_The following article has been submitted to APL Materials. After it is
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# Epitaxial growth, optical and electrical conductivity of the metallic
pyrochlore Bi2Ru2O7 on Y-stabilized ZrO2 substrate.

Marita O’Sullivan<EMAIL_ADDRESS>Department of Physics, University
of Liverpool, Oxford Street, Liverpool, L69 7ZE, United Kingdom  Matthew S.
Dyer  Department of Chemistry, University of Liverpool, Crown Street,
Liverpool, L69 7ZD, United Kingdom  Michael W. Gaultois  Department of
Chemistry, University of Liverpool, Crown Street, Liverpool, L69 7ZD, United
Kingdom  Leverhulme Research Centre for Functional Materials Design, The
Materials Innovation Factory, University of Liverpool, 51 Oxford Street,
Liverpool, L7 3NY, United Kingdom  John B. Claridge  Department of Chemistry,
University of Liverpool, Crown Street, Liverpool, L69 7ZD, United Kingdom
Matthew J. Rosseinsky<EMAIL_ADDRESS>Department of Chemistry,
University of Liverpool, Crown Street, Liverpool, L69 7ZD, United Kingdom
Jonathan Alaria  Department of Physics, University of Liverpool, Oxford
Street, Liverpool, L69 7ZE, United Kingdom

###### Abstract

Epitaxial heterostructures composed of complex correlated metal oxides grown
along specific crystallographic orientations offer a route to investigating
emergent phenomena such as topological states and spin liquids through
geometrical lattice engineering. A2Ru2O7 pyrochlore ruthenates in particular
exhibit a metal-insulator transition with varying A cation whose mechanism is
not fully understood. We report on the epitaxial growth, structural and
electrical properties of metallic pyrochlore bismuth ruthenate
heterostructures grown along both the [001] and [111] directions. Ordered
pyrochlore thin films were obtained with highly oriented texture along the
[001] and [111] crystallographic directions. Density functional theory
calculations of the electronic band structure and density of states indicated
that Bi2Ru2O7 is semimetallic and that hybridization of the Ru 4$d$ and Bi
6$p$ orbitals via the anion network at the Fermi energy was responsible for
the metallicity. Electrical conductivity measurements confirmed that the
compound is weakly metallic in agreement with the reported conductivity for
the stoichiometric bulk compound. The carrier concentration and mobility of
the electrons compared favorably with previous reports on bulk material and
indicate strong electron-electron interactions. The measured and computed
optical conductivities were found to share coincident spectral features and
confirm the electronic correlation. Comparison of the electrical and optical
properties of the two distinct orientations indicates differences that cannot
be attributed to differences in crystalline quality or dislocations and may
indicate anisotropy in the electronic structure of Bi2Ru2O7. This study will
enable access to the kagome lattice arising naturally in the 111 planes of the
pyrochlore B cation sublattice which may be used to uncover emergent
topological properties.

††preprint: APLMat/OSULLIMBRO

##  I Introduction

Oxides with the statistical formula A2B2O7 crystallizing with the pyrochlore
structure have shown wide-ranging properties suitable for applications such as
oxide ion conductivityLi  _et al._ (2013), metallic conductivity as thick film
electrodesZhang  _et al._ (2021), ferroelectricityDong  _et al._ (2009), and
thermoelectricityYasukawa  _et al._ (2003); Akhbarifar  _et al._ (2020). They
also offer a rich playground to explore more fundamental physical properties
with potential topological materialsPesin and Balents (2010); Yang and Nagaosa
(2014); Chu  _et al._ (2019); Guo and Franz (2009a); Hu  _et al._ (2015) and
canonical spin ice behaviorBovo  _et al._ (2014).

The A2Ru2O7 pyrochlore ruthenates in particular exhibit electrical
conductivity that verges between localized and itinerant behavior and has led
to numerous studies into the evolution of their electronic structures with
varying A cation to understand the mechanism of the Mott metal-insulator
transition. Bi2Ru2O7-y and Pb2Ru2O6.5, for example, are weakly metallic Pauli
paramagnetsYamamoto  _et al._ (1994); Kobayashi  _et al._ (1995), while
Y2Ru2O7 and Ln2Ru2O7 (Ln = Pr–Lu) exhibit semiconducting behavior with
spontaneous antiferromagnetic orderBouchard and Gillson (1971); Gökaǧaç and
Kennedy (1994); Gaultois  _et al._ (2013). Electrical conduction in the
metallic ruthenates is known to take place via the Ru-O band states in the
Ru2O6 networkLee  _et al._ (1997). In photoemission spectroscopy and high-
resolution electron energy-loss spectroscopy studies, Cox $et$ $al.$
identified a decrease in the density of states at the Fermi energy,
$E_{\textnormal{F}}$, from Pb2Ru2O6.5 to Bi2Ru2O7 to Y2Ru2O7 with electron-
electron correlation yielding a Mott insulator for Y2Ru2O7Cox  _et al._
(1983). They posited that mixing of the A 6$s$ and Ru 4$d$ bands via the
A–O–Ru interaction had the effect of broadening the Ru $t_{2g}$ block bands
arising from the octahedral crystal field Cox  _et al._ (1983), however
changes to the bandwidth or band splittings can be observed as a function of
the A cation. It was noted that increasing the A site radius has the effect of
opening the Ru-O-Ru bond angle thereby increasing the Ru 4$d$/O 2$p$ orbital
overlap and broadening the bandwidth to delocalize the carriersLee  _et al._
(1997). It was therefore concluded that metallic ruthenate pyrochlores are
characterized by relatively short Ru-O bonds ($\sim$1.95 Å), less distorted
RuO6 octahedra, and more open Ru-O-Ru angles ($>$ 133°) compared with longer
bonds ($\sim$1.98 Å), greater octahedral distortions, and smaller angles ($<$
133°) in the semiconducting analoguesFacer  _et al._ (1993); Kanno  _et al._
(1993); Kennedy and Vogt (1996); Okamoto  _et al._ (2004); Lee  _et al._
(1997).

Self-consistent first principles calculations of the electronic band structure
of metallic pyrochlore ruthenates using the pseudofunction method, however,
were used to argue that the A 6$s$ bands are too deep to mix with Ru 4$d$
bandsHsu  _et al._ (1988). Local-density approximation density functional
theory calculations suggested that the unoccupied A 6$p$ states positioned
slightly above the Fermi energy, $E_{\textnormal{F}}$, could hybridize with
the Ru 4$d$ $t_{2g}$ states via the O 2$p$ and contribute band filling charge
resulting in metallic conductivityIshii and Oguchi (2000); Lee  _et al._
(2005). Indeed the position of the A cation orbitals relative to the Ru $d$-O
$p$ antibonding states is an important consideration in understanding the
mechanism of the metal-insulator transition in these pyrochlore ruthenium
oxides. It was noted however that the A cation radius alone could not explain
the observed nonlinear crossover from metallic to insulating regime Laurita
_et al._ (2019), but that the stereochemical activity of the Bi3+ 6$s^{2}$
lone pair electrons leads to local disorder and indirectly increases the Ru-O-
Ru covalency driving a metallic state in Bi2Ru2O7Lee  _et al._ (2005); Avdeev
_et al._ (2002); Shoemaker  _et al._ (2011); Laurita  _et al._ (2019).

Metallic Bi2Ru2O7 is widely used as a thick film resistorCarcia  _et al._
(1982); Pike and Seager (1977); Stanimirović and Stanimirović (2020), and has
further applications as a catalystHorowitz  _et al._ (1983), a cathode
material for solid oxide fuel cells Takeda  _et al._ (2002); Esposito  _et
al._ (2006), an electrode for pyrochlore based dielectric material such as
Bi1.5Zn1.0Nb1.5O7Nakajima  _et al._ (2014) and has been predicted to host
fragile band topology Song  _et al._ (2020). Although the electrical
properties of polycrystalline films have been previously studied in
detailCarcia  _et al._ (1982); Řehák  _et al._ (1984) there are limited
studies dedicated to heteroepitaxial Bi2Ru2O7 thin film growth focusing on
(111) oriented heterostructures prepared by chemical vapor deposition
methodsNakajima  _et al._ (2014); Chiba  _et al._ (2019). Pulsed laser
deposition (PLD) is a physical vapor deposition method which is well suited to
the deposition of high quality oxide thin films and has been used to obtain
epitaxial pyrochlore filmsIto  _et al._ (2021), however the high volatility of
bismuth and ruthenium makes the stoichiometric transfer of Bi2Ru2O7
challenging.

In this report we have studied the heteroepitaxial synthesis of pyrochlore
Bi2Ru2O7 thin films by PLD on Y-stabilized ZrO2 (YSZ) single crystals with two
different orientations, (001) and (111). By tuning the deposition conditions,
a narrow growth region has been identified where single phase, highly-oriented
films could be obtained. The electrical and optical conductivities were
measured, and the carrier concentration, obtained from Hall effect
measurement, together with the observed optical transition is in good
agreement with the calculated electronic structure. The high quality of the
thin film samples will therefore allow for further experimental studies to
understand the rich electronic structure embedded in this system.

