# Strain-induced effects on the magnetic and electronic properties of
epitaxial Fe1-xCoxSi thin films

P. Sinha<EMAIL_ADDRESS>School of Physics & Astronomy, University of Leeds,
Leeds, LS2 9JT, UK  N. A. Porter  School of Physics & Astronomy, University of
Leeds, Leeds, LS2 9JT, UK  C. H. Marrows<EMAIL_ADDRESS>School of
Physics & Astronomy, University of Leeds, Leeds, LS2 9JT, UK

###### Abstract

We have investigated the Co-doping dependence of the structural, transport,
and magnetic properties of $\epsilon$-Fe1-xCoxSi epilayers grown by molecular
beam epitaxy on silicon (111) substrates. Low energy electron diffraction,
atomic force microscopy, X-ray diffraction, and high resolution transmission
electron microscopy studies have confirmed the growth of phase-pure, defect-
free $\epsilon$-Fe1-xCoxSi epitaxial films with a surface roughness of $\sim
1$ nm. These epilayers are strained due to lattice mismatch with the
substrate, deforming the cubic B20 lattice so that it becomes rhombohedral.
The temperature dependence of the resistivity changes as the Co concentration
is increased, being semiconducting-like for low $x$ and metallic-like for
$x\gtrsim 0.3$. The films exhibit the positive linear magnetoresistance that
is characteristic of $\epsilon$-Fe1-xCoxSi below their magnetic ordering
temperatures $T_{\mathrm{ord}}$, as well as the huge anomalous Hall effect of
order several $\mu\Omega$cm. The ordering temperatures are higher than those
observed in bulk, up to 77 K for $x=0.4$. The saturation magnetic moment of
the films varies as a function of Co doping, with a contribution of $\sim
1~{}\mu_{\rm B}$/ Co atom for $x\lesssim 0.25$. When taken in combination with
the carrier density derived from the ordinary Hall effect, this signifies a
highly spin-polarised electron gas in the low $x$, semiconducting regime.

###### pacs:

68.55.-a, 72.20.My, 73.50.Jt

##  I introduction

The rich behaviour shown by ferromagnetic semiconductors arise from an
interesting interplay of their electronic density of states and magnetic
interactions within the crystal structure, offering new possibilities for
spintronics.Ohno (2010) Whilst most magnetic semiconductors to date are based
on compound or oxide materials, the transition metal monosilicides are
promising candidates in that they are based on silicon, by far the most common
commercial semiconductor. These materials crystallize in cubic B20 structure,
the $\epsilon$-phase, and which belongs to the space group $P2_{1}3$.Al-Sharif
_et al._ (2001) They are continuously miscible with each other and form an
isostructural series compounds with endmembers MnSi (a metallic helimagnet),
FeSi (a paramagnetic narrow-gap semiconductor), and CoSi (a metallic
diamagnet).Manyala  _et al._ (2000) They have been studied for many years as
they exhibit wide variety of different aspects of condensed matter physics
including paramagnetic anomalies,Wertheim  _et al._ (1965); Jaccarino  _et
al._ (1967) strongly correlated/Kondo insulator-like behaviour,Schlesinger
_et al._ (1993); Paschen  _et al._ (1997); DiTusa  _et al._ (1997); Aeppli and
DiTusa (1999) non-Fermi liquid behaviour,Pfleiderer  _et al._ (2001); Manyala
_et al._ (2008); Ritz  _et al._ (2013a) unusual magnetoresistance,Manyala  _et
al._ (2000); Onose  _et al._ (2005); Porter  _et al._ (2012) and helical
magnetismBeille  _et al._ (1981, 1983); Uchida  _et al._ (2006); Grigoriev
_et al._ (2009) with skyrmion phasesMühlbauer  _et al._ (2009); Münzer  _et
al._ (2010); Yu  _et al._ (2010); Milde  _et al._ (2013) that have associated
topological Hall effects.Lee  _et al._ (2009); Neubauer  _et al._ (2009); Ritz
_et al._ (2013b)

Almost all work to date on the monosilicide materials has been carried out
using bulk single crystal samples. For technological applications, thin films
that can be patterned into devices with conventional planar processing
techniques are required. Epilayers of the helimagnetic metal MnSi have been
grown by using molecular beam epitaxy (MBE) by Karhu et al.,Karhu  _et al._
(2010, 2011, 2012) Li et al.,Li  _et al._ (2013) and Engelke et al.Engelke
_et al._ (2012) The properties are broadly comparable to those of the bulk
material, including the presence of chiral magnetismKarhu  _et al._ (2011) and
a topological Hall effect.Li  _et al._ (2013) Other monosilicides have
received less attention to date. The family of alloys Fe1-xCoxSi should be of
particular interest for spintronics: whilst both endmembers are non-magnetic,
magnetic ordering is evident at almost all intermediate values of $x$.Manyala
_et al._ (2000) For low doping levels of Co in the semiconducting parent FeSi,
a magnetic semiconductor with a half-metallic state is expected.Manyala  _et
al._ (2000); Guevara  _et al._ (2004) Polycrystalline thin films of Fe1-xCoxSi
have been grown by pulsed laser deposition,Manyala  _et al._ (2009) and
sputtering,Morley  _et al._ (2011) but with properties that fall short of
those in single crystal samples due to microstructural disorder and lack of
phase purity.

Here we report on the properties of epitaxial $\epsilon$-Fe1-xCoxSi layers
grown on commercial (111) Si substrates, across the doping range $0\leq x\leq
0.5$, using the growth methods we have previously developed.Porter  _et al._
(2012) The films are phase pure, with a B20 lattice that is distorted by
biaxial in-plane epitaxial strain to have a rhombohedral unit cell. Although
Fe1-xCoxSi is known to possess a helimagnetic ground state,Beille  _et al._
(1981, 1983); Uchida  _et al._ (2006); Grigoriev  _et al._ (2009) we focus
here on the properties in fields large enough to generate a uniformly
magnetized ferromagnetic state, which are modest in size. We find that these
epilayers display the full range of properties expected of this material,
including a characteristic temperature dependence of resistivity,Onose  _et
al._ (2005), positive linear magnetoresistance,Manyala  _et al._ (2000); Onose
_et al._ (2005), and a very large anomalous Hall effect.Manyala  _et al._
(2004) Measurements of the number of Bohr magnetons ($\mu_{\mathrm{B}}$) of
magnetic moment and electron-like carriers per Co indicate the presence of a
highly spin-polarised electron gas in the low doping ($x\lesssim 0.25$)
regime,Manyala  _et al._ (2000); Morley  _et al._ (2011) where the half-
metallic state is expected.Guevara  _et al._ (2004) Nevertheless, the presence
of epitaxial strain, giving rise to an expanded unit cell volume, leads to
some quantitative changes, the most prominent of which is a substantial
enhancement of the magnetic ordering temperature with respect to bulk
crystals. These epilayers are suitable for patterning into nanostructures that
may find use as spin injectors into siliconMin  _et al._ (2006); Appelbaum
_et al._ (2007); Huang  _et al._ (2007) or exploit the chiral nature of the
magnetism at low fields in skyrmion-based devices.Kiselev  _et al._ (2011);
Fert  _et al._ (2013); Lin  _et al._ (2013)

##  II Growth and structural characterisation

The Fe1-xCoxSi thin films were prepared by simultaneous co-evaporation of Fe,
Co, and Si by MBE on a lightly n-doped silicon (111) substrates with
$2000$-$3000~{}\Omega$cm resistivity at room temperature. The level of Co-
doping $x$ of the various Fe1-xCoxSi films was determined by controlling the
individual rates of incoming flux. We adopted the growth protocol described by
Porter et al. in Ref. Porter  _et al._ , 2012. The base pressure of the growth
chamber remained within the range $2.8$-$4.8\times 10^{-11}$ mbar. Prior to
the deposition of the film, the substrates were annealed at 1200∘C until a
well ordered $7\times 7$ reconstructed Si (111) surface was obtained. A low
energy electron diffraction pattern demonstrating this reconstruction is shown
in Fig. 1(c). The films were then grown by depositing a seed layer of Fe of
$\sim 5.4$ Å thickness at room temperature, followed by the deposition of a
$\sim 50$ nm thick Fe1-xCoxSi layer at a net flux rate of $\sim 0.4$ Å/s at
400 ∘C . The films were then further annealed at 400∘C for 15 minutes, before
being allowed to cool to room temperature for further characterisation.

The films grow in the (111) orientation and are $\epsilon$-phase pure, as can
be seen from the Cu $K_{\alpha}$ X-ray diffraction (XRD) spectrum shown in
Fig. 1(a). In-plane epitaxy of the Fe1-xCoxSi films is seen to be achieved by
a 30∘ in-plane rotation of the surface unit cell with respect to the Si, such
that the Fe1-xCoxSi [112̄] direction is aligned parallel to Si [11̄0],
demonstrated by the LEED pattern of a completed epilayer in Fig. 1(d). Atomic
force microscopy (AFM) was used to map the surface topography of the films: an
representative micrograph is shown in Fig. 1(b). The root mean square (rms)
roughness of the films were estimated from these images to be around 1 nm.

