
The laser excitation wavelength was 532 nm, and the
laser power was around 0.1 W. Raman spectra were
collected in the range of 400 to 4000 cm–1. The slit
width was 2.5 μm, and the working distance was deter-
mined by a 100× objective of the microscope. Sixty-
four spectral acquisitions were carried out. Samples
were placed on the microscope stage and a laser beam
was focused at a specimen surface. Each sample was
investigated in three different regions.
Scanning electron microscopy (SEM) imaging was
performed using a Vega 3 instrument (Tescan) in the
secondary electron detection mode, with the acceler-
ating voltage being 30 kV. Atomic force (AFM) and
magnetic force (MFM) microscopies were carried out
on a XE-120 microscope (Park System Corporation)
in the contactless mode. For these investigations, we
used a MAGT cantilever with a coated tip (a 40 nm
thick CrCo layer) with a radius of curvature <40 nm
(AppNano). Before use, the tip was magnetized along
its vertical axis in a magnetic field with B = 0.5 T.
MSM imaging followed the surface topography imag-
ing and was performed at a probe-to-surface distance
of 200 nm.
Magnetic measurements were carried out in the
temperature range of 2–300 K in the magnetic fields
up to 9 T using the vibrating-sample magnetometer
option of a Physical Property Measurement System
(Quantum Design).
Temperature and magnetic field dependences of
electrical resistivity R(T, B) were measured by the
four-point probe method in the temperature range of
2 to 300 K and in a transversal magnetic field with
magnetic flux density B up to 8 T using a noncryo-
genic measuring system (Cryogenics Ltd) on the basis
of a closed-cycle refrigerator. In studying ρ(T, B) and
RH(T, B) dependences, current through a sample was
controlled and measured using a Keithly 6430 appara-
tus, which enabled us to measure the electrical resis-
tance in the range of 100 μΩ to 10 GΩ with an accu-
racy of at least 0.1%. The temperature of samples was
measured using LakeShore thermal diodes calibrated
to an accuracy of 0.0005 K and having a precision of
0.001 K, which enabled us to stabilize and measure the
temperature using a LakeShore 331 temperature con-
troller. The accuracy of resistivity measurements and
the Hall coefficient was at least 5%, with the main fac-
tors contributing to the experimental error being inac-
curacies in the measurements of the sample geometri-
cal dimensions, width of probable electrical contacts,
and distance between them.
3. RESULTS AND DISCUSSION
The structure of samples of CVD graphene with
deposited Co nanoparticles (Co–Gr/SiO2) was inves-
tigated using Raman spectroscopy, and the results are
shown in Fig. 1.
Overall, the characteristics of our Gr/SiO2 and
Co–Gr/SiO2 samples are typical of monolayer
graphene, as was confirmed by a number of methods.
The number of graphene layers was determined by
evaluating the shape and measuring the width of the
370
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
FEDOTOVA et al.
2D peak [14], as well as by using the intensity ratio
between the 2D and G peaks [15, 16]. The 2D band in
the Raman spectra of the Gr/SiO2 and Co–Gr/SiO2
samples represents a Lorentzian with a full width at
half-maximum of ≈40 cm–1, which are the features
typical of monolayer graphene [14]. On the other
hand, the intensity ratio for Gr/SiO2 and Co–Gr/SiO2
samples is on average I2D/IG > 2, another indicator of
monolayer graphene [15, 16]. At the same time, the
sample contains regions (Fig. 1а, curve 2) with char-
acteristics of bilayer graphene: the intensity ratio is
I2D/IG = 1.595 (for bilayer graphene, 1 < I2D/IG < 2),
and the 2D peak is broader. The intensity ratio
between D and G peaks (i.e., ID/IG) enables us to esti-
mate the amount of defects in a graphene sample. For
the Gr/SiO2 sample, we have the intensity ratio ID/IG<
0.2, a value typical of large-area polycrystalline films
with a fairly decent sample quality [17]. The Co–
Gr/SiO2 sample exhibits a slight increase in the ID/IG
ratio, but can still be considered as having a fairly
decent quality.