##  II Methods

###  II.1 Experimental methods

Thin film deposition was carried out using a polycrystalline Bi2Ru2O7 source
target synthesized following a previously reported solid state methodAvdeev
_et al._ (2002). Stoichiometric quantities of the dried binary oxides, Bi2O3
and RuO2, were mixed, ground, pressed and calcined at 750 ℃ for 24 hours in
air. The resultant pellets were ground, pressed and fired once again in air at
900 ℃ for 24 hours, this process was repeated at 950 ℃ for 72 hours with a
final sinter at 975 ℃ for 24 hours to form a dense ceramic pellet. The phase
purity of the obtained target was confirmed by X-ray diffraction (XRD, X’Pert
Pro, Panalytical, Co $K_{\alpha 1}$ radiation) and a lattice parameter $a$ =
10.2972(2) Å was obtained in agreement with previous values reported in the
literature, 10.2934(1) ÅKanno  _et al._ (1993) and 10.28974(3) - 10.28976(7)
ÅAvdeev  _et al._ (2002). The O Wyckoff position at the 48$f$ site (x, 1/8,
1/8) was found to be x = 0.315(2) which is comparable to the reported figures
of 0.32652(6) - 0.32649(6) Avdeev  _et al._ (2002). Thin films were grown on
(001) and (111) oriented 8 mol.% Y-stabilized zirconia (YSZ) single crystal
wafers from Crystal GmbH. The deposition was carried out in a PVD high vacuum
chamber with a base pressure of $1\cdot 10^{-7}$ Torr using a KrF excimer
laser ($\lambda$ = 248 nm) with a fixed repetition rate of 2 Hz. The substrate
surfaces were prepared by annealing in air at 1150 ℃ for 3 hours prior to
deposition to achieve atomically flat surfaces which were confirmed by atomic
force microscopy. A range of substrate temperatures ($T_{S}$ = 675 – 750 ℃),
oxygen partial pressures ($P_{O_{2}}$ = 1 – 50 mTorr), and laser energy
densities ($J$ = 1.0 – 1.6 J/cm2) were explored to determine the optimum
growth conditions. After deposition the samples were cooled in the same oxygen
partial pressure at a rate of 10 ℃/minute. The quality (phase and mosaicity)
of the films was assessed using a high-resolution four-circle diffractometer
(Smartlab, Rigaku, 16 kW rotating anode Cu $K_{\alpha 1}$ radiation). The
thickness, $d$, was measured using X-ray reflectometry ($d<$ 170 nm) and
profilometry (Ambios XP – 200 stylus profilometer, $d>$ 170 nm). The
electrical transport properties were measured in the Van der Pauw
configuration Van der Pauw (1958) with a 14 T Quantum Design Dynacool ETO
using In solder, Au wires and an AC excitation with an amplitude of 0.5 mA and
a frequency of 9.15527 Hz. The antisymmetric component of the transverse Hall
magnetoresistance was used to calculate the carrier concentration of the
films. The optical properties of the Bi2Ru2O7 films and YSZ substrate were
measured using spectroscopic ellipsometry (J. A. Woollam M200UI, wavelength
range 240 – 1700 nm (0.73 – 5.14 eV)) with photon energies between 0.74 – 5.86
eV) at three different angles (65, 70 and 75 °).

###  II.2 Computational methods

Plane-wave based periodic density functional theory calculations were
performed using VASPKresse and Furthmüller (1996) with the PBE
functionalPerdew  _et al._ (1996). The projector augmented wave approachKresse
and Joubert (1999) was used with the inclusion of spin-orbit coupling.
Calculations were performed in the primitive unit cell with a
32$\times$32$\times$32 k-point grid and a plane-wave cutoff energy of 550 eV.
Prior to the calculation of density of states and band structure, the lattice
parameters and atomic positions were optimized until all forces fell below
0.001 eV Å-1.

##  III Results and discussion

The A2B2O6O' pyrochlore structure presented in Fig. 1(a) is a face-centered
cubic structure which can be viewed as independent interpenetrating A2O' and
B2O6 sublattices based on a 3-dimensional framework of corner-sharing BO6
octahedra that are linked into zigzag chainsSubramanian  _et al._ (1983);
Kennedy and Vogt (1996); Kanno  _et al._ (1993); Yamamoto  _et al._ (1994).
The larger A cations occupy the 16$d$ sites at (1/2, 1/2, 1/2) in eight-fold
scalenohedral coordination where each A cation is at the centre of an
octahedron of O squashed along the $<$111$>$ axis and capped by two axial O'
atoms slightly closer to the A cation. The smaller B cations occupy the 16$c$
sites at (0, 0, 0) assuming trigonal antiprism coordination with the anions,
while O and O' occupy the 48$f$ (x, 1/8, 1/8) and 8$b$ (3/8, 3/8, 3/8) sites
respectively in the $Fd\bar{3}m$ space group symmetry. The defect pyrochlore
Bi2Ru2O7 is formed when there are disordered oxygen vacancies on the O' 8$b$
site. The B cation sublattice is composed of alternating triangular and kagome
structural motifs along the [111] direction, and tight-binding calculations
have shown that a two-dimensional kagome lattice with spin-orbit coupling can
potentially exhibit topological insulator behaviorGuo and Franz (2009b).

###  III.1 Electronic structure

The electronic band structure along selected high symmetry directions of the
Brillouin zone and density of states (DOS) of Bi2Ru2O7 are shown in Fig. 1(b)
and (c), where the reference energy of the vertical axis is the Fermi energy,
$E_{\textnormal{F}}$. The electronic bands positioned between -8 eV and -2 eV
(Fig. 1(b)) are composed primarily of O 2$p$ states bonding with Ru $d$
orbitals at the lower levels and with a Bi 6$s$ contribution in the higher
energy region with corresponding DOS shown in Fig. 1(c). The Fermi level lies
between two localized DOS peaks attributed to antibonding Ru $d$ states which
are strongly hybridized with O and Bi $p$ states, consistent with previously
reported electronic structure calculations using LDAIshii and Oguchi (2000),
PBEsolLaurita  _et al._ (2019) and tight-binding linear muffin-tin orbital
methodAvdeev  _et al._ (2002). It is also worth noting some mixing of the Bi
$s$ states exists in the $d$ bands above the Fermi level especially around the
$\Gamma$ and L points. This leads to an almost semimetallic state with four
bands crossing $E_{\textnormal{F}}$, two small electron pockets along the
$\Gamma-$K and W$-$L directions and two hole pockets along the $\Gamma-$X and
K/U$-$X paths. The bandwidth of the Ru $t_{2g}$ block bands around the Fermi
level at the $\Gamma$ point is 2.5 eV which is consistent with reported values
for LDA Ishii and Oguchi (2000) and PBEsolLaurita  _et al._ (2019).