Figure 1: (Color online) Structural characterisation of the 50 nm thick
Fe1-xCoxSi epilayers. (a) XRD spectrum of a $x=0.5$ film, illustrating the
phase purity of the B20 structure and the (111) epitaxial orientation of the
film. (b) Atomic force micrograph of the top surface of an Fe1-xCoxSi epilayer
with $x=0.5$. (c) LEED pattern of an annealed Si (111) substrate prior to film
growth. The $7\times 7$ surface reconstruction is evident. (d) LEED pattern
from an Fe1-xCoxSi film $x=0.3$, demonstrating epitaxial growth in the (111)
orientation.

For further structural verification, high resolution transmission electron
microscopy (HRTEM) and energy dispersive X-ray analysis (EDX) were carried out
on cross-section specimens prepared by focussed ion beam (FIB). Fig. 2(a) and
(b) show the top and bottom interfaces of a Fe1-xCoxSi film with $x=0.5$. The
films look well-ordered throughout and epitaxial growth can be observed with
the orientation (111)Fe1-xCoxSi$\|$(111)Si : [112̄]Fe1-xCoxSi$\|$[11̄0]Si.
Sample cross sections were mapped with EDX which confirmed the homogeneous
distribution and chemical composition of the films. In-plane (110) lattice
parameters were determined from the HRTEM images, which we discuss below.

Figure 2: HRTEM of an Fe1-xCoxSi epilayer with $x=0.5$ on the [112] zone axis,
showing the upper (a) and lower (b) interfaces.

##  III Strain characterisation

Heteroepitaxy gives rise to strained growth of films as a result of the
lattice mismatch between substrate and the film. The lattice parameter of Si
is 5.431 Å, whilst that of bulk FeSi is 4.482 Å. It is to accommodate this
large difference that the film grows with the 30∘ in-plane rotation
demonstrated above by LEED (see Fig. 1(c) and 1(d)) and HRTEM (Fig. 2(a) and
2(b)). This gives rise to an in-plane lattice mismatch of $5.6\%$ at the
interface. Inspection of the LEED patterns shows that this is relaxed to $\sim
3.7\%$ at the surface of a 50 nm thick film (see above). The heteroepitaxy
induces biaxial tensile strain in the in-plane directions of the Fe1-xCoxSi
layers, with corresponding compression in the out-of-plane direction, which
distorts the cubic B20 lattice to have a rhombohedral form.

The position of the Fe1-xCoxSi [111] and [222] Bragg peaks, obtained from
$\theta$-$2\theta$ high angle XRD scans, were used to determine the out-of-
plane [111] lattice parameter of Fe1-xCoxSi films using the Bragg law. In
order to make quantitative comparisons of our samples, we define the parameter
$a^{hkl}$, the lattice constant, assuming a cubic unit cell, that is
determined from a measured interplanar spacing $d^{hkl}$ associated with a
particular set of lattice planes $(hkl)$. A systematic decrease in out-of-
plane lattice constant, $a^{111}$ is observed with increasing Co content $x$
in the films, as shown in Fig. 3(a). The linear variation of the out-of-plane
lattice parameter with $x$ shows that Vegard’s law is followed, as is the case
in bulk crystals of this material.Shinoda (1972) However, there is also the
large in-plane lattice mismatch with the Si substrate that was discussed above
in the case of thin films. The in-plane lattice parameter $a^{110}$ at the
surface of the Fe1-xCoxSi films, shown in Fig. 3(b), varies from
$4.45\pm~{}0.02$ Å for $x=0$ to $4.64\pm 0.02$ Å for $x=0.5$, as determined
from analysis of the LEED patterns, using the ($7\times 7$) reconstructed Si
(111) pattern to provide a calibration. Overall we see that the in-plane
lattice parameter of epitaxial Fe1-xCoxSi is larger than the corresponding
out-of-plane lattice parameter and is closer to that of Si (5.431Å). The
variation with $x$ is plotted in Fig. 3(b).

Figure 3: (Color online) Strain analysis. (a) Out-of-plane lattice parameter
(LP) $a^{111}$ of Fe1-xCoxSi films based on data from XRD. (b) In-plane
lattice parameter (LP) $a^{110}$ at the surface of the film, based on data
from LEED. (c) Out-of-plane of strain in the unit cell. (d) In-plane strain in
the unit cell. (e) Rhombohedral unit cell volume as a function of $x$. (f)
Rhombohedral angle as a function of $x$. The solid lines are linear best fits,
the dashed lines are guides to the eye.

Based on data from Fig. 3(a) and 3(b), the out-of-plane compressive,
$\varepsilon_{\perp}$, and in-plane tensile, $\varepsilon_{\|}$, strains in
the crystal structure were calculated, with the results shown in Fig. 3(c) and
(d), using the following expression:

$\varepsilon^{hkl}=\frac{a^{hkl}_{\mathrm{epi}}-a^{hkl}_{\mathrm{bulk}}}{a^{hkl}_{\mathrm{bulk}}},$
(1)

where $a^{hkl}_{\mathrm{epi}}$ is the lattice parameter as measured for a
given epilayer and $a^{hkl}_{\mathrm{bulk}}$ is the corresponding lattice
parameter in the bulk (Manyala  _et al._ , 2004). In both the cases strain
follows a nonlinear relationship with the Co-doping level $x$. For higher
values of $x$ the out-of-plane lattice constant is more compressed, whilst the
in-plane lattice is extended.

The different methods we have used to determine the lattice constants give
information about different parts of the film. Using the TEM images as shown
in Fig. 2(b) it is possible to determine the lattice constant of the
Fe1-xCoxSi near the Si substrate. In Fig. 4(a), we plot the unit cell face
diagonal $d^{\prime}_{110}$ for selected values of $x$ as obtained from TEM.
For $x=0$ and $x=0.2$, $d^{\prime}_{110}$ is measured to be $6.62\pm~{}0.02$ Å
and $6.66\pm~{}0.02$ Å respectively. These values are seen to match well to
the Si (112) face diagonal (6.6501 Å), which it must for heteroepitaxial
growth. Our LEED data are surface sensitive, however. Measuring
$d^{\prime}_{110}$ from our LEED patterns shows considerable variation with
$x$ (Fig. 4(a)). For $x=0$, there is a good match to the bulk value for this
crystallographic distance, if we assume a cubic crystal structure. We can
conclude from this comparison that the Fe1-xCoxSi films are strained at the Si
interface to adapt to the lattice constant of Si substrate. At greater
distances from the interface with the substrate, the lattice relaxes
throughout the 50 nm film thickness, and adapts to its own strained lattice
constant for a rhombohedral crystal structure which is somewhere in between
that of Si and the Fe1-xCoxSi cubic assumption of crystal structure. The
variation of volume strain with shear strain in Fe1-xCoxSi film is shown in
the Fig. 4(b) for various Co doping ranging from $x=0$ to $x=0.5$. The
linearity in the relationship confirms that the epitaxial strain in Fe1-xCoxSi
film changes only the angle of the unit cell as shown in Fig. 3(f) and that
there are no structural phase changes associated with the strain. Thus, even
though the strained Fe1-xCoxSi films have rhombohedral unit cell but they are
phase pure as shown in the Fig. 1(a).

Figure 4: (Color online) Epitaxial strain analysis. (a) Comparison of
evolution of unit cell face diagonal $d^{\prime}_{110}$ of Fe1-xCoxSi films as
a function of cobalt content from data obtained by LEED, TEM and theoretical
prediction. b) Variation of volume strain with shear strain for various Co
doping in Fe1-xCoxSi films. The dashed line is a straight line best fit to the
data.

Knowledge of the in-plane and out-of-plane lattice constants give a full
determination of the geometry of the rhombohedral unit cell. The volume of the
unit cell as function of $x$ is plotted in Fig. 3(e). The unit cell volume
increases in a monotonic but non-linear fashion with $x$. We have also
calculated the variation of the rhombohedral angle as a function the varying
Co doping, shown in Fig. 3(f). The angle increases from little more than $90$∘
for $x=0$ to $\sim 92$∘ for $x=0.5$. Since the in-plane strain is determined
from LEED, these values apply close to the top surface of the epilayer. These
changes in unit cell geometry induced by epitaxial strain can be expected to
give rise to modifications to various properties such as the band structure,
density of states, transport properties, magnetization and magnetic
anisotropy, which we will explore in remainder of the paper.

