Magnetism of Ir 5 + -based double perovskites: Unraveling its nature and the inﬂuence of structure

A combination of x-ray-diffraction, x-ray absorption, x-ray magnetic circular dichroism, macroscopic magnetization, and muon-spin relaxation measurements is used to investigate the interplay between structure (both crystallography and microstructure) and magnetism in Sr 2 YIrO 6 as a function of both chemical (Ca-doping) and physical (hydrostatic) pressure. X-ray absorption spectroscopy clearly shows that the physical pressure is more effective in modifying the structure. On the other hand, the dichroic measurements evidence a constant magnetic signal with physical pressure and strong differences with Ca-doping. Muon-spin relaxation reveals the presence of magnetic order, even when this is hidden in the magnetization data. From the combined analysis, the magnetic results are explained in terms of the presence of Ir 6 + or Ir 4 + ions in magnetic clusters, most likely located at and triggered by antisite disorder. The measurements under high physical pressure indicate that the magnetic state is independent of the crystallographic details such as Ir-O distances and Ir-O-Y angles.

(Received 17 September 2019; published 30 January 2020) A combination of x-ray-diffraction, x-ray absorption, x-ray magnetic circular dichroism, macroscopic magnetization, and muon-spin relaxation measurements is used to investigate the interplay between structure (both crystallography and microstructure) and magnetism in Sr 2 YIrO 6 as a function of both chemical (Ca-doping) and physical (hydrostatic) pressure. X-ray absorption spectroscopy clearly shows that the physical pressure is more effective in modifying the structure. On the other hand, the dichroic measurements evidence a constant magnetic signal with physical pressure and strong differences with Ca-doping. Muon-spin relaxation reveals the presence of magnetic order, even when this is hidden in the magnetization data. From the combined analysis, the magnetic results are explained in terms of the presence of Ir 6+ or Ir 4+ ions in magnetic clusters, most likely located at and triggered by antisite disorder. The measurements under high physical pressure indicate that the magnetic state is independent of the crystallographic details such as Ir-O distances and Ir-O-Y angles. DOI: 10.1103/PhysRevB.101.014449

I. INTRODUCTION
In the past decade, the discovery of new spin-orbit-related phenomena has led to increasing interest in materials containing Ir [1][2][3][4][5][6][7][8]. However, little work has focused on the iridates having pentavalent Ir 5+ ions (5d 4 electronic configuration) as they are expected to be in a Van Vleck nonmagnetic state in the atomic limit, in both the weakly and the strongly interacting regimes. In the strong spin-orbit coupling (SOC) regime, the J = 0 state on pentavalent Ir 5+ ions arises from the splitting of the t 2g shell: the lower j = 3/2 subshell is fully filled by the four electrons while the upper j = 1/2 subshell remains empty. In the Coulomb dominated regime, the first two Hund's rules require each Ir 5+ ion to be in a total S = 1 and total L = 1 oppositely aligned to S, yielding a J = 0 state. Recently, however, several experimental counterexamples are casting into doubt this notion. Ca 2 RuO 4 (with Ru d 4 electronic configuration) is found to display a moment of 1.3μ B [9], and double-perovskite iridate Sr 2 YIrO 6 (SYIO) has been reported to show well-formed magnetic moments at Ir sites (μ eff = 0.91μ B /Ir) that order below 1.3 K (T N = 1.3 K, θ CW = −229 K) [10]. This work on SYIO suggested that small structural distortions have the potential to leverage large changes in magnetic behavior (from J = 0 to a significant * anlaguna@unizar.es magnetic moment that can be ordered). This has not only basic scientific interest but also undoubted practical potential in spintronics. Consequently, interest in 5d 4 magnetism has been boosted following this publication [11][12][13][14][15][16][17][18][19].
From the experimental point of view, several compounds of the Sr 2−x Ba x YIrO 6 series have been revisited in the past four years, but controversial and contradictory magnetic behavior has been reported. Terzic et al. reported long-range magnetic order at temperatures below 2 K for several compounds in the Sr 2−x Ba x YIrO 6 series [11]. Ranjbar et al. and Phelan et al., by contrast, did not observe any signature for long-range magnetic order in polycrystalline Sr 2−x Ba x YIrO 6 samples [12,13], but they did not investigate properties below 2 K. Corredor et al. and Dey et al. studied the Sr 2 YIrO 6 and Ba 2 YIrO 6 (BYIO) compounds, respectively, and concluded that although long-range magnetic order is absent, correlated magnetic moments (0.2-0.5μ B /Ir) are present [14,15].
Several explanations have been proposed to explain the observed magnetism in Ir 5+ systems. Initially, it was argued that the root cause for the quenching of the J = 0 state was the distortion of the IrO 6 octahedra. In particular, the noncubic crystal field created by the distortion would give rise to the partial quenching of the orbital angular momentum [10]. However, studies on Sr 2−x Ba x YIrO 6 , where the distortion is gradually decreased down to a perfect cubic situation in Ba 2 YIrO 6 , found that the moment shows little dependence on the chemical pressure [12,14,15]. This suggests that distortions of the octahedra are not responsible for the magnetic moment formation. Theoretical works on the effects of noncubic distortion also report uncertain results. Bhowal et al. found that the splitting between the levels due to the noncubic distortion in SYIO is too small, ∼10 meV, to be responsible for the breakdown of the J = 0 state [20]. By contrast, it has been reported that the trigonal distortion in Sr 2 GdIrO 6 gives rise to a splitting of ∼0.1 eV, one order of magnitude larger than that found for SYIO [20]. Therefore, distortions of the IrO 6 octahedra should still be considered as a possible factor affecting the magnetic state. In relation to the distortion of the IrO 6 octahedra, it should also be noticed that, in addition to chemical substitution, the presence of antisite disorder could also lead to significant local lattice distortions, which can partially quench the orbital angular momentum, thus restoring the magnetic moment [21].
Several experimental groups have proposed that the magnetism observed in their Sr 2−x Ba x YIrO 6 samples is ascribed to Ir 6+ and/or Ir 4+ paramagnetic impurities (estimated to be <5% in all cases) [12][13][14][15][16]18] caused by chemical disorder and/or off-stoichiometry. While the presence of Ir 6+ and/or Ir 4+ impurities cannot be a priori ruled out, identifying them as the origin of magnetic correlations is not without controversy.
Alternatively, magnetism in d 4 -based oxides has been proposed to arise from condensation of J = 1 triplon excitations [22,23]. In this scenario, if the energy of the J = 1 state is sufficiently small, the interatomic exchange due to electron hopping may lead to the onset of (anti)ferromagnetism. Regarding the works that focused on iridates, Bhowal et al. studied through first-principles calculations the electronic structure of double-perovskite iridates with Ir 5+ and found a finite moment at the Ir site that was attributed to a band-structure effect [20]. Later calculations, however, called into question the breakdown of the J = 0 state in double-perovskite iridates as they found that Ir-Ir hopping is too small to give rise to bandwidths that can overcome the singlet-triplet gap of ∼200 meV [24,25]. Density-functional theory (DFT) calculations by Chen et al. [26] also suggest that magnetic condensation is unlikely in perfect SYIO and BYIO systems. However, they also suggest that Y/Ir intersite disorder can induce magnetism (J = 1 triplon) inside the intersite disordered clusters because of enhanced interactions due to increased orbital overlap and an increased number of orbitals mediating the interactions. It should be noticed, therefore, that there are two mechanisms that could possibly link antisite disorder and the formation of magnetic moments, namely via distortions or via triplon condensation.
There are other possible mechanisms that could contribute to stabilize a magnetic moment in pentavalent Ir systems: a volume contraction would result in an increment of the hybridization, which could not only reduce the orbital angular momentum but also increase the electron hopping and the bandwidth of the 5d subshells. Taking into account the extended nature of the 5d orbitals, it cannot be discarded beforehand that this structural modification changes the delicate balance between interactions present in these systems, destabilizing the J = 0 state. Doping is an alternative mechanism. Chaloupka et al. have carried out a theoretical study of the effect of light doping with d 5 ions (J = 1/2 states, assuming strong SOC), and they found that the interaction between J excitons and doped carriers may convert the nonmagnetic and insulating parent into a ferromagnetic metal [27].
From the above scenario, it is inferred that the key questions remain unsolved: What are the root causes of the magnetism in these 5d 4 compounds? Can 5d 4 iridates become magnetic through structural (lattice contraction, distortions, defects, etc.) modification? Our work aims to provide insight into both questions. Regarding the origin of the magnetism, we present, in addition to bulk magnetometry, results from muon-spin relaxation and x-ray magnetic circular dichroism (XMCD) measurements to get further insight and better identify the origin of the magnetic behavior. Regarding the link between structure and magnetism, it is to be expected that both the crystal field and the hopping will become more important factors in determining the electronic structure of these compounds as the lattice volume is reduced. For this purpose, we have tracked the changes in the net magnetic moment per Ir as the lattice volume decreases from the initial SYIO by applying both chemical (newly synthesized Ca-doped Sr 2−x Ca x YIrO 6 ) and physical pressure. We explore whether the volume contraction or the structural distortions cause any change in the magnetic response.