Figure 1: (a) Pyrochlore Bi2Ru2O7 crystal structure. (b) Bi2Ru2O7/YSZ
heterostructure viewed towards the (2$\overline{1}\overline{1}$) plane with
the (111) along the vertical axis. (c) Bi2Ru2O7/YSZ heterostructure viewed
towards the (010) plane with (001) along the vertical axis. (d) Electronic
band structure of Bi2Ru2O7 calculated by density functional theory. (e)
Partial densities of states (DOS) of the constituent elements.

###  III.2 Thin film growth

Fluorite YSZ substrates were selected due to the crystal structure similarity
and low lattice mismatch of 0.2 %, to the Bi2Ru2O7 pyrochlore phase as
illustrated for (111) and (001) orientations in Fig. 1(d) and (e). Optimal
growth was achieved at a temperature of 710 ℃ under an oxygen partial pressure
of 15 mTorr and a laser fluence of 1.6 J/cm2 giving a growth rate of 0.205
Å/pulse for the (001) oriented film and 1.4 J/cm2 giving a growth rate of
0.167 Å/pulse for the (111) oriented film. The relatively high oxygen partial
pressure and moderate growth temperature were found necessary both to avoid
reduction of the films and to minimize variation in relative stoichiometry of
the two volatile cations which led to splitting of the Bragg peaks in the XRD
patterns indicative of a stoichiometric inhomogeneity. Higher oxygen pressure
was observed to result in an additional Bi3Ru3O11 impurity phase. Target
polishing was required between depositions to avoid stoichiometric variation
in the thin film composition.

Figure 2: (a) $\theta$-2$\theta$ X-ray diffraction scan for optimized growth
of (111) oriented Bi2Ru2O7/YSZ heterostructure. The film reflections are
labelled and the (*) indicates the substrate peaks. (b) Rocking curve of (222)
reflection of (111) oriented Bi2Ru2O7/YSZ heterostructure (black line and
circle) with pseudo-Voigt peak fit (red line). (c) Reciprocal space map
showing the asymmetric Bi2Ru2O7 (484) and the YSZ (242) reflections.

The out-of-plane $\theta-2\theta$ XRD pattern for Bi2Ru2O7 on (111) YSZ under
optimized growth conditions, presented in Fig. 2(a), shows that the obtained
film is single phase and follows the orientation of the substrate with only
$hhh$ Bragg reflections observed. The presence of strong odd $hhh$ reflections
confirms the cation ordering in the pyrochlore structure rather than the
disordered defective fluorite which was obtained in zirconate pyrochlore
heterostructures grown by PLDO’Sullivan  _et al._ (2016). An out-of-plane
lattice parameter of $a$ = 10.47936 Å for the (111) oriented film was observed
to be larger than the reported bulk valueAvdeev  _et al._ (2002) and likely
due to slightly off-stoichiometric cation transfer due to the high vapor
pressure of Bi and Ru, and variation in anion content. The quality of the
heterostructure was assessed by a rocking curve measurement on the (111)
Bi2Ru2O7 Bragg reflection shown in Fig. 2(b). The peak exhibits a broad base
with a narrow component which can be fitted using a pseudo-Voigt profile with
Gaussian and Lorentzian widths of $w_{G}$ = 0.025(3)° and $w_{L}$ = 0.121(2)°
respectively. The high intensity, narrow component is caused by the
diffraction of (111) planes and the broad, lower intensity component is
attributed to diffuse scattering originating from interface roughness, high
dislocation density and strain in quasi-epitaxial thin filmsBläsing  _et al._
(2009). The crystalline quality of these films is superior to the previously
reported (111) oriented Bi2Ru2O7 films which presented rocking curve peak
widths of 0.2°Nakajima  _et al._ (2014); Chiba  _et al._ (2019). The
reciprocal space map collected around the (242) YSZ Bragg reflection is
presented in Fig. 2(c) and shows that the (111) oriented Bi2Ru2O7 film is
strained to the substrate. An in-plane lattice parameter of $a$ = 10.420 Å was
observed which is close to the out-of-plane component and the grown film can
be considered a close equivalent to a bulk Bi2Ru2O7 single crystal.

Figure 3: (a) $\theta$-2$\theta$ X-ray diffraction scan for optimized growth
of (001) oriented Bi2Ru2O7/YSZ heterostructure. The (00$l$) film reflections
are labelled and the (*) indicates the substrate peaks. Inset shows the
rocking curve of the (004) reflection of (001) oriented Bi2Ru2O7/YSZ
heterostructure (black line and circle) with pseudo-Voigt peak fit (red line).
(b) Reciprocal space map showing the asymmetric Bi2Ru2O7 (111) reflection of
the (001) oriented Bi2Ru2O7/YSZ heterostructure confirming the cation ordering
in the pyrochlore crystal structure. (c) Reciprocal space map showing the
asymmetric Bi2Ru2O7 (048) and the YSZ (024) reflections in the (001) oriented
Bi2Ru2O7 film.