##  IV Transport Properties

The transport properties of our Fe1-xCoxSi films were measured in a gas-flow
cryostat with a base temperature of 1.4 K capable of applying magnetic fields
of up to 8 T. The films were patterned into Hall bars which were $5~{}\mu$m
wide using optical lithography, etched by Ar ion milling, and bonded onto a
chip carrier for measurement.

Measurements of the electrical resistivity $\rho(T,H)$ of the films as a
function of temperature $T$ and magnetic field $H$ applied perpendicular to
the sample plane are shown in Fig. 5. A bias current of $30~{}\mu$A was used.
The solid lines show the $\rho(T)$ in absence of magnetic field and the dashed
lines show $\rho(T)$ in presence of an 8 T magnetic field. Fig. 5(a) shows the
resistivity variation of an FeSi film. FeSi is a narrow band-gap
semiconductor,Jaccarino  _et al._ (1967) and upon decreasing the temperature
the resistivity increases reaching $3700~{}\mu\Omega$cm at 1.4K. We determined
the band-gap of the epitaxial FeSi to be $\Delta=30.1\pm 0.2$ meV using the
following relation:

$\ln\rho\propto\left(\frac{\Delta}{2k_{\mathrm{B}}T}\right),$ (2)

where $k_{B}$ is the Boltzmann constant, fitted to the high temperature data
(above about 50 K).

Doping FeSi with Co introduces electron-like carriers and a lowered
resistivity. At the opposite extreme, the $\rho(T)$ relation for the film with
$x=0.5$ has a metallic form, shown in Fig. 5(f), increasing with $T$ for all
temperatures. Intermediate values of $x$ yield hybrid $\rho(T,0)$ dependences,
with a gradual crossover from semiconductor-like to metal-like behavior as $x$
rises. For these values of $x$ the $\rho(T,0)$ curve is often non-monotonic,
combining regions with both positive and negative temperature coefficients of
resistance. The curves are similar to those measured for bulk crystals at a
qualitative level,Manyala  _et al._ (2000); Onose  _et al._ (2005) but differ
quantitatively.

Figure 5: (Color online) Temperature dependence of resistivity in $\sim$ 50 nm
films of Fe1-xCoxSi in magnetic fields of 0 T (solid lines) and 8 T (dashed
lines). Increasing cobalt concentration $x$ changes the temperature
coefficient of resistivity from negative (semiconductor-like) for $x=0$ to
positive (metallic-like) for $x=0.5$, with mixed behavior seen for
intermediate values of $x$. $\uparrow$ and $\downarrow$ illustrate
respectively temperatures of minima, $T_{res}$, and maxima in the resistivity.

In the intermediate doping regime ($0.15<x<0.3$), we observe some distinctive
features such as points of local maximum ($T_{\mathrm{max}}$) and minimum
($T_{\mathrm{res}}$) resistivity that vary with the degree of Co doping. For
instance, in Fig. 5(b) (for $x=0.15$) we observe a broad maximum in $\rho$
around 125 K. As the Co doping increases this maximum shifts towards higher
temperatures, reaching 175 K for $x=0.3$, then becoming less pronounced until
it vanishes for $x=0.5$. The observed broad maximum is a feature reminiscent
of the narrow band-gap semiconducting parent compound FeSi Onose  _et al._
(2005). The maxima and associated temperature shift can be explained in the
framework of epitaxial strain and Co doping. Substituting Co for Fe not only
introduces volume strain (as previously shown in Fig. 4(b)), but also changes
the band structure, resulting in a broadening of bands and reduced band
gap.Forthaus  _et al._ (2011) Thus, increased Co doping provides more carriers
to be available for conduction, giving rise to the hybrid semiconducting-
metallic behaviour that we see. It is the competition between the temperature
dependence of mobility, importance of thermally activated carriers
(particularly at low $x$) and the carrier concentration that gives rise to
such difference in $\rho(x,T)$. Fe1-xCoxSi films thus lose the low $T$
insulating behaviour of FeSi as $x$ rises.

As the temperature is reduced further below $T_{\mathrm{max}}$, the
resistivity decreases until a minimum ($T_{\mathrm{res}}$) is reached. This
minimum in the resistivity curve is related to the magnetic behaviour of the
films and signifies the onset of magnetic ordering in the Fe1-xCoxSi crystal
structure.Forthaus  _et al._ (2011) The position of the minimum
$T_{\mathrm{res}}$ varies with Co doping and is found to follow the same trend
as the magnetic ordering temperature $T_{\mathrm{ord}}$, as we shall discuss
later in §VII. Ideally, $T_{\mathrm{res}}\approx T_{\mathrm{ord}}$, but in the
samples studied here, we find that $T_{\mathrm{res}}$ is actually slightly
higher. The value of $T_{\mathrm{res}}$ increases with increasing Co doping
and reaches the maximum value of $\sim 92$ K for $x=0.4$ before decreasing
again. The transport properties of Fe1-xCoxSi epilayers are dominated by
short-ranged ferromagnetic interactions in the crystal structure.(Onose  _et
al._ , 2005) When the mean free path is of the same order as the ferromagnetic
correlation length, $T_{\mathrm{ord}}$ and $T_{\mathrm{res}}$ almost coincide,
as is the case for $x=0.1,0.5$. However, if the mean free path is longer, then
$T_{\mathrm{res}}$ is higher than $T_{\mathrm{ord}}$, as we observe for
Fe1-xCoxSi films in the range $0<x<0.5$ (and discuss later in §VII). Also this
may be due to magnetic fluctuations occurring above the ordering temperature
which may contribute to the discrepancy between the magnetic ordering
temperature and $T_{\mathrm{res}}$ (Pfleiderer  _et al._ , 2001) . When the
temperature is decreased below $T_{\mathrm{res}}$, the resistivity further
increases for the Fe1-xCoxSi films with $0<x<0.5$, as pointed out in the
previous studies.(Beille  _et al._ , 1983; Manyala  _et al._ , 2000)

Overall we observe semiconducting behaviour of the films for low $x$ and
metallic for high $x$. This remains the case when the measurements were
performed under a $\mu_{0}H=8$ T field applied perpendicular to the sample
plane (dashed lines in Fig. 5). In the high temperature region (above $\sim
T_{\mathrm{max}}$), the resistivity is almost unchanged with field for all our
Fe1-xCoxSi films. In the lower temperature regime, after the onset of magnetic
ordering, magnetoresistance gradually rises in the semiconducting regime,
washing out any maximum $\rho(T,\mathrm{8~{}T})$. Positive magnetoresistance
is a very typical property of the Fe1-xCoxSi system, and shall be discussed in
more detail in the next section.

##  V Magnetoresistance

Unlike most other ferromagnetic metals, which show negative magnetoresistance
(MR) at high fields,Raquet  _et al._ (2002) Fe1-xCoxSi systems show unusual
positive MR in the form of bulk crystals and epilayers.Manyala  _et al._
(2000); Onose  _et al._ (2005); Porter  _et al._ (2012) The high field
magnetoresistance in these Fe1-xCoxSi samples, shown in Fig. 5 for a
perpendicular field orientation, is not only linear for $x>0$ , but also
isotropic for $T<T_{\mathrm{res}}$. For an FeSi film, which is a paramagnet,
the MR has a quadratic dependence on magnetic field. Introducing Co doping to
FeSi, changes the nature of the curve from quadratic to linear at $x=0.1$,
with a large MR ratio of almost 12% in an 8 T field at 5 K.

Figure 6: (Color online) Magnetoresistance. a) MR isotherms at 5 K for
Fe1-xCoxSi films of varying Co doping $x$. b) MR ratio at 8 T and 5 K as a
function of cobalt concentration $x$.

Fig 6(a) shows the magnetoresistance ratio observed in Fe1-xCoxSi epilayers
for different Co doping for a field of 8 T at 5 K. As the Co content is
increased from $x=0.1$ to $x=0.5$, we observe that the MR remains linear at
low temperatures ($T<T_{\mathrm{res}}$), i.e. in the presence of magnetic
ordering. (As the temperature is increased the linearity of the MR is lost,
and above $T_{\mathrm{max}}$ it becomes quadratic for all our Fe1-xCoxSi
films.) The maximum magnetoresistance should be observed near the metal-
insulator transition, where there is the highest Coulomb interaction. This is
observed here for $x=0.1$, as shown in Fig. 6(b) where we observe an MR ratio
of almost 12%. The MR ratio decreases with increasing Co content up to
$x=0.3$, and then flattens off at a level of $\sim 5$% for all higher values
of $x$. The explanation of this low $T$ positive linear magnetoresistance is
contested: both quantum interference effects,Manyala  _et al._ (2000) and
Zeeman splitting of the majority and minority spin bands, which reduces the
high mobility minority spin carriers and in turn increases the
resistivity,Onose  _et al._ (2005) have been cited as causes.