II. EXPERIMENT
Polycrystalline samples of Sr 2−x Ca x YIrO 6 were prepared by solid-state reaction. The appropriate stoichiometric mixture of SrCO 3 (Aldrich, 99.99%), CaCO 3 (Aldrich, 99.99%), Y 2 O 3 (Aldrich, 99.999%), and Ir metal (Aithaca, 99.9%) was weighed and finely mixed by hand in an agate mortar. Prior to weighing the reagents, CaCO 3 and SrCO 3 were dried at 150 • C for 12 h and Y 2 O 3 was heated at 1000 • C for 12 h. The samples were placed in alumina crucibles and heated at 650 • C for 12 h and 850 • C for 12 h with intermediate regrinding. After mixing again, the samples were pressed into 20 mm pellets and heated in air at 1050 • C for 24 h, 1200 • C for 72 h, and 1400 • C for 72 h. Synchrotron x-ray diffraction (SXRD) experiments were carried out in transmission mode on the BL04-MSPD beamline [28] of the ALBA synchrotron (Barcelona, Spain) using the highest angular resolution mode as provided by the multianalyzer detector (MAD) setup. Fine powder was sealed in 0.7-mm-diam quartz capillaries. Data were collected while rotating the sample to increase powder averaging. The beam energy was 38 keV (λ = 0.325 11 Å), selected to optimize absorption. Temperature-dependent SXRD patterns were collected at 25 • C for Sr 2−x Ca x YIrO 6 (x = 0, 0.2, 0.4, and 0.6), and then at 200, 400, 600, and 800 • C for the x = 0 sample. The diffraction patterns were Rietveld-refined using the FULLPROF code [29].
The extended x-ray absorption fine structure (EXAFS) spectra at the Ir L 3 absorption edge were recorded at ambient pressure and room temperature (RT) as well as under applied high pressures (from 2.5 GPa up to 43 GPa) and low temperature (T = 10 K) at the BM23 [30] and ID24 [31] beamlines of the ESRF (Grenoble, France), respectively. In the first case the incoming energy was selected by using a Si (111) double-crystal monochromator, and higher-order harmonics were rejected by a Si mirror set at 2.2 mrad. Measurements were performed in transmission using ionization chambers. An ID24 energy-dispersive spectrometer was used to perform the low-temperature and high-pressure x-ray absorption spectroscopy (XAS) measurements. The measurements were also performed in transmission by using a one-dimensional Hamamatsu CCD camera. We used nanopolycrystalline diamond anvils [32] to avoid glitches from the anvils on the EXAFS spectra and a He-flow cryostat. Ruby chips were used as pressure markers and Ne gas was used as a pressure-transmitting medium. The EXAFS spectra were analyzed according to standard procedures [33] using the HORAE-IFEFFIT (Athena, Artemis) program package [34,35]. For the analysis of the EXAFS spectra at the Ir L 3 edge, a cluster 7 Å in size was used in calculating theoretical standards.
The magnetic properties were studied with a commercial superconducting quantum interference device (SQUID) magnetometer from Quantum Design. The magnetic susceptibility was measured both in zero-field-cooled (ZFC) mode and fieldcooled (FC) mode in the 5 T 300 K range under an applied magnetic field of 1000 Oe. Isothermal magnetization curves were obtained for magnetic fields in the −50 to 50 kOe range at 5 and 1.8 K.
Muon-spin relaxation (μSR) experiments were carried out using the GPS instrument at the Swiss Muon Source, Paul Scherrer Institute, Villigen, Switzerland. Spin-polarized positive muons (+, mean lifetime 2.2 s, momentum 28 MeV/c) were implanted into the powdered sample. The time evolution of the muon-spin polarization [the asymmetry function, A(t )] is calculated by counting emitted decay positrons forward ( f ) and backward (b) of the initial muon-spin direction with scintillation counters. The asymmetry measurements were performed in the temperature range between 5 and 300 K and in a zero-field configuration. Two additional measurements with applied 50 G transverse field were performed to get the value of α (experimental calibration constant) and the volume fractions.
The XANES/XMCD measurements under high pressure were carried out at beamline 4-ID-D of the Advanced Photon Source, Argonne National Laboratory. The spectra were recorded at the Ir L 2,3 absorption edges (2p 1 2 , 3 2 →5d transition) to probe the Ir 5d states. Circularly polarized x rays were generated using phase-retarding optics [36,37]. Harmonic rejection was achieved by the combined effects of x-ray reflection from two Pd mirrors at a 3.1 mrad incidence angle and detuning of the second crystal in the Si(111) doublecrystal monochromator. XMCD was measured by switching x-ray helicity (13.1 Hz) and detecting the related modulation in absorption coefficient with a lock-in amplifier [38]. All the measurements were done in transmission geometry, at low temperature (10 K) and under a magnetic field of 3.5 T applied along the x-ray propagation direction. For the highpressure measurements, the powdered samples were loaded on copper-beryllium diamond anvil cells (DACs) fitted with 300-μm culet anvils and a Re gasket [39]. Ne gas was used as the quasihydrostatic pressure transmitting medium and ruby spheres for in situ pressure calibration. Low temperature was reached using a He-flow cryostat, and pressure was controlled remotely using a He-gas membrane.

A. Chemical pressure
For all the Sr 2−x Ca x YIrO 6 samples, where x indicates nominal compositions, the structure at RT is described in a monoclinic unit cell, P2 1 /n space group (no. 14), and the main parameters are summarized in Table I (see the Supplemental Material for details [40]). As expected, the substitution of Sr 2+ ions by smaller Ca 2+ ions causes a small, monotonic decrease in the three lattice parameters. This reduction, however, is not the same in the three directions. For x = 0.6, a 0.51%, 0.41%, and 0.38% reduction is obtained for the a, b, and c parameters, respectively. In addition, the β angle increases. This implies a slightly increasing distortion in the crystal structure, as expected from the concomitant reduction of the tolerance factor upon introducing a smaller ion. As shown in Table I, according to the x-ray diffraction (XRD) data, not only does the structural distortion increase because of the increment of the octahedral tilting (i.e., reduction of the Ir-O-Y bond angle), but also the octahedron itself becomes more distorted upon Ca introduction.
Additionally, the Y/Ir antisite has been explored in the four samples, finding that it is small (<1%) in all the cases. For x = 0, we have 0.6 ± 0.2 % of the Ir sites occupied by Y. Regarding the effect of doping, no monotonic evolution is found as a function of doping. On the other hand, as the doping level of Ca increases, a part of it is incorporated at the octahedral sublattice instead of Y: 4.2% Ca at Y sites is found for the x = 0.2 compound and 11% for the x = 0.4 and 0.6 compounds. This favors the formation of disordered regions and implies that Ir is partially oxidized to Ir 6+ .
At first glance, the EXAFS spectra show no substantial changes with Ca-doping (see Fig. 1). To correlate the spectral features with specific structural or compositional changes, we take advantage of the Fourier transform (FT), which provides a measure of the radial distribution function around the Ir atom. In addition, taking as a starting point the SYIO crystal structure [13], we have considered a simplified model that includes the contributions to the EXAFS signal coming from four single scattering (SS) paths up to 6 Å (that is, O, Sr/Ca, Y, and Ir coordination shells around the absorbing Ir) as well as the (quasi)collinear, focusing multiple scattering (MS) paths involving the same atoms from which the SS occurs (i.e., O-Ir abs -O, Y-O, and O-Y-O scattering paths). Each coordination shell has one unique average distance (R j ) and one Debye-Waller (DW) factor. The R j lengths and DW factors of the MS paths are parametrized in terms of the SS paths in a similar manner to that described in Refs. [41,42], but the Ir-O-Y angle in our case remains fixed to that derived from the crystal structure refinement. Other models dividing the coordination shells into several subshells (thus increasing the number of SS paths) were tested but gave worse fitting parameters. The best-fit values are summarized in Table II for the end members of the series. Comparison of the two panels in Fig. 2 clearly shows that the evolution with Ca [panel (a)] is very well reproduced in the fits [panel (b)].
The first peak on the FT curve corresponds to the first coordination shell around Ir, that is, the octahedral IrO 6 environment. As can be seen in the FT represented in Fig. 2(a), no shift is observed in the first peak, indicating no measurable modification of the average Ir-O distance. The intensity shows only very small differences (whose trend is in agreement with the distortion parameter obtained by XRD), and the width of the peak remains constant. This indicates that the distortion TABLE II. Values of the best-fit structural parameters: half path lengths/interatomic distances [R j , in (Å)] and Debye-Waller factors [σ 2 , in (Å 2 )] for the Sr 2−x Ca x YIrO 6 samples. The number of atoms at mean distances R j around the absorbing atom (N j ) is fixed in the model. S 2 0 = 0.89 and E 0 (eV) = 6.23 have been fixed to the values obtained for the SYIO sample measured at ambient pressure. The Rfactor, which is a measure of the misfit between the data and theory, is 0.02 for the ambient data and 0.04 for HP data.  (9) 3.47 (7) 3.21(6) R 3 Ir-Y 4.05(5) 3.95(4) 4.00 (9) 3.56 (3) 4.33(9) R 4 Ir-Ir 5.76(6) 5.75 (7)   of the IrO 6 octahedra does not have any significant variation with Ca-doping. It should be noted, however, that the spatial resolution in our EXAFS is ∼0.1 Å, so very small distortions could be hidden in our data.
According to our analysis results, the main contribution to the R ∼ 2.2-3.4 Å range comes from the MS O-Ir-O path. The Sr atoms also contribute at this R range, but the intensity of its contribution is small as reflected by the large DW values (Table II). This agrees well with the fact that the structure of SYIO [13] actually presents four different Ir-Sr distances spanned in a broad range. As a consequence, substituting Sr by Ca in the model does not make any noticeable difference. The main contribution to the feature at R ∼ 3.9 Å is associated with the Y shell (and its concomitant SS and MS paths), and the features at R ∼ 5.6 Å and R ∼ 7.0 Å are due to the scattering coming from the Ir atoms. As shown in Fig. 2(a), the main spectral modification is located around 3.4-4.2 Å, which noticeably shifts toward lower R. Our analysis of the EXAFS spectra indicates that the differences observed with Ca-doping are not due to the chemical substitution itself but are associated with structural changes related to the Ir-O-Y angle. In particular, the fact that the length of the Y-related scattering paths decreases clearly more than the rest (see Table II) suggests that the main structural change is an increase of the Ir-O-Y tilting. This is in agreement with the evolution of ϕ found by XRD (Table I).