The sample deposited on the (001) YSZ substrate under the optimized
temperature and partial pressure yielded a phase pure Bi2Ru2O7 film, as shown
in the out-of-plane XRD pattern in Fig. 3(a). The observation of ($00l$)
Bi2Ru2O7 Bragg reflections alone confirm that it is highly oriented and the
extracted lattice parameter, $a$ = 10.47388 Å, which is close to that of the
(111) oriented film, indicates a comparable stoichiometric transfer for both
orientations. The rocking curve measured on the (004) Bi2Ru2O7 reflection is
shown in the inset of Fig. 3(a) and a fit to a pseudo-Voigt function resulted
in widths of $w_{G}$ = 0.377(2)° and $w_{L}$ = 0.323(5)°. In this case the two
components are almost equal and the rocking curve is broader than that
obtained for the (111) oriented film. The inferior crystallinity of the (001)
oriented sample could be due to the mixed cation composition in the (111)
planes of the structure (Fig. 1(e)) compared to uniquely cationic layers
alternating with complete layers of anions in the (001) planes (Fig. 1(d))
which may introduce stacking faults. It could also originate from the
crystallization of the defective fluorite structure where the Bi and Ru atoms
occupy the same crystallographic site. Since the ($002n$) reflections are
forbidden by symmetry, it is not possible to distinguish (001) oriented
Bi2Ru2O7 pyrochlore and defective fluorite out-of-plane. The cation ordering
in the film was confirmed with the observation of the (111) Bi2Ru2O7
reflection presented in Fig. 3(b) and the film was found to be fully relaxed
with an in-plane lattice parameter of $a$ = 10.395 Å extracted from the
Bi2Ru2O7 peak in the reciprocal space map measured around the (024) reflection
of the YSZ substrate.

###  III.3 Electrical properties

Both film orientations show a similar metallic temperature dependence in the
electrical resistivity with a small negative temperature coefficient across
the measured temperature range (Fig. 4). This cannot be explained by a
thermally activated semiconducting mechanism and is similar to previously
reported thin film Nakajima  _et al._ (2014); Chiba  _et al._ (2019) and
polycrystalline samples prepared in air Carbonio  _et al._ (1999). Resistivity
values of $\rho$ = 0.54(3) m$\Omega$cm and $\rho$ = 0.43(3) m$\Omega$cm were
obtained for the (001) and the (111) oriented layers respectively at 300 K, in
close agreement with the values reported in polycrystalline samples Kanno  _et
al._ (1993); Carbonio  _et al._ (1999), single crystals Tachibana  _et al._
(2006) and thin films Nakajima  _et al._ (2014); Chiba  _et al._ (2019). The
reduced resistivity observed in the (111) oriented film could be attributed to
lower scattering from dislocations as the crystallinity of this film is
superior.

Figure 4: (a) Temperature dependence of electrical resistivity of (111)
oriented (red squares) and (001) oriented (black circles) Bi2Ru2O7/YSZ
heterostructures.

To our knowledge, the carrier concentration in this compound has only been
estimated through spectroscopic measurements Cox  _et al._ (1983) and the thin
film configuration in this study permits measurement of the effective carrier
concentration using conventional Hall effect. The magnetic field dependence of
the Hall resistance, shown in Fig. 5(a) is linear with a negative slope
indicating the majority charge carriers are electrons. The temperature
dependence of the effective carrier concentration calculated from the Hall
resistance for both (001) and (111) orientations is presented in Fig. 5(b).
The samples exhibit an increase in carrier concentration with increasing
temperature, differing from the nearly constant carrier concentration expected
for a metal or degenerate semiconductor. The carrier concentrations measured
at 5 K are 7.5(5)$\cdot 10^{22}$ cm-3 and 3.6(2)$\cdot 10^{22}$ cm-3 for the
(111) and (001) oriented films respectively. These values are close to the
carrier concentration extracted from spectroscopic measurements Cox  _et al._
(1983) and the theoretical carrier concentration of 5.9$\cdot 10^{22}$ cm-3
expected for four free electrons per Ru. Carrier concentrations of
2.9(2)$\cdot 10^{23}$ cm-3 and 1.20(8)$\cdot 10^{24}$ cm-3 were observed at
300 K for the (001) and (111) oriented heterostructures respectively which may
arise due to thermal broadening of the Fermi distribution in the higher
temperature region. The temperature dependence of the extracted Hall mobility
is presented in Fig. 5(c) for both orientations showing an increase in the
mobility as the temperature is reduced towards a saturation values of 0.17 and
0.28 cm2V-1s-1 for the (111) and (001) oriented samples respectively at low
temperature. This suggests that the dominant mechanism limiting the mobility
is phonon scattering at high temperature and neutral impurities at low
temperature. The low mobility values are consistent with the reported
conductivity and large effective mass of 2.9 $m_{0}$ observed in
polycrystalline samples Kanno  _et al._ (1993); Cox  _et al._ (1983).

Figure 5: (a) Hall resistivity of a (001) oriented Bi2Ru2O7/YSZ
heterostructure measured in the Van der Pauw geometry. (b) Carrier mobility
and (c) carrier concentration of (111) oriented (red squares) and (001)
oriented (black circles) Bi2Ru2O7/YSZ heterostructures extracted from Hall
effect measurements.

