#  Tuning the structural, electronic and magneto-transport properties of spin-
orbit Mott insulator Sr2IrO4

Priyamedha Sharma1 Saurabh Singh2,3 Kentaro Kuga2,3 Tsunehiro Takeuchi2,3 R.
Bindu1 Corresponding author<EMAIL_ADDRESS>1School of Basic Sciences,
Indian Institute of Technology Mandi, Kamand, Himachal Pradesh- 175005,
India2Toyota Technological Institute, Nagoya, Aichi 468-8511, Japan3Japan
Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan

###### Abstract

In this work, we investigate the tunability of the structural, electronic and
magneto transport properties of polycrystalline Sr2IrO4. Both the compounds
exhibit transition from paramagnetic to canted antiferromagnetic (AFM)
structure $\sim$240 K. At low temperatures, the extent of the bifurcation of
the magnetisation curves during the field cooled and zero field cooled cycles
establishes that the magnetic anisotropy in the _as prepared_ sample is more
as compared to the _vacuum annealed_ one. Based on the behaviours of the
structural parameters and the magnetic studies, our results show that the
canted AFM structure is stabilized in a larger temperature range in the case
of the _annealed_ sample ($\sim$165K) as compared to the _as prepared_ one
($\sim$115K). At low temperatures, for both the samples, a phase, of glassy
nature competes with the canted AFM phase. The temperature extent to which
both these phases coexist for the _as prepared_ and the _annealed one_ is
$\sim$115K and $\sim$70K, respectively. We also observe the importance of
hybridization of the Ir 5 _d_ and O 2 _p_ states in the canted AFM phase. Our
results show a strong link between the extent of magnetic anisotropy and the
difference in the in-plane Ir-O-Ir bond angles between these two samples.The
transport studies reveal that for both the samples, in the high temperature
region of study, the conduction mechanism is governed by Arrhenius model. In
the intermediate temperature range, variable range hopping (VRH) and Arrhenius
models govern the transport in the _as prepared_ and the _annealed ones_ ,
respectively. At low temperatures, the conduction mechanism occurs through
Efros–Shklovskii-VRH and VRH mechanisms for the _as prepared_ and the
_annealed_ samples, respectively.The magneto resistance measurements indicate
higher negative magneto resistance in the annealed at all temperatures which
can be explained by larger reduction in spin dependent scattering and a higher
sensitivity of Ir-O-Ir in-plane bond angle to the applied magnetic field. The
field dependence of magneto resistance at 10K suggests a co-existing glassy
magnetic phase along with canted antiferromagnetic structure in the as
prepared sample and a suppression of this glassy magnetic phase in the
annealed sample. The combined analysis of all the results highlight the role
of disorder for the magnetic and transport properties of this compound.

###### pacs:

61.05.cp,75.47,71.27.+a,73.43.Qt

##  I Introduction

Iridates have attracted significant amount of research due to its
unconventional properties like stabilization of different topological phases
of matter, superconductivity, spin liquid behaviours, kitaev modes
etc.Witczak-Krempa  _et al._ (2014); Rau  _et al._ (2016); Cao and Schlottmann
(2018) These properties emerge due to strong interplay between the spin-orbit
coupling (SOC), on-site Coulombic interaction, Hund’s coupling and crystal
field interactions. In the case of Ruddlesden popper series Srn+1BnO3n+1, for
n=1 that represent the dimensionality, as one varies the transition metal ion,
B from having electronic character 3d to 5d, unique properties emerge due to
strong interplay of various energy scales as mentioned above. The
distinguishing factors are observation of charge gap for Sr2IrO4 despite the
extended nature of the 5d states in comparison to the 3d statesKim  _et al._
(2008); observation of high magnetic transition temperatures but with low
moment values; the canting of the magnetic moment follows the rotation of the
IrO6 octahedra; weak coupling between the transport and magnetism; saturating
resistivity at low temperatures etc.Ye  _et al._ (2013); Cao and Schlottmann
(2018)

Interest in Sr2IrO4 compound were driven initially due to its structural
analogue with high Tc cuprate based superconductor from the structural,
magnetic and electronic point of view.Huang  _et al._ (1994); Cava  _et al._
(1994); Cao  _et al._ (1998) Many theoretical studies predicted a possibility
of superconductivity upon electron or hole doping in Sr2IrO4.Wang and Senthil
(2011); Yang  _et al._ (2014); Gao  _et al._ (2015) In contradiction to these
results, the transport and magnetic measurements on the doped bulk samples did
not show superconductivity. In this compound, electron doping can be achieved
by substituting La in the place of Sr ion or by introducing oxygen
vacancies.Chen  _et al._ (2015); De La Torre  _et al._ (2015); Pincini  _et
al._ (2017); Gretarsson  _et al._ (2016) The hole doping is realized by
substituting Ru/Rh at Ir site or K at Sr site.Klein and Terasaki (2008);
Calder  _et al._ (2015); Lee  _et al._ (2012); Yuan  _et al._ (2015) It has
been observed that even a small amount of chemical doping led to the evolution
of spin-orbit Mott insulating state into an exotic metallic state with the
increase in the doping level. On the other hand, oxygen deficient single
crystals produced by annealing in vacuum exhibited a metal to insulator
transition at low temperatures.Korneta  _et al._ (2010) The nature of the
metallic state induced by these electron or hole doping is a subject of
interest in recent years due to their novel properties such as robust AFM
metallic state,Wang  _et al._ (2018) phase separationChen  _et al._ (2015);
Calder  _et al._ (2015) etc,.

The ground states of the 5d systems are governed by the hopping of the
electrons through direct d-d overlap and/or through the intervening oxygen
ions. Such overlap is strongly dependent on the local structural parameters.
Hence, strain and/or disorder play critical role in deciding the physical
properties. One of the novel properties observed in Sr2IrO4 is its unusual
link between its exotic properties and the structural aspects through the spin
orbit coupling (SOC). At room temperature (RT) this compound stabilizes in
tetragonal structure with I41/acd spacegroup.Crawford  _et al._ (1994); Huang
_et al._ (1994) The characteristics of this space group is that there occurs
antiphase rotation of the corner linked IrO6 octahedra along the layering axis
and there by leading to the doubling of the c-parameters in comparison to the
high temperature high symmetric structural phase (T$>$ 1000 K) with space
group I4/mmm.Ranjbar and Kennedy (2015) This leads to uniaxial negative
thermal expansion (along the c-axis) and hence an increase in the unit cell
volume. The octahedral rotation breaks the inversion center on oxygen atom
connecting the two Ir atoms which leads to the appearance of Dzyaloshinskii-
moriya (DM) interactionDzyaloshinsky (1958) along with the super exchange
interaction between the Jeff=1/2 pseudospins.Jackeli and Khaliullin (2009);
Katukuri  _et al._ (2014) The DM interaction induces a canting of
antiferromagnetically coupled Jeff=1/2 spins leading to the appearance of a
weak ferromagnetism below $\sim$240K. The Jeff=1/2 moments track the in-plane
octahedral rotation through a strong magnetoelastic coupling.Ye  _et al._
(2013) It is important to note that the structural transition from I4/mmm to
I41/acd space group is of second order kind where a variation in the
transition temperature is expected to occur at local scale due to
disorder.Rocha-Rodrigues  _et al._ (2020) It has also been realized that
positive thermal expansion occurs in the I4/mmm phase. Such thermal tendencies
due to local disorder can give rise to unconventional behaviours.

In single crystal samples of Sr2IrO4, the reported magnetization curves along
a and c axes, exhibit distinct features at around $\sim$100K and $\sim$25K, in
addition to the weak ferromagnetic transition at $\sim$240K. These features
are attributed to a spin reorientation transition leading to a decrease of
magnetic anisotropy along a and c axes.Ge  _et al._ (2011) Also, temperature
dependent dielectric constant measurementsChikara  _et al._ (2009) shows a
peak at $\sim$100K with a strong frequency dependence, indicating a
frustrating magnetic order at low temperatures. There are also reports of co-
existence of cluster glass phase present along with canted AFM phase at low
temperatures in polycrystalline samples.Manna  _et al._ (2014) All these
results indicate a complex magnetic structure at low temperatures and it
fairly deviates from the canted AFM structure with moments confined to the
_ab_ -plane.

There are contradictory reports in literature with regard to conduction
mechanism in single crystal as well as polycrystalline samples. Three
temperature regions with different thermal activation behaviour is observed in
single crystal specimens.Ge  _et al._ (2011) In the case of polycrystalline
samples, Bhatti _et al_ Bhatti  _et al._ (2014) have reported 2-dimensional
(2D) variable range hopping(VRH) in three different temperature regions with
different localization lengths. But Kini _et al_ Kini  _et al._ (2006) have
observed resistivity proportional to ln(T) in the paramagnetic phase and
Arrhenius behaviour in the intermediate temperature range, followed by a
3D-VRH mechanism at low temperatures. On the other hand, thin film samples
exhibit a thickness dependent transition from 3D-VRH behaviour to
Efros–Shklovskii variable range hopping behaviour.Lu  _et al._ (2014) These
diverse reports suggest a role of sample preparation conditions and sample
quality (defects, disorder etc) in deciding the nature of conduction at
different temperature intervals. Although a change in conduction mechanism has
been observed across the magnetic transition in all the cases, there is no
apparent correlation between nature of conduction mechanism and the magnetic
ordering.

As already mentioned, Ir-O-Ir bond angle plays a crucial role in deciding the
magnetic and transport properties in this compound. The knowledge of
temperature evolution of structural parameters and the bond angle is necessary
to have a clear understanding of coupling between structure and physical
properties. An earlier neutron diffractionCrawford  _et al._ (1994) and a
synchrotron x-ray diffractionRanjbar and Kennedy (2015) (xrd) studies have
reported a decrease in this bond angle with the decrease in temperature. On
the contrary, an xrd(Bhatti  _et al._ , 2014) study has reported an increase
in the bond angle with the reduction in temperature.

Figure 1: The crystal and magnetic structure of Sr2IrO4.(a)Conventional unit
cell of Sr2IrO4 (b)A part of unit cell in _ab_ -plane showing in-plane
rotation of IrO6 octahedra (c)A part of the unit cell in _bc_ -plane showing
different bonds (d)Canted AFM structure of Sr2IrO4 as reported in the
literature,Ye  _et al._ (2013) arrows on the right hand side indicate the
direction of net magnetic moment from individual layers in the _ab_ -plane.

The chemical substitution introduces disorder in the system which alters the
magnetic and transport properties. Often, undoped parent compounds possess
stoichiometric disorder. Recently, a suppression of metal-insulator transition
has been reported in pyrochlore iridates (R2Ir2O7) due to changes in R/Ir
ratio.Sleight and Ramirez (2018) Although there are many reports on
polycrystalline Sr2IrO4 with attempts of different chemical substitutions in
search of superconductivity, there is a lack of studies focussing on the
effect of disorder in this system. Apart from these behaviours, from the
technological aspect, the system with compositional disorder has variation in
its bond strengths. Hence, one can expect emergent phenomena at different
length scales and hence exploiting the required properties as per our need.
Towards this, we aim at studying the electronic, magnetic properties and its
interplay in Sr2IrO4 compounds which are prepared under different preparation
conditions.

Keeping all these above mentioned aspects in mind we have investigated the
structural, magnetic, transport and magneto-transport properties of
polycrystalline Sr2IrO4 and explore the effect of vacuum annealing on these
properties. Annealed polycrytalline samples of Sr2IrO4 were found to be more
insulating than the as-prepared samples in contrast to what has been observed
in single crystal samples. The central findings of this work are : (a)Vacuum
annealing reduces Sr/Ir ratio in addition to incorporating oxygen vacancy and
enhances the tetragonality (c/a ratio) of the unit cell; (b) The annealed
samples exhibit enhanced magnetization and resistivity at all temperatures;
(c) connectivity between magnetic anisotropy and Ir-O-Ir (in-plane) bond
angles; (d)The temperature dependence of transport behaviour is affected by
annealing with implications of lesser disorder in annealed sample; (e)The
magneto-transport studies have shown a significant enhancement in the negative
magnetoresistance in the vacuum annealed sample. All these changes are
associated with the changes in Ir-O-Ir in-plane bond angle and other
structural parameters extracted from low temperature xrd measurements. The
combined analysis of all the results suggests a disorder induced phase
separated state at low temperatures in _as-prepared_ samples which gets
suppressed after vacuum annealing.

##  II Experimental

The polycrystalline samples of Sr2IrO4 were prepared by solid state reaction
method using stoichiometric amounts of IrO2 (99.9$\%$ pure) and
SrCO3(99.995$\%$ pure). A stoichimoetric mixture of the raw materials were
ground for about 3 hours before calcining at 900∘C for 24 hours followed by
1000∘C for 24 hour and 1100∘C for 24 hours with intermediate grindings. The
latter heat treatments were done in the pellet form. Heating and cooling rates
utilized are 2∘C/minute and 1∘C/minute respectively. This method of
preparation has been frequently employed in the literature for synthesizing
polycrystalline Sr2IrO4 samples.Klein and Terasaki (2008); Bhatti  _et al._
(2014) To incorporate oxygen deficiency, the pellets of the samples were
heated in an evacuated quartz tube ($\sim$10-5mbar) at 600∘C for two different
time intervals of 2.5 hours and 5 hours. The properties of the samples heated
for 2.5 hours were similar to that of the as prepared compound. Hence we shall
present a comparative study of the as prepared Sr2IrO4 (_SIO-as prep_) and the
sample which is vacuum annealed for 5 hours (_SIO-anneal_).

The temperature dependent xrd patterns of all the samples were collected using
Smart Lab 9kW rotating anode x-ray diffractometer with Cu-K$\alpha$ radiation.
All the patterns were collected in the 2$\Theta$ range of 10∘ \- 90∘ with the
step size of 0.02∘. The scanning speed during the measurements was 1∘/minute.
The low temperature measurements were performed inside a cryostat from RT to
12K for 15 different temperatures.

The energy dispersive x-ray analysis (EDS) measurements were performed on Nova
Nano SEM-450 which is fitted with an energy dispersive x-ray spectrometer.

