Evolution of Magnetism in the N a 3−d N a 1−x M g x I r 2 O 6 Series of Honeycomb Iridates
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r Evolution of Magnetism in the Na − δ (Na − x Mg x )Ir O Series ofHoneycomb Iridates
David C. Wallace a,b , Craig M. Brown c,d , Tyrel M. McQueen a,b a Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA b Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University,Baltimore, MD 21218, USA c NIST Center For Neutron Research, Gaithersburg, MD, 20899, USA d Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716,USA
Abstract
The structural and magnetic properties of a new series of iridium-based honeycomb lat-tices with the formula Na − δ (Na − x Mg x )Ir O (0 ≤ x ≤
1) are reported. As x and δ areincreased, the honeycomb lattice contracts and the strength of the antiferromagnetic inter-actions decreases systematically due to a reduction in Ir–O–Ir bond angles. Samples withimperfect stoichiometry exhibit disordered magnetic freezing at temperatures T f between3.4 K and 5 K. This glassy magnetism likely arises due to the presence of non-magnetic Ir ,which are distributed randomly throughout the lattice, with a possible additional contri-bution from stacking faults. Together, these results demonstrate that chemical defects andnon-stoichiometry have a significant effect on the magnetism of compounds in the A IrO materials family. Keywords:
Honeycomb, Iridium, Magnetic Frustration, Disorder
1. Introduction d transition metal oxide materials have recently attracted significant interest due tothe comparable energy scales of crystal field stabilization, electronic correlations (HubbardU), and spin-orbit coupling [1]. In particular, iridium oxides are of great interest due tothe ability of Ir to adopt a d electronic configuration in its 4+ oxidation state, yielding asingly-occupied orbital with non-trivial spin texture in the strong spin-orbit coupling limit.This electronic configuration has been predicted to give rise to an unusual pattern of su-perexchange interactions, resulting in magnetic frustration and possible spin liquid behavior[2, 3, 4]. For this reason, the A IrO ( A = Li, Na) family of layered honeycomb materialshave been the subject of intense scrutiny [5, 6, 7, 8, 9].The majority of experimental work on Na IrO and Li IrO has focused on single-crystalline specimens grown via “self-flux.” Despite strong antiferromagnetic interactionsin Na IrO , evidenced by a reported large negative Weiss temperature θ W = -116 K, long-range antiferromagnetic order is only present below a N´eel temperature of T N = 15 K, Email address: [email protected] (Tyrel M. McQueen)
Preprint submitted to Journal of Solid State Chemistry June 9, 2018 emonstrating that that Na IrO is in a magnetically frustrated regime [10, 11]. A studyof the (Na − x Li x ) IrO solid solution revealed that θ W as well as T N vary significantly with x , and the magnetism reaches a peak in frustration at the intermediate value of x = 0.7[12]. Isovalent substitution of Li for Na in the A IrO structure presumably has the effectof modulating the exchange interaction strengths between neighboring Ir sites, however thiseffect has not been systematically explored. Recently, a broad variety of new ternary Iroxides with the formula Na − δ M Ir O ( M = Zn, Cu, Ni, Co, Fe and Mn) were reported [13],but no unifying picture of the magnetism demonstrated by this family can yet be drawn.Here, we report another new member of this chemical family, Na − δ (Na − x Mg x )Ir O , inwhich Mg substitutes for Na in the honeycomb planes and the Na content between planes isvariable (Fig. 1(a)). Aliovalent substitution of Mg for Na in the honeycomb plane offers a con-venient and controllable method by which to tune the lattice parameters of the unit cell and,in doing so, vary the exchange interactions between neighboring Ir sites. Additionally, weresolve the discrepancy in magnetic behavior between polycrystalline and single-crystallinesamples of Na IrO , where the former are spin glasses and the latter exhibit long rangeantiferromagnetic (AFM) order [10], by showing that Na IrO decomposes rapidly in air aspreviously reported, and that this decomposition destroys AFM order [14].
