Disordered dimer state in electron-doped Sr 3 Ir 2 O 7
Tom Hogan, Rebecca Dally, Mary Upton, J. P. Clancy, Kenneth Finkelstein, Young-June Kim, M. J. Graf, Stephen D. Wilson
DDisordered dimer state in electron-doped Sr Ir O Tom Hogan,
1, 2
Rebecca Dally,
1, 2
Mary Upton, J. P. Clancy, KennethFinkelstein, Young-June Kim, M. J. Graf, and Stephen D. Wilson ∗ Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA Materials Department, University of California, Santa Barbara, California 93106, USA. Advanced Photon Source, Argonne National Laboratory, Chicago, Illinois, 60439 USA Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 Cornell High Energy Synchrotron Source, Cornell University, Ithaca, New York 14853
Spin excitations are explored in the electron-doped spin-orbit Mott insulator (Sr − x La x ) Ir O .As this bilayer square lattice system is doped into the metallic regime, long-range antiferromagnetismvanishes, yet a spectrum of gapped spin excitation remains. Excitation lifetimes are strongly dampedwith increasing carrier concentration, and the energy integrated spectral weight becomes nearlymomentum independent as static spin order is suppressed. Local magnetic moments, absent in theparent system, grow in metallic samples and approach values consistent with one J = impurity perelectron doped. Our combined data suggest that the magnetic spectra of metallic (Sr − x La x ) Ir O are best described by excitations out of a disordered dimer state. PACS numbers: 75.40.Gb, 75.10.Kt, 75.50.Ee, 75.70.Tj
Models of Heisenberg antiferromagnets on a bilayersquare lattice have generated sustained theoretical andexperimental interest due to their rich variety of groundstates [1–5]. In zero field, an instability occurs abovea critical ratio of interlayer to intralayer magnetic ex-change that transitions spins from conventional antifer-romagnetism into a dimer state comprised of spin singlets[1, 6]. These singlets may interact and form the basis fornumerous uncoventional ground states such as valencebond solids [7, 8], quantum spin liquids [4], Bose-glass[9], and other quantum disordered states [8]. Realiza-tions of bilayer systems inherently near the critical ratioof interlayer to intralayer coupling however are rare, pri-marily due to orbital/exchange anisotropies strongly fa-voring either interplane or intraplane exchange pathwaysin accessible compounds [10–12]. J eff = moments are arranged onto a bilayer squarelattice within the n = 2 member of the Sr n +1 Ir n O n +1 Ruddlesden-Popper series, Sr Ir O (Sr-327) [13]. Thestrong spin-orbit coupling inherent to the Ir cationsin cubic ligand fields renders a largely three dimensionalspin-orbit entangled wave function [14, 15]. This com-bined with the extended nature of its 5 d valence elec-trons presents Sr-327 as an interesting manifestation ofthe bilayer square lattice—one where appreciable inter-layer coupling potentially coexists with strong intralayerexchange inherent to the single layer analogue Sr IrO (Sr-214) [16].While its ground state is antiferromagnetic (AF) [17–19], measurements of magnetic excitations in Sr Ir O observe anomalous spectra with large spin gaps (∆ E ≈
90 meV) whose values exceed that of the single magnonbandwidth [20, 21]. This has led to models shown inFigs. 1 (a) and (b) that cast the underlying exchangeinto two extremes: A linear spin wave approach (LSW)with a large anisotropy gap and predominantly intra- plane exchange [20] versus a bond operator (BO) meanfield approach [22] with a dominant interplane, dimer-like, exchange [21, 23]. Recently, an additional excita-tion attributed to a longitudinal mode associated withtriplon excitations was observed supporting the latterapproach[24].The comparable ability of both LSW and BO ap-proaches to capture major features of the magnetic spec-tra of Sr-327 invites further study. In particular, consid-erable insight can be gained by probing the evolution ofspin dynamics as static AF order is suppressed. Recentwork has shown that, unlike Sr-214, Sr-327 can be driveninto a homogenous metallic state with no static spin or-der via La-substitution [25, 26]. Local moment behavior,notably absent in parent Sr-327 [27], appears in theseelectron-doped samples and hints at an unconventionalmetallic state [25].Here we utilize resonant inelastic x-ray scattering(RIXS) to explore the spin dynamics of (Sr − x La x ) Ir O as it transitions from an AF insulator into a paramag-netic metal. Beyond x = 0 .