The temperature dependent dc magnetization measurements were performed using
Magnetic Properties Measurement Systems (MPMS) in the temperature range of 300
K to 2 K at an applied magnetic field of 1T. The magnetic moment measuring
system is from Quantum design, USA. The temperature dependent resistivity
measurements were carried out using four probe method using commercial
physical properties measurement system from Quantum design, USA. The
magnetoresistance measurements were carried out at temperatures 300 K, 180 K,
150 K and 10 K, the magnetic field was applied up to 9 Tesla.

##  III Results and Discussions

The crystal structure of Sr2IrO4 is shown in Fig.1(a).In Fig.2(a-b), we show
the Reitveld refinement of the _xrd_ pattern of _SIO-as prep_ and _SIO-anneal_
samples collected at 300K. The experimental spectra shows a good agreement
with tetragonal _I4 1/acd_ structural model, in line with the
literature.Crawford  _et al._ (1994); Klein and Terasaki (2008); Bhatti  _et
al._ (2014) The refined RT structural parameters along with the R-factors of
refinement are shown in Table-I. The RT xrd pattern of _SIO-as prep_ as well
as _SIO-anneal_ also indicated the presence of small but identical amounts of
SrIrO3 impurity as shown in the inset of Fig.2(a). These impurities at
2$\theta$ $\sim$19.5∘ and $\sim$32.15∘ correspond to monoclinic C2/c phase of
SrIrO3 compound.Longo  _et al._ (1971)

Figure 2: Reitveld refinement of room temperature xrd pattern of (a)_SIO-as
prep_ (b)_SIO-anneal_. Experimental patterns are fitted to I41/acd tetragonal
structure. The open and the line symbols correspond to the observed and
calculated patterns, respectively. The Bragg reflections and the residual are
given in black and green colours, respectively. The insets display enlarged
view of the pattern with arrows indicating the positions of SrIrO3 impurity
phase.

The compositional analysis of the samples were carried out by Energy
dispersive x-ray analysis (EDS) technique. The expected atomic percentages of
Sr, Ir and O for a stoichiometric Sr2IrO4 are respectively, 28.57, 14.28 and
57.14. The atomic percentages of Sr, Ir and O obtained for _SIO-as prep_ are
respectively $\sim$24.09, $\sim$11.61 and $\sim$64.3 while for _SIO-anneal_ ,
they are $\sim$25.21, $\sim$12.5 and $\sim$62.2. The composition values
indicate deficiency of Sr and Ir in both the samples. However, the ratio Sr/Ir
is $\sim$2.08(9) in _SIO-as prep_ sample while it is $\sim$2.02(9) for _SIO-
anneal_ sample. Although this ratio is similar within the error bar, there is
a decreasing trend from _SIO-as prep_ to _SIO-anneal_ sample. Hence, _SIO-
anneal_ has improved stoichiometry in comparison to _SIO-as prep_ sample. The
atomic percentage values of oxygen are very much larger than the expected
value in both the samples. This arises due to limited sensitivity of EDS to
oxygen. The vacuum annealing process is expected to incorporate oxygen
deficiency and the obtained atomic percentage values indicate a relatively
lesser oxygen in _SIO-anneal_ sample. A possible reason for the observed off-
stoichiometry in Ir may be due to the volatile nature of IrO2 at high
temperatures as reported in other Ir based oxides.Sleight and Ramirez (2018)
The presence of Ir vacancy may result in the change of oxidation state of some
Ir+4 ions to non-magnetic Ir+5. In essence, vacuum annealing has reduced the
oxygen content along with a reduction of Sr/Ir ratio from $\sim$2.08 to
$\sim$2.02.

Table 1: Crystallographic information for _SIO-as prep_ and _SIO-anneal_
samples at RT obtained from Rietveld refinement using _I4 1/acd_ space group.
The atomic positions of Sr, Ir, O1 and O2 are
(0,0.25,z),(0,0.25,0.375),(0,0.25,z) and (x, x+0.25,0.125)

|  | _SIO-as prep_ |  |  |  |  |  | _SIO-anneal_ |  |  |
---|---|---|---|---|---|---|---|---|---|---|---
Lattice parameters |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
a |  |  |  |  | 5.4975 Å |  |  |  |  |  |  |  |  | 5.4968 Å |  |  |
c |  |  |  |  | 25.791 Å |  |  |  |  |  |  |  |  | 25.799 Å |  |  |
Atomic positions |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Sr |  | z |  |  | 0.5506 |  |  |  |  |  |  |  |  | 0.5499 |  |  |
O1 |  | z |  |  | 0.4692 |  |  |  |  |  |  |  |  | 0.4697 |  |  |
O2 |  | x |  |  | 0.1977 |  |  |  |  |  |  |  |  | 0.1944 |  |  |
Refinement R factors |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Rp |  |  |  |  | 9.42$\%$ |  |  |  |  |  |  |  |  | 10.7$\%$ |  |  |
Rwp |  |  |  |  | 11.5$\%$ |  |  |  |  |  |  |  |  | 13.5$\%$ |  |  |
Rexp |  |  |  |  | 7.55$\%$ |  |  |  |  |  |  |  |  | 7.39$\%$ |  |  |

Fig.3(a) shows the zero-field cooled(ZFC) and field-cooled(FC) magnetization
curves for _SIO-as prep_ and _SIO-anneal_ samples at an applied magnetic field
of 1T. Both the samples exhibit magnetic transition below around $\sim$238 K
as seen from the inflexion point in the derivative of the ZFC magnetization
curve, inset of Fig.3(a). The inverse susceptibility shown in Fig.3(c) do not
obey Curie-Weiss behaviour in the entire paramagnetic region of both the
samples, but in a limited temperature region. The transition temperature (TN)
obtained from the fitting are 233.7 K and 233.8 K, respectively for _SIO-as
prep_ and _SIO-anneal_ samples. The estimated effective paramagnetic moment
$\mu_{eff}$ value for _SIO-as prep_ is $\sim$0.58$\mu_{B}$ which is close to
reported valuesBhatti  _et al._ (2014) while $\mu_{eff}$ for SIO-anneal is
$\sim$0.60$\mu_{B}$,higher than _SIO-as prep_. The transition temperature
marks the transition from paramagnetic to canted antiferromagnetic structure.
The rise in the dc magnetization below TN suggests weak ferromagnetic
behaviour arising due to the canted antiferromagnetic structure. The magnetic
structure of Sr2IrO4 compound is shown in Fig.1(d). The Jeff=1/2 pseudospins
are rotated in the _ab_ -plane by about 13∘ and are locked to in-plane IrO6
octahedral rotation due to strong spin orbit coupling.Ye  _et al._ (2013) This
canting of spins results in a net magnetic moment along _b_ -direction in each
Ir-O layer which are arranged in
($\uparrow\downarrow\downarrow\uparrow$)manner along _c_ -direction as shown
in Fig.1(d).Ye  _et al._ (2013); Kim  _et al._ (2009) The intralayer magnetic
interaction which is dominated by Heisenberg exchange coupling ($\sim$60meV)
is stronger compared to interlayer interaction.Haskel  _et al._ (2020) Both
these interactions (intra and interlayer) are proposed to be necessary to
stabilize the observed canted AFM magnetic structure.Katukuri  _et al._ (2014)
The canting of moments in the _ab_ -plane arises due to DM-interaction which
is responsible for weak ferromagnetic behaviour of the compound.