Additionally, we estimated the number of graphene
layers using the relationship ωG = 1581.6 + 11/(1 +
n1.6 ), where ωG is the G band position and n is the
number of graphene layers [18]. The position of G
band in the spectra of Co–Gr/SiO2 sample agrees well
with the theory, which additionally corroborates that
our samples are monolayer graphene with inclusion of
bilayer regions. For the Gr/SiO2 sample, however, the
G band has a lower Raman shift (i.e., 1577 cm–1),
which is out of the range predicted by the theory, and
this deviation was attributed to changes in the carrier
concentration [19]. Deposition of cobalt particles
value for the layer Hall coefficient RHd (which is neg-
ative) to increase. The latter was measured at room
temperature in a magnetic field B = 1 T, and the values
were 126 and 485 m4/C for the Gr/SiO2 and
Co‒Gr/SiO2 samples, respectively.
A surface topography SEM image of the Co–
Gr/SiO2 sample is shown in Fig. 2a. The analysis of
contrast features in the image showed that the Co
deposition produced mainly isolated particles with a
size of around 50 nm and agglomerates (size up to
500 nm) consisting of prolate particles. The regions
with a bright contrast in the image may correspond to
completely or partially oxidized particles, and the lat-
ter are likely represent the Co core–CoO shell type
structure, as was proven in [5]. The results of SEM
agree well with AFM images (Fig. 2b). These AFM
images show that the particles and their agglomerates
are not spherical, because their size in the image plane
exceeds their height by 30–40%. Contrast features
seen in MFM images (Fig. 2c) are typical when imag-
ing is performed using a probe magnetized perpendic-
ularly to the sample’s plane; these are characteristic of
cobalt island nanostructures that have their easy mag-
Fig. 1. Raman spectra for (a) Gr/SiO2 and (b) Co–
Gr/SiO2 samples.
0
0
0.5
0.5
1.0
1.0
I/I2D
I/I2D
1000
1000
2000
2000
3000
3000
(a)
(b)
2D
2D
G
D
1
1
2
2
3
3
λ, cm1
λ, cm1
G
D
Fig. 2. Morphology of Co–Gr/SiO2 sample: (a) SEM,
(b) AFM, and (c) MFM images.
(a) (b)
(c)
1 m
2 m
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
EFFECT OF MAGNETIC Co–CoO PARTICLES ON THE CARRIER TRANSPORT 371
netization axis in the sample’s plane [20, 21]. In this
instance, large agglomerations (size, 400–500 nm) of
deposited particles are seen as regions with bright con-
trast at one end and dark contrast on the other end,
which corresponds to a strong interaction between the
probe and magnetic poles of nanostructures that have
their magnetic moments lying in the sample’s plane
(i.e., a magnetic dipole response) [22]. Isolated
nanoparticles and smaller agglomerates are likely to be
magnetically soft, exhibit a weak interaction with the
tip, and do not exhibit noticeable magnetic contrast.
The magnetic state of Co–Gr/SiO2 samples was
zation curves for these samples were recorded in the
temperature range of 3–300 K and are shown in
Fig. 3a. The magnetization curves m(B) recorded at
room temperature (T = 300 K) are nearly symmetric
(relative to B = 0 T). They are characterized by coer-
civity BC ≈ 38 mT and saturations at relatively small B
(around 0.4 T), suggesting that the remaining unoxi-
dized cobalt makes a sufficient contribution to the
magnetization of Co–Gr/SiO2 samples. As the tem-
perature T is reduced below 100 K, the m(B) curves
become asymmetric relative to the zero B field. This
suggests the presence of exchange bias that reaches
field strengths HEB up to 146 Oe at T = 10 K (Fig. 3b).
The observed exchange bias and sufficiently large
coercivity HC (up to 880 Oe at 20 K) are most likely
due to exchange interaction at the Co core/CoO shell
interface. Similar results were obtained for Co parti-
cles electrodeposited onto twisted graphene [5]. Con-
sidering that HEB is inversely prop ortional to the size of
ferromagnetic particles [23], the relatively small values
of HEB, with respect to for example HEB = 6.5 kOe for
Co–CoO particles at T = 10 K [24], are indicative of
quite a large size of Co cores in the deposited Co–
CoO particles.
In addition, the m(T) curves recorded at T 100 K
show a inflection at fields around B = 0.15 T. This
shape of the curves may be suggestive of the nonuni-
form size of the deposited particles due to their com-
plex core–shell type structure. In this instance, non-
oxidized cobalt cores undergo remagnetization at
smaller B f ields, while the inf lection on m(T) curves
corresponds to the beginning of remagnetization in
regions close to the oxide shell which exhibit a harder
magnetic behavior due to the effect of spin pinning at
the core–shell interface. The fact that the inflection
on the curves occurs below the Néel temperature (TN)
for CoO [25] supports this hypothesis.
The temperature dependences of sheet resistance
for Gr/SiO2 (curve 1) and Co–Gr/SiO2
(curve 2) samples are shown in Fig. 4 in normalized
(Fig. 4a) and semilogarithmic (Fig. 4b) coordinates.
The linearity of current–voltage curves shown in the
inset in Fig. 4b is indicative of the ohmic behavior of
electrical contacts. The shape of curves 1 and 2 sug-
gests that increased after electrodeposition of par-
ticles and that the shape of dependence is asso-
ciated with a semiconducting behavior at temperatures
below 150–200 K. Moreover, the data of Fig. 4 show
an abrupt drop in the resistance in curve 2 (see the
inset to Fig. 4a) at temperatures above 260 K, which
may be related to the phase transition in the CoO shell
(or isolated CoO particles) from the antiferromagnetic
to paramagnetic state at a temperature above the Néel
temperature [25]. We note that the observed increase
in the electrical resistance of Co–Gr/SiO2 sample,
compared to its Gr/SiO2 counterpart, may be due to
the presence of CoO. We also note that, as the tem-
h
()
RT
h
h
()
RT
Fig. 3. Co–Gr/SiO2 sample: (a) m(B) magnetization curves and (b) temperature dependences of coercive field Hc and exchange
bias (magnetic field) HEB.
0.5 0 0.5
0.05
0
0.05
B, T T, K
,
,
,
,
,
,
,
, , ZFC T = 3 K
(a) (b)
0 100 200 300
250
500
750
1000
Hc, HEB, Oe
m, μA m2
T= 3 K
T= 20 K
T= 10 K
T= 200 K
T= 100 K
T= 50 K
T= 300 K
Hc
HEB
372
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
FEDOTOVA et al.
perature is raised (above 225 K for Gr/SiO2 and 290 K
for Co–Gr/SiO2), the sign of temperature coefficient
of electrical resistance flips from positive to negative,
which points to a metal-like behavior of these samples
at elevated temperatures.
The important feature of samples under study is
that the dependences shown in Fig. 4b (i.e., in
the –logT semilog coordinates) tend to exhibit
a linear behavior (corresponding curve regions are
marked with colored lines) and the tendency to satu-
ration, as the temperature is reduced. The observation
of linear regions on the curves presented in the
–logT coordinates is usually ascribed to the
presence of quantum corrections to the Drude model
subject to the condition of weak localization [6–8,
26]. The estimative calculations provided below sug-
gest that incoherence of the phase of electrons that are
h
()
RT
h
()
RT
h
()
RT
related to the mentioned linear contribution (behav-
ior) is due to their elastic scattering on phonons [27].
The likelihood of this scenario is also indicated by a
fairly broad linear behavior range for the –logT
dependences (i.e., from 5 to 100 K). Such a behavior is
not uncommon for graphene [28], which places it in
stark contrast to metals and semiconductors, for
which weak quantum localization effects are observed
at temperatures no more than 10–15 K [29]. This fact
can be linked to specific features of the phonon spec-
trum of carbon nanolayers, and in particular to that
the Debye temperature θD for graphene is much higher
than that for any other quasi-two-dimensional systems
on the basis of metals or semiconductors. For
graphene, θD reaches 1200–2300 K [30]. As a result,
even at temperatures around 200 K, the energy and
density of excited phonons are low enough to result in
quasi-elastic scattering of electrons on phonons [27].
The saturation behavior of curves (Fig. 4b)
may be due to a drop in the conductivity of graphene
layer to the minimum for disordered metallic systems
(the so-called minimum metallic conductivity σmin),
as the temperature tends to the absolute zero [27]. An
alternative explanation of the observed saturation is
that the free path becomes comparable to the grain
size in graphene, as the temperature is lowered [31].
Knowing that disorder may break the weak local-
ization conditions and lead to a strong localization
which prepares ground for hopping conductivity in
graphene, we tested this hypothesis by fitting the
curves with the known formula
(1)
In this formula, the model parameters α, , and
depend on the mechanism of hopping conductivity,
the dimensionality (1, 2, or 3) of samples under study,
and the energy-dependence of density of localized
states involved in hopping. In the Mott model of vari-
able-range hopping conductivity, parameter α can
take values of 0.25 or 0.33 for the 3D and 2D variants,
respectively, while the Shkolovskii–Efros model gives
0.5 and 0.33 for α for the 3D and 2D variants, respec-
tively [9, 10, 32]. We note that, in the conventional
band model of conductivity, parameter α = 1.
To identify possible involvement of one of the
mentioned models of variable-range hopping conduc-
tivity, relationships are conventionally plotted
in so-called Mott coordinates, i.e., ln( )–(1/T)α,
in which low-temperatures regions of Mott curves are
linearized for one of the indicated values of α in the
exponent in Eq. (1). The slope of these linear sections
in the Mott coordinates (i.e., ln( )–(1/T)α) can
be used to estimate parameters and , which
determine the probability of hopping and the wave
h
()
RT
h
()
RT
h
()
RT
α







0
0
() exp .
D
DT
RT R T
0
D
R
0
D
T
h
()
RT
h
()
RT
h
()
RT
0
D
R
0
D
T
Fig. 4. Temperature dependences of sheet resistance
(T) in (a) normalized and (b) semilog coordinates for
(1) Gr/SiO2 and (2) Co–Gr/SiO2 samples. Inset to Fig. 4a:
a magnified view of (T) dependence in the range of
240–300 K. Inset to Fig. 4b: current–voltage curve for the
Co–Gr/SiO2 sample recorded at room temperature.
0.2
0
0.2
,
1
2
02112
U, V
0100
10
200
100
300
1.0
1.1
5
1.2
6
250 275 300
0.99
1.00
1.01
1
2
1
2
(a)
(b)
R(T)/R250
Ru, k/u
Ru, k/u
R(T)/R250
11
10
9
8
T, K
T, K
I, 105 A
T, K
h
R
h
R
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
EFFECT OF MAGNETIC Co–CoO PARTICLES ON THE CARRIER TRANSPORT 373
function localization radius in the corresponding
models. The dependences in Fig. 5 show us that
our experimental data in low-temperature ranges are
consistent with none of the mentioned models, since
no linear sections of these curves are observed. This
means that, for our graphene samples, the shape of
curves at lower temperatures is mainly deter-
mined by the theory of quantum corrections to the
Drude model of conductivity.
To reaffirm the validity of this statement, we ana-
lyze the field-dependences of sheet resistance (B)
and relative magnetoresistance MR(B) = [ (B, T) –
(0, T)]/ (0, T) for the Gr/SiO2 and Co–Gr/SiO2
samples under study, which are shown in Figs. 6 and 7,
respectively. As Fig. 6 shows, the initial graphene (i.e.,
Gr/SiO2) is characterized by two contributions to the
h
()
RT
h
()
RT
h
h
h
h
magnetoresistance effect: the negative (NMR) and the
positive (PMR) one. For the Gr/SiO2 sample, the
NMR is observed in only weak fields (up to 0.4
0.8 T), but here it covers almo st the entire temp erature
range under study (up to 250 K, as the PMR starts to
take place from this temperature upward). These two
effects compete at low temperatures (2–175 K), so that
the PMR starts dominating in magnetic fields with
flux density more than 1 T. That being so, the MR(B)
dependences in the range of very low temperatures
(i.e., 2–5 K) in fields higher than 4–5 T are quite lin-
dependence in fields <4 T, which may be suggestive of
the Lorentz force acting upon electrons. For the
Co‒Gr/SiO2 sample, the (B) and MR(B) depen-
dences tend to a plateau at low temperatures (2–10 K)
and in magnetic fields higher than 6 T (curves 13
in Fig. 7).