##  VI Hall effect

Hall measurements were made simultaneously with the longitudinal resistivity
measurements. As an example, the Hall resistivity $\rho_{xy}(H)$ for an
Fe1-xCoxSi thin film with $x=0.4$ is shown in Fig. 7(a) for various
temperatures. There is low field hysteresis (for fields $\mu_{0}H\lesssim 0.3$
T) and a high field linear regime. (Inset in Fig.7(a) are data measured at 5 K
showing the high field response.) The high field slope is due to the ordinary
Hall effect. This high field Hall slope, measured at 5 K for Fe1-xCoxSi films
with different values of $x$, was used to determine the type of charge carrier
and carrier density, as shown in Fig. 7(b), and was combined with the
longitudinal resistivity to give the mobility of the carriers in the film, as
shown in Fig. 7(c). In the bulk, each Co dopant contributes one conduction
electron to the electron gas over the whole $x$ range.Manyala  _et al._ (2000)
The data shown in Fig. 7(b) show that there is a small shortfall in our
samples, with close to, but not quite, one electron-like carrier per Co
dopant. It is possible that there are defects in our film, too subtle to pick
up by XRD or HRTEM, that act as traps preventing all the electrons released by
the Co dopants from acting as carriers. As shown in Fig. 7(c), the mobility
$\mu$ of the charge carriers drops with increasing Co doping in the films,
which can be accounted for if the Co dopants act as scattering centres.

Figure 7: (Color online) Hall measurements. (a) Hall resistivity $\rho_{xy}$
as a function of field for Fe1-xCoxSi epilayers with $x=0.4$ for selected
temperatures. Hysteresis is observed in the extraordinary Hall effect which
diminishes at elevated temperatures. The ordinary Hall effect was extracted at
high fields above the saturation field. A measurement at 5 K is shown inset up
to higher magnetic fields. (b) Charge carrier density expressed as electrons
per formula unit inferred from measurements of the high field ordinary Hall
effect at 5 K. The dashed line illustrates the ideal case of one electron
added to the electron gas per cobalt atom. (c) Carrier mobility $\mu$ as a
function of cobalt doping $x$ at 5 K.

The hysteretic part of the the Hall signal arises due to the anomalous Hall
effect that is present in magnetically ordered materials.Nagaosa  _et al._
(2010) The Hall resistivity in a ferromagnetic material is given by

$\rho_{xy}=R_{\mathrm{o}}\mu_{0}H+4\pi R_{\mathrm{s}}M,$ (3)

where $R_{\mathrm{o}}$ is the ordinary Hall coefficient and $R_{\mathrm{s}}$
is the anomalous Hall coefficient. The anomalous contribution to the Hall
resistivity $\rho_{\mathrm{AH}}=4\pi R_{\mathrm{s}}M$ was determined by
extrapolating the high field Hall slope to $H=0$, where the magnetisation is
saturated, so any topological contribution of the Hall resistivityNeubauer
_et al._ (2009); Lee  _et al._ (2009) is neglected in the present analysis.
(We will discuss it elsewhere.) $\rho_{\mathrm{AH}}$ for the $x=0.4$ sample,
shown in Fig. 7(a), is as large as $2~{}\mu\Omega$cm at 5 K, and diminishes as
$T$ rises, becoming almost negligible at 100 K or beyond. As shown in Fig.
8(a), even larger values of $\rho_{\mathrm{AH}}$ can be found for lower values
of $x$. Fe1-xCoxSi layers with $x\lesssim 0.3$ have $\rho_{\mathrm{AH}}\sim
5~{}\mu\Omega$cm. The highest value we observe is $5.5~{}\mu\Omega$cm for
$x=0.25$. In Fig. 8(b) we plot anomalous Hall coefficient $R_{\mathrm{s}}$ as
a function of $x$ and observe that highest value is reached for $x=0.1$, up to
$0.67~{}\pm~{}0.04~{}cm^{3}C^{-1}$ before decreasing almost linearly to
$0.09~{}\pm~{}0.01~{}cm^{3}C^{-1}$ for $x=0.5$. The large value of
$R_{\mathrm{s}}$ observed in our epilayers is of the similar order but a
little higher than that observed in bulk Fe1-xCoxSi crystals by Manyala et
al.Manyala  _et al._ (2004) This could be attributed to the strained epitaxial
structure of Fe1-xCoxSi films, in which strain increases the effective spin-
orbit coupling.

Figure 8: (Color online) Anomalous Hall effect. (a) Variation of anomalous
Hall resistivity $\rho_{\mathrm{AH}}$, and (b) anomalous Hall coefficient
$R_{\mathrm{s}}$ as a function of $x$ at 5 K for Fe1-xCoxSi films.

##  VII Magnetic properties

Magnetic characterisation was carried out using a vibrating sample
magnetometer (VSM) with a sensitivity of $10^{-6}$ emu and a SQUID
magnetometer with a sensitivity of $10^{-8}$ emu. For measurements in the VSM,
several pieces of sample cut from the same wafer were stacked up to increase
the signal. The temperature dependences of the magnetisation of the films were
measured with a 10 mT field applied in the film plane, the results are shown
in Fig. 9(a). It is straightforward to determine the critical temperature for
magnetic ordering from these curves. Since Fe1-xCoxSi is helimagnetic, we
refer to an ordering temperature $T_{\mathrm{ord}}$, rather than a Curie
temperature. The values of $T_{\mathrm{ord}}$ obtained for the various films
have been plotted as a function of Co content $x$ and shown in Fig. 9(b). When
compared with corresponding data for bulk samples,Onose  _et al._ (2005);
Grigoriev  _et al._ (2007) we see that for our Fe1-xCoxSi epilayers
$T_{\mathrm{ord}}$ has been significantly increased, and is as high as 77 K
for the $x=0.4$ epilayer. Enhanced ordering temperatures with respect to bulk
have also been observed in MnSi epilayers by Engelke et al.Engelke  _et al._
(2012)

Figure 9: (Color online) Magnetic characterisation of the Fe1-xCoxSi
epilayers.(a) Magnetisation as a function of temperature in an in-plane 10 mT
field. The Co concentration, $x$, of the films is labeled on the graph. Larger
error bars correspond to measurements by VSM. b) The ordering temperature
$T_{\mathrm{ord}}$ of the epitaxial thin films shows an enhancement magnetic
ordering temperature bulk material.Onose  _et al._ (2005); Grigoriev  _et al._
(2007) $T_{\mathrm{res}}$, determined as discussed in §IV, is up to 10 K
higher than $T_{\mathrm{ord}}$. The dashed lines are guide to the eye. (c) The
saturation magnetisation at 5 K, extracted from hysteresis loops of the films,
expressed in Bohr magnetons per formula unit. The value is close to
$1~{}\mu_{\mathrm{B}}$ per cobalt dopant atom (ideal relationship shown by the
dashed line), in good agreement with bulk,Manyala  _et al._ (2000) for
$x\lesssim 0.25$.

We attribute this increased stability of the magnetic ordering in our
Fe1-xCoxSi epitaxial films to their epitaxial strain. As shown in Fig. 3(e),
the biaxial in-plane strain increases the unit cell volume. Studies of bulk
crystals of Fe1-xCoxSi under hydrostatic pressure show that compressing the
unit cell volume suppresses magnetic order and can even induce a quantum phase
transition in the system.Forthaus  _et al._ (2011) Based on this argument, we
conclude that the epitaxial strain in these Fe1-xCoxSi systems stabilises the
magnetic order and increases $T_{\mathrm{ord}}$ for the whole range of $x$.

We determined the magnetic moment, in units of Bohr magnetons
($\mu_{\mathrm{B}}$) per formula unit(f.u.), from these hysteresis loops. The
results are plotted as a function of $x$ in Fig. 9(c). Our results are
comparable to the findings of Manyala et al. for bulk crystals,Manyala  _et
al._ (2000) and largely in line with theoretical expectations.Guevara  _et
al._ (2004) As found previously, we see that each Co atom contributes $\sim
1~{}\mu_{\mathrm{B}}$ up to a limit of $x\approx 0.25$. Beyond this point, the
total moment is roughly constant at $\sim 0.25~{}\mu_{\mathrm{B}}$ per formula
unit (f.u.). The dashed line in Fig. 9(c) represents the ideal result of
exactly $1~{}\mu_{\mathrm{B}}$/f.u. We can see that in the low $x$ range there
is a small excess of moment per Co above the ideal result, suggesting that the
Co dopants could be weakly magnetising nearby Fe atoms in this regime.

##  VIII Discussion and Conclusions

In the early report of Manyala et al., the finding of one electron-like
carrier and one $\mu_{\mathrm{B}}$ of magnetic moment per Co atom dopant in
Fe1-xCoxSi (at least in the regime $x\lesssim 0.25$) was interpreted as
indicating the presence of a fully spin-polarised electron gas.Manyala  _et
al._ (2000) This half-metallic state was retrodicted by band structure
calculations a few years later,Guevara  _et al._ (2004) and its presence
explains the greater stability of the magnetic order against pressure for low
$x$ samples.Forthaus  _et al._ (2011) We previously detected evidence for the
partial preservation of this state in non-phase-pure sputtered Fe1-xCoxSi
polycrystalline films.Morley  _et al._ (2011)

In Fig. 10 we show the magnetic moment per electron-like carrier as a function
of $x$ for our epilayer samples. The moment is determined from the
magnetometry results in Fig. 9(c) and the number of carriers from the Hall
effect, as given in Fig. 7(b).

