performance of piezo-based devices.

  12. 12.

Reducing the maintenance cost, enhancing the lifespan, ameliorating the
performance, analysis of government supports, the cost-benefit balance, and
investigations of piezo-harvesting from energy policy viewpoint.

  13. 13.

Thermal design of piezo-systems including the temperature-dependent properties
and high-temperature harvesting limitations.

  14. 14.

Fabrication of new piezo-materials with the non-linear behavior, larger
displacements, lower frequencyies, wider operation bandwidth, and the
frequency self-adaptation capabilities.

  15. 15.

Use of meta-materials, non-toxic, biocompatible, printable piezo-materials,
nanofibers, lead-free and high-piezoelectric coefficient materials.

  16. 16.

Improving the design of electrical circuitry and managing rectification and
storage losses.

  17. 17.

Modification of structural designs including fracture-fatigue studies to
increases reliability, stability, and durability of the device.

  18. 18.

Design of efficient control techniques.

  19. 19.

Extending the application of piezo-materials in novel fields such as internet
of things.

  20. 20.

Paying close attention to the use of unimorph design for high-energy
harvesting rate, obtaining realistic resonance data in order to reach
compactness, investigating energy output much lower than 1mW, and step-by-step
report of successive energy flow or efficiency from input mechanical energy to
the final electric energy in a rechargeable battery.

  21. 21.

Focusing on applications involving elimination, restriction, and replacement
of toxic materials and environmental pollution.

  22. 22.

Development of designs exhibiting the highest electromechanical coupling
factor.

  23. 23.

Considering mechanical impedance matching, electromechanical transduction,
electrical impedance matching and priority of these factors.

  24. 24.

Development of other applications as energy harvesting devices with low energy
demand.

  25. 25.

Designing a grid of nano-devices (thousands) or thick films (10 to 30 microns)
to generate minimum 1mW power (the required electric energy to operate a
typical energy harvesting electric circuit with a DC/DC converter).

  26. 26.

General development directions may be remote signal transmission, and energy
saving in rechargeable batteries.

However, the research on piezoelectric energy harvesting is not mature enough
and many interdisciplinary active research fields are currently available. It
should be mentioned that the progress of small-scale devices with very low
power need is tightly tied to the revolution in design of efficient high-
output power piezoelectric energy harvesters. It is recommended to lie on
fundamental principles in order to obtain unique designs for future research.

## Acknowledgment

This research was supported by the Iran National Science Foundation (Grant
number 98017606).

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# The Co2+-Ir5+ orbital hybridization in LaCaCoIrO6 double perovskite

L. Bufaiçal<EMAIL_ADDRESS>L. S. I. Veiga  J. R. L. Mardegan  T. Pohlmann
S. Francoual  S. S. Dhesi  M. B. Fontes  E. M. Bittar  Instituto de Física,
Universidade Federal de Goiás, 74001-970 , Goiânia, GO, Brazil  Diamond Light
Source, Chilton, Didcot, Oxfordshire, OX11 0DE, United Kingdom  Deutsches
Elektronen-Synchrotron DESY, Notkestra$\beta$e 85, 22607, Hamburg, Germany
Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180,
Rio de Janeiro, RJ, Brazil

###### Abstract

Here, we report on the structural, electronic, and magnetic properties of a
polycrystalline sample of the LaCaCoIrO6 double-perovskite investigated by
means of synchrotron x-ray powder diffraction, x-ray absorption spectroscopy,
and x-ray magnetic circular dichroism at the Co and Ir $L_{2,3}$ edges,
magnetometry, and electrical transport. Our results indicate a configuration
of nearly Co2+/Ir5+ configuration for the transition-metal ions, with spin
canting within the Co antiferromagnetic superstructure responsible for the
ferromagnetic-like behavior observed below 100 K. The highly insulating
character of LaCaCoIrO6 and its positive magnetoresistance further suggest
that this antiferromagnetic superexchange interaction occurs through an
indirect hybridization between the Co $e_{g}$ orbitals.

###### keywords:

Double-perovskite; Cobalt; Iridium; Orbital hybridization

††journal: Journal of Magnetism and Magnetic Materials

, , ,, , , , ,

##  1 Introduction

There has recently been a great attention directed towards iridates driven by
the the peculiar interplay between the spin-orbit coupling (SOC), the crystal
field and the on-site Coulomb repulsion. This interplay leads to the splitting
of the Ir $t_{2g}$ levels, resulting in a lower-energy fourfold state with
$j_{eff}$ = 3/2 and an upper-energy twofold state with $j_{eff}$ = 1/2 [1]. In
Ir4+ (5$d^{5}$)-based oxides it has been reported, for instance, a $j_{eff}$ =
1/2 Mott insulating state in Sr2IrO4 [2], and a possibly Kitaev spin liquid
state in Cu2IrO3 [3]. But unusual magnetism can also occur in Ir5+-based
systems. For example, there is an ongoing discussion concerning a possible
excitonic magnetic ground state for Ir 5$d^{4}$ in Sr2YIrO6 and Ba2YIrO6
double perovskites (DP), which from a $j_{eff}$ perspective should result in a
$J$ = 0 state [4, 5, 6].