04 (6% electrons/Ir), AForder vanishes, yet robust magnetic excitations persistdeep into the metallic regime. Excitations become over-damped as carriers are introduced, yet the large spin gapinherent to the AF parent state survives into the disor-dered regime. The spectral weight of magnons in themetallic state becomes nearly momentum independentand exhibits a dispersion best described using the BOrepresentation appropriate for a dimer state [21]. Sup-porting this, static spin susceptibility measurements re-solve the emergence of local moments which grow withincreasing La-content and are consistent with a picturewhere each electron doped breaks a dimer and creates anuncompensated moment. Our aggregate data are bestunderstood in the framework of a disordered dimer stateemergent upon electron substitution in La-doped Sr-327. a r X i v : . [ c ond - m a t . s t r- e l ] A ug J c J J E n e r gy ( m e V ) (π,0) (π,π) (π/2, π/2) (0,0) (π,0) (π/2, π/2) (0,0) ( π,π ) (2 π,0 )( π,0 ) J (a)(b) (c)(d) Momentum (H ,K)
AcousticOpticalLongitudinalTransverse
Linear spin wave model
Kim et al. , Phys. Rev. Lett. 109, 157402 (2012)
Quantum dimer model
Moretti Sala et al. , Phys. Rev. B 92, 024405 (2015)
FIG. 1. Magnon dispersion relations for Sr-327 plotted for (a)LSW model of Kim et al. , with data reproduced at L = 26 . et al. , with data reproduced at L = 28 . Resonant inelastic x-ray scattering (RIXS) measure-ments were performed at 27-ID-B at the Advanced Pho-ton Source at Argonne National Lab and resonant elasticx-ray scattering (REXS) measurements were performedat C1 at CHESS. Details regarding the experimental se-tups are in supplementary information [28]. Inelasticspectra were collected near the Ir L edge (11.215 keV)in a geometry with an energy resolution at the elasticline ∆ E res = 32 meV [28]. RIXS spectra were collectedat T = 40 K for two La-doped Sr-327 concentrations: x = 0 .
02, an AF insulator ( T AF ≈
240 K) and x = 0 . H, K ) wave vectors in the ap-proximate tetragonal unit cell ( a ≈ b ≈ . A ) and, un-less stated otherwise, momentum scans were collected at L = 26 . x = 0 .
02 and x = 0 . Q = ( π, π ) andzone boundary Q = ( π,
0) cuts are shown with the elas-tic line ( E ), single magnon ( M ), proposed multimagnon( M ∗ ), and d − d excitations ( D ) shaded. Excitations werefit to a Lorenztian of the form I Q ( E ) = Aπ Γ Q E − E Q ) +Γ Q multiplied by the Bose population factor (1 − e − EkBT ). Theinverse lifetime values Γ Q for all excitations were substan-tially greater than the instrumental resolution.The dispersions of the M and M ∗ peaks along the highsymmetry directions illustrated in Fig. 1 (d) are plottedfor both samples in Fig. 3. Energies of M (squares)and M ∗ (circles) peaks are shown with the Γ Q associ-ated with M peaks illustrated via the larger shaded re-gions. Only one feature associated with a single magnon (π, π) x = 0.02 C oun t s ( A . U . ) (π, 0) x = 0.02 C oun t s ( A . U . ) -300 -200 -100 0 100 200 (π, 0) x = 0.07 C oun t s ( A . U . ) -1500 -1000 -500 0 500 (π, π) x = 0.07 C oun t s ( A . U . ) Energy Transfer (meV)Energy Transfer (meV) (a)(b)(c)(d)
EEMMM* M* M EMM* EM* DD DD
FIG. 2. Representative energy scans collected at 40 K at fixed Q for samples with x = 0 .
02 and x = 0 .
07. Panels (a) and (b)show scans performed at the AF zone center ( π, π ) and zoneboundary ( π , 0) for AF insulating x = 0 .
02 respectively whilepanels (c) and (d) show the same scans for paramagnetic,metallic x = 0 .
07. Features labeled E , M , M ∗ , and D denotescattering from the elastic line, single magnon, multimagnon,and d − d excitations respectively. excitation could be identified, and no additional acous-tic/optical branches associated with spin waves from abilayer or longitudinal modes associated with triplon ex-citations were isolated. Similar to the parent material,the M peaks were independent of L within the zones ex-plored [20, 28]. Any weak additional modes are obscureddue to the overdamping of the M excitations as carriersare introduced [28]—an effect which partially convolvesthe M and M ∗ features.Despite the absence of this second mode, tests canstill be made within the RIXS spectra regarding thesuitability of the LSW and BO approaches to the bi-layer square lattice Heisenberg Hamiltonian with inplaneexchange constants J , J , J , interplane exchange J c ,and an anisotropy term θ as illustrated in Fig. 1 (c)[20, 21]. Specifically, the data show that the gap ener-gies of M -peaks at the ( π, π ) and (0 ,
0) positions becomeincreasingly inequivalent upon doping. For the x = 0 . Transverse Mode (Fit) Longitudinal Mode (Calculated) E n e r gy ( m e V ) (π, 0) (π, π) (π/2, π/2) (0, 0) (π, 0) (π/2, π/2) Momentum (H, K)
Transverse Mode (Fit) Longitudinal Mode (Calculated) x = 0.07 x = 0.02 (a)(b) M* peakM peak
FIG. 3. Dispersion of M and M ∗ features for (a) x = 0 . x = 0 .