Figure 10: (Color online) Magnetic moment per carrier of the electron gas in
Fe1-xCoxSi as a function of cobalt doping $x$.

The data show an approximately linear decrease as the Co content $x$ rises.
For $x\gtrsim 0.25$, in the metal-like regime, the behavior is much as
expected: the moment per carrier ratio drops, falling to only about 0.5
$\mu_{\mathrm{B}}$ per electron for $x=0.5$. The decrease in the spin-
polarization for high $x$ has been previously observed and explained as being
due to local disorder in the crystal structure induced by addition of Co
atoms.Guevara  _et al._ (2004); Forthaus  _et al._ (2011)

In the low-doping semiconductor-like regime ($x\lesssim 0.25$), the ratio of
moment per carrier exceeds unity, arising from the small shortfall in carriers
per Co that was found in the data presented in Fig. 7(b), and slight excess
moment observed in Fig. 9(c). Physically, the underlying mechanism is not
clear. A plausible picture might be that there are a low number of Co atoms on
Si antisites or in interstitial positions, too few to be readily detected by
XRD or HRTEM, that act both as charge traps and possess local moments
exceeding 1 $\mu_{\mathrm{B}}$ (either alone or by weakly polarising
neighbouring Fe sites). More detailed studies, such as ab initio calculations,
would be required to confirm this scenario. Nevertheless, it is clear that in
this regime, we have a highly spin-polarized electron gas.

To summarize, we have grown a set of Fe1-xCoxSi epitaxial thin films, and
studied the variation in the structural, transport, and magnetic properties in
the range $0\leq x\leq 0.5$. The epilayers are $\epsilon$-phase pure, but with
a deformation of the B20 unit cell into an rhombohedral form by the epitaxial
strain. Qualitatively, the properties of our epilayer samples are similar in
many ways to those of bulk crystals. In particular, we found the metal-
insulator transition to lie in the middle of this range, with a high spin-
polarization in the semiconducting regime ($x\lesssim 0.25$). However there
are quantitative differences, the most important of which is the stabilisation
of magnetic order up to much higher temperatures than in bulk crystals. The
availability of thin films amenable to planar processing techniques is an
important step to realising spintronic devices based on the remarkable physics
of these B20-ordered materials.Jonietz  _et al._ (2010); Schulz  _et al._
(2012); Fert  _et al._ (2013)

###### Acknowledgements.

We acknowledge support from the EPSRC (grant EP/J007110/1) and Marie Curie
Initial Training Action (ITN) Q-NET 264034. We would also like to thank Dr G.
Burnell for useful discussions, Dr M. Ward for TEM sample preparation and
imaging, and Dr D. Alba Venero for help with SQUID measurements.

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# (Mis)perceptions and Engagement on Twitter: COVID-19 Vaccine Rumors on
Efficacy and Mass Immunization Effort

Filipo Sharevski  School of Computing
DePaul University
Chicago, IL
<EMAIL_ADDRESS>Alice Huff
School of Computing
DePaul University
Chicago, IL
<EMAIL_ADDRESS>Peter Jachim  School of Computing
DePaul University
Chicago, IL
<EMAIL_ADDRESS>Emma Pieroni  School of Computing
DePaul University
Chicago, IL
<EMAIL_ADDRESS>
###### Abstract

This paper reports the findings of a 606-participant study where we analyzed
the perception and engagement effects of COVID-19 vaccine rumours on Twitter
pertaining to (a) vaccine efficacy; and (b) mass immunization efforts in the
United States. Misperceptions regarding vaccine efficacy were successfully
induced through simple content alterations and the addition of popular anti
COVID-19 hashtags to otherwise valid Twitter content. Twitter’s misinformation
contextual tags caused a “backfire effect” for the skeptic, vaccine-hesitant
participants reinforcing their opposition stance. While the majority of the
participants staunchly refrained from engaging with the COVID-19 rumours, the
vaccine-hesitant ones were open to comment, re-tweet, like and share the
vaccine efficacy rumors. We discuss the implications of our results in the
context of broadening the effort for dispelling rumors about COVID-19 on
social media.

###### Index Terms:

soft moderation, Twitter, misinformation, COVID-19, rumors

##  I Introduction

COVID-19, as an unprecedented threat to public health, has been surrounded
with many unverified claims about: the virus propagation, mutations, long-term
effects, vaccine development and mass immunization. These ambiguities allowed
for misinformation and rumours to proliferate alongside public health
authority’s claims. Mindful of this “infodemic,” Twitter in time responded by
issuing warnings - in form of contextual tags or interstitial covers - on
Tweets deemed as spreading misinformation related to the COVID-19 pandemic and
vaccine [1, 2]. However, there is no evidence that these warnings are as
effective as anticipated. An early investigation of misinformation warnings on
social media suggest that they may actually “backfire,” i.e. convince people
to believe the misinformation even more than if the label were not there. One
reason for this result is because the warnings were primarily focused on
battling political misinformation, versus COVID-19, which has shown to be
incredibly divisive [3]. This backfiring of warnings led users that believed
whatever stance the misinformation declared to lose trust in the social media
site’s judgment. Instead of halting the spread, this lack of trust culminated
in proliferating the misinformation.

There are real world implications of (mis)information and unverified rumors
having a direct impact on public health in terms of hesitancy to receive a
COVID-19 vaccine. For this reason, we wanted to explore if (a) carefully
altered Twitter content in the form of a rumour could cause misperceptions
about the COVID-19 vaccination, and (b) initiate a desire to engage with this
rumor, even in the presence of warnings in a form of contextual tags. We
focused specifically on COVID-19 vaccines because of the relevance linked to
development and deployment of several vaccines available at the time of the
study in early 2021 [4]. The other leading factor for testing vaccine specific
content was the existing evidence of polarized discourse surrounding the
federal vaccination effort on Twitter. Recent studies have shown that valid
Twitter content on vaccines could be altered to cause a misperception about
the relationship between vaccines and autism [5]. Therefore, we sought to see
how participants might respond to efficacy rumours and whether it would
illicit a desire to engage in the discourse on Twitter. Engagement, whether
for purposes of negating the information or not, aids in further dissemination
of that information, and early evidence showed that Tweets labeled as
misinformation generate more engagement than regular Tweets [6]. Because of
the confines of Twitter interactions, we focused our study on comments, likes,
re-tweets, and sharing actions.

Our results suggest that people are overly sensitive to pessimistic rumours
about the COVID-19 vaccine, as well as alternative hashtags [7]. Our results
showed that it was sufficient for a Tweet to cause a misperception of
otherwise valid content was not very accurate through the inclusion of popular
alternative hashtags #COVIDIOT and #covidhoax. The participants in our study
were also unable to shed their staunch notions about general vaccination
efficacy when interpreting COVID-19 vaccination information on Twitter. The
participants who have existing skepticism of the likelihood of a successful
COVID-19 vaccine being produced (“vaccine hesitant participants”), were more
inclined to accept a pessimistic alteration of COVID-19 vaccine content. The
findings of our study add more evidence to the phenomenon of belief echoes on
Twitter. We found that despite the contextual tags, there was sustained
hesitancy to receive a vaccination personally or for children to receive one.
Additionally, pre-existing beliefs about COVID-19 rumors, alternative
narratives and misinformation were unaltered by the contextual tags.

##  II COVID-19 Content on Twitter

As one of the mainstream social media sites in the United States, Twitter
became a battleground of the COVID-19 online discourse. This heated discourse
required someone to assume the role of taming uncertainties. This duty fell on
public healthcare authorities like the Centers for Disease Control (CDC) and
the World Health Organization(WHO). Tasked with the righting of wrongs, public
health officials timidly and cautiously joined the battle. But because of the
initial lack of information surrounding COVID-19, they did so inconsistently,
e.g. expressing reservations about effectiveness of masks to prevent the
spread of the virus, later changing their view to proclaim masks’ prevention
efficacy [8]. Accordingly, this provided an opportunity to hijack the COVID-19
discourse. It allowed dissenting users to spread rumors and disinformation
regarding the virus, using the official’s mistakes as fodder for their
defense. Due to the majority of the public being at home with unlimited
Internet access and time to kill, the discourse spread like wildfire [9].

Twitter was initially hesitant to implement hard moderation (account bans)
knowing dissenting users’ valid argument for protection of free speech.
Instead Twitter opted to suspend accounts on the grounds that content was
violating the platform’s terms of use. This in and of itself was an enormous
task to undertake due to the amount of nuanced material to comb through.
However, COVID-19 misinformation quickly became an “infodemic,” which forced
the platform to monitor COVID-19 content for false or misleading information
that was not corroborated by public health authorities or subject matter
experts. Their attempt was to apply warnings in a form of interstitial covers
or contextual tags underneath unverified information [1]. The supposed aim of
these warnings is to reduce misleading or harmful information that could
incite people to action and cause widespread panic, health anxiety, and fear
that could lead to social unrest or large-scale disorder.

However, one study found that Twitter’s content with contextual tags generated
more action than content without said labels [6]. Meaning that the
misinformation was spreading more due to the tag. Despite the public health
risk, the study found a mere 1% of the Tweets gathered (a total of 18,765
Tweets) were contextually tag with a COVID-19 warning. A number of these 187
some Tweets were found to be mislabeled simply because they contained the
words “oxygen” and “frequency.” One such Tweet specifically was attempting to
show the failures of the soft moderation for COVID-19 misinformation and
invited others to test the keywords as well, i.e. by writing about mountain
climbing “oxygen” levels and “frequency” to monitor gear. Another study found
that a number of users did not trust the soft moderation intervention because
it opposed their personal beliefs. Consequently, they felt that Twitter itself
was biased and purposefully mislabeling valid content [10].

The effort to tame the uncertainty surrounding COVID-19 and related
vaccinations is a convoluted affair. Even with the attempt of soft moderation
to emphasize invalid COVID-19 information, there exists the possibility for
undetected circulation of COVID-19 misinformation or at least unverified
rumors. These realizations led us to question the probability of bad actors
responding to this demand for information through intentional spreading of
rumors regarding COVID-19 on the social media platform Twitter. In order to
evaluate the results of this threat we chose to analyze participants’
reactions to altered content of Tweets as well as implementation of the
contextual tags to rumors. We were also interested in investigating the level
of engagement of Twitter users initiated by the perception of COVID-19
vaccination information pertaining to (a) vaccine efficacy; and (b) mass
immunization effort.

##  III Research Study

###  III-A COVID-19 Vaccine Misperceptions

We set to examine the possibility for inducing misperceptions regarding the
efficacy of the COVID-19 vaccines as well as the political context of the
COVID-19 mass immunization. We selected two verified content Tweets to act as
the controls (Figure 1 and Figure 3). The first Tweet seen in Figure 1 was a
Tweet reporting the efficacy of the Oxford/Astra-Zeneca COVID-19 vaccines.
This content was selected owing to the controversy surrounding the large-scale
trials for this particular COVID-19 vaccine, its diminished effectiveness
against new variants, as well as the mixed interpretation of the results for
elderly [11]. By the time of the study, this vaccine has not received an
approval by the Food and Drug Administration [12]. This controversy created a
polarized debate on Twitter and we explored if an alteration of the Tweet
feeding into the downplay of its’ effectiveness, shown in Figure 2, would
suffice in affecting the perceived accuracy of the content. We tested the
following hypothesis, accordingly:

  * $H1$: There will be no difference in the perceived accuracy between an altered Tweet containing misleading information about the effectiveness of a COVID-19 vaccine relative to a Tweet containing valid information about the effectiveness of a COVID-19 vaccine.

To remove any bias or control for the “influencer” effect, all Tweets tested
appear to come from a verified account named “VaccinateNow” and indicate a
relatively high level of interaction with 15.3k re-tweets, 17.2 quotations,
and 6.8K likes. This level of engagement is appropriate when compared to
comparable Tweets with important COVID-19 vaccine information previously
observed on Twitter by [6]. For the opposing Tweet, the software from [5] was
utilized to swap the word “robust” with the word “mild,” to correspond to the
differences in responses with the administration of full and half doses [13].
The software also negated the word “could” to “couldn’t” and inserted the word
“lasting” before the word “immunity” to emphasize the lack of evidence about
the length of the immunity provided by this particular COVID-19 vaccine at the
time of the study [14]. The software also inserted two trending hashtags among
top alternative COVID-19 Twitter users, #COVIDIOT and #covidhoax [7, 15].

Figure 1: Verified Vaccine Efficacy Information Tweet. Figure 2: Altered
Efficacy Information Tweet.

The misinformation labels on Twitter gained widespread attention with the soft
(and later hard) moderation of political content [1]. Twitter applied a
similar approach of soft moderation to any unverified claim about the COVID-19
vaccines by applying labels with an exclamation mark and a link where users
can “get the facts about COVID-19.” With the stark political division over the
federal COVID-19 mass immunization [16], we wanted to test the effect of label
alteration in addition to the altering of Twitter COVID-19 vaccine content. We
selected a Tweet, shown in Figure 3, reporting the intentions of the
president-elect Joe Biden to drop the name “Operation Warp Speed” from the
federal vaccine effort to “combat the populist management of the COVID-19
pandemic by the previous administration of Donald Trump” [17] (we are
apolitical as researchers and take no preference in political figures).
Naturally, this turned into ammunition for sustaining the political/mass
vaccination on Twitter. We explored if an alternation of the Tweet – dropping
the key word “name,” shown in Figure 4 – might cause confusion that the effort
for mass vaccination under the new administration is in jeopardy. We also
explored a variation of the modified misinformation Tweet with the addition of
a contextual tag (Figure 5) in order to see if users will heed a
misinformation warning. We tested the following hypotheses, accordingly:

  * $H2$: There will be no difference in the perceived accuracy between an altered Tweet containing misleading information about the COVID-19 mass immunization relative to a Tweet containing valid information about the COVID-19 mass immunization.

  * $H3$: There will be no difference in the perceived accuracy between an altered Tweet containing misleading information and a COVID-19 misinformation contextual tag relative to a Tweet containing valid information about the COVID-19 mass immunization.

Figure 3: Verified Mass Immunization Information Tweet. Figure 4: Altered Mass
Immunization Information Tweet Without a Contextual Tag Figure 5: Altered Mass
Immunization Information Tweet With a Contextual Tag

Because the Tweet’s content is on COVID-19 vaccination, we tested the
relationship between one’s hesitancy to receive a COVID-19 vaccination
(personally and a vaccination for children) as well as their beliefs on
production of safe and effective vaccines and the perceived accuracy of the
Tweets in Figure 1 - 5 with the following hypotheses:

  * $H4_{1}$: There will be no difference in the perceived accuracy of an altered Tweet containing misleading information about the COVID-19 vaccines between Twitter users that are personally hesitant and users that are willing to receive the COVID-19 vaccine for themselves.

  * $H4_{1}$: There will be no difference in the perceived accuracy of an altered Tweet containing misleading information about the COVID-19 vaccines between Twitter users that are hesitant and users that are willing to administer the COVID-19 vaccine to children.

  * $H4_{3}$: There will be no difference in the perceived accuracy of a Tweet containing valid information about the COVID-19 vaccines between Twitter users that believe a safe and effective COVID-19 vaccine is possible and the users that believe that’s not possible.

###  III-B COVID-19 Vaccine Twitter Engagement

Engagement with soft-moderated Twitter content and misinformation content was
found to be high among Twitter users [6]. Therefore, we also explored the
intended engagement with the Tweets in Figure 1 - 5. We assessed the
likelihood of commenting, re-tweeting, liking, and sharing the Tweets to test
the following hypotheses:

  * $H5$: There will be no difference in the likelihood for engagement (commenting, re-tweeting, liking, and sharing) between an altered Tweet containing misleading information about the COVID-19 vaccines relative to a Tweet containing valid information about the COVID-19 vaccines.

  * $H6_{1}$: There will be no difference in the engagement (commenting, re-tweeting, liking, and sharing) with an altered Tweet containing misleading information about the COVID-19 vaccines between hesitant and non-hesitant Twitter users, both personally and for children.

  * $H6_{2}$: There will be no difference in the engagement (commenting, re-tweeting, liking, and sharing) with a Tweet containing valid information about the COVID-19 vaccines between hesitant and non-hesitant Twitter users, both personally and for children.

  * $H7_{1}$: There will be no difference in the engagement (commenting, re-tweeting, liking, and sharing) with an altered Tweet containing misleading information about the COVID-19 vaccines between Twitter users that believe a safe and effective COVID-19 vaccine is possible and the users that believe that’s not possible.

  * $H7_{2}$: There will be no difference in the engagement (commenting, re-tweeting, liking, and sharing) with a Tweet containing valid information about the COVID-19 vaccines between Twitter users that believe a safe and effective COVID-19 vaccine is possible and the users that believe that’s not possible.