To get further evidence, we have simulated the FT profile assuming a perfectly collinear Y-O-Ir angle. We have fixed all the parameters to those in Table II, but the Y-related MS paths have been modified to be perfectly collinear (and with a total length equal to that in the SS path) and their DW factors have been increased. According to the simulation in the inset of Fig. 2(b), as the angle decreases the feature at R ∼ 3.9 Å shifts toward lower R. This further supports an increasing tilting of the Ir-O-Y angle with Ca-doping.

B. Physical pressure
In contrast to the Ca-doping case, a gradual evolution of the EXAFS oscillations is observed as the pressure is increased (Fig. 3). This indicates that the application of hydrostatic pressure gives rise to larger changes in the structure than applying chemical pressure. To further analyze the effect of physical pressure on the structure, the same model as for chemical pressure has been used (with the same ranges and parameters). The best-fit values for three representative pressures have been included in Table II, and the fits can be observed in Fig. 4(b).
Regarding the octahedral IrO 6 environment, a shift is observed in the first peak, indicating a reduction of the average Ir-O distance [ Fig. 4(a)]. According to our analysis, the average Ir-O distance in the IrO 6 octahedra reduces by 0.05 Å, i.e., a 2.6% reduction. The intensity also tends to decrease with increasing pressure. This is typically indicative of an increasing distortion of the IrO 6 octahedra, but it can also indicate an increasing pressure gradient along the sample.  Table II) and the Ir-O-Y angle are modified to a greater extent by hydrostatic pressure than by chemical pressure.

A. Ambient pressure
Our measurements on Sr 2 YIrO 6 indicate the lack of longrange magnetic order at least to 1.8 K. The magnetization at 014449-5  [15]. Other values reported for Ba 2−x Sr x YIrO 6 and LaSrBIrO 6 samples are also in the 0.16-0.63μ B /Ir range [14,16,26]. On the other hand, Cao et al. found higher μ eff (μ eff = 0.91μ B /Ir) as well as long-range magnetic order below 1.8 K [10,11].
In all those cases in which the magnetic response has been reported to be ascribed to paramagnetic impurities, a small percentage, 5%, has been estimated [13][14][15][16]18]. Following these works, the amount of magnetic centers would be ∼3% in our Sr 2 YIrO 6 sample [estimated from μ eff and assuming Ir 4+ ions, this value is smaller if estimated from M(H ) data].
While no data have been reported for the Ca-doped samples so far, our results show that Ca-doping does not induce any magnetic transition or drastic change of the magnetic behavior. As can be seen in Figs. 5 and 6, no evidence of longrange magnetic order is observed down to T = 1.8 K. Despite that, the magnetization values at T = 5 K and H = 50 kOe (Fig. 5) and the effective magnetic moment (Fig. 6) of the doped samples are somewhat larger than those found in our Sr 2 YIrO 6 sample. M = 0.043μ B /f.u. and μ eff ∼ 0.6μ B /Ir for Additionally, it should be noted that the shape of our M(H ) and M(T ) curves, slightly departing from a perfect canonical paramagnetic behavior, indicates the presence of correlated magnetic moments, in agreement with that found by Dey et al. and Corredor et al. [14,15].
The XMCD measured on Sr 2 YIrO 6 consists of a small but clear negative peak at the Ir L 3 edge, while no signal is observed at the L 2 edge. By contrast, the doped sample shows XMCD signals with similar intensity and opposite sign at the Ir L 3 and L 2 edges. Application of sum rules [43,44]  T z / S z = 0.056 [45]; if T z = 0 is used we obtain m S ∼ 0.0051μ B and m S ∼ 0.0130μ B , respectively). While the total magnetic moments obtained from XMCD are slightly different from magnetometry, it confirms an increase of the net magnetization in the doped sample. There is also a drastic quenching of the Ir orbital magnetic moment, with the m l / m s ratio dropping by more than a factor of 10 from x = 0 to 0.4 ( m l / m s ∼ 0.69 and 0.06, respectively). The XMCD spectra in Fig. 7, therefore, show an unexpectedly different nature of the magnetic moment for x = 0 and 0.4 samples.