The addition of a second transition-metal (TM) ion in Ir-DPs increases the
complexity of the system’s electronic and magnetic structures. In contrast to
3$d$-3$d$ systems where the main exchange interactions involve the $e_{g}$
orbitals, for 3$d$-5$d$ systems may involve the $t_{2g}$ orbitals. As a
result, the conventional Goodenough-Kanamori-Anderson rules often fail to
describe the magnetic coupling between the TM ions [7, 8, 9]. A recent study
on LaSrNiIrO6, for instance, has shown an antiferromagnetic (AFM)
superstructure at the Ni2+ site through the Ni2+–O–Ir5+–O–Ni2+ path [10]. On
the other hand, the complete substitution of Sr2+ by a rare-earth A3+ element
in A2NiIrO6 DPs leads to a magnetic Ir4+ state, which couples AFM with the
Ni2+ ions to produce a ferrimagnetic (FIM) behavior whose strength increases
as the A-site ionic radius decreases [11]. Because the Ni2+ (3$d^{8}$)
$t_{2g}$ orbitals are completely filled, the hybridization with Ir $j_{eff}$ =
1/2 necessarily occurs via its half-filled $e_{g}$ orbitals [12].

Another example of interesting Ir5+-based DP is Sr2FeIrO6, for which an AFM
coupling between the Fe3+ ions occurs at $T_{N}$ $\simeq$ 120 K [13, 14, 15].
This suggests strong magnetic exchange between the widely separated Fe $d$
ions through the Fe–O–Ir–O–Fe pathway. Here, Fe3+ presents empty states at
both $t_{2g}$ and $e_{g}$ orbitals, and based on existing repors, it remains
unclear whether the $t_{2g}$ orbitals or the $e_{g}$ orbitals are more
favorable for hybridization with Ir5+. The same situation holds for
LaSrCoIrO6, for which neutron powder diffraction (NPD) and x-ray magnetic
circular dichroism (XMCD) confirm an AFM arrangement for the Co ions, but the
preferable path of hybridization between the TM ions remains unknown [16, 17].

Thereby, compelling question for this work is what constitutes the most
relevant channel of hybridization between the TM ions in a scenario where Ir5+
is the 5$d$ element and the 3$d$ ion presents empty states in both $t_{2g}$
and $e_{g}$ orbitals. Our case study is the LaCaCoIrO6 (LCCIO) DP, for which
the presumably Co2+/Ir5+ configuration leads to two fully occupied $t_{2g}$
orbitals and one half-filled $t_{2g}$ orbital for the high spin (HS) Co2+
(3$d^{7}$: $t_{2g}^{5}e_{g}^{2}$) ion. Conversely, for the low spin (LS) Ir5+
(5$d^{4}$: $t_{2g}^{4}e_{g}^{0}$) the four valence electrons occupy lower
$j_{eff}$ = 3/2, leaving the $j_{eff}$ = 1/2 levels unoccupied. We thoroughly
investigate the structural, electronic, and magnetic properties of a
polycrystalline sample of LCCIO by means of synchrotron x-ray powder
diffraction (SXRD), x-ray absorption spectroscopy (XAS), and XMCD at the Co
and Ir $L_{2,3}$-edges, magnetometry, and electrical transport measurements to
unravel the main exchange interactions between the TM ions present within this
system.

##  2 Experimental details

The polycrystalline LCCIO sample was synthesized by conventional solid-state
reaction, as described elsewhere [18]. High-resolution SXRD data were recorded
on beamline XPD at the Brazilian Synchrotron Light Laboratory (LNLS). The SXRD
patterns were obtained using the Bragg-Brentano geometry with wavelength
$\lambda$ = 1.3736 Å, at temperatures ranging from 300 K down to 25 K, using a
DE-202 cryostat (ARS Cryo) with a HOPG(002) analyzer. Rietveld refinements
were performed using the GSAS software and its graphical interface program
[19].

Room temperature Co $L_{2,3}$-edge XAS was carried on beamline I06 at Diamond
Light Source (DLS), where a fine powder of LCCIO was spaded on conductive
carbon tape and measured in total electron yield (TEY). The XMCD measurements
at the same absorption edge were performed at 2 K with an $\pm$ 5 T external
magnetic field applied along the beam axis to reach saturation. The Ir
$L_{2,3}$-edge XAS and XMCD were collected at beamline P09 of PETRA III at
DESY [20], where the powder was mixed and pressed into a low-Z BN material to
produce a pellet for transmission measurements. The Ir $L_{2,3}$ XMCD
measurements were performed at 5 K by fast-switching the beam helicity between
left and right circular polarization [21]. To align the magnetic domains and
correct for nonmagnetic artifacts, an external magnetic field of $\pm$ 5 T was
applied parallel and antiparallel to the incident beam wave vector $k$ using a
6T/2T/2T vector magnet.