By comparing Figs. 6 to 7, we can see that electro-
deposition of cobalt nanoparticles on graphene leads
to narrowing both the temperature and magnetic field
ranges for NMR—below 75 K and 0.5 T, respec-
tively—and enhancement of the contribution of PMR
to the total magnetoresistance. In contrast to the
Gr/SiO2 sample, for which the MR grew by only 23%,
a marked increase of 80% was registered for the
Co‒Gr/SiO2 sample in a field of 8 T (i.e., in the PMR
region). The presence of this enhancement may tell us
that the effect of Lorentz force on the electrons in
CoO cores is implicated in the PMR effect in samples
under discussion, which, in turn, means that the shell
is not continuous and has pinholes that result in a
direct electrical contact between graphene and
Co cores.
The effects that magnetic field and electrodeposi-
tion of oxidized cobalt particles have on the type of
magnetoresistance effect (i.e., a switch from NMR to
PMR) and can be appreciated from temperature
dependences MR(T) registered at different B (Fig. 8).
In the low-temperature range, in which the PMR is
dominant, MR(T) for the Gr/SiO2 sample initially
increases and then tends to saturation (curves 1 and 2
in Fig. 8a). The transition to PMR, occurring as the
temperature is raised, causes the MR to increase in
response to raising the temperature or increasing the
applied magnetic field (curves 36 in Fig. 8a), reach-
ing saturation at room temperatures as well. At the
same time, we can see that (Fig. 8b), for samples with
deposited oxidized cobalt particles, MR grows at all
temperatures and the MR(T) dependences exhibit a
marked change in their shape. Although these curves
continue to exhibit a saturation behavior at small B, in
stronger f ields, i.e., B > 3 T, they have maxima that
tend to shift toward lower temperatures: starting from
220 K at B= 4 T to 150 K at B = 8 T.
To identify the role that temperature plays in switch-
ing the type of magnetoresistance effect from NMR to
PMR, in Fig. 9, we show the dependences for MRmin
h
Fig. 5. Temperature dependences (T) in the Mott coor-
dinates (ln( (T))–(1/T)α) for (a) Gr/SiO2 and (b)
Co‒Gr/SiO2 samples at different values for exponent α in
Eq. (1): (1) 1, (2) 1/2, (3) 1/3, and (4) 1/4.
0
0
0.4
0.4
0.8
0.8
1.0
1.0
1.2
1.3
(a)
(b)
14
4
2
2
3
3
1.2
1.1
1
1.1
R(T)/R250
R(T)/R250
T , K
T , K
h
R
h
R
374
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
FEDOTOVA et al.
(curves 1) and Bmin (curves 2) at the minima of MR(B)
dependences shown in Figs. 6 and 7 for the two sam-
ples. It can be seen that absolute values of both MRmin
and Bmin drop rapidly (nearly linearly) as the tempera-
ture is raised in the range of 2 to 50 K (curves 1), reach-
ing zero above 50 K, the region in which NMR van-
ishes almost completely and PMR emerges. That
being so, in contrast to the initial graphene sample
(Fig. 9a, curve 1) for which, as we noted above, the
NMR exists almost throughout the studied tempera-
ture range, electrodeposition of cobalt particles
(Fig. 9b, curve 1) suppresses the NMR effect totally at
temperatures as low as 130–140 K. Moreover, for the
MR to f lip the sign from negative to positive, the
Co‒Gr/SiO2 sample requires weaker fields (Fig. 9b,
curve 2) than the initial graphene does (Fig. 9a,
curve 2). As can be seen, the most dramatic drop in
Bmin is observed when the temperature is raised in the
range of 2–5 K, the range in which (T) curves tend
to saturation as the samples are cooled down (Fig. 4).
The presence of NMR in the region of relatively
low magnetic fields is typically seen as a manifestation
of contributions due to quantum corrections. It was
reported [8] that commonly the following types of
quantum corrections are considered in graphene with
a high carrier mobility (e.g., in mechanically exfoli-
ated graphene): weak localization as such and the one
allowing for electron–electron coupling [6, 7, 33, 34];
the intervalley distance and break of chirality [34];
weak antilocalization [33, 34]; and more. According to
the cited works, the listed contributions to the tem-
perature dependences of graphene electrical resistance
h
Fig. 6. Dependences of (a) sheet resistance (B) and
(b) relative magnetoresistance MR = [ (B) –
(0)]/ (0) on magnetic flux density B for Gr/SiO2
sample at different temperatures covering the range of 2–
300 K: (1) 2, (2) 7, (3) 10, (4) 25, (5) 50, (6) 75, (7) 125, and
(8) 275 K. Inset to Fig. 6b: MR curves in the range of mag-
netic flux density of –2 B 2 T.