###  III-C Sampling and Instrumentation

Prior to initiating the study, we received approval from our local
Institutional Review Board. We set to sample a population that met the
following base requirements: participant was 18 years old or above, was a
Twitter user, and has encountered at least one Tweet in their Twitter feed
that relates to COVID-19 vaccines. These requirements were implemented using
metric tools as part of survey posting on Prolific and “Human Intelligence
Tasks” (HITs) posting on Amazon Mechanical Turk (“MTurk”). We crafted the
content of the Tweets to be relevant to the participants, such that they may
wish to meaningfully engage with the Tweet’s content (i.e., their responses
are not arbitrary).

To assess the perceived accuracy we used the questionnaire from [3] for each
of the Tweets on a 4-point Likert scale (1-not at all accurate, 2-not very
accurate, 3-somewhat accurate, 4-very accurate). To assess participants’
hesitancy and beliefs regarding the COVID-19 vaccine, we used the
questionnaire from [18]. To assess the subjective attitudes we asked if the
participants (a) expect efficacious vaccine to be developed (Yes/No); (b) will
receive a COVID-19 vaccine (Yes/No/I Don’t Know); and (c) if children should
receive a COVID-19 vaccine too (Yes/No). To gauge whether participants’ would
engage with the Tweet, we used a standardized questionnaire for Twitter
engagement on a 7-point Likert scale (1-extremely likely; 7-extremely
unlikely) [5]. We utilized an experimental design where participants were
randomized into one of five groups: (1) verified vaccine efficacy information
Tweet; (2) altered vaccine efficacy information Tweet; (3) verified mass
immunization information Tweet (4) altered mass immunization information Tweet
without a warning tag; (5) altered mass immunization information Tweet with a
warning tag.

##  IV Results

We conducted an online survey (N = 606) in January and February 2021. The
break down of participants’ sex were as follows: 54% male, 43.9% female, and
2.1% participants identified as non-cis, non-binary or preferring not to
answer. The age brackets were distributed as follows: 20.0% [18 - 24], 37.5%
[25 - 34], 25.5% [35 - 44] and 16.8% [45 - above]. The political leaning of
the sample was skewed towards liberals: 51.8% participants identified as
liberal-leaning, 22.4% identified as moderate and 25.8% participants
identified as conservative-leaning.

###  IV-A COVID-19 Vaccine Perceptions on Efficacy

Initially we hypothesized that there would be no difference in the perceived
accuracy between an altered Tweet containing misleading information and an
original Tweet containing valid information about the effectiveness of a
COVID-19 vaccine. We found a significant difference in the perceived accuracy
between the Tweets in Figure 1 and Figure 2 ($U=981$,
$p=.000^{*},(\alpha=0.05)$, Cohen’s $d=0.832$ large). Based on this result, we
reject our first hypothesis and accept the alternative where the contextual
rewording was perceived as “not at all accurate,” whereas the original Tweet
was perceived as “somewhat accurate” on average. Perception of accuracy was
altered through 1) swapping the word “robust” with “mild,” 2) the rewording to
emphasize the lack of evidence of lasting immunization, 3) implementation of
the most popular COVID-19 alternative hashtags (#COVIDIOT and #covidhoax).
Either the participants in the altered Tweet group were overly sensitive to a
pessimistic COVID-19 vaccine outlook, or a simple inclusion of alternative
hashtags signaled “opposition, fake news” (recalling our liberal-leaning
sample) [19].

Hesitancy to receive the vaccine proved to be a decisive factor in how the
altered Tweet was perceived. We found a statistically significant difference
between the pro-vaccination and anti-vaccination participants for both
condition of receiving a COVID-19 vaccination personally and administering one
to children ($U=567$, $p=.017^{*},(\alpha=0.05)$, Cohen’s $d=0.4$ medium) and
($U=954$, $p=.033^{*},(\alpha=0.05)$, Cohen’s $d=0.4$ medium), respectively.
Rejecting $H4_{1}$ and $H4_{2}$ hypotheses, we accept the alternative
hypothesis that one’s hesitancy to receive a vaccine factors into how COVID-19
information is perceived. The hesitant participants perceived the altered
Tweet as “somewhat accurate,” while the pro-vaccination participants perceived
it as “not very accurate.” This comes as no surprise given that the
pessimistic rewording confirms the suspicions of the overall COVID-19
vaccination effort [20]. To underline this point, we also had to reject the
$H4_{3}$ hypothesis and accept the alternative. The alternative suggested that
the participants with a pre-existing skepticism of the possibility of a safe
and efficacious vaccine also deemed the alternative Tweet as ”somewhat
accurate” ($U=266$, $p=.030^{*},(\alpha=0.05)$, Cohen’s $d=0.3$ small).

###  IV-B COVID-19 Vaccine Perceptions on Mass Immunization

To investigate the possibility for misperceptions further we next hypothesized
that there will be no difference in the perceived accuracy between an altered
and original Tweet on the topic of mass immunization. For the second test of
misperception of COVID-19 vaccines we opted to test a more politicized Tweet.
COVID-19 was one of the main focal points of the political battle during and
after the U.S. elections in 2020 that naturally flooded over to Twitter [7].
Therefore, we tested a Tweet regarding the new administration’s intentions for
renaming “Operation Warp Speed,” the Department of Defense’s effort for rapid
U.S. mass immunization [21]. Here we took a slightly more adversarial approach
in attempting to muddy the waters about what the President-elect had reported
to drop - just the name or perhaps the entire operation, given his open
criticism of the operation overall [22].

We found a significant difference in the perceived accuracy between the Tweets
in Figure 3 and Figure 4 ($U=1845.5$, $p=.023^{*},(\alpha=0.05)$, , Cohen’s
$d=0.619$ medium). Based on this result, we reject our second hypothesis and
accept the alternative one where the contextual rewording was perceived as
“not very accurate,” whereas the original Tweet was on average considered
“somewhat accurate.” This is a promising result suggesting that Twitter users
in our liberal-leaning sample can accurately assess an attempt for spreading
rumours about this vital operation for mass immunization. Perhaps this is an
expected result given that liberal-leaning, and possibly moderate users, are
sensitive to any attempt to tarnish the actions of Donald Trump, who is widely
accepted as the top misinformation machine over the last four years[7]. Or
these participants closely monitor mainstream media compared to their
conservative counterparts [23].

Indeed, the participants heeded the contextual tag applied to the altered
variant of the Tweet (Figure 5). We found a significant result in the
perceived accuracy for the labeled Tweet and the original Tweet in Figure 3
($U=2825$, $p=.002^{*},(\alpha=0.05)$, Cohen’s $d=0.532$ medium). We rejected
the third hypothesis and accepted the alternative, that the warning tag indeed
nudged the participants to perceive the Tweet as “not at all accurate.” This
evidence goes along with the observation that misinformation labels on social
media works, if that label aligns with one’s biases and receptivity to the
content at stake [3]. This finding indicates that the liberal-leaning and
moderate participants trust Twitter and the soft moderation of COVID-19
vaccination content. This is contrary to the evidence of opposition sentiment,
that did not trust the soft moderation intervention and felt that Twitter
itself was biased and mislabeling content [24]. As we previously found,
hesitancy to receive the vaccine again proved to be a decisive factor in how
the misinformation labeled Tweet was perceived. We found a statistically
significant difference between the pro-vaccination and anti-vaccination
participants for both condition of receiving a COVID-19 vaccination personally
and administering one to children ($U=453$, $p=.033^{*},(\alpha=0.05)$,
Cohen’s $d=0.4$ medium) and ($U=608$, $p=.014^{*},(\alpha=0.05)$, Cohen’s
$d=0.233$ small), respectively. Rejecting $H4_{1}$ and $H4_{2}$ hypotheses, we
accept the alternative hypothesis that one’s hesitancy factors into how
COVID-19 information is perceived. The vaccine hesitant participants perceived
the altered Tweet as “somewhat accurate,” while the pro-vaccination
participants viewed it as “not very accurate.” Again, this breakdown reveals
that heeding a misinformation warning relies on the biases regarding the
content of the Tweet [3]. We also had to reject the $H4_{3}$ hypothesis and
accept the alternative one suggesting that the vaccine hesitant participants
deemed the altered Tweet claiming Operation Warp Speed as “somewhat accurate”
despite the soft moderation warning ($U=266$, $p=.030^{*},(\alpha=0.05)$,
Cohen’s $d=0.3$ small).

###  IV-C COVID-19 Vaccine Twitter Engagement

To test the likelihood of engagement with each of our Tweets in the study, we
hypothesised that there will be no difference in level of commenting, re-
tweeting, liking, and sharing between an altered and the original versions of
the Tweets in Figures 1-5. Comparing the engagement with the Tweets on
COVID-19 vaccine efficacy (Figure 1 and Figure 2), we observed a statistical
difference in the case of re-tweeting ($U=986.1$, $p=.002^{*},(\alpha=0.05)$,
Cohen’s $d=0.2$ small), liking ($U=165.9$, $p=.000^{*},(\alpha=0.05)$, Cohen’s
$d=0.23$ small), and sharing ($U=1007$, $p=.002^{*},(\alpha=0.05)$, Cohen’s
$d=0.267$ small0), where the altered Tweet was “extremely unlikely” to be
engaged with, compared with the “somewhat unlikely” with the original Tweet.
Comparing the engagement with the Tweets on the COVID-19 mass immunization, we
didn’t observe any statistical difference.