The magnetization and electrical transport measurements were performed on a
Quantum Design’s Physical Property Measurement System (PPMS) coupled with a
VSM-head. The magnetization as a function of magnetic field [M(H)] curves were
carried after zero-field-cool (ZFC) the sample, while the magnetization as a
function of temperature [M(T)] curves were measured in both ZFC and field-
cooled (FC) modes. The electrical transport data were carried out using
platinum wires and silver paste for the contacts to produce a four-contact
configuration.

##  3 Results

Fig. 1(a) shows the SXRD pattern taken at 300 K, together with its Rietveld
refinement in the $P2_{1}/n$ space group. The match between the observed and
calculated patterns confirms that LCCIO grows in the monoclinic space group,
in agreement with previous reports [18]. The antisite disorder (ASD) at the
Co/Ir sites is estimated from the refinement to be $\sim$6.7%, which is within
the values found for other 3$d$/Ir-based DPs [12, 16, 22, 23]. The SXRD data
carried out at lower temperatures ($T$) show no evidence of any structural
transition. The main parameters obtained from the Rietveld refinements are
displayed in Table 1. As Table 1 and Fig. 1(b) show, the unit cell volume
($V$) decreases with $T$, as expected. Although Figs. 1(b) and (c) seem to
evidence some changes in the slope of curves for $V$ and Co/Ir–O bond lengths
at the magnetic transition temperature, more data points would be necessary to
ensure a conclusive interpretation. Besides the magnetic ordering, such
changes in the slope of the curves may stem from the progressive freezing of
phonons that occurs at low temperatures, causing the observed flattening of
the structural evolution.

Figure 1: (a) Rietveld refinement fitting of the room temperature SXRD of
LCCIO. The vertical lines represent the Bragg reflections for the $P2_{1}/n$
space group. (b) Unit cell volume (V) as a function of $T$. (c) Average Co–O
and Ir–O bond lengths as a function of $T$. (d) Average Co–O–Ir bond angle as
a function of $T$. (e) ($a$+$b$)/2$c$ as a function of $T$.

Interestingly, the average Co–O–Ir bond angle monotonically increases as $T$
decreases to 100 K, below which it it continues to increase, albeit at a lower
rate. This suggests a tendency toward a constant value caused by the Co–Ir
magnetic coupling (mediated by the intervening oxygen ions) that naturally
strengthens at temperatures below the magnetic ordering. Such an increase of
the Co–O–Ir angle may indicate a flattening of the oxygen octahedra, related
to the fact that the reduction in lattice parameter $c$ is proportionally more
pronounced than the changes in $a$ and $b$. This can be observed in Fig. 1(e)
showing ($a$+$b$)/2$c$ as a function of $T$. This term, which is equal to 1
for a cubic system, can be used as a measure of the tetragonal distortion. As
it can be seen, this parameter gets closer to 1 as $T$ decreases,
corresponding to a decrease in the tetragonal distortion.

Table 1: Main results obtained from the Rietveld refinements of the SXRD data. The number in parenthesis represents the standard uncertainties in the last decimal digits. $T$ (K) | 300 | 200 | 100 | 75 | 50 | 25
---|---|---|---|---|---|---
$a$ (Å) | 5.52494(18) | 5.51829(25) | 5.51343(21) | 5.51264(21) | 5.51200(22) | 5.51168(22)
$b$ (Å) | 5.60612(21) | 5.60675(30) | 5.60824(25) | 5.60903(26) | 5.60860(26) | 5.60919(27)
$c$ (Å) | 7.83541(43) | 7.82556(64) | 7.81955(51) | 7.81877(55) | 7.81788(54) | 7.81738(54)
$V$ (Å3) | 242.69(2) | 242.12(3) | 241.79(2) | 241.76(2) | 241.69(2) | 241.68(2)
$\beta$ (∘) | 90.033(2) | 90.027(2) | 90.032(2) | 90.032(2) | 90.027(2) | 90.028(2)
$\langle$Co-O$\rangle$ (Å) | 2.17518(5) | 2.17354(7) | 2.17256(5) | 2.17250(6) | 2.17229(6) | 2.17228(6)
$\langle$Ir-O$\rangle$ (Å) | 1.95069(3) | 1.94904(5) | 1.94804(5) | 1.94794(5) | 1.94773(5) | 1.94771(5)
$\langle$Co-O-Ir$\rangle$ (∘) | 147.508(1) | 147.516(2) | 147.523(1) | 147.525(2) | 147.525(1) | 147.526(1)
$R_{wp}$ (%) | 13.6 | 12.9 | 12.9 | 13.4 | 13.4 | 13.4
$R_{p}$ (%) | 8.7 | 8.2 | 8.7 | 9.0 | 9.1 | 9.2