(a)
(b)
840
5.75
4.75
0.2
0.1
0
5.50
5.00
5.25
84
Ru, kΩ/u
MR
B, T
840 84
B, T
MR
h
R
h
R
h
R
h
R
Fig. 7 Dependences of (a) sheet resistance (B) and
(b) relative magnetoresistance MR = [ (B) –
(0)]/ (0) on magnetic f lux density B for Co–Gr/SiO2
sample at different temperatures covering the range of 2
300 K: (1) 2, (2) 7, (3) 10, (4) 25, (5) 50, (6) 75, (7) 125, and
(8) 275 K. Inset to Fig. 7b: MR curves in the range of mag-
netic flux density of –2 B 2 T.
16
12
14
0
0.2
0.4
0.6
0.8
10
(a)
(b)
1
2
3
MR Ru, kΩ/u
4
5
6
7
8
1
2
3
4
5
6
78
20
МR
0.05
0
0.05
0.10
1
2
3
4
5
6
7
8
112
840 84
B, T
B, T
840 84
B, T
h
R
h
R
h
R
h
R
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
EFFECT OF MAGNETIC Co–CoO PARTICLES ON THE CARRIER TRANSPORT 375
can be both positive and negative. These are usually
described by relationships of the type [35]
(2)
where
and the characteristic fields determine the phase
incoherence of charge carriers for the corresponding
process.
For the weak localization contribution, the time is
given by the formula
(3)
ϕϕ ϕ

 
Δσ =

 

π++
 

2
2,
2
*
i
eB B B
FF F
hB BB BB
=+ψ+
1
() ln() (0.5 ),
Fx x x
ϕ
ϕ
τ=
4
.
eDB
At the same time, within the quantum correction the-
ory [36–38], the temperature dependences of phase
incoherence time τϕ of electron wave functions follow
a power law:
(4)
where parameter p is determined by the mechanism
underlying phase incoherence of electron wave func-
tions, and the range predicted by the theory for this
parameter is 1 < p < 2 [27].
Equation (4) includes corrections due to weak
localization (the first term), weak localization allow-
ing for electron–electron coupling (the second term),
and the effects of chirality and corrugations (the third
term) [35, 39, 40]. With Eqs. (2) and (3), by perform-
ing data fitting, we can estimate the characteristic
times of phase incoherence for the different contribu-
tions. The results of data fitting in the range of weak
magnetic fields (B < 1, i.e., the range of existence of
the NMR) are shown in Fig. 10. These corroborated
ϕ
τ
()~ ,
p
TT
Fig. 8. Temperature dependences of relative magnetoresis-
tance MR(T) for (a) Gr/SiO2 and (b) Co–Gr/SiO2 samples
in different magnetic fields B: (1) 0.5, (2) 1, (3) 2, (4) 4,
(5)6, and (6) 8 T.
0 100 200 300
0
0.1
0.2
(a)
(b)
MR
1
2
3
4
5
6
T, K
T, K
0 100 200 300
0
0.4
0.8
MR
1
2
3
4
5
6
Fig. 9. Temperature dependences of (1) MRmin and (2)
magnetic field Bmin in minima of the MR(B) curves shown
in Figs. 7 and 8 for (a) Gr/SiO2 and (b) Co–Gr/SiO2 sam-
ples, respectively.
0 100 200 300
0
0.02
(a)
MRmin
Bmin, T
Bmin, T
MRmin
0.04
0
0.5
1.0
0 100 200 300
0
0.03
(b)
0.06
0
0.4
0.6
0.2
1
2
1
2
T, K
T, K
376
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
FEDOTOVA et al.
the power law for the temperature dependence of
phase incoherence time given by Eq. (6) and enabled
us to determine the values for parameter p: 1.07 for the
initial graphene (line 1) and 0.71 for graphene with
deposited cobalt particles (line 2). Thus, the tempera-
ture dependence of (T) in combination with mag-
netic field dependences MP(B) suggest that the quan-
tum corrections play a key role in the carrier transport
at low temperatures in both the initial and cobalt
nanoparticle-decorated graphene samples. The data
fitting showed that in fields below 1 T and tempera-
tures below 75 K the contribution of other terms enter-
ing Eq. (2) was no more than 0.1% of weak localization
contribution. Their effect on low-temperature carrier
transport may manifest in the PMR region, i.e., in
stronger magnetic fields.