###  III.4 Optical properties

The real $\epsilon_{1}$ and imaginary $\epsilon_{2}$ parts of the dielectric
function obtained from ellipsometry data for both (001) and (111) orientations
are shown in Fig. 6(a) and (b) respectively. The raw ellipsometry data were
fitted with a combination of Drude and Lorentz oscillators in a combined model
for the substrate and the film to extract the complex dielectric function. A
blank substrate was measured to determine the dielectric function and a model
using three Tauc-Lorentz oscillators, similar to what is reported for c-ZrO2
Synowicki and Tiwald (2004), was fixed together with the film thickness in the
heterostructure models. The film layer models were constructed from a Drude
oscillator combined with a series of five Lorentz oscillators. The real
components of the optical conductivity spectra $\sigma_{1}$ were calculated
and shown in Fig. 6(c) together with the optical conductivity extracted from
the DFT calculation and that of a previous study performed on a
polycrystalline sample Lee  _et al._ (2005). The reduced plasma energy
$E(\omega_{p}$), defined as the energy at which the real part of the complex
dielectric function $\epsilon_{1}$ is equal to zero, was measured to be 1.17
eV for the (111) oriented film and 1.34 eV for the (001) oriented sample.
These values are comparable to the reported electron energy-loss spectral
(EELS) peak of 1.25 eV for a polycrystalline sample which was associated with
excitation of the conduction-electron surface plasmon Cox  _et al._ (1983).
The red shift in the plasma energy from the (001) to the (111) oriented film
together with the elevated carrier concentration observed in the
magnetotransport measurements in the latter film and must indicate a
coincident increase in electron effective mass which is inversely proportional
to the plasma frequency. Despite the superior crystalline quality of the (111)
heterostructure, demonstrated by the narrow rocking curve, the Fermi surface
of the (111) planes could have a higher concentration of carriers together
with a diminished carrier mobility compared with the (001) if either the
effective mass was sufficiently large or the scattering time was sufficiently
enhanced in an electronically anisotropic crystal structure.

Figure 6: Ellipsometry measurements showing the real $\epsilon_{1}$ and
imaginary $\epsilon_{2}$ parts of the dielectric function for (a) (001) and
(b) (111) oriented Bi2Ru2O7/YSZ heterostructures. (c) Calculated optical
conductivity $\sigma(\omega)$ for (001) and (111) oriented Bi2Ru2O7/YSZ
heterostructures compared with the optical conductivity extracted from the DFT
calculations and that of a polycrystalline sample studied by Lee $et$ $al.$
Lee  _et al._ (2005).

Electronic band structure calculations indicate deep bands composed of O 2$p$
bonding with Ru $d$ orbitals and some contribution from Bi 6$s$ at levels well
below $E_{\textnormal{F}}$. Closer to $E_{\textnormal{F}}$ the bands consist
mainly of a Ru 4$d$ $t_{2g}$ block with a bandwidth of 2.5 eV at $\Gamma$. The
$E_{\textnormal{F}}$ lies between two localized density of states peaks
indicating that the material is semimetallic, this corresponds to Ru 4$d$
states which are hybridized with Bi 6$p$ states via the anion network in
agreement with more recent theoretical studies Hsu  _et al._ (1988); Ishii and
Oguchi (2000). Epitaxial films of (001) and (111) oriented Bi2Ru2O7/YSZ
heterostructures have been grown by PLD. Both films crystallized with the
ordered pyrochlore structure with lattice parameters that were larger than the
reported bulk figures Avdeev  _et al._ (2002). The (111) oriented film had a
superior crystallinity and was strained to the substrate. The films were
weakly metallic with resistivity profiles in agreement with previously
reported electrical measurements Carbonio  _et al._ (1999). They had low
electron mobilities, consistent with optical spectroscopy reports of high
carrier effective masses Cox  _et al._ (1983); Kanno  _et al._ (1993), and
they had carrier concentrations in agreement with the theoretical
concentration with thermally activated carriers at higher temperature. The
reduced plasma energies extracted from the real component of the dielectric
function were close to the EELS surface plasmon excitation energy previously
reported Cox  _et al._ (1983). The spectral features of the experimental
optical conductivity of the films were reproduced in the DFT computed model.
Differences in the magnetotransport parameters and the optical properties
between the two orientations which cannot be explained by differences in
crystallinity indicate a degree of electrical and optical anisotropy in the
electronic structure.

##  IV Conclusions

In summary, we have grown epitaxial heterostructures of pyrochlore Bi2Ru2O7
along [111] and [001] directions of YSZ single crystals by PLD. The structural
properties, crystalline quality and strain in the heterostructures have been
examined by XRD. The electrical resistivity has been measured and the carrier
type, mobility and concentration have been determined by Hall effect
measurement as a function of temperature. The optical conductivity and reduced
plasma energy have been determined by ellipsometry measurements. The transport
and optical parameters have been compared for the two orientations and a
degree of anisotropy in the crystal structure is evident. The measured optical
conductivities have also been compared with the DFT calculated optical
conductivity and the observed optical transitions have been reproduced at
coincident energies in the computed electronic structure. Investigation of the
effect of Bi off-centering on the electronic structure and optical
conductivity would give useful insights into what drives the metallicity in
this system. The ability to access distinct structural motifs such as the
kagome lattice which is peculiar to the B cation planes of the (111)
orientation of the pyrochlore crystal structure could lead to new and
interesting physical properties relating to the symmetry of this structure.
Recent computational studies into the 3-dimensional pyrochlore niobate systems
suggest that topological phases can be tuned by shifting the A cation away
from the centrosymmetric position along the [111] axisZhang  _et al._ (2019);
Zhou  _et al._ (2019), indicating the potential of this crystal system to
demonstrate exciting symmetry-protected band structure features.

## Acknowledgements

This paper is dedicated to Sir A.K. Cheetham in celebration of his 75th
birthday.

The authors would like to acknowledge funding from the Engineering and
Physical Sciences Research Council (EPSRC) Programme Grants (EP/N004884 and
EP/V026887). The X-ray diffraction facility used to characterize the films was
supported by EPSRC (grant EP/P001513/1). We thank the Leverhulme Trust for
funding via the Leverhulme Research Centre for Functional Materials Design.
MOS acknowledges financial support from the EPSRC as part of a Daphne Jackson
Fellowship.

## Authors declaration

### Conflict of interest

The authors have no conflicts to disclose.

### Author contributions

Marita O’Sullivan: Conceptualization; Formal analysis; Investigation; Writing
- Original Draft; Visualization. Matthew S. Dyer: Formal analysis;
Investigation; Writing - Review & Editing; Visualization. Michael W. Gaultois:
Writing - Review & Editing. John B. Claridge: Conceptualization; Writing -
Review & Editing. Matthew J. Rosseinsky: Conceptualization; Resources; Writing
- Review & Editing; Project administration; Funding acquisition. Jonathan
Alaria: Formal analysis; Writing - Original Draft.

## Data availability

The data that support the findings of this study are openly available in

## References

## References

  * Li  _et al._ (2013) B. Li, J. Zhang, T. Kaspar, V. Shutthanandan, R. C. Ewing, and J. Lian, Phys. Chem. Chem. Phys. 15, 1296 (2013).
  * Zhang  _et al._ (2021) Z. Zhang, S. L. Hsu, V. A. Stoica, H. Paik, E. Parsonnet, A. Qualls, J. Wang, L. Xie, M. Kumari, S. Das, Z. Leng, M. McBriarty, R. Proksch, A. Gruverman, D. G. Schlom, L. Q. Chen, S. Salahuddin, L. W. Martin, and R. Ramesh, Adv. Mater. 33, 2006089 (2021).
  * Dong  _et al._ (2009) X. W. Dong, K. F. Wang, S. J. Luo, J. G. Wan, and J. M. Liu, J. Appl. Phys. 106, 104101 (2009).
  * Yasukawa  _et al._ (2003) M. Yasukawa, S. Kuniyoshi, and T. Kono, Solid State Commun. 126, 213 – 216 (2003).
  * Akhbarifar  _et al._ (2020) S. Akhbarifar, W. Lutze, N. A. Mecholsky, and I. L. Pegg, Mater. Lett. 275, 128153 (2020).
  * Pesin and Balents (2010) D. Pesin and L. Balents, Nat. Phys. 6, 376 (2010).
  * Yang and Nagaosa (2014) B. J. Yang and N. Nagaosa, Phys. Rev. Lett. 112, 246402 (2014).
  * Chu  _et al._ (2019) J. H. Chu, J. Liu, H. Zhang, K. Noordhoek, S. C. Riggs, M. Shapiro, C. R. Serro, D. Yi, M. Mellisa, S. J. Suresha, C. Frontera, E. Arenholz, A. Vishwanath, X. Marti, I. R. Fisher, and R. Ramesh, New J. Phys. 21, 113041 (2019).
  * Guo and Franz (2009a) H.-M. Guo and M. Franz, Phys. Rev. Lett. 103, 206805 (2009a).
  * Hu  _et al._ (2015) X. Hu, Z. Zhong, and G. A. Fiete, Sci. Rep. 5, 11072 (2015).
  * Bovo  _et al._ (2014) L. Bovo, X. Moya, D. Prabhakaran, Y. A. Soh, A. T. Boothroyd, N. D. Mathur, G. Aeppli, and S. T. Bramwell, Nat. Commun. 5, 3439 (2014).
  * Yamamoto  _et al._ (1994) T. Yamamoto, R. Kanno, Y. Takeda, O. Yamamoto, Y. Kawamoto, and M. Takano, J. Solid State Chem. 109, 372 (1994).
  * Kobayashi  _et al._ (1995) H. Kobayashi, R. Kanno, Y. Kawamoto, T. Kamiyama, F. Izumi, and A. W. Sleight, J. Solid State Chem. 114, 15 (1995).
  * Bouchard and Gillson (1971) R. J. Bouchard and J. L. Gillson, Mater. Res. Bull. 6, 669 (1971).
  * Gökaǧaç and Kennedy (1994) G. Gökaǧaç and B. J. Kennedy, J. Electroanal. Chem. 368, 235 (1994).
  * Gaultois  _et al._ (2013) M. W. Gaultois, P. T. Barton, C. S. Birkel, L. M. Misch, E. E. Rodriguez, G. D. Stucky, and R. Seshadri, J. Condens. Matter Phys. 25, 186004 (2013).
  * Lee  _et al._ (1997) K.-S. Lee, D.-K. Seo, and M.-H. Whangbo, J. Solid State Chem. 131, 405 (1997).
  * Cox  _et al._ (1983) P. A. Cox, R. G. Egdell, J. B. Goodenough, A. Hamnett, and C. C. Naish, J. Phys. C Solid State Phys. 16, 6221–6239 (1983).
  * Facer  _et al._ (1993) G. R. Facer, M. M. Elcombe, and B. J. Kennedy, Aust. J. Chem. 46, 1897 – 1907 (1993).
  * Kanno  _et al._ (1993) R. Kanno, Y. Takeda, T. Yamamoto, Y. Kawamoto, and O. Yamamoto, J. Solid State Chem. 102, 106 (1993).
  * Kennedy and Vogt (1996) B. J. Kennedy and T. Vogt, J. Solid State Chem. 126, 261 (1996).
  * Okamoto  _et al._ (2004) J. Okamoto, T. Mizokawa, A. Fujimori, T. Takeda, R. Kanno, F. Ishii, and T. Oguchi, Phys. Rev. B 69 (2004), 10.1103/PhysRevB.69.035115.
  * Hsu  _et al._ (1988) W. Hsu, R. Kasowski, T. Miller, and T.-C. Chiang, Appl. Phys. Lett. 52, 792 – 794 (1988).
  * Ishii and Oguchi (2000) F. Ishii and T. Oguchi, J. Phys. Soc. Japan 69, 526 – 531 (2000).
  * Lee  _et al._ (2005) J. S. Lee, S. J. Moon, T. W. Noh, T. Takeda, R. Kanno, S. Yoshii, and M. Sato, Phys. Rev. B 72, 035124 (2005).
  * Laurita  _et al._ (2019) G. Laurita, D. Puggioni, D. Hickox-Young, J. M. Rondinelli, M. W. Gaultois, K. Page, L. K. Lamontagne, and R. Seshadri, Phys. Rev. Mater. 3 (2019), 10.1103/PhysRevMaterials.3.095003.
  * Avdeev  _et al._ (2002) M. Avdeev, M. K. Haas, J. D. Jorgensen, and R. J. Cava, J. Solid State Chem. 169, 24 (2002).
  * Shoemaker  _et al._ (2011) D. P. Shoemaker, R. Seshadri, M. Tachibana, and A. L. Hector, Phys. Rev. B 84 (2011), 10.1103/PhysRevB.84.064117.
  * Carcia  _et al._ (1982) P. F. Carcia, A. Ferretti, and A. Suna, J. Appl. Phys. 53, 5282 (1982).
  * Pike and Seager (1977) G. E. Pike and C. H. Seager, J. Appl. Phys. 48, 5152 (1977).
  * Stanimirović and Stanimirović (2020) Z. Stanimirović and I. Stanimirović, IEEE Trans. Electron Devices 67, 600 (2020).
  * Horowitz  _et al._ (1983) H. S. Horowitz, J. M. Longo, and H. H. Horowitz, J. Electrochem. Soc. 130, 1851 (1983).
  * Takeda  _et al._ (2002) T. Takeda, R. Kanno, K. Tsubosaka, and Y. Takeda, Electrochem. 70, 969 (2002).
  * Esposito  _et al._ (2006) V. Esposito, B. H. Luong, E. Di Bartolomeo, E. D. Wachsman, and E. Traversa, J. Electrochem. Soc. 153, A2232 (2006).
  * Nakajima  _et al._ (2014) M. Nakajima, R. Ikariyama, P. S. Sankara Rama Krishnan, T. Yamada, and H. Funakubo, Appl. Phys. Lett. 104, 022908 (2014).
  * Song  _et al._ (2020) Z.-D. Song, L. Elcoro, Y.-F. Xu, N. Regnault, and B. A. Bernevig, Phys. Rev. X 10, 031001 (2020).
  * Řehák  _et al._ (1984) B. Řehák, K. Horčic, M. Frumar, and L. Koudelka, J. Cryst. Growth 68, 647 (1984).
  * Chiba  _et al._ (2019) H. Chiba, R. Ikariyama, S. Yasui, and H. Funakubo, Thin Solid Films 669, 471 (2019).
  * Ito  _et al._ (2021) H. Ito, T. Fujita, and M. Kawasaki, APL Mater. 9 (2021), 10.1063/5.0060084.
  * Van der Pauw (1958) L. J. Van der Pauw, Philips Technical Review 20, 220 (1958).
  * Kresse and Furthmüller (1996) G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
  * Perdew  _et al._ (1996) J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
  * Kresse and Joubert (1999) G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
  * Subramanian  _et al._ (1983) M. A. Subramanian, G. Aravamudan, and G. V. Subba Rao, Prog. Solid State Chem. 15, 55 (1983).
  * Guo and Franz (2009b) H.-M. Guo and M. Franz, Phys. Rev. B 80, 113102 (2009b).
  * O’Sullivan  _et al._ (2016) M. O’Sullivan, J. Hadermann, M. S. Dyer, S. Turner, J. Alaria, T. D. Manning, A. M. Abakumov, J. B. Claridge, and M. J. Rosseinsky, Nat. Chem. 8, 347 – 353 (2016).
  * Bläsing  _et al._ (2009) J. Bläsing, A. Krost, J. Hertkorn, F. Scholz, L. Kirste, A. Chuvilin, and U. Kaiser, J. Appl. Phys. 105 (2009), 10.1063/1.3074095.
  * Carbonio  _et al._ (1999) R. Carbonio, J. Alonso, and J. Martínez, J. Condens. Matter Phys. 11, 361 – 369 (1999).
  * Tachibana  _et al._ (2006) M. Tachibana, Y. Kohama, T. Shimoyama, A. Harada, T. Taniyama, M. Itoh, H. Kawaji, and T. Atake, Phys. Rev. B 73, 193107 (2006).
  * Synowicki and Tiwald (2004) R. Synowicki and T. Tiwald, Thin Solid Films 455-456, 248 – 255 (2004).
  * Zhang  _et al._ (2019) W. Zhang, K. Luo, Z. Chen, Z. Zhu, R. Yu, C. Fang, and H. Weng, Npj Comput. Mater. 5, 105 (2019).
  * Zhou  _et al._ (2019) Y. Zhou, K. H. Jin, H. Huang, Z. Wang, and F. Liu, Phys. Rev. B 99, 201105 (2019).