Fig. 2(a) shows the Co $L_{2,3}$-edges XAS of LCCIO together with those of CoO
and LaCoO3, measured as references for Co2+ and Co3+ oxidation states,
respectively [24, 25]. The spectral features of LCCIO are closer to that of
CoO and to that of other Co2+-based DPs [24, 26]. For the XMCD signal depicted
in Fig. 2(b), the black and red curves stand respectively for parallel
($\mu^{+}$) and antiparallel ($\mu^{-}$) alignments between the photon spin
and the external magnetic field ($H$), and the difference spectra
$\Delta\mu=\mu^{+}-\mu^{-}$ is represented by the blue line. The shape of the
XMCD curve is also very similar to that of Co-based DPs for which the bivalent
Co state dominates [24, 26, 27]. Particularly, the $L_{3}$-edge XMCD exhibits
a shoulder at $\sim$780 eV that is characteristic of Co2+ [24, 26] but is
usually absent in Co3+-based systems [28]. These results strongly indicate a
nearly Co2+ state in LCCIO, although the presence of small amounts of Co3+ can
not be totally ruled out.

Figure 2: (a) Co $L_{2,3}$-edge XAS spectra of LCCIO, CoO (Co2+) and LaCoO3
(Co3+). (b) XMCD of LCCIO, taken at 2 K with $H$ = 5 T. The photon spin was
aligned parallel ($\mu^{+}$, black) and antiparallel ($\mu^{-}$, red) to $H$,
and the difference spectra are shown in blue. The dotted line is a guide to
the eye.

As Fig. 2(b) shows, the Co $L_{2}$ XMCD signal is weakly positive while the Co
$L_{3}$ is largely negative, giving evidence of a significant orbital
contribution to Co magnetic moment. In order to get a quantitative estimate of
the spin and orbital magnetic moments, we performed sum rules calculations
developed by B. T. Thole et al. [29] and P. Carra et al. [30], which provide
the following orbital and spin contributions to the magnetization.

$m_{l}=-\frac{4\int_{L_{3}+L_{2}}(\mu^{+}-\mu^{-})d\omega}{3\int_{L_{3}+L_{2}}(\mu^{+}+\mu^{-})d\omega}N_{h},$
(1)
$m_{s}=-\frac{6\int_{L_{3}}(\mu^{+}-\mu^{-})d\omega-4\int_{L_{3}+L_{2}}(\mu^{+}-\mu^{-})d\omega}{\int_{L_{3}+L_{2}}(\mu_{+}+\mu_{-})d\omega}\times
N_{h}\left(1+\frac{7\langle T_{z}\rangle}{2\langle
S_{z}\rangle}\right)^{-1},\\\ $ (2)

where $m_{l}$ and $m_{s}$ are the angular and spin magnetic moments in units
of $\mu_{B}$/atom, $S_{z}$ denotes the projection along $z$ of the spin
magnetic moment, $N_{h}$ represent the number of empty 3$d$ states, $T_{z}$
denotes the magnetic dipole moment, and $L_{2}$ and $L_{3}$ represent the
integration ranges.

Here, we assumed $T_{z}$ to be negligible compared to $S_{z}$, as usual for
3$d$ TM ions in octahedral symmetry [31, 32]. Thus, using $N_{h}$ = 3, which
is an approximated atomistic value for Co2+ state corresponding to 3 holes in
the 3$d$ level, we obtain $m_{l}$ $\simeq$ 0.14 $\mu_{B}$ and $m_{s}$ $\simeq$
0.29 $\mu_{B}$, revealing a significant orbital moment, as expected.
Considering sources of deviations such as electronic interactions, imprecision
in the integral calculations, and the $N_{h}$ value assumed, we estimate an
uncertainty of 10$\%$ on these values [31, 32] (see table 2).

Table 2: Co and Ir BR, orbital ($m_{l}$), spin ($m_{s}$) and total ($m_{t}$) magnetic moments obtained from the Co and Ir $L_{3,2}$ XAS and XMCD. Ion |  $m_{l}$ ($\mu_{B}$) |  $m_{s}$ ($\mu_{B}$) |  $m_{t}$ ($\mu_{B}$) | $m_{l}/m_{s}$ | BR
---|---|---|---|---|---
Co | 0.141$\pm$0.014 | 0.286$\pm$0.029 | 0.427$\pm$0.032 | 0.49 | 5.5
Ir | -0.022$\pm$0.002 | -0.015$\pm$0.002 | -0.037$\pm$0.003 | 1.47 | 4.6

The orbital and spin magnetic moments obtained are relatively close but
smaller than those reported by Min-Cheol Lee et al. for La2CoIrO6 ($m_{l}$ =
0.18 $\mu_{B}$, $m_{s}$ = 0.31 $\mu_{B}$ [24]. Such difference could be
related to some internal field-induced contribution since for La2CoIrO6; the
neighboring Ir ions are mainly in the tetravalent state. In contrast, for
LCCIO they are majoritarian in pentavalent $J$ = 0 states, as will be
discussed later. In any case, the total magnetic moment obtained for LCCIO
from the sum rules, $m_{t}$ $\simeq$ 0.43 $\mu_{B}$, falls significantly below
the $\sim$3 $\mu_{B}$ value expected for Co2+. This disparity indicates an AFM
arrangement of the Co ions, in agreement with other analogue CoIr-based DPs
where the small Co contribution to the magnetisation is attributed tospin
canting [16, 33].

Fig. 3(a) shows the Ir $L_{2,3}$-edge XAS of LCCIO. Its spectral lineshape is
qualitatively very similar to that of both Ir4+\- and Ir5+-based DPs [18, 28,
17, 34, 35]. Indeed, the similarity of the $L_{3}$-edge XAS is characteristic
of Ir and other 5$d$ ions, being related to the diffuse 5$d$ valence orbitals
[18, 36]. However, a closer inspection of the $L_{3}$ absorption threshold for
LCCIO, as compared with that of IrO2 measured as a reference for Ir4+ state
[inset of Fig. 3(a)], reveals a shift of $\sim$0.8 eV between the white lines.
Although such displacement lies within the instrumental resolution ($\sim$1.5
eV), it indicates a tendency toward Ir5+ in our system, but some small amount
of Ir4+ may be also present, since in octahedral coordination it is usually
observed a shift of $\sim$1 eV or more toward higher energies for the Ir5+
$L_{3}$ XAS spectra with respect to that of Ir4+ [18, 23, 28]. This, in turn,
suggests the presence of a small fraction of Co3+ and/or oxygen vacancy.

We can further scrutinize the tendency toward Ir5+ in LCCIO and, additionally,
get further insight into the strength of the SOC by computing the branching
ratio BR = $I_{L_{3}}$/$I_{L_{2}}$, where $I_{L_{3}}$ and $I_{L_{2}}$ are the
integrated white line intensities calculated from the $L_{3}$ and $L_{2}$
absorption edges, respectively. The value here found, BR $\simeq$ 4,6, is
larger than that observed for Ir4+ but similar to those of Ir5+ in DPs [23].
This tends to confirm that Ir ions are majoritarian in the pentavalent state.
Importantly, this value is much larger than the statistical BR $\simeq$ 2
observed for Ir in metals [37] and alloys [38], suggesting a strong SOC. From
the BR we can estimate the ground-state expectation value of the angular part
of the SOC by using the equation BR = (2 + $\langle$ L $\cdot$ S
$\rangle$/$N_{h}$)/(1 - $\langle$ L $\cdot$ S $\rangle$ / $N_{h}$). Assuming
$N_{h}$ $\simeq$ 6 (i.e. an Ir formal valence close to +5), we have $\langle$
L $\cdot$ S $\rangle$ $\simeq$ 2.8 $\hbar^{2}$. This high value tends to
corroborate with a $j_{eff}$ description for the Ir electronic configuration
in LCCIO [23, 39, 40].

Figure 3: (a) Ir $L_{3}$-edge XAS of LCCIO and and IrO2 standard. Inset shows
a magnified view of the absorption edges to compare their positions in energy.
(b) $L_{2,3}$-edge XMCD spectra of LCCIO, measured at 5 K and under $H$ = 5 T.

Fig. 3(b) shows the Ir $L_{2,3}$-edge XMCD signal for LCCIO, measured at 5 K
with $H$ = 5 T. Differently from previous report on the same compound [18], a
non-negligible $L_{3}$ signal is observed. Such discrepancy is most likely
related to the fact that in Ref. [18] the XMCD was carried out at a different
condition, with $H$ = 0.9 T at 60 K. Our $M(T)$ and $M(H)$ data, along with
element-specific XMCD hysteresis curves reported for the resemblant compounds
La2CoIrO6 [17], La1.5Ca0.5CoIrO6 and La1.5Ba0.5CoIrO6 [34], suggest that the
Ir moments in LCCIO are far from reaching saturation with $H$ = 0.9 T at 60 K.
Interestingly, it can be noticed a relatively large Ir $L_{2}$ signal. For
other Ir5+-based DPs, usually the $L_{3}$ and $L_{2}$ signals have opposite
signs, leading to a vanishing XMCD integrated intensity and, consequently, to
a small orbital moment [28, 17]. In contrast, for LCCIO, the $L_{3}$ and
$L_{2}$ XMCD signals have the same sign, resulting in a noticeable orbital
moment. It is important to mention that the sign of the Ir XMCD signal is
opposite to that of Co, further indicating an AFM coupling between these ions.

We performed the sum rules calculations for a quantitative estimate of the Ir
orbital moment. Assuming $N_{h}$ = 6 in Eq. 1 yields $m_{l}$ = -0.022
$\mu_{B}$. Using $\langle$$T_{z}$$\rangle$/$\langle$$S_{z}$$\rangle$ = 0.056
as previously obtained from configuration interaction calculations for
Ir5+-based DPs [6, 23, 39] we get $m_{s}$ = -0.015 $\mu_{B}$ (using
$\langle$$T_{z}$$\rangle$ = 0 would lead to $m_{s}$ = -0.018 $\mu_{B}$, a
difference of 20%), resulting in a large orbital to spin ratio typical of
5$d$-based materials presenting strong SOC [41, 42]. Although the magnetic
moments here obtained are much smaller than those found for Ir4+ [34, 17],
they are somewhat larger than those usually reported for Ir5+ [6, 23, 39]. The
recent discussion concerning excitonic magnetism for Ir5+ in some DPs [4, 5,
6, 15] indicates that non-negligible magnetism in Ir5+ can not be completely
ruled out in our sample. However, we believe that any interpretation of our
data in this way would be merely speculative since the Ir $L_{2,3}$-edge XAS
suggests the presence of some tetravalent Ir ions. The relatively large moment
found is most likely related to the presence of magnetic Ir4+. Again, the
magnetic moments obtained from sum rules are just rough estimates. Considering
sources of imprecision such as the calculated XAS and XMCD integrated
intensities, the $N_{h}$ and $\langle$$T_{z}$$\rangle$ values assumed, we
estimate an uncertainty of $\sim$ 20% on these values.

The ZFC and FC M(T) curves of LCCIO, measured with $H$ = 0.1 T, are displayed
in Fig. 4(a). The FC curve exhibits an FM-like ordering at $\sim$87 K followed
by a rough plateau-like behavior below $\sim$24 K. In contrast, the ZFC curve
shows an anomaly at $\sim$87 K corresponding to the material’s conventional
magnetic ordering and a pronounced cusp at $\sim$24 K. Previous AC
susceptibility measurements performed on this compound confirmed that the low-
temperature cusp is related to the emergence of a spin glass (SG) phase,
making of this a re-entrant SG system [18].

The inset shows 1/($\chi$-$\chi_{0}$) $vs$ temperature, where the $\chi_{0}$
term represents a $T$-independent contribution due to the combined effects of
the core diamagnetic susceptibility and a Van Vleck paramagnetic
susceptibility [4, 5, 28]. The straight line represents the best fit of the
paramagnetic region of the curve with the Curie-Weiss (CW) law, from which we
obtain $\chi_{0}$ = 3.9 $\times$ 10-4 emu/mol$\cdot$Oe, with this value being
in the range usually found for Ir5+-based DPs [5, 28, 43]. The negative sign
of the CW temperature extracted from the fit, $\theta_{CW}$ = -74 K, indicates
a predominance of AFM coupling in LCCIO, in agreement with other DPs
containing a 3$d$ TM ion and Ir5+ such as LaSrNiIrO6, Sr2FeIrO6, and
Sr2CoIrO6, for which it is attributed an AFM arrangement of the 3$d$ ions,
with the Ir5+ being presumably in the $J$ = 0 state [10, 15, 28]. Despite our
low-temperature magnetization being somewhat larger than what is observed in
the materials mentioned above, it remains considerably lower than the value
expected for FM or even FIM arrangements. The FM-like qualitative features
observed in our study are most likely related to spin canting in an AFM
superstructure at the Co site, reminiscent of findings reported for LaSrCoIrO6
[16, 17].

Figure 4: (a) ZFC-FC $\chi_{dc}$ M(T) curves for LCCIO measured with $H$ = 0.1
T. The inset shows 1/($\chi$-$\chi_{0}$) and the fit of its PM region with the
CW law. (b) M(H) curve measured at 10 K. The inset shows the evolution of
$H_{C}$ and $M$(7T) with temperature. The lines are guides for the eye.