In summary, we can state that the decoration with
cobalt particles has a considerable effect on both the
temperature and field dependences of magnetization
and sheet resistance of our samples; the effect is, how-
ever, different in different ranges of the temperature
and magnetic flux density. Figure 11 shows tempera-
ture dependence of the difference of relative mag-
netoresistance effect—defined as [MRCo–Gr(T, 8 T)–
MRGr(T, 8 T)]—for the Gr/SiO2 and Co–Gr/SiO2
samples in magnetic field B = 8 T, which enabled us to
identify the contribution of cobalt particles to the
magnetotransport in these samples. It can be seen that
the curve has a maximum in a temperature range
around 100 K, its position corresponding to the end of
temperature range for the NMR in the Co–Gr/SiO2
sample. As the temperature is raised above 250–
275 K, the curve exhibits a sharp drop that coincides
with a similar drop in sheet resistance (T) (curves 2
in Fig. 4), which we previously related to the transition
h
h
of CoO from the antiferromagnetic to paramagnetic
state at a temperature above the Néel temperature.
We note that the decrease in the [MRCo–Gr(T, 8 T) –
MRGr(T, 8 T)] observed with increasing the temperature
above 100 K can be considered as another argument in
favor of the Lorentz mechanism contributing to the
increase in PMR due to the influence of cobalt core,
albeit we cannot fully eliminate the possibility of posi-
tive quantum corrections contributing to PMR [28].
4. CONCLUSIONS
We showed that electrochemical deposition onto
CVD graphene in the pulse-reverse mode from
an electrolyte containing CoSO4·6H
2O produced
Co–CoO particles (with size up to 500 nm) on the
graphene surface consisting of polydisperse agglomer-
ates with prolate shapes. For the Co–Gr/SiO2 sample,
the surface oxidation of cobalt particles is revealed in
asymmetry in magnetization curves M(H) and a dra-
matic decrease in sheet resistance R(T) below the Neel
temperature on their temperature dependences.
The deposition of Co–CoO particles was shown to
increase the resistance of graphene samples due to a
lower electron concentration. For the Gr/SiO2 and
Co–Gr/SiO2 samples, we revealed the existence of a
competition between the NMR and PMR contribu-
tions to the observed magnetoresistance effect and
showed that the low-temperature carrier transport in
the NMR region was due to quantum localization cor-
rection to the Drude model of conductivity, while the
enhancement in PMR after depositing Co–CoO par-
ticles onto graphene may be attributed to the Lorentz
mechanism operating within Co cores.
Fig. 10. Temperature dependences of phas e incoherence
times for the weak localization contribution to quantum
corrections for (1) Gr/SiO2 and (2) Co–Gr/SiO2 samples.
57610
1.6
2.0
1.2
, 1013 s
0.8
0.4
89
1
2
T, K
Fig. 11. Temperature dependences of the difference in rel-
ative magnetoresistance between Gr/SiO2 and Co–
Gr/SiO2 samples, i.e., [MRCo–Gr(T, 8 T) – MRGr(T, 8 T)],
in a magnetic field B = 8 T. The critical temperature of
NMR-to-PMR transition and the Néel temperature (TN)
for CoO are indicated with arrows.
NMR–PMR
TN
0 100 200 300
0.4
0.5
0.6
T, K
MRCo–Gr(B) MRGr(B)
PHYSICS OF THE SOLID STATE Vol. 62 No. 2 2020
EFFECT OF MAGNETIC Co–CoO PARTICLES ON THE CARRIER TRANSPORT 377
FUNDING
The work was supported by the State Committee on Sci-
ence and Technology, Republic of Belarus (agreement no.
F18PLShG-005), within the state research programs “Pho-
tonics and Opto- and Microelectronics” (assignment no.
3.3.01), and within a contract (no. 08626319/182161170-74)
with the Joint Institute for Nuclear Research, Russia.
CONFLICT OF INTEREST
The authors declare that they have no conflicts of interest.
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Translated by A. Kukharuk
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