2. Materials and Methods
Polycrystalline Na IrO was prepared via a method similar to what was previously re-ported [10]: Na CO (NOAH Technologies Corp., 99.9%) , MgO (NOAH Technologies Corp.,99.99%) and Ir black (J&J Materials Inc.) were intimately ground using an agate mortarand pestle and pelletized. The sample was heated in a covered alumina crucible to 750 ◦ Cover a period of 4 hrs, held at that temperature for 30 hrs, then quenched in air. The pelletwas then reground with an additional 5 mol % Na CO , pelletized, and placed into a furnacepreheated to 900 ◦ C where it dwelled for and additional 48 hrs. After the final heating,samples were removed from the furnace and allowed to cool in an argon filled glovebox toprevent reaction with laboratory air. Polycrystalline samples of Na − δ (Na − x Mg x Ir )O wereprepared via a similar method: Na CO , MgO and Ir metal powder were intimately groundand pelletized. Samples were heated in covered alumina crucibles to 750 ◦ C over a periodof four hrs, held at that temperature for 30 hrs, then quenched in air. Samples were thenreground, pelletized, and placed into a furnace preheated to 900 ◦ C where they dwelled forbetween 48 and 96 hrs, followed by quenching in air. The 900 ◦ C heating was repeatedwith intermediate regrindings until the laboratory x-ray powder diffraction (XRPD) datashowed no impurity phases and no change in lattice parameters or relative peak intensitiesbetween subsequent heatings. After the final heating, samples were processed and stored inan argon-filled glovebox to prevent reaction with air. Samples of suitable size for neutronpowder diffraction (NPD) were prepared via a similar method, but with an additional twoweek heating at 900 ◦ C. Certain commercial suppliers are identified in this paper to foster understanding. Such identificationdoes not imply recommendation or endorsement by the National Institute of Standards and Technology, nordoes it imply that the materials or equipment identified are necessarily the best available for the purpose. α radiation with λ = 1.5406 ˚A and λ = 1.5445 ˚A and equipped with a LynxEye CCD detec-tor. Rietveld refinements to laboratory XRPD data were performed using TOPAS (BrukerAXS). NPD data were collected at the NIST Center for Neutron Research using the BT-1high-resolution powder diffractometer with an incident wavelength of λ = 1.5419 ˚A usinga Cu (311) monochromator and with 15’ and 60’ for primary and secondary collimation,respectively. Rietveld refinements to NPD data were performed in GSAS/EXPGUI [16, 17].Samples were loaded into vanadium cells and sealed in an inert helium glovebox to preventexposure to air. DC and AC magnetization measurements were carried out using a QuantumDesign Physical Properties Measurement System. Elemental analyses were performed viainductively-coupled plasma optical emission spectroscopy (ICP-OES) by Evans AnalyticalGroup. XRPD simulations were performed using DIFFaX [18].
3. Results and Discussion
The structure of the A IrO family of materials is derived from the layered triangularlattice compound α –NaFeO (Fig. 1(a)): when Na substitutes for one third of the Fe sitesin NaFeO in an ordered fashion, a layered honeycomb lattice is formed and the chemicalformula becomes Na FeO . For this reason, the structural formula of A IrO can be de-scribed more intuitively as A A ′ Ir O , where electronically active A ′ Ir O honeycomb layers,comprised of tilted, edge-sharing octahedra, are separated by electronically inert layers of A cations. The honeycomb order in these layers is energetically favorable due to the largedifferences in atomic radii and oxidation states of Ir in comparison to the A ′ cation. Becauseelectronically active honeycomb layers are separated by electronically inert triangular layers,the A IrO family are essentially layered two dimensional materials. This fact can give riseboth to interesting physics, and to complex structural disorder.Fig. 2(a) shows simulated XRPD data that demonstrate how disordered stacking arrange-ments affect the observed XRPD pattern. When honeycomb lattices are stacked in a perfectlyordered manner, sharp reflections are observed in the XRPD data between scattering angle2 θ = 19 ◦ and 32 ◦ – these are often referred to as supercell reflections, as the arise from theadditional honeycomb ordering within the triangular layer. This structure (Fig. 1(a)) canbe accounted for by a larger R3 m cell where the a axis is expanded by √ m cell, or to lower symmetry variations such as the monoclinic C2/ m or C2/ c cells commonly observed (Fig. 1(b)) [11, 19]. If stacking faults are introduced, even with alow probability of occurrence, the supercell reflections become broadened and attenuated asshown in Fig. 2(a) with 5% stacking faults. Fig. 2(b) shows XRPD data collected on threedifferent samples of Na IrO , each with a different degree of structural disorder. Rietveldrefinement to data collected on a sample with stacking faults can incorrectly account for theobserved loss in supercell reflection intensity by introducing cation site mixing in the hon-eycomb plane. The energy cost associated with producing a stacking fault in Na IrO andstructurally analogous systems is very small, and is thus significantly more likely to occurthan antisite disorder [11, 15]. Similarly, a refinement can give the illusion of small particlesize in order to account for the observed broadening of the supercell reflections. The sameeffect is observed in neutron diffraction, though the honeycomb order may be less apparent3f atoms in the honeycomb layer have similar neutron scattering cross sections. It is there-fore quite difficult to make accurate structural characterizations of samples with significantstacking disorder using neutron or x-ray diffraction techniques.Fig. 3 shows NPD datasets collected on Na Mg . Ir O at T = 5, 100, and 295 K, alongwith Rietveld refinements to the data. Small supercell reflections were observed that couldnot be indexed using the standard R3 m cell for a triangular lattice. To account for this,a refinement was attempted using an R3 m cell with a √ a -axis fromthe corresponding triangular cell, but this did not accurately index the observed supercellreflections. The reflections were properly indexed using the lower symmetry monoclinic spacegroup C2/ m (12). In order to determine cation site occupancies, it was assumed that nosite mixing occurs between sites in the honeycomb plane (4 g and 2 a ), and the 4 g site wasfixed at full Ir occupancy. The 2 a site was assumed to have mixed Na/Mg occupancy. Itwas further assumed that Mg only substitutes for Na at the 2 a site. The interplane Nasites (2 d and 4 h ) were constrained to have the same occupancy, as were the O1 and O2sites (8 j and 4 i ). Occupancies were then allowed to refine freely within the constraints. Theoccupancies determined from refinement to the T = 5 K data were then fixed in refinementsto data collected at higher temperatures. Due to the high correlation between isotropicdisplacement and occupancy, occupancies were determined with fixed U iso = 0.005, then U iso was allowed to refine freely. The results of these refinements are listed in Table 1. Fig. 4shows NPD datasets collected on Na . MgIr O at T = 5 K and 100 K. Rietveld refinementsto these datasets were carried out in the same way as for the previous sample, however, asmall IrO impurity was present in this sample, and was included as a separate phase in therefinements. The results of these refinements are listed in Table 2. Lattice parameters forNa . MgIr O at room temperature were determined from laboratory XRPD data collectedusing an air-free sample holder sealed under argon.To confirm the compositions of the samples used for NPD, elemental analyses were per-formed via ICP-OES. The results of these analyses are shown in Table 3. Initial attempts todissolve the samples were unsuccessful, and the samples had to be recovered and re-dissolvedusing microwave digestion. While the Na/Mg ratios agree well with the compositions deter-mined from NPD, the Ir content is anomalously low for both samples, which is likely due tothe difficulty associated with fully dissolving Ir and its oxides.The structures of all other samples in the series were characterized via laboratory XRPD.Rietveld refinements were carried out using the reported structure for Na IrO (space groupC2/ m ) [11]. However, because Ir is the dominant x-ray scatterer and stacking disorder ispresent, the a and b lattice parameters of the monoclinic cell were first obtained by performinga Le Bail fit to the data using space group R3 m , where the a -axis is the nearest-neighbordistance in the honeycomb lattice. The resulting a lattice parameter was converted to thethe a and b lattice parameters of the monoclinic cell, which were then fixed for the remainderof the refinement. In this way, site mixing between the 4 g and 2 a sites can be introduced inorder to improve relative peak intensities without adversely affecting the lattice parameters.This is particularly important when comparing compounds within a series that may havevarying degrees of stacking disorder and site mixing. For reporting purposes, we refer to theresulting site-mixing percentages as the percent of disorder, as they are likely due to stackingfaults rather than site mixing. The lattice constants and percents of disorder determined forthese compounds are listed in Table 4. 