The fit of the PM region with the CW law yields an effective magnetic moment
$\mu_{eff}$ = 4.9 $\mu_{B}$/f.u, which is somewhat larger than the value
expected from a spin-only approximation for Co2+, $\mu$ = 3.9 $\mu_{B}$ [44],
and considering a $J$ = 0 state for the Ir5+. Notwithstanding its 3$d$
character, Co2+ usually exhibits unquenched orbital contribution to its
magnetic moment in octahedral coordination [25]. Furthermore, our XAS data
suggest small fractions of Ir4+ and Co3+, helping to explain the $\mu_{eff}$
value found. In its turn, the presence of mixed valences and ASD at Co/Ir
sites would lead to competing magnetic phases and, consequently, to the
emergence of the SG phase observed at lower temperatures [18].

Fig. 4(b) shows the M(H) curve measured at 10 K. As can be seen, the loop
shows some hysteresis characteristic of FM or FIM. But again, the small
magnetization values, together with the linear dependence of the curve with
$H$ at high fields, suggest AFM coupling, with the FM-like behavior possibly
coming from spin canting at the Co moment [16, 33]. The inset of Fig. 4(b)
shows the evolution of the coercive field ($H_{C}$) with temperature, as well
as the magnetization at $H$ = 7 T, $M$(7T). A large coercivity at low
temperatures can be noticed, which can be anticipated as due to strong
magnetic anisotropy caused by significant orbital contribution from both Co
and Ir ions [12, 28, 34, 45]. The changes in the slopes of $M$(7T) and $H_{C}$
curves below the freezing temperature of the SG state ($\sim 24$ K) indicate
intrinsic blocking mechanisms related to local frustration effects of the
glassy magnetism [46].

The electrical resistivity measurements show semiconductor-like behavior for
LCCIO, as observed in Fig. 5(a). At room temperature, the resistivity is
$\rho$ $\simeq$ 0.8 $\Omega\cdot$cm and increases exponentially with
decreasing temperature down to $\sim$30 K, below which it exceeds the
instrumental limit of detection. The inset of Fig. 5(a) shows $ln\rho$ vs.
$T^{-1}$, from which the high temperature data ($T$ $>$ 150 K) was fitted with
the Arrhenius equation $\rho(T)$ $\propto$ exp($E_{g}/2k_{B}T$), where $E_{g}$
is the energy bandgap and $k_{B}$ is the Boltzmann constant. The best-fit
yields $E_{g}$ $\simeq$ 0.13 eV, a value similar to that of other Ir-based DPs
[16, 43, 47]. However, the fitting of $ln\rho$ on a $T^{-1/4}$ scale, also
shown at the inset, results in a significantly better agreement. This
indicates that the electrical transport of LCCIO is better described by a
variable-range hopping mechanism [48] rather than by a thermally activated
model.

Figure 5: (a) Electrical resistivity ($\rho$) as a function of temperature,
measured with $H$ = 0 and 9 T. (b) Magnified view of the low $T$ region,
highlighting the positive MR. (c) MR as a function of $H$, measured at 50 K
and 120 K.

The application of a magnetic field leads to a subtle increase of $\rho$,
which is unnoticed in the scale of Fig. 5(a) but can be visualized in the
zoom-in view of the low-temperature region, Fig. 5(b). This positive
magnetoresistance occurs along the whole investigated temperature interval but
is larger below $T_{N}$. This can be observed in Fig. 5(c), where isothermal
$\rho$ vs $H$ curves measured at 50 K ($<$ $T_{N}$) and 120 K ($>$ $T_{N}$)
are depicted. At 50 K, the magnetoresistance, $MR(H)$ = 100$\times$[$\rho(H)$
\- $\rho(0)$]/$\rho(0)$, is of $\sim$0.6% for $H$ = 9 T, while at 120 K it is
about five times smaller.

##  4 Discussion

A recent study of first-principles calculations on La2CoIrO6 indicates that
the energy of Ir $t_{2g}$ states reside in between those of Co $t_{2g}$ and
$e_{g}$ states. In contrast, the Ir $e_{g}$ states lie farther above, making
these last orbitals irrelevant to our discussion [49]. From the experimental
side, we came to a similar conclusion using XAS, XMCD and magnetometry
experiments on La${}_{1.5}A_{0.5}$CoIrO6 ($A$ = Ba, Ca) DPs, for which the Co
$e_{g}$ – Ir $t_{2g}$ ($j_{eff}$ = 1/2) AFM coupling seems to be the most
relevant path of hybridization between Co2+/3+ and Ir4+ [34]. Also recently, a
study of XAS and magnetotransport on strained Sr2CoIrO6 films has shown that
for compressively strained films the Co3+ moments points perpendicular to the
surface of the film within an AFM superstructure. Moreover, applying a
magnetic field along this direction results in a positive magnetoresistance
that gradually increases with increasing the field strength. This enhancement
is attributed to the progressive rotation of the moments, originally oriented
in an antiparallel direction, towards the alignment with the applied magnetic
field [47].

Figure 6: Schematic diagram of the mechanisms of the virtual electron hopping
between Co ions via (a) the $t_{2g}$ orbitals, resulting in FM coupling, and
(b) the $e_{g}$ orbitals, leading to AFM. The intermediate Ir and O ions are
omitted for simplicity.

Although the Co2+/Ir5+ valence states in LCCIO differ from those found in
La2CoIrO6 (Co2+/Ir4+), La1.5(Ba,Ca)0.5CoIrO6 (Co2+/3+/Ir4+) and Sr2CoIrO6
(Co3+/Ir5+), we can use the information discussed above to address the
mechanisms of hybridization in our compound. Co2+ (3$d^{7}$) has two
completely filled and one half filled $t_{2g}$ orbital, while both its $e_{g}$
orbitals are half filled. For Ir, the SOC lifts the $t_{2g}$ degeneracy into a
fourfold $j_{eff}$ = 3/2 and a twofold $j_{eff}$ = 1/2 state. In LCCIO, the Ir
valence is close to +5 (5$d^{4}$), with the $j_{eff}$ = 3/2 orbitals full and
the $j_{eff}$ = 1/2 ones empty. This means that the non-magnetic Ir (here
neglecting any possible excitonic magnetism for Ir5+) is just an intermediate
path for the exchange interactions between the Co ions. Thereby, the virtual
electron hopping through the pseudolinear Co–O–Ir–O–Co or the orthogonal
Co–O–O–Co paths can occur via the Co $t_{2g}$ or $e_{g}$ orbitals, as
schematically depicted in Fig. 6. Importantly, despite the fact that the
$t_{2g}$-$t_{2g}$ hybridization is, in principle, precluded by symmetry in a
cubic perovskite, it becomes possible with the tilting and rotation of the
oxygen octahedra [50, 51], as is the case for the distorted monoclinic
structure of LCCIO.

The upper panel of Fig. 6 shows the exchange interaction between Co $t_{2g}$
orbitals, while the bottom panel depicts the exchange coupling via the Co
$e_{g}$ orbitals. As can be seen, the $t_{2g}$–$t_{2g}$ hybridization should
result in FM coupling between the Co ions, whereas for the Co $e_{g}$–$e_{g}$
interaction, an AFM coupling is predicted. The small magnetization values
observed by magnetometry and XMCD suggest that FM is unlikely in LCCIO, which
favors the AFM structure for the Co ions. This is corroborated by the positive
magnetoresistance found in the electrical transport data, since for an FM
arrangement of the Co ions through $t_{2g}$ orbitals, one should expect an
increase in the conductivity when $H$ is applied. Conversely, in the presence
of AFM coupling, a strong external field acts to align the spins, thus
inhibiting the virtual electron hopping through $e_{g}$ orbitals and
consequently increasing the material’s resistivity. All together, our results
indicate that the Co $e_{g}$–$e_{g}$ AFM hybridization, mediated by the
intervening O 2$p$ and Ir $t_{2g}$ ($j_{eff}$ = 1/2) orbitals, is the most
relevant in Co2+/Ir5+ systems.

##  5 Summary

In summary, we thoroughly investigated the structural, electronic, and
magnetic properties of polycrystalline LaCaCoIrO6 (LCCIO) using SXRD, M(T) and
M(H) measurements, Co and Ir $L_{2,3}$-edge XAS and XMCD, and electrical
transport. LCCIO crystallizes in the monoclinic $P2_{1}/n$ space group with
$\sim$6.7% of ASD at the Co/Ir sites. The XAS and XMCD results indicate a
nearly Co2+/Ir5+ configuration, with possibly small fractions of Co3+ and Ir4+
ions. The weak FM-like behavior observed in the M(T) and M(H) curves is most
likely related to spin canting at the Co sites. The positive magnetoresistance
observed in the electrical transport data suggests an AFM arrangement of the
Co ions via hybridization between its $e_{g}$ orbitals and the Ir $t_{2g}$
($j_{eff}$ = 1/2) orbitals.

ACKNOWLEDGEMENTS

This work was supported by the Brazilian funding agencies: Fundação Carlos
Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) [Nos.
E-26/202.798/2019 and E-26/211.291/2021], Fundação de Amparo à Pesquisa do
Estado de Goiás (FAPEG) and Conselho Nacional de Desenvlovimento Científico e
Tecnológico (CNPq) [No. 400633/2016-7]. We thank Diamond Light Source for time
on beamline I06 under proposal MM29620-1. We acknowledge DESY (Hamburg,
Germany), a member of the Helmholtz Association HGF, for providing
experimental facilities. Parts of this research were carried out at beamline
P09 under proposal I-20200348, and we would like to thank J. Bergtholdt and O.
Leupold for assistance in setting up the experiment and 6T/2T/2T vector
magnet, respectively.

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