Apart from this, the FC and ZFC magentization curves show bifurcation below
$\sim$140K (Tirr) in both the samples. The ZFC curve exhibits a dip below
$\sim$65K in both the samples. It can also be seen that the difference between
FC and ZFC curves is higher for _SIO-as prep_ below $\sim$40K, Fig.3(b). The
observation of the bifurcation in the FC and ZFC magentization curves suggest
magnetic anisotropyJoy  _et al._ (1998) existing in these systems. Based on
the extent of bifurcation of the FC and ZFC magnetizations one can conclude
that the magnetic anisotropy is more in the case of _SIO-as prep_ as compared
to the _SIO-anneal_ sample.

In the system that is magnetically isotropic, in the presence of the external
magnetic field, the system shows no directional dependence in terms of the
alignment of the spins while in the case of the system that exhibit magnetic
anisotropy, there occurs preferential alignment of the spin along a particular
direction in response to the external field. Magnetic anisotropy is usually
observed in the systems that display properties like spin glass, cluster
glass, superparamagnetism, have strong spin orbit coupling or any short range
magnetic ordering etc. When the sample is cooled in zero field, the spins are
randomly oriented but cooling the sample in the presence of field leads to the
tendency of the spins to align in the direction of the applied field. This
tendency depends on the magnetic anisotropy of the system and the strength of
the applied field. If the system shows more anisotropy, higher fields are
required to align the spins in the direction of the applied field and hence to
higher magnetisation.

In the compound under study, reports show that the magnetic anisotropy is
driven mainly by (a) strong spin orbit coupling, below TN which leads to
canted antiferromagnetic structure and (b) possibility of stabilisation of
frustrating magnetic orderChikara  _et al._ (2009) and co-existence of cluster
glass phase along with canted AFM phaseManna  _et al._ (2014) at low
temperatures.

Figure 3: (a)ZFC and FC magnetization curves for SIO-parent and SIO-anneal
samples at 10kOe field, inset shows the derivative of ZFC magnetization curve
for both the samples; (b)Difference between FC and ZFC for both the samples;
(c) Inverse susceptibility vs temperature curves, solid lines indicate Curie-
Weiss fit to the experimental data

The stabilisation of spin orbit coupling in the compounds under study is
expected to manifest in the structural parameters. Towards this, we now
investigate the results of the temperature dependent x-ray diffraction
experiments collected on both the samples. Figs.4(a-d) shows the temperature
variation of lattice parameters, unit cell volume and c/a ratio of _SIO-as
prep_ and _SIO-anneal_ samples, extracted from the Rietveld refinement of
temperature dependent xrd measurements. The a-parameter shows a decreasing
trend while the c-parameter increases with the decrease in temperature, in
agreement with the literature. The a-parameter decreases monotonically until
around 80K with a variation rate of $\Delta$a/a $\sim$0.24$\%$ in both the
samples. While, below 80K, this rate of variation is reduced significantly
($\Delta$a/a $\sim$0.02$\%$). Similarly, the c-parameter also decreases from
RT to around 270K in both the samples. Around the region of TN, we observe a
change in slope of a-parameter and a small hump in c-parameter, insets of
Fig.4(a) and Fig.4(b), respectively. Below 250K to around 60K, c-parameter
increases with a variation rate of $\sim$0.03$\%$ in both the samples. Below
60K, rate of variation decreases and the c-parameter of _SIO-as prep_ sample
increases by about 0.008$\%$ while that of _SIO-anneal_ by 0.005$\%$. The unit
cell volume decreases while the c/a ratio which is a measure of tetragonality
of the system increases with the decrease in temperature. The a-parameter is
lower in _SIO-anneal_ sample compared to _SIO-as prep_ whereas the c-parameter
is lower in _SIO-as prep_ at all temperatures. The effect of annealing is the
preservation of the unit cell volume, while the tetragonality c/a increases
when we go from _SIO-as prep_ to _SIO-anneal_ sample at all temperatures,
Fig.4(c and d). The anisotropic temperature behaviour of lattice parameters
can be explained on the basis of temperature evolution of relevant bond
distances and bond angles.

Figure 4: (a-d) Temperature evolution of lattice parameters, unit cell volume
and c/a ratio of _SIO-as prep_ and _SIO-anneal_ samples obtained by Reitveld
refinement. The error bar is within the symbol size. The line represents guide
to the eye.  Figure 5: Temperature evolution of bond lengths and bond angle in
_SIO-as prep_ sample (a) Ir-O2 basal bond length; (b) Ir-O2-Ir in-plane bond
angle; (c) Ir-O1 apical bond length; (d) Sr-O1 bond length parallel to _c_
-axis; (e) Sr-O2 shorter bond length; (f) Sr-Sr bond length parallel to _c_
-axis; (g) Ir-Ir out of plane bond distance.The line represents guide to the
eye. Figure 6: Temperature evolution of bond lengths and bond angle in _SIO-
anneal_ sample (a) Ir-O2 basal bond length; (b) Ir-O2-Ir in-plane bond angle;
(c) Ir-O1 apical bond length; (d)Sr-O1 bond length parallel to _c_ -axis; (e)
Sr-O2 shorter bond length; (f) Sr-Sr bond length parallel to _c_ -axis; (g)
Ir-Ir out of plane bond distance;(h) Comparison of the difference in the
irreversible magnetization between both the samples and the difference in the
in-plane Ir-O2-Ir bond angles between both the samples.The line represents
guide to the eye.

There are two kinds of Ir-O, Sr-O1 and Sr-O2 bonds as shown in Fig.1(c). The
temperature evolutions of some of these bonds are shown in Fig. 5(a-g) for
_SIO-as prep_ and Fig.6(a-g) for _SIO-anneal_ samples. The Ir-O2 in-plane bond
length shows negligible variation from RT to around 80K for _SIO-as prep_
sample, Fig.5(a). At the same time, there is a overall decrease in Ir-O2-Ir
in-plane bond angle from RT to $\sim$80K, Fig.5(b). Below 80K, Ir-O2 bond
length shows a decreasing trend while Ir-O2-Ir bond angle increases. Hence,
from RT to $\sim$80K, the decrease in a-parameter is dominated by decrease in
Ir-O2-Ir bond angle while below 80K, the increase in Ir-O2-Ir bond angle along
with the decrease in Ir-O2 results in lesser variation of a-parameter.

In general, lattice parameters are expected to decrease with the decrease in
temperature due to reduction in lattice vibrations. The negative thermal
expansion in the c-parameter has been attributed to the in-plane rotations of
the IrO6 octahedra as allowed by the space group _I4 1/acd_. At the local bond
length level, such increment in the c-parameter can be understood as follows.
The Ir-O1 and Sr-O1 bonds shown in Fig.5(c-d), which are parallel to c-axis
exhibit opposite temperature dependence and hence do not contribute to
increase in _c_ -parameter. On the other hand, Sr-Sr bonds increase with the
decrease in temperature as shown in Fig.5(f). This increase in Sr-Sr distance
is related to the Ir-O2-Ir in-plane bond angle variation with temperature. The
Ir-O2-Ir bond angle changes due to change in the position of O2 in the ab-
plane. The temperature variations of Sr-O2 bond lengths follow the Ir-O2-Ir
bond angle variation. The bond angle variation causes the shorter Sr-O2 bond
length to decrease with temperature from RT to $\sim$80K, Fig.5(e). Hence, it
is favourable for the Sr ions parallel to _c_ -axis to move away from each
other for minimizing repulsion with basal oxygen ion cloud. This leads to the
unusual expansion of the c-axis with the reduction in temperature. Below 80K,
the increase in Ir-O2-Ir bond angle increases Sr-O2 shorter bond which further
leads to lesser variation in Sr-Sr bond length. Hence c-parameter variation is
suppressed at low temperatures.

Similar to _SIO-as prep_ sample, Ir-O2 bond length and Ir-O2-Ir bond angle
decide temperature dependence of _a_ -parameter in _SIO-anneal_ sample,
Fig.6(a-b). The increase in c-parameter with temperature can be explained in a
similar manner as that of _SIO-as prep_ sample. The Ir-O1 and Sr-O1 bonds
which are parallel to z-axis show opposite temperature behaviour, Fig.6(c-d).
The Sr-O2 shorter bond length shows a decreasing trend which leads to the
increase of Sr-Sr bond length, Fig.6(e-f).

In _SIO-anneal_ sample, we have seen that c/a ratio increases at all
temperatures compared _SIO-as prep_. When we compare the lattice parameters of
both the samples, we observed that the a-parameter is larger in the case of
the _SIO-as prep_ as compared to the _SIO-anneal_ sample while for the case of
the c-parameter, the behaviour is opposite. Such behaviour could be due to the
changes in the composition of the sample. From the compositional analysis, the
_SIO-as prep_ has Ir vacancies due to which Ir+5 ions can be present in the
sample. Annealing process has improved the stoichiometry thereby converting
some of Ir+5 to Ir+4. The ionic radius of Ir+4 is higher than that of Ir+5
which results in the increase of Ir-O1 and Ir-O2 bond distances in _SIO-
anneal_ sample. The decrease in a-parameter of _SIO-anneal_ is due to the
decrease in Ir-O2-Ir bond angle which dominates the increase in Ir-O2 bond
length. The increase in Ir-O1 bond length contributes to increase in _c_
-parameter of _SIO-anneal_ sample.

Now we shall explain the consequences of structural parameter variation on the
magnetic properties of _SIO-as prep_ and _SIO-anneal_ samples. The magnetism
in Sr2IrO4 is stabilized by a stronger intralayer and weaker interlayer
exchange interactions leading to a planar canted AFM structure with Jeff-1/2
moments in the ab-plane and ($\uparrow\downarrow\downarrow\uparrow$) alignment
of net moments along the c-direction, as shown in Fig.1(d). The strong spin
orbit coupling, locks the moments to the IrO6 octahedral rotation. Hence, the
decrease in Ir-O2-Ir bond angle with temperature suggests an increase in
canting angle until $\sim$125K in _SIO-as prep_ sample. Such a decrease in
Ir-O2-Ir bond angle in Sr2IrO4 is observed in previous neutron diffraction
measurements.Crawford  _et al._ (1994) This decrease in bond angle is
accompanied by decrease in Ir-Ir out of plane bond length until $\sim$125K as
shown in Fig.5(g), strengthening the interlayer coupling. The decrement of
both the Ir-O2-Ir bond angle and the Ir-Ir bond distances suggests the setting
up of the intralayer and interlayer interactions and hence the setting up of
canted AFM structureManna  _et al._ (2014). In the temperature range 125 to
80K, Ir-O2-Ir bond angles remain almost the same suggesting a competing
interaction at play. Below $\sim$125 K, the Ir-Ir bond lengths exhibit an
increment down to low temperatures. The increase in Ir-O2-Ir bond angle
suggests a decrease in canting and increase in Ir-Ir out of plane distance
further weakens interlayer exchange interaction. These results indicate a
deviation from canted AFM structure in _SIO-as prep_ sample below $\sim$80K.

The Ir-O2-Ir bond angle for _SIO-anneal_ samples are less than that for _SIO-
as prep_ sample at all temperatures, Fig.6(b). This indicates an increased
canting and consistent with the observation of higher magnetization for _SIO-
anneal_ compared to _SIO-as prep_ sample. With the decrease in temperature,
the Ir-O2-Ir bond angle in _SIO-anneal_ shows an increment $\sim$150K and then
a decrement upto $\sim$75K. In the temperature range 75 to 40 K, the Ir-O2-Ir
bond angles remain almost the same. This suggests a competing interaction that
opposes the stabilization of canted AFM structure. Below $\sim$30K , a small
increasing trend is observed. There is an overall decrease in the bond angle
indicating a dominant canted AFM phase until $\sim$75K. The Ir-Ir out of plane
bond length decreases from RT to around 230K with a pronounced feature
$\sim$240K, Fig.6(g). From 230K to $\sim$90K this bond length shows a
negligible variation. Below 90K, an increasing trend is observed. The
magnitude of increase in this bond length below 90K to low temperature is
lesser compared to that observed in _SIO-as prep_ sample. All these results
suggest a dominant canted AFM magnetic structure in _SIO-anneal_ sample until
$\sim$75K, below which magnetic structure may deviate as reported in the
literatureManna  _et al._ (2014); Chikara  _et al._ (2009) with the
possibility of stabilisation of disordered magnetic phase along with the
canted antiferromagnetic structure. It is interesting to note that below Tirr,
the behaviour of the difference in the irreversible magnetisation between both
the samples is in line with the difference in the Ir-O2-Ir bond angle between
both the samples, Fig.6(h).The structural link with the magnetism is
summarised pictorially in Fig.7. From this figure, it is clear that with
vacuum _annealing_ , the range of stabilisation of canted AFM structure is
enhanced by 50 K as compared to the _as prepared_ sample and hence the
strength of the canted AFM structure. From Fig.7, it is interesting to note
that in SIO-as prep and SIO-anneal samples, $\sim$ 175 K and 150 K,
respectively a slight increment in the Ir-O2-Ir bond angles is observed. Such
an increment suggests the role of hybridisation between the Ir 5d and O 2p
orbitals in the setting up of the intralayer exchange interaction.

Figure 7: Pictorial representation of the results of the transport,magnetic
properties,Ir-O2-Ir bond angle and Ir-Ir out of plane bond distances as a
function of temperature for _SIO-as prep_ (upper panel) and _SIO-anneal_
(lower panel) samples.The line represents guide to the eye.

We now investigate the link between the magnetic and structural properties on
to the transport properties. Fig.8 shows the resistivity variation of _SIO-as
prep_ and _SIO-anneal_ samples with temperature. Both the samples exhibit
semiconducting like behaviour in the entire temperature range. The resistivity
of _SIO-anneal_ sample is higher than that of _SIO-as prep_ at all the
temperatures. It can be seen that resistivity rises very rapidly below around
100K upto the lowest temperature studied.

Figure 8: Resistivity variation with temperature for _SIO-as prep_ and _SIO-
anneal_ samples.  Figure 9: Upper panel-resistivity variation of _SIO-as prep_
showing (a)Arrhenius behaviour in the range 300K to 253K (b) Variable range
hopping from $\sim$200K to 80K (c)Efros–Shklovskii (ES) variable-range hopping
at low temperature. Lower panel-resistivity fitting for _SIO-anneal_ sample:
Arrhenius equation fitting in (a) from 300K to 253K (b) from 200K to 75K and
(c)Variable range hopping at low temperatures. Solid line indicates the fit
and the symbols are experimental data.

It is possible to identify three different temperature regions having a
distinct resistivity behaviour in both samples as shown in Fig.9(a-c) for
_SIO-as prep_ sample and in Fig.9(d-f)in _SIO-anneal_ sample. In the
paramagnetic phase of both the samples, resistivity can be modeled by
Arrhenius equation given by $\rho=\rho_{0}\ \exp(E_{a}/k_{B}T)$, where $E_{a}$
is the activation energy, $k_{B}$ is Boltzmann constant and $\rho_{0}$ is a
constant. In Arrhenius hopping model, the charge carriers undergo thermal
excitations of charge carriers from localized state to the extended states. A
plot of $ln\rho$ vs 1/T is shown in Fig.9(a) and Fig.9(d) for _SIO-as prep_
and _SIO-anneal_ samples respectively, which are straight lines in the
temperature range of 300K to $\sim$253K. The activation energy obtained from
the fitting are 107 meV and 130 meV for _SIO-as prep_ and _SIO-anneal_
samples, respectively. These values are closer to the reported values for
single crystal samplesGe  _et al._ (2011) and also to those obtained from
optical absorption measurements.Kim  _et al._ (2008)

Below the magnetic transition temperature, from 200K to $\sim$80K, _SIO-as
prep_ obeys Mott’s variable range hopping (VRH) equation given by,Mott (1968)

$\rho(T)=\rho_{0}\ \exp(T_{M}/T)^{1/p+1}$

where $\rho_{0}$ is a constant, _p_ is the dimensionality of the system and
$T_{M}$ is a characteristic temperature which is related to electron
localization length $\xi$. VRH model is applicable in temperature region where
there is slowly varying DOS around the region of the Fermi level and the
electrons at the Fermi level are localized. In this model, conduction occurs
through hopping of the charge carriers from one localized state to another
localized state. In 3-dimensions (_p=3_ , the relation between the
localization length $\xi$ and TM is given by the equation,Rosenbaum (1991)

$T_{M}=18/[k_{B}\xi^{3}N(E_{f})]$

Here, $N(E_{f})$ is the number of available electron states per unit volume at
the fermi level, $E_{f}$. In 2-dimension (_p=2_), it is given byPepper  _et
al._ (1974)

$T_{M}=27/[k_{B}\xi^{2}N(E_{f})]$

Here, $N(E_{f})$ is the number of available energy states per unit area at the
fermi level, $E_{f}$.

The plots of both ln$\rho$ with $T^{-1/3}$ and with $T^{-1/4}$ are straight
lines as shown in the Fig.8(b) in almost the same temperature range from
$\sim$200K to $\sim$80K. We have obtained a value of $\rho_{0}$=0.01456
$\Omega$-cm and 0.08713 $\Omega$-cm respectively for 3D and 2D VRH fitting.
Also, the obtained values of $T_{M}$ for 2D and 3D cases are respectively
$3.67\times 10^{5}K$ and $20.737\times 10^{3}K$. Lu _et al_ Lu  _et al._
(2014) have reported similar values of 3D-VRH fitting parameters for epitaxial
thin film samples in the higher thickness limit while Bhatti _et al_(Bhatti
_et al._ , 2014) have obtained similar 2D-VRH parameters in the bulk sample
and in the intermediate temperature range.

Our results show that we could fit the resistivity curves in the temperature
range 200 to 80 K using both 2D and 3D VRH models. It is important to note
that in this compound where SOC plays important role, there is a strong link
between the transport and the magnetic properties. The canted AFM structure is
known to exhibit weak ferromagnetic behaviour. With decrease in temperature,
the rise in the dc magnetization around 240 K is due to the weak
ferromagnetism and further decrement in the temperature leads to the setting
up of the antiferromagnetic interaction between the layers. Hence, data fitted
with both 2D and 3D VRH mechanism suggest the setting up of the magnetic
interactions both within and between the layers.It is important to note that
the interaction between the layers is a weak one.

Using the co-efficient of electronic part of specific heat $\gamma$, the
estimated density of states per unit volume at $E_{f}$ is $\sim$ 6 $\times$
1028/eV m3.(Kini  _et al._ , 2006; Bhatti  _et al._ , 2014) The electron
localization length $\xi$ obtained using $T_{M}$ and $N(E_{f})$ for 3D case is
$\sim$2.12Å, which is very close to in-plane Ir-O bond length. It is important
to note that the value of $\xi$ may deviate due to deviation in $N(E_{f})$
from the actual value in the temperature domain of VRH fitting. The ratio of
mean hopping distance $R_{M}$ to electron localization length $xi$ given by,

$R_{M}/\xi=(3/8)(T_{M}/T)^{1/4}$

is always greater than 1 in the temperature range 200K to 80K, which supports
the applicability of Mott’s VRH equation.Rosenbaum (1991) We could not
calculate the corresponding localization length for the 2D case due to lack of
information regarding $N(E_{f})$.

The cross over from Arrhenius behaviour to variable range hopping mechanism of
resistivity is generally observed in disordered semiconductors with VRH
occurring at low temperatures.Mott and Davis (2012) As we have seen in EDS
analysis, _SIO-as prep_ has stoichiometric disorder in the form of Ir
deficiency. This may be the reason behind the occurrence of VRH behaviour at a
relatively higher temperature. On the other hand, in almost the same
temperature interval, _SIO-anneal_ sample follows Arrhenius equation similar
to that in the paramagnetic phase but with a lesser activation energy of 50
meV, Fig.9(e). The observation of Arrhenius behaviour in the intermediate
temperature range is previously reported by Kini _et al._ Kini  _et al._
(2006) in polycrystalline Sr2IrO4 prepared by solid state reaction method
starting from Ir metal and with a relatively lower temperature of heat
treatment compared to the present study. It is to be noted that, EDS analysis
indicated a change in the $Sr/Ir$ ratio from $\sim$2.08 for _SIO-as prep_ to
$\sim$2.02 for _SIO-anneal_. Hence, _SIO-anneal_ is less disordered than _SIO-
parent_ leading to Arrhenius behaviour in the intermediate temperature range.