A simple profile comparison with other spectra corresponding to Ir 4+ , Ir 5+ , and Ir 6+ double-perovskite iridates [46] (the particular case of Sr 2 ZnIrO 6 has been directly included in Fig. 7) allows us to undoubtedly rule out the presence of Ir 6+ ions in Sr 2 YIrO 6 while its presence is evidenced in Sr 1.6 Ca 0.4 YIrO 6 . Regarding the possible presence of Ir 4+ ions in Sr 2 YIrO 6 , the similar profiles of Ir 4+ and Ir 5+ XMCD spectra [46] prevent us from straightforwardly discarding the presence of Ir 4+ ions in the undoped sample. It is worth noticing at this point that Fuchs et al. reported a major Ir 6+ contribution in the nondistorted Ba 2 YIrO 6 sample [18].
The muon-spin relaxation (μSR) technique is used to study the spin order and dynamics arising from the Ir moment. The muon asymmetry spectra for SYIO in zero applied magnetic field are shown in Fig. 8(a). Unambiguous oscillations are observed for temperatures below 50 K, indicating the presence of magnetic order even when this is not observed in dc magnetization measurements. It should be noted here that the characteristic time windows corresponding to the two techniques are rather different: 10 −1 -10 2 s in the case of the SQUID magnetometry and 10 −5 -10 −3 s for μSR.
The time dependence of the muon-spin polarization in Fig. 8(a) is found to be best described by the following two-component functional form: 11  where j 0 is a Bessel function, A 1 and λ 1 are the amplitude and damping rate of the oscillating (magnetic) fraction, and A 2 and λ 2 are the amplitude and relaxation rate of the relaxing (nonmagnetically ordered) fraction. The results of the fit analysis are shown in Fig. 9.
The value of A 1 obtained from the fits, and reflecting the percentage associated with the volume fraction of the magnetically ordered phase, is 15% at low temperature [ Fig. 8(b)]. This is in agreement with the percentage obtained by measuring the muon asymmetry under a weak external field H ext . The amplitude of the muon signal precessing under H ext reflects the volume fraction of the sample that is paramagnetic or not ordered magnetically. Therefore, to determine the fraction of magnetic and nonmagnetic phases, the asymmetry at 300 and 5 K under a weak (H ext = 50 Oe) transverse applied field has been measured. From the data in Fig. 8(b), we obtain that the volume fraction of the magnetic phase at T = 5 K is 17%. This volume fraction implies that the magnetic signal is not coming from the majority of the Ir 5+ ions. That is to say, the magnetic response is not homogeneous throughout the sample. At the same time, a 17% volume fraction of magnetically ordered phase is in disagreement with a tiny percentage of isolated paramagnetic centers.
As for the magnitude of the local magnetic field at the muon site in SYIO, the value obtained from the fit [ Fig. 9(a)] is very close to the 958 Oe reported for La 2 CuIrO 6 [47]. Despite the fact that this Ir 4+ compound crystallizes in the triclinic P1 space group, which presents a reduced symmetry relative to the P2 1 /n, and in spite of the presence of magnetic Cu 2+ ions (μ Cu = 0.69μ B ; μ Ir = 0.45μ B ) [47], which does not allow us to assume the same magnetic structure, we can still reasonably assume a similar muon site for both compounds and a similar magnetic moment of the iridium atoms in both compounds, or at least a sizable magnetic moment for the Ir ions in our compound. In addition, a well-defined oscillation frequency indicates the development of one distinct internal magnetic field at the muon site. This seems to rule out the possibilities of a spin-glass state or an incommensurate state, confirming a commensurate magnetic order instead. On the other hand, the fact that the spectra are better fit to a Bessel function could indicate very inhomogeneous behavior across the SYIO sample. λ 1 accounts for the relaxation of the oscillation and is a measure of the width of the static Gaussian field distribution. Dynamical effects are also present in λ 1 . Interestingly enough, the damping rate peaks at T = 100 K [ Fig. 9(b)] and not in the T = 20-50 K range, where the oscillation disappears and one could expect a magnetic transition. The thermal evolution of λ 1 suggests the onset of magnetic correlations or dynamic local order already at 200 K. The change from a slowly relaxing behavior at 300 K to a fast-relaxing behavior at 200 K in Fig. 8(a) also supports this idea.
Overall, the magnetic signal in the μSR data can be better explained as coming from segregated magnetic clusters. In addition, the analysis of these data suggests a sizable Ir magnetic moment and the presence of magnetic correlations (or even well-developed dynamic magnetic order) at temperatures below 200 K.

B. Physical pressure
As shown in Fig. 10, as the pressure increases, the intensity of the x-ray absorption near-edge structure (XANES) signal at the Ir L 3 edge undergoes a slight, gradual decrease (∼0.19%/GPa), while at the L 2 edge it remains invariable. This implies a gradual decrease of the ground-state expectation value of the angular part of the spin-orbit coupling L · S , calculated via BR = (2 + L · S /n h )/(1 − L · S /n h ) [48], from ∼3.1 down to ∼2.2 (∼0.5%/GPa). A 30% reduction is significant and may be indicative of an increasing bandwidth and/or an incipient mixing of j = 1/2 and 3/2 subbands. Nevertheless, the L · S values remain large, which indicates that the system still stays in the high SOC regime and is closer to the J = 0 state. Compared to this, the reduction of L · S with Ca-doping is smaller: ∼2% for x = 0.4.