4n order to distinguish between the effects of Mg substitution and Na deficiency, twoseries of compounds were prepared using the exact same heating schedule. The first serieswere prepared with the nominal formula Na Na − x Mg x Ir O , and the second series hadthe nominal formula Na − δ Na . Mg . Ir O . Plots of lattice parameters versus nominalcomposition demonstrate the influence of both Mg substitution (Fig. 5(a)) and Na-deficiency(Fig. 5(b)) on the lattice parameters. Substitution of Mg for Na in the honeycomb planecauses the a - and b -axes to contract, and the c -axis to expand slightly. This result supportsthe assumption that Mg substitutes into the honeycomb plane, as substitution between theplanes would cause the c -axis to contract due to electrostatics and the reduced size of Mgrelative to Na. Similarly, Na-deficient samples show a contraction of the a - and b -axes andan expansion of the c -axis. Because both Na and Mg contents are variable, compounds inthe Na − δ (Na − x Mg x )Ir O series have a broad range of possible unit cell parameters. To investigate the influence of lattice geometry on the magnetic properties of the A IrO family, zero-field-cooled (ZFC) magnetization data were collected under an applied magneticfield of µ H = 1 T on each of the compounds in the Na − δ (Na − x Mg x )Ir O series. Fig. 6shows plots of inverse magnetic susceptibility ( χ − ≈ HM ) versus temperature for all com-pounds studied in this work. Datasets are staggered along the y-axis for visibility. Linearfits to the data in the paramagnetic regime ( T >
60 K) yield the Curie constant C , theWeiss temperature θ W , and the temperature-independent susceptibility χ (Table 5). θ W ,a measure of the average magnetic interaction strength, is negative for all members of theseries, indicating that antiferromagnetic interactions dominate in these materials. Fig. 7shows a plot of θ W versus the average nearest neighbor Ir–Ir distance for all members of theNa − δ (Na − x Mg x )Ir O series. There is a clear trend in the magnitude of θ W as a functionof Ir–Ir distance, illustrated with a solid red line. Contraction of the honeycomb plane re-sults in a decrease in the magnitude of θ W . The change in interaction strength is likely dueto modulation of the Ir–O–Ir bond angles, which become narrower as the lattice contracts.Contraction of the lattice causes these angles to decrease, resulting in increased ferromag-netic exchange and a concomitant decrease in the magnitude of θ W . To illustrate this effect,the average Ir–O–Ir bond angles at T = 5 K are given on the plot for the two samples thatwere analyzed via NPD, along with the average of the two angles reported for Na IrO [11].The Curie constant C is directly related to the number of Ir species in the sample, asIr , Na, and Mg are all diamagnetic. We therefore use both the nominal compositions andthe calculated values for C to estimate the ratio of Ir to Ir , using the compounds whosecompositions are known (Na IrO , Na Mg . Ir O and Na . MgIr O ) as reference points(Table 5). It must be noted that in the strong spin-orbit coupling limit there is a substan-tial orbital contribution to the observed susceptibility of the Ir electrons. Nevertheless,these estimates show unambiguously that a significant quantity of low-spin Ir can exist asnon-magnetic “holes” in A IrO honeycomb lattices. This is unsurprising from a chemicalstandpoint, as the Ir /Ir redox cycle is well documented in the literature, and has evenbeen studied for use in water oxidation catalysis [20]. It is likely that the reduced Ir speciesare distributed in a disordered manner throughout the lattice, which would explain the originof the spin glass-like behavior observed in many low quality Na IrO samples.5amples in the Na − δ (Na − x Mg x )Ir O series exhibit spin glass-like behavior. Fig. 8 (a)shows AC magnetic susceptibility data collected on Na Mg . Ir O and Na . MgIr O . Inboth sets of data there is a broad peak in the real component of the AC susceptibility χ ′ atlow temperatures, the position T f and height χ ′ max of which vary as a function of the fre-quency ω of the AC field. Analysis of the data in the context of a canonical spin glass usingthe Vogel–Fulcher law or standard theory for dynamical scaling yield unphysical parametersand therefore little insight [21]. The linear relationship between of ln( ω ) and T f indicates anArrhenius–type activation barrier, with activation energies E a between 100 K and 300 K andcharacteristic frequencies ω on the scale of 10 Hz to 10 Hz [22] (Fig. 8 (b)). While theselarge values, located in Table 6, are clearly unphysical, they do imply that the frozen, disor-dered magnetic state observed in these and other iridates is closer to superparamagnetismthan to spin glass. This implication is best understood by considering the two major sourcesof disorder in honeycomb iridates: stacking faults (Fig. 9(a)) and non-magnetic Ir “holes”(Fig. 9(b)). Stacking faults occur due to the negligible energy difference between all possiblestacking arrangements, but may have little influence on magnetic order because exchangeinteractions between neighboring layers are small compared to the interactions within eachtwo dimensional layer. Non-magnetic Ir “holes” are also likely to exist due to the easewith which Ir can be reduced. This type of defect, in contrast to stacking faults, can havea significant effect on magnetic order even at low levels, as it gives rise to the possibility ofisolated antiferromagnetic domains [6]. Such a picture could explain the apparent proximityto a superparamagnetic state which in fact arises due to a distribution of local AF domainsizes.Fig. 10 (a) shows XRPD data collected over the 2 θ range 10 ◦ to 50 ◦ in six minutes on anearly pristine sample of Na IrO , collected immediately upon removal from an argon-filledglovebox, where the sample was ground and prepared after heating at 900 ◦ C. XRPD datacollected on powder from the same sample after eight hours of exposure to laboratory air showsignificant changes in the relative intensities of the Bragg peaks, as well as the developmentof broad new peaks, however there is only a minor change in the lattice parameters of theNa IrO unit cell over this time period. In contrast, the magnetic properties are significantlyaffected by the reaction. When handled properly, polycrystalline Na IrO exhibits long rangeAFM order, as evidenced by the local peak in the magnetic susceptibility data below T N =15 K (Fig. 10(b)). After eight hours of exposure to air, there is no such local maximum.Curie-Weiss fitting to the linear region of the data above T = 60 K shows that θ W decreasessubstantially as a result of the reaction (Fig. 10(c)). The Curie constant also decreasessignificantly, suggesting that the average oxidation state of Ir is changing as a result of thereaction, resulting in fewer S = Ir species. The fact that the lattice parameters of theNa IrO cell do not change significantly as a result of exposure to air suggests that thisis not simply a result of hydration, as one might expect from experience with structurallyanalogous systems [23]. The appearance of new peaks suggests that a chemical reaction isoccurring between one or more components of laboratory air and Na IrO , a possibility thatwas very recently explored in detail [14]. This result suggests the origin of the discrepancybetween magnetic data collected on single crystalline and polycrystalline samples: the smallsurface area to volume ratio of single crystalline samples hinders the reaction, leaving muchof the sample’s bulk unreacted. Unfortunately, this implies that previous studies on the6agnetic properties and structure of single-crystalline Na IrO may have yielded inaccuratedata due to sample inhomogeneity.
4. Conclusions
A new series of compounds based on the A IrO prototype with the formula Na − δ (Na − x Mg x )Ir O (0 ≤ x ≤
1) were synthesized and characterized using NPD, XRPD, ICP-OES, and magne-tometry. Substitution of Mg for Na results in contraction of the a - and b -axes and expansionof the c -axis, suggesting that Mg substitution occurs primarily in the honeycomb plane.Similarly, Na deficiency between honeycomb planes contracts the a - and b -axes and expandsthe c -axis. All samples exhibit stacking disorder, which complicates structural characteri-zation. Magnetic data collected on the compounds studied in this series suggest that thereare two main variables that determine the magnetic properties of compounds in the A IrO family: (1) the strength of the magnetic superexchange interactions between neighboring S = Ir species is dependent on the angle of the Ir–O–Ir bonds, for which the in planelattice parameters a and b are a good structural marker, and (2) the number of S = Ir sites is influenced by the chemical composition of the compound because the oxidation stateof Ir is variable. This demonstrates that chemical defects can lead to significant numbers ofnon-magnetic “holes”, which are likely the root of the pseudo-superparamagnetic behaviorobserved in many polycrystalline samples. We further showed that Na IrO reacts quicklywith laboratory air, producing significant changes in its magnetic behavior, and reportedmagnetic data on high-quality polycrystalline Na IrO , which shows long-range AFM order.Together, our results demonstrate that defects and disorder have significant effects of themagnetism of the A IrO family, and that these materials can be chemically tuned to inorder to explore experimentally what may prove to be a rich magnetic phase diagram.
5. Acknowledgements
Acknowledgement is made to the donors of the American Chemical Society PetroleumResearch Fund and the David and Lucille Packard Foundation for support of this research.
References [1] G. Jackeli & G. Khaliullin, Mott Insulators in the Strong Spin-Orbit Coupling Limit:From Heisenberg to a Quantum Compass and Kitaev Models.
Physical Review Letters IrO . Physical Review Letters A IrO . Physical Review Letters A IrO . Physical Review Letters Ir − x Ru x O . arXiv:1311.7317 (2013)[9] V. M. Katukuri, et al. , Kitaev interactions between j = 1/2 moments in honeycombNa IrO are large and ferromagnetic: Insights from ab initio quantum chemistry calcu-lations. arXiv:1312.7437 (2013)[10] Y.Singh & P. Gegenwart, Antiferromagnetic Mott insulating state in single crystals ofthe honeycomb lattice material Na IrO . Physical Review B , 064412 (2010)[11] S. K. Choi et al. , Spin Waves and Revised Crystal Structure of Honeycomb IridateNa IrO . Physical Review Letters , 127204 (2012)[12] G. Cao et al. , Evolution of Magnetism in Single-Crystal Honeycomb Iridates.arXiv:1307.2212v1 (2013)[13] K. Baroudi et al. , Structure and Properties of α -NaFeO -type Ternary Sodium Iridates.arXiv:1312.0995 (2013)[14] J. W. Krizan, J. H. Roudebush, G. M. Fox, R. J. Cava., The Chemical Instability ofNa IrO in Air. arXiv:1312.1637 (2013)[15] J. Br´eger et al. , High-resolution X-ray diffraction, DIFFaX, NMR and first principlesstudy of disorder in the Li MnO –Li[Ni / Mn / ]O solid solution. Journal of Solid StateChemistry , , 2575 (2005)[16] A. C. Larson, R. B. Von Dreele, Los Alamos National Laboratory Report LAUR , 86–748.(2000)[17] B. H. Toby, EXPGUI, a graphical user interface for GSAS,
J. Appl. Crystallogr. , ,210–213. (2001)[18] M. M. J. Treacy, J. M. Newsam & M. W. Deem, A general recursion method for cal-culating diffracted intensities from crystals containing planar faults. Proceedings of theRoyal Society, London
A433 , 499-520 (1991)[19] E. Climente-Pascual, et. al , Spin Delafossite Honeycomb Compound Cu SbO , Jour-nal of Inorganic Chemistry , , 557 (2012)820] J. D. Bakemore, et al , Half-Sandwich Iridium Complexes for Homogeneous Water-Oxidation Catalysis. Journal of the American Chemical Society , , 16017 (2010)[21] J. A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor and Francis Inc.(1993) ISBN 0-7484-0038-9[22] K. Binder, A. P. Young, Spin glasses: Experimental facts, theoretical concepts, andopen questions. Rev. Mod. Phys. , , 801 (1986)[23] J. W. Lynn et al. , Structure and dynamics of superconducting Na x CoO hydrate andits unhydrated analog., Physical Review B , , 214516 (2003)
6. Tables and Figures Mg . Ir O ( C2 / m (12)) 5 K 100 K 295 K a (˚A) 5.3565(3) 5.3585(3) 5.3621(5) b (˚A) 9.3172(5) 9.3216(5) 9.3294(9) c (˚A) 5.6032(3) 5.6069(4) 5.6186(4) β ( ◦ ) 108.617(7) 108.632(8) 108.58(1)Na1 (2 d ) ,0, occ. 0.81(1) 0.81(1) 0.81(1)U iso h ) , y , occ. 0.81(1) 0.81(1) 0.81(1) y iso a ) 0,0,0 occ. 0.54/0.46 0.54/0.46 0.54/0.46U iso g ) , y ,0 y iso j ) x , y , z x y z iso i ) x ,0, z x z iso ◦ ) 99.1(4) 97.5(3) 100.7(6)Ir–O–Ir 2( ◦ ) 94.0(3) 95.0(3) 93.8(3) χ R wp R p Table 1: Results of Rietveld refinement to NPD data collected on Na Mg . Ir O (sample 7). . MgIr O ( C2 / m (12)) 5 K 100 K a (˚A) 5.3084(6) 5.3091(5) b (˚A) 9.197(1) 9.1992(9) c (˚A) 5.6461(3) 5.6473(3) β ( ◦ ) 108.440(7) 108.441(6)Na1 (2 d ) ,0, occ. 0.77(1) 0.77(1)U iso h ) , y , occ. 0.77(1) 0.77(1) y iso a ) 0,0,0 occ. 0/1 0/1U iso g ) , y ,0 y iso j ) x , y , z x y z iso i ) x ,0, z x z iso ◦ ) 97.8(6) 99.5(5)Ir–O–Ir 2 ( ◦ ) 94.4(4) 93.9(3) χ R wp R p Table 2: Results of Rietveld refinement to NPD data collected on Na . MgIr O (sample 11). Sample No. NPD Formula
Na : Mg : Ir molar ratio7 Na . Na . Mg . Ir O ICP-OES
NPD . MgIr O ICP-OES
NPD
Table 3: results of ICP-OES elemental analysis performed on Na Mg . Ir O and Na . MgIr IrO comparedwith compositions determined from Rietveld refinement to NPD data. Ir contents determined from ICP-OESare anomalously low due to complications which arose in the dissolution process. ample No. Target Stoichiometry a (˚A) b (˚A) c (˚A) β ( ◦ ) % Disorder NaIr O NaIr O (8h in air) 5.4270(1) 9.3999(1) 5.6135(2) 108.991(5) 20%3 Na Na . Mg . Ir O Na . Mg . Ir O Na . Mg . Ir O Na . Mg . Ir2O . Na . Mg . Ir O * 5.3621(5) 9.3294(9) 5.6186(4) 108.58(1) –8 Na Na . Mg . Ir O . Na . Mg . Ir O . Na . Mg . Ir O . MgIr O * 5.3171(1) 9.2094(1) 5.6707(3) 108.499(6) 32% Table 4: Target stoichiometries and unit cell parameters determined from XRPD data collected at roomtemperature of all compounds studied in this work. Compositions marked with an asterisk were determinedby Rietveld refinement to NPD data collected on the final product and verified via ICP-OES. The 4 g /2 a sitemixing percentages, referred to as “% Disorder,” are a rough measure of the amount of structural disorderpresent in the sample. Sample No. Target Stoichiometry χ ( emumolIr · K ) C ( emu · KmolIr · Oe ) θ W (K) Ir :Ir ( ± NaIr O · − NaIr O (8h in air) -5(2) · − Na . Mg . Ir O -9(1) · − Na . Mg . Ir O -9(1) · − . Na . Mg . Ir O -6(1) · − . Na . Mg . Ir2O · − . Na . Mg . Ir O * 3.7(8) · − Na . Mg . Ir O -3.4(6) · − . Na . Mg . Ir O -9(1) · − . Na . Mg . Ir O -1.2(9) · − . MgIr O * -1.1(7) · − Table 5: Curie-Weiss parameters determined from linear least-squares fitting to inverse magnetic suscepti-bility data in the paramagnetic regime.
Sample No. Target Stoichiometry T f (100 Hz) E a (K) ω (Hz)5 Na Na . Mg . Ir O Na . Mg . Ir2O . Na . Mg . Ir O * 4.9 190(13) 10 Na . Mg . Ir O . Na . Mg . Ir O
11 Na . MgIr O * 3.4 187(11) 10 Table 6: Freezing temperatures T f , activation energies E a , and characteristic frequencies ω deter-mined from an Arrhenius analysis of AC magnetic susceptibility data collected on members of theNa − δ (Na − x Mg x )Ir O series. igure 1: (a) A simple triangular lattice can be described by an R -3m unit cell (green) with in-plane latticeparameter a . Formation of honeycomb order by substitution of one third of the atoms in the triangularlattice is accommodated by a √ -3m unit cell(red). Different stacking arrangements (not shown) can require a lower symmetry unit cell, such as the C2/ m cell shown (blue). (b) The structure of Na − δ (Na − x Mg x )Ir O is described by the C2/ m cell shown in the ab -plane. Oxygen atoms above the honeycomb plane are bonded to Ir with thick black lines, while thosebelow the plane are bonded to Ir with thin lines. IrO octahedra share edges to form a honeycomb lattice,highlighted by a light blue hexagon. Two distinct Ir–O–Ir bond angles, labeled 1 and 2, are possible in thisstructure. The structure is also shown in the ac -plane to highlight the stacking arrangement correspondingto the C2/ m cell.Figure 2: (a) XRPD patterns simulated using DIFFaX are shown for layered structures of the followingtypes: triangular (green), ordered honeycomb (blue), and ordered honeycomb with 5% stacking faults (red).The influence of honeycomb ordering on the XRPD pattern is most apparent in the shaded region between2 θ = 18 ◦ and 22 ◦ . (b) XRPD data collected on three different samples of Na IrO with varying degrees ofstructural disorder. The top sample has the fewest stacking faults, as illustrated by the sharp peaks in theshaded region between 2 θ = 18 ◦ and 22 ◦ . igure 3: NPD data (black circles) collected on Na Mg . Ir O at T = 5 K, 100 K, and 295 K are shownalong with Rietveld refinements (red) and the difference between the data and the fit (green). Tick marks(gray) indicate the positions of expected Bragg reflections.Figure 4: NPD data (black circles) collected on Na . MgIr IrO at T = 5 K and 100 K are shown along withRietveld refinements (red) and the difference between the data and the fit (green). A small ( ∼ impurity was present in the sample, and was included as a separate phase in the refinements. Tick marks(gray) indicate the positions of expected Bragg reflections. Tick marks corresponding to the IrO impuritypeak positions are located below the tick marks for the structure. igure 5: Plots of lattice parameters vs. nominal chemical composition for the cases of varied Mg substitution(Na (Na − x Mg x )Ir O ) (a) and varied Na-content (Na − δ (Na . Mg . )Ir O ) (b) . Substitution of Mg forNa in the honeycomb plane causes the a - and b -axes (black diamonds and red circles, respectively) to contractand the c -axis (blue squares) to expand. Decreasing the amount of sodium in the lattice has a similar effect. igure 6: Inverse magnetic susceptibility is plotted