In contrast to the evidence of high engagement with alternative and soft
moderated Tweets [6], our sample appeared quite reserved in terms of
engagement with the content offered. The unwillingness to engage with the
twitter rumors is otherwise consistent with the spiral-of-silence effect
observed for the general vaccination debate in [5]. The evidence of high
engagement was reported in the context of mocking the original poster and
attempting to correct or debunk the perceived misinformation. However, our
sample group was observed to have no intention of commenting or replying to
either of the altered Tweets directly in order to take said actions.

This could be a result of social network fatigue being a year into social
media coverage of COVID-19 [25]. Otherwise, we observed a significant
difference in engagement when we controlled for the hesitancy of COVID-19
vaccination, both personally and for children. The vaccine hesitant
participants were “somewhat likely” to comment, re-tweet, like or share the
altered Tweet seen in Figure 2. The ones with little belief for a production
of safe and efficacious vaccines were also significantly more inclined to
comment and re-tweet the altered Figure 2 Tweet, but not to like or share it.
Rejecting the $H6_{1}$ and $H7_{1}$ hypotheses only for the pessimistic case,
but not the other alterations including the soft moderated Tweet, we suspect
is due to subjective interpretation of the content, as we noted previously.

##  V Discussion

###  V-A Broader Context of the Results

In this study, we attempted to manufacture “misinformation” that essentially
categorizes as a rumor more so than any of the other alternative narrative
types [26]. The deliberate choice for a nuanced modification of small,
seemingly inconsequential changes in the content was made to capture the
zeitgeist of uncertainty surrounding COVID-19 vaccination. This is especially
prevalent in the politicization of the mass immunization effort. In order to
capture the perceptions and the intent for engagement with content that is not
clear cut, we chose this more nuanced approach versus blatant misinformation
like the predominant COVID-19 vaccine sentiment on Parler [27]. Yet another
study of testing the claim that “the COVID-19 vaccine will infect you with
HIV” with our liberal-leaning, dominantly young sample, would not have
adequately yielded the perception whims and engagement avoidance proclivity.
Finally, the more divisive misinformation might not have accurately assessed
the vaccine hesitant participants’ true inclinations and ways of interpreting
information that fits broadly into a skeptic outlook of the mass COVID-19
vaccination.

In terms of perceptions of COVID-19 rumors as Twitter content, this study
helped conclude that existing biases, such as reservations of government’s
intention or skepticism of vaccine efficacy, have an impact on perception.
Those with pre-existing skepticism and a hesitancy to personally receive a
COVID-19 vaccine or administer one to children were more accepting of the
altered Tweets presented. Those with no hesitancy in receiving a COVID-19
vaccine, and who believed in efficacy of existing vaccines, in contrast
decisively did not accept the rumors. This example shows the effect of rumor
propagation via echo chambers on social media [28].

While other studies implied that there would be heavy engagement with
misinformation, even for those who may disagree or not believe the
misinformation, we found that most Twitter users in our sample were unlikely
to comment, like, re-weet or share altered Tweets. Perhaps the rumors give
people a pause because they cannot immediately infer the weaponizing value of
the Tweet for their expression on Twitter versus the clear cut misinformation
like “5G causes coronavirus.” The study showed that only those with skepticism
were willing to engage with the Tweets. Another reason why the majority of the
sample group, beyond the spiral-of-silence, may have been less inclined to
engage may have to do with “social network fatigue” [25]. The outcome of this
fatigue is that social network users may skim or skip irrelevant information
or even avoid some information, and exhibit ignoring and avoidance behaviors.

###  V-B Usable Security Implications

We also focused on soft moderation, as an early effort to regulate the
COVID-19 information, since misinformation could have ramifications beyond the
microblogging sphere for the health of the general public. The majority of our
participants were receptive to the soft moderation, which is a promising
result and we acknowledge and support this effort for misinformation warnings.
That being said, young liberal-leaning people do not make up the whole of the
population. The concern we have is with the minority of our sample that chose
to ignore these warnings. Efforts have been invested in increasing the clarity
of the messages and design of soft moderation warnings to attract attention
and motivate users. However, old habits die hard and habituation is a complex
problem transcending security designs.

The contextual tag implemented by Twitter in blue font appears as a banner
after the Tweet content and any images/links with a favicon of an encircled
exclamation point stating “Get the facts about COVID-19,” which redirects
users to verified public health official’s information. This design and
formatting can be observed as innocuous, and does not explicitly address that
the Tweet’s content aims to mislead users about COVID-19 or its vaccines. A
similar visual formatting is used for labeling Tweets with unverified
political claims, e.g. “Get the facts about mail-in ballots” [1]. Research has
shown that even if people are exposed to misinformation multiple times, it can
alter their memories [29]. For this reason, it may be worth exploring the
potential benefits of adding the contextual tag above the content versus below
it to assess if it hinders users from reading the misinformation.

Twitter just recently decided to up the ante in tagging intentional content-
level exploits about COVID-19. The moderation is changing to a hybrid between
hard and soft moderation, with a “striking system” that results in an ultimate
ban from the platform after 5 strikes [30]. It is interesting to research both
the positive and negative externalities of this hybrid moderation effort. The
hybrid moderation might restore the balance on Twitter, but further push the
polarization between platforms that was already observed with the formation of
a sizable Parler community of skeptic, COVID-19 vaccine-hesitant communities
on Parler [27].

###  V-C Future Research

Extensive further research should be done investigating the full ramifications
of misinformation and soft/hybrid moderation by social media platforms. A
promising line of research is the combination of soft and hard moderation,
given that Twitter has exercised the right to ban or suspend accounts
indefinitely that have been tagged for misinformation in the past, like in the
case of Donald Trump. Twitter is going to implement a strike system for
misinformation Tweets [30] and research could probe the warning
tagging/covering algorithm and reverse engineer it to find if a strike system
will be more effective in curbing users posting misinformation, before the
account gets permanently banned.

Soft moderated content is typically closely related to trolling content, so
there is room for exploration of this relationship, such as understanding if
warning tagged/covered Tweets provoke emotional response and if so, what kind.
Similar to research conducted on the evolution of COVID-19 information, the
warning tagging/covering could be associated with an evolution of political
information operations on Twitter. It would be beneficial to trace the
relationship between actual users and social bots rigging the engagement
metrics as in the previous vaccine debates on Twitter [5].

###  V-D Scope Limitations

We used Tweets that were tied to a particular vaccine vendor and a single
decision regarding the public relations of United States mass immunization
efforts during the period of January-February 2021. Twitter content tested did
not include the actual operational changes promised or undertaken by then
President Biden, which could be perceived with a different level of accuracy
after a certain period of time. It is possible that other vaccines from
various non-US vendors like Sanofi, Sinopharm or Galeneya, could yield
different perception of accuracy or strength of soft moderation. Overall, the
findings in the present study may be specific to the alterations we tested,
and cannot be generalized to other alterations, for example swapping the word
“Warp” with ‘Top” in the second Tweet. Participants who are frequent social
media users in general may be desensitized to the information presented in the
Tweets. Which seems likely considering the breakdown of political leanings and
age bracket of the majority of the test sample. The participants may also have
been biased from heightened exposure to mainstream media and social network
information about COVID-19 vaccines and the Biden administration mass
immunization efforts. Both of these factors may have limited participants’
perceptions and desire to engage with the content presented irrespective of
the alterations.

##  VI Conclusion

This study showed that a majority of participants were able to recognize
rumors and had no inclination to engage with those rumors (they did not have a
desire to like, comment, re-tweet, or share the content). However, the
majority of the participants identified as pro-vaccine and our sample was
skewed towards the liberal-leaning. These existing biases likely impacted
their perceptions and lack of motivation to engage. The more participants who
showed hesitancy to personally receiving a vaccine or administering them to
children found the rumors more “accurate” and had more of an appetite to
engage with the altered Tweets. While the skeptic, vaccine-hesitant
participants were in the minority in our study and might well be a minority on
twitter, that is not necessarily the makeup of the entire social media user
base, especially considering alternative platforms like Parler. It is
important to consider the potential consequences for overall public health of
the soft moderation. While it is reassuring that majority of the participants
had enough COVID-19 literacy to recognize rumors, this does not solve the
problem of misinformation spreading on Twitter and the spill over on other
alternative platforms. Nor does it alter the existing opinions of the opposing
population with hesitancy to receive vaccination. Therefore, we an improved
soft/hybrid moderation should be extensively explored in future towards
effective eradication of valid COVID-19 vaccine information.

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