As the pressure increases there is also a slight, gradual shift (∼0.012 eV/GPa) of the Ir L 3 -edge XANES toward higher energies. As demonstrated by XMCD (see below), the spectral shift observed at the XANES is purely due to Ir-O bond length 11 contraction [49] and is not related to an evolution from Ir 5+ to Ir 6+ . Figure 11 shows the XMCD as a function of applied pressure. No spectral modification is observed as the pressure increases. This shows that no electron transfer from the Ir ion occurs. Indeed, the lack of electron transfer is not surprising in this system given the fully occupied electronic configuration of the different (Sr,O,Y) elements. More importantly, Fig. 11 demonstrates that the large structural modification observed by EXAFS spectroscopy does not cause any observable modification of the magnetic state.

V. DISCUSSION
Regarding the origin of the magnetism in these samples, the analysis of the ambient-pressure XMCD data reveals striking results. As seen in Fig. 7, the match between Sr 1.6 Ca 0.4 YIrO 6 and Sr 2 ZnIrO 6 samples is quite remarkable, thus being strong evidence that the signal comes from Ir 6+ for x = 0.4. This, in turn, indicates that (i) the Ir 5+ ions do not have any significant contribution to the XMCD, even when they are the majority, and (ii) the XMCD of the Sr 2 YIrO 6 sample does not rule out the presence of small amounts of Ir 4+ ions. The stark difference between Sr 1.6 Ca 0.4 YIrO 6 and Sr 2 YIrO 6 XMCD spectra reinforces this idea. Incidentally, in light of these results the conclusions regarding the Ir 5+ iridates in Ref. [46] should be revisited.
Following this line of argument, the differences in the XMCD recorded for Sr 1.6 Ca 0.4 YIrO 6 and Sr 2 YIrO 6 suggest an explanation in terms of unsystematic microstructural differences driven by the particular growth conditions. This could also explain the differences observed between the four samples in Fig. 5, as well as the dispersion in M(H, T ) found in the literature and why Fuchs et al. reported a major Ir 6+ contribution in the nondistorted Ba 2 YIrO 6 sample [18].
The presence of Ir 6+ in Sr 1.6 Ca 0.4 YIrO 6 can result from cation vacancies or from partial substitution of Ir by Y ions or Y by Ca ions. In our Sr 1.6 Ca 0.4 YIrO 6 , 11% of Ca at Y sites is found by XRD. On the other hand, the formation of Ir 4+ ions in SYIO would be favored by both oxygen vacancies and partial substitution of Y by Ir atoms. Y/Ir antisite disorder would also favor Ir 4+ , locally. No evidence of off-stoichiometry is found in our SYIO. Similarly, in several works, the inclusion of off-stoichiometry on the refinements of XRD and neutron powder diffraction (NPD) data was reported not to lead to better fit results [11,13,14]. Dey et al. did not notice any change in the magnetic properties before and after annealing their Ba 2 YIrO 6 sample [14], and Chen et al. found that their EDX measurements do not suggest any deviation of Ba, Sr, Y, and Ir from stoichiometry [26]. Nevertheless, it should be noticed that (i) there is limited accuracy in the occupancy factors of oxygen atoms from XRD measurements, and (ii) the amount of defects needed is very low. For instance, only 0.25% oxygen vacancies would result in 3% of Ir 4+ . Regarding the Y/Ir antisite, a 0.6% swap is obtained in SYIO.
Can the magnetism observed in Sr 2−x Ca x YIrO 6 be assigned to the presence of a few percent ( 3% in the case of our SYIO) of isolated paramagnetic Ir 4+ and/or Ir 6+ centers? If we assume that this small number of impurities are randomly distributed through the sample, the existence of magnetic correlations is rather puzzling. If verified, this would imply that these centers can establish magnetic correlations at remarkably long distances. This would be quite a notable result. On the other hand, μSR experiments evidence an inhomogeneous behavior with the presence of magnetic order in a ∼17% fraction of the sample. In addition, the analysis of these data suggests a sizable Ir magnetic moment and the presence of magnetic correlations even at temperatures below 200 K. The behavior observed by μSR is better explained in terms of small magnetic domains locally ordered, i.e., shortrange order or short-range correlations.