At low temperatures, below $\sim$35K, the resistivity of _SIO-as prep_ can be
described with the Efros–Shklovskii (ES) variable-range hopping equation given
by,Éfros and Shklovskii (1975)

$\rho(T)=\rho_{0}\ \exp(T_{ES}/T)^{1/2}$

where, TES is a characteristic temperature. A plot of ln$\rho$ vs $T^{-1/2}$
is shown in Fig.9(c) which fits fairly well with a straight line. In the ES
VRH model, Coulomb gap appears in the region around the Fermi level. This
arises due to the introduction of long-range Coulomb interaction between the
electrons in the localized states.Éfros and Shklovskii (1975) A value of
TES=487.52K is obtained from the fitting. The ratio of average hopping
distance $R_{ES}$ to the localization length $\xi$ must be greater than 1 in
the temperature range of fitting for the validity of ES-VRH hopping. This
ratio is given by,

$R_{ES}/\xi=(1/4)(T_{ES}/T)^{1/2}$

Using the value of $T_{ES}$, we found this ratio to be greater than 1 upto
$T\leq 30K$. Thus, in _SIO-as prep_ sample ES-VRH picture is valid from the
lowest temperature to 30K. The expression for the Coulomb gap $\Delta_{CG}$ is
given by,

$\Delta_{CG}\simeq k_{B}(T^{3}_{ES}/T_{M})^{1/2}$

The value of this gap is found to be $\sim$1.5meV. Recently, a similar
temperature dependence and a cross over from Mott 3D-VRH to ES-VRH mechanism
at low temperatures has been reported in thin film samples of Sr2IrO4Lu  _et
al._ (2014) and also in La-doped single crystal samples.Chen  _et al._
(2015)In literature, T-1/2 behaviour is also observed in granular metal
systems consisting of metallic grains embedded in an insulating media.Sheng
_et al._ (1973) A similar phase separation has been observed in La-doped
single crystal samples probed by scanning tunnelling microscopy along with
magneto-transport and neutron diffraction measurements.Chen  _et al._
(2015)Thus the observation of ES-VRH hopping may also be due to inhomogeneity
at the electronic or magnetic level or at both levels. However, further
experiments are required to confirm this.

In _SIO-anneal_ sample, there is a cross over from Arrhenius behaviour in the
intermediate temperature region to Mott’s VRH mechanism at low temperatures,
Fig.9(f). As observed in _SIO-as prep_ sample, it is possible to model the
resistivity variation by using both 2D and 3D VRH limits in the temperature
range from $\sim$36K to 8K. A value of $\rho_{0}$=0.0042(0.2943)$\Omega$-cm
and $T_{M}=14.14\times 10^{5}(3.48\times 10^{4})$K is obtained from the
fitting 3D (2D)-VRH fitting. The 3D fitting parameters obtained here matches
with those reported by Kini _et al_ Kini  _et al._ (2006) in a similar
temperature range and in polycrystalline samples. The calculated localization
length $\xi$ from the 3D-VRH fitting parameters is $\sim$1.35$A^{\circ}$ which
is even smaller than Ir-O nearest in-plane bond length. But similar to the
case of _SIO-as prep_ , the ratio of mean hopping distance to localization
length $R_{M}/\xi$ is greater than 1 in the temperature range of fitting which
validates the use of 3D VRH model. We now investigate the effect of magnetic
field on to the transport properties.

Fig.10(a-b) shows the percentage magnetoresistance for _SIO-as prep_ and _SIO-
anneal_ samples at few selected temperatures, MR =
$100\times\rho(H)-\rho(0)/\rho(0)$, where $\rho(H)$ is the resistivity in the
presence of applied magnetic field H and $\rho(0)$ is the resistivity at H=0T.
In Fig.10(c), an expanded view of MR at low field is shown for _SIO-as prep_
sample and Fig.10(d) shows the same for _SIO-anneal_ sample. Both the samples
exhibit negative MR whose magnitude increases with the decrease in
temperature. At 300K, both the samples exhibit a negligible MR and as the
temperature is lowered, there is an enhancement. At 180K and 150K, the field
dependence of the MR is similar where the MR decreases sharply at low fields
until $\sim$0.3T and the rate of decrease slows down towards high field. On
the other hand, at 10K, MR exhibits small positive values in low fields upto
$\sim$0.3T and then decreases towards high field in _SIO-as prep_ sample,
Fig.10(c). For _SIO-anneal_ , MR at 10K decreases slowly in low fields,
Fig.9(d), and then rapidly drops at high fields. The magnitude of MR at 9T in
_SIO-as prep_(_SIO-anneal_) sample are $\sim$2.5$\%$($\sim$6.1$\%$),
$\sim$3.7$\%$($\sim$8$\%$) and $\sim$10$\%$($\sim$18$\%$), respectively at
180K, 150K and 10K. The observed values of MR in _SIO-anneal_ are higher than
the previously reported values for polycrystalline samples, while MR of _SIO-
as prep_ sample are similar to the literature.(Bhatti  _et al._ , 2014)

Figure 10: Magnetoresistance(MR) upto 9T of (a) _SIO-as prep_ and (b) _SIO-
anneal_ at different temperatures. The expanded view of MR at low fields in
(c)_SIO-as prep_ (d)_SIO-anneal_ samples

The origin of negative MR has been attributed to reduction in spin dependent
scattering and a slight increase in Ir-O-Ir bond angle by the application of
magnetic field though strong magneto-elastic coupling.Ge  _et al._ (2011)

A larger bond angle favours electron hopping resulting in lower resistivity.
Our results can also be explained by similar lines in both the samples. At
$\sim$0.3T it is known that Sr2IrO4 undergoes a metamagnetic transition where
($\uparrow\downarrow\downarrow\uparrow$)arrangement of net magnetic moments in
the _ab_ -plane changes to ($\uparrow\uparrow\uparrow\uparrow$) configuration
between the adjacent IrO6 octahedral layers.Kim  _et al._ (2009)This results
in a sharp drop of MR at low fields. The difference in conduction mechanism
has no effect on the nature of MR at 180K and 150K between the two samples.
The higher magnitude of MR observed in _SIO-anneal_ sample can be explained
based on its higher magnetization due to lower Ir-O-Ir bond angle which
enhances ferromagnetic polarization of the domains and thus reduces spin
dependent scattering to a larger extent compared to that in _SIO-as prep_
sample.Ge  _et al._ (2011); Chen  _et al._ (2015) Also, from structural
analysis we have seen that c/a ratio and Ir-Ir interlayer distance is higher
in _SIO-anneal_ sample which weakens the interlayer magnetic interaction.
Hence,it is easier to increase Ir-O-Ir bond angle by the applied magnetic
field resulting in enhanced electron hopping.Ge  _et al._ (2011)

The field dependence of MR that we see here is an average behaviour that has
been reported for single crystal samples for MR along crystallographic a and c
directions. In particular, MR along a-direction in single crystal samples at
10K shows an increasing trend at low fields and then decreases as the field
strength increases. The positive MR at low fields and then becoming negative
at high fields has been previously observed in spin glass systems such as AuFe
and NiMn alloys,Nigam and Majumdar (1979) where a competing glassy magnetic
phase and a ferromagnetic phases are present in the sample. In our case,
canted AFM phase gives rise to negative MR with field dependence as observed
in 180K and 150K. At 10K, there seems to be a positive component which is
dominant at low fields and decreases towards high fields in _SIO-as prep_
sample in addition to the negative component contributed by canted AFM phase.
In the case of _SIO-anneal_ sample, the positive component in MR is lesser
than that of _SIO-as prep_ and its MR at 10K behaves much similar to those of
180K and 150K. Thus magneto-transport at 10K suggests the presence of co-
existing glassy and canted AFM phase in _SIO-as prep_ sample and this glassy
magnetic phase is suppressed in _SIO-anneal_ sample. This is clear from Fig.7,
that shows the extent of stabilisation of the coexisting phases in the case of
_SIO-as prep_ is more as compared to the _SIO-anneal_ sample. A similar MR
behaviour at low temperatures has been reported in La doped Sr2IrO4 single
crystals which also shows spin-glass behaviour. Such glassiness is in line
with the increase in the bifurcation of the FC and ZFC magnetization curves of
the _SIO-as prep_ sample.