against temperature for each member of the series.Datasets are shifted along the y-axis for visibility. Linear fits to inverse magnetic susceptibility data overthe range T = 60 K to 300 K yield the Curie constant C and the Weiss temperature θ W for each member ofthe series. Datasets are shifted along the y-axis for visibility. The Weiss temperatures θ W for each memberof the series are indicated by red circles, corresponding to the x-intercept of the linear extrapolation fromthe Curie-Weiss regime. igure 7: Plot of the Weiss temperature θ W versus the average nearest neighbor Ir–Ir distance for allcompounds studied in this work. Negative values of θ W indicate that antiferromagnetic interactions dominatethe magnetic susceptibility of these layered honeycomb iridates, and the magnitude of θ W is a measure ofthe strength of these interactions. Expansion of the honeycomb plane increases the overall antiferromagneticinteraction strength as Ir–O–Ir bond angles deviate from 90 ◦ . Average Ir–O–Ir bond angles, determinedfrom analysis of NPD data, are shown for two points on the plot, as well as the reported value for Na IrO ,denoted by red boxes [11]. θ W is largest in Na IrO and is diminished by chemical substitution and sodiumvacancies, as well as decomposition in air. The smooth curve through the data is a guide to the eye. igure 8: (a) AC susceptibility data collected on two representative samples from the Na − δ Na − x Mg x Ir O series under an applied field of H = 796 A/m (10 Oe) with amplitude of H = 398 A/m (5 Oe). Both samplesshow a peak in the real component χ ’ of the AC susceptibility at the freezing temperature T f , and themagnitude of the peak decreases and shifts to higher temperatures as the frequency of the AC field isincreased, consistent with a spin glass-like transition (inset). (b) A plot of ln( ω ) versus T f yields a roughlylinear dependence, indicating proximity to a super paramagnetic regime, and the slope and intercept of thelinear fit yield activation energy E a and the characteristic frequency ω for spin reorientation. igure 9: Common types of disorder in A IrO honeycomb iridates. (a) In a fully ordered sample, hon-eycomb layers are stacked in a perfectly repeating pattern (ABCABCABC, for example). Stacking faults(ABCCACBCA, here) complicate structural characterization as they masquerade as (Na/Mg) mixing ontothe Ir site. (b)
Non-magnetic Ir also exist due to chemical defects. These “holes” perturb the magneticorder in A IrO materials, and can lead to the disordered freezing of spins commonly observed in polycrys-talline samples. We speculate that this type of disorder leads to the formation of isolated “islands” of AFMorder, which vary in size and interact weakly with one another, which is one possible explanation for thepseudo–superparamagnetic behavior observed in AC magnetic susceptibility measurements. igure 10: (a) XRPD data collected over the 2 θ range 10 ◦ to 50 ◦ in six minutes on Na IrO immediatelyafter removal from an argon-filled glovebox (blue, bottom) and after eight hours of exposure to laboratoryair (red, top). A reaction occurs between Na IrO and one or more components of the air that causes therelative intensities of the C2/ m reflections to change, and new reflections emerge, highlighted with grayarrows. Small circles indicate reflections due to crystalline Silicon, which was used as an internal standardfor the purpose of Rietveld refinement. (b) The magnetic susceptibilities of polycrystalline Na IrO (bluecircles) and the same powder after eight hours of exposure to air at room temperature (red diamonds) arecompared. When handled in air-free conditions, Na IrO exhibits long-range AFM order, as evidenced bythe local maximum in the magnetic susceptibility at T N = 15 K. (c) A plot of inverse magnetic susceptibilityversus temperature, along with linear fits to both datasets above T = 60 K yield the Weiss temperature θ W and Curie constant C for Na IrO before (blue circles) and after (red diamonds) exposure to air.before (blue circles) and after (red diamonds) exposure to air.