These small domains could originate by the formation of antisite disordered regions. According to Chen et al. [26], the formation of magnetic moments would be favored in the Y/Ir antisite disordered clusters because of enhanced interactions due to increased orbital overlap and an increased number of orbitals mediating the interactions. In the case of SYIO, the level of Y/Ir antisite, 0.6%, is smaller than the ∼2.4% needed to explain the ∼17% volume fraction of magnetically ordered phase observed by μSR. While the observed Y/Ir antisite certainly contributes to the formation of magnet clusters, additional mechanisms, which are unclear to date, must also be contributing. Besides, in perovskites with partial ordering, it is not unusual for the degree of antisite mixing to be sensitive to variations in synthesis conditions [50]. Regarding the Ca-doped samples, the enhanced magnetic response relative to SYIO that is observed in Figs. 6 and 5 can also be explained (and at least partially) in terms of antisite-induced magnetic clusters. As the doping level of Ca increases, an increasing part of it is incorporated at the Y sites. This implies an increasing formation of disordered regions containing Ir 6+ ions that may interact magnetically (or even might polarize the Ir 5+ ions around). Alternatively, Chaloupka et al. propose that light doping with d 5 ions (J = 1/2 states) could be another mechanism to create magnetic clusters. In particular, they found that the interaction between J excitons and doped carriers may convert the nonmagnetic parent into a ferromagnet [27]. Nevertheless, further work would still be needed to better clarify the role of Ir 4+ /Ir 6+ ions in the formation and behavior of magnetic clusters.
With respect to the role of structure, as shown by XRD and EXAFS results, the structural modification caused by physical pressure is larger than that due to Ca-doping. In particular, the IrO 6 octahedron becomes smaller and more distorted applying hydrostatic pressure. Similarly, the Ir-O-Y angle undergoes a more drastic modification when physical pressure is applied. These structural changes could be expected to modify both the crystal field and the magnetic exchange. Despite that, the magnetism of the SYIO sample remains constant as hydrostatic pressure is applied, as clearly shown in Fig. 11. Therefore, it can be concluded that the magnetism of the Ir 5+ ions in double perovskites cannot be tuned through small structural distortions. Neither volume contraction nor the structural distortions cause any change in the magnetic response. Similarly, it can be concluded that physical pressure does not affect either of the Ir 4+ ions present in the SYIO sample.
On the other hand, the J eff = 1/2 state of Ir 4+ relies on a nearly cubic crystal field, and substantial distortions of the IrO 6 octahedron are expected to destroy the J eff state, leading to a quenched orbital moment [51]. However, the exact relationship between noncubic distortions and the J eff = 1/2 state is currently unknown. While even a small tetragonal distortion, as observed in Sr 2 IrO 4 and Sr 3 Ir 2 O 7 , can lead to some orbital mixing [52], a dominant J eff = 1/2 character is preserved even within the distorted octahedra of the A 2 IrO 3 (A = Li,Na,Cu) family [53,54]. Nevertheless, it is well established that, in transition-metal oxides, the local structure ∼1 nm around a dopant can be highly distorted [41]. Thus, one could speculate that the quenched m L seen in Sr 1.6 Ca 0.4 YIrO 6 occurs due to Ir 4+ ions placed in highly distorted octahedra. The fact that the EXAFS does not see any distortion might simply be because it is difficult to distinguish the disordered octahedra (i.e., the EXAFS would not have enough resolution). However, while we cannot categorically dismiss such a scenario, we note that Ca-doping has a minor effect on L · S , which is difficult to reconcile with a quenched m L . Besides, the physical HP-XMCD results seem to disagree with this hypothesis and support the microstructural origin, as discussed above.
Finally, the possible emergence of excitonic magnetism (J = 1 exciton) induced by Ca-doping is discussed. According to our EXAFS results, the Ca-doping does not cause any measurable modification of the IrO 6 octahedra, but it increases the tilting of the Ir-O-Y angles. Therefore, we can reasonably assume that the spin-orbit-coupling (SOC), crystal electric field (CEF), on-site Coulomb interactions (U), and Hund's coupling (J H ) remain constant as the Ca-doping increases. The interatomic exchange, on the other hand, can be expected to decrease as a consequence of the larger Ir-O-Y tilting observed. Since the reduction of the interatomic exchange is a hindrance against the condensation of J = 1 triplon excitations, we can rule out that the enhanced magnetization signal in the doped samples is related to the onset of excitonic magnetism.

VI. CONCLUSIONS
Our XMCD data reveal that the magnetic signal comes from Ir 6+ (Ir 4+ ) ions for x = 0.4 (x = 0). The Ir 5+ ions do not have any significant contribution to the XMCD even when they are the majority. In addition, macroscopic magnetization, XMCD, and μSR experiments show that the magnetic response in Sr 2−x Ca x YIrO 6 samples is rooted in the formation of magnetic clusters. The disparity found for different Cadopings indicates the crucial role of microstructural details (antisite disorder, and off-stoichiometry) in defining the overall magnetic response.
On the other hand, from the results obtained under physical pressure, it can be clearly concluded that the nonmagnetic state of the Ir 5+ ions in these double perovskites is robust and not dependent on the structural details (Ir-O distances and Y-O-Ir angles). As a result, it cannot be tuned through small structural distortions. Neither volume contraction nor the structural distortions cause any change in the magnetic response.