Now we attempt to establish a connection between the results obtained by the
different experiments performed on both the samples. We have prepared
polycrystalline samples of Sr2IrO4 using using solid state reaction method and
have studied the effect of vacuum annealing on its structural and magneto-
transport properties. The xrd results indicate that both the samples exhibit
tetragonal _I4 1/acd_ crystal structure along with a presence of very small
amounts of SrIrO3 impurity. The compositional analysis by EDS technique
indicates off-stoichiometry in the as prepared sample and the process of
annealing brings the sample closer to stoichiometry. This off-stoichiometry
may lead to the presence of Ir+5 ions in the _as prepared_ sample which are
smaller in size compared to Ir+4 ions and are also non-magnetic. Annealed
samples indicate higher value of magnetization as well as higher effective
paramagnetic moment. Higher magnetization value is due to increased canting of
moments caused by the smaller Ir-O2-Ir in-plane bond angle at all
temperatures. On the other hand, higher effective paramagnetic moment might be
due to conversion of some of the non-magnetic Ir+5 ions into magnetic Ir${+4}$
ions by the removal of oxygen during vacuum annealing. The higher magnitude of
Ir-O1 and Ir-O2 bond lengths in the annealed sample also supports this
scenario.

The process of annealing has enhanced c/a ratio and preserved the unit cell
volume at all temperatures. On the structural side, a-parameter exhibits a
slope change while the c-parameter exhibits a kink at the magnetic ordering
temperature showing a response to antiferromagnetic ordering in both the
samples. In the _as prepared_ sample, the Ir-O2-Ir in-plane bond angle
decreases until around 125K thereby enhancing the canting. The bond angle
remains unchanged until 80K and below this temperature, it increases
signalling the deviation from canted AFM structure.In the case of _annealed_
sample, there is an overall decrease in the bond angle until around 80K which
suggests the dominance of canted AFM structure. In the temperature range 80 to
30K, the bond angle remains almost the same. Below 30K, the increment in the
bond angle suggests another phase competing with the canted AFM structure. The
higher magnitude of Ir-Ir out of plane bond distances in the _annealed_ sample
indicates a weaker inter-planar coupling in comparison to the _as prepared_
sample. Thus the _annealed_ sample is expected to possess higher magnitude of
magnetic anisotropy. But from the behaviour of the bifurcation in the
magnetisation curves collected during FC and ZFC cycles suggests opposite
behaviour for T$\leq$ 40K. Such behaviour could be due to the nature of the
glassy phase stabilised at low temperatures.In the canted AFM phase, our
results show the importance of the hybridisation of the Ir 5 _d_ and O 2 _p_
states.

The resistivity of the _as prepared_ sample is lower than the annealed sample
at all temperatures. There are three temperature regions with a distinct
transport behaviour in both the samples. From 300K to $\sim$253K, resistivity
obeys Arrhenius behaviour in both the samples. From $\sim$200K to $\sim$80K,
the _as prepared_ sample exhibits Mott’s variable range hopping behaviour
while the annealed samples show Arrhenius behavior with different activation
energy compared to the previous high temperature region. Although there is an
ambiguity with regard to dimensionality limit of hopping conduction, the
change in conduction mechanism from VRH to Arrhenius behaviour in the
intermediate temperature region is an indication of higher disorder present in
the _as prepared_ sample compared to the annealed sample. This is also in line
with the higher off-stoichiometry in the as prepared sample as observed in EDS
measurements. At low temperatures, below $\sim$35K, _as prepared_ compound
exhibits ES-VRH (T-1/2 dependence) mechanism, while the annealed sample
exhibits variable range hopping. The T-1/2 dependence is generally observed in
granular metals which contain phase separated metallic and insulating domains.
This result corroborates with the field dependence of magneto resistance at
10K for the _as prepared_ sample which indicates a co-existing glassy and
canted AFM phases. The lowest temperature magneto resistance for annealed
sample indicates a suppression of the glassy magnetic phase and a dominance of
canted AFM structure.This deviation in the ground state magnetic structure is
also reflected in the increase in Ir-O2-Ir bond angle below $\sim$80K in the
_as prepared_ compound. All these results suggest an electronically phase
separated ground state which is probably originated by higher disorder in the
_as prepare_ d sample.

The lowest temperature MR for annealed sample indicates a suppression of the
glassy magnetic phase which is also in line with the resistivity and bond
angle behaviours. The magnitude of negative MR is higher for annealed sample
at all temperatures. This is due to lower Ir-O2-Ir in-plane bond angle in
_annealed_ sample which results in higher canting of moments and hence higher
value of ferromagnetic magnetization value. At 10K, the observed magnitude of
MR at 9T is around 18$\%$ which is nearly 10$\%$ higher than those reported
earlier for polycrystalline sample of Sr2IrO4. The higher sensitivity of
transport property to the applied magnetic field in the annealed samples may
be useful for device applications especially in spin-orbit coupling driven AFM
based spintronics.

##  IV Summary

We have explored the effect of _vacuum annealing_ on the magnetic, structural,
transport and magneto-transport properties of polycrystalline Sr2IrO4 prepared
by solid state reaction method. EDS analysis indicates that _annealed_ samples
are closer to stoichiometry than the _as prepared_ sample. A higher effective
paramagnetic moment as well as magnetization is observed in the _annealed_
sample. The _vacuum annealing_ enhances the resistivity over the entire
temperature range and both the samples exhibit distinct transport behaviour in
three different temperature regions. From 300K to $\sim$253K, both the samples
obey Arrhenius equation while in the intermediate temperature range from 200K
$\sim$80K there is a change over from Mott’s variable range hopping (VRH) to
Arrhenius behaviour with the annealing. At low temperatures below $\sim$35K,
the _as prepared_ sample obeys ES-VRH model while the _annealed_ samples show
Mott’s VRH behaviour. Our results show that vacuum annealing has increased the
temperature range of stabilisation of the canted AFM phase. For both the
samples we observe a signature of phase that competes with the canted AFM
structure. The change in Ir-O2-Ir bond angle with annealing follow the change
in the extent of magnetic anisotropy. There is an enhancement in the magnitude
of magneto resistance in the annealed samples which is higher than previously
reported values for the polycrystalline sample of Sr2IrO4. The higher magneto-
resistance is explained based on larger reduction in spin dependent scattering
and higher sensitivity of Ir-O2-Ir bond angle in the annealed samples. The
combined analysis of magnetic, structural, transport and magneto transport
results suggest a disorder induced phase separation in as prepared samples
with glassy and canted AFM phases while vacuum annealing suppresses this phase
separation.

##  V Acknowledgments

Priyamedha Sharma thanks UGC-DAE CSR Indore for financial support.

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