07 samples. M and M ∗ peaks are plotted assquares and circles respectively, each with accompanying er-rors. The larger shaded regions about the M -dispersion arethe excitations’ FWHM. Solid lines denote fits to the trans-verse modes using the BO model and dashed lines denote thepredicted positions of longitudinal modes. sample, the AF zone center ( π, π ) gap value decreasesto E π,π = 73 ± ,
0) gapremains nearly unchanged from the parent system at E , = 89 ± M peaks at these two points suggest that a simple LSWmodel cannot account for the dispersion [20]. In a naiveLSW approach, the combined optical plus acoustic spec-tral weight should remain degenerate at the ( π, π ) and(0 ,
0) positions, which for the x = 0 .
07 sample wouldviolate the assumption that both an acoustic and opti-cal mode are convolved within the largely L -independent M excitations [20, 28]. The BO approach however al-lows for nondegenerate spectral weight at these positionsthrough inequivalent transverse mode E π,π and E , gapvalues whose ratio is governed by the anisotropy term cot ( θ ) = E , /E π,π . Therefore, to parameterize the dis-persion in electron-doped Sr-327 samples, the BO modelwas utilized [21, 23].Fits using the BO generated dispersion relations alongthe pathways illustrated in Fig. 1 (d) are shown as solidlines in Figs. 3 (a) and (b). Due to the suppressed spec-tral weight expected for the longitudinal mode [21, 28]and the broadened Γ values inherent to doped sam-ples, the predicted longitudinal branches lie convolved C oun t s ( A . U . ) (π, 0) (π, π) (π/2, π/2) (0, 0) (π, 0) (π/2, π/2) Momentum (H, K) x = 0.02 x = 0.07 (a) S = 1/2 limit (c) (d)
Insulator (H, H, 19) σ−σ (H, H, 18) σ−π × 1/50 x = 0.05 (b) T = 7 K E = 11.218 keV T = 40 K E = 11.215 keV ( χ - χ P ) - ( m o l / e m u ) • Temperature (K) x = 0.035 x = 0.042 x = 0.050 x = 0.058 x = 0.071 L o ca l M o m e n t ( μ B / L a ) La Concentration ( x )Metal C oun t s ( A . U . ) FIG. 4. (a) Energy integrated spectral weight of M peaksacross the AF zone. Data for x = 0 .
02 (blue circles) show amaximum at the zone center consistent with its AF orderedground state. Data for x = 0 .
07 (red circles) show a nearlyQ-independent response. (b) REXS data showing the absenceof AF correlations in the x = 0 .
05 sample. Black circles de-note H -scans through the AF position (0.5, 0.5, 18) in the σ − π channel. Red circles denote the structural reflection at(0.5, 0.5, 19) in the σ − σ channel scaled by 1 /
50 for clarity.Background has been removed from the data. (c) Curie-Weissfits to high temperature susceptibility with a temperature in-dependent χ term removed and collected under H = 5 kOe.(d) Local moments µ eff /La extracted from fits in panel (c). either within the FWHM of the M mode or M ∗ fea-ture. Fits were therefore performed only to the transversemodes’ dispersion, and the predictions for the accompa-nying longitudinal modes are plotted for reference. Us-ing this parameterization, the coupling constants evolvefrom J = 37 . J = − . J = 4 . J c = 87 . x = 0 .
02 sample to J = 29 . J = − . J = 5 . J c = 80 . x = 0 .
07 sample. The anisotropy term de-creased slightly from θ = 41 . x = 0 .
02 to θ = 37 . x = 0 .
07. The inverse lifetimes of the M -excitationsare largely Q -independent and increase from an averagevalue of Γ avg = 75 meV for x = 0 .
02 to Γ avg = 124 meVfor x = 0 .
07 [28].While electron-doping drives a subtle shift in the M dispersion, the bandwidth is largely unaffected upontransitioning from the AF insulating regime ( x = 0 . x = 0 . x = 0 .
07 sample [25]. The distribu-tion of the spectral weights of M peaks in both samplesfurther reflect this fact and are plotted in Fig. 4 (a). Inthe AF x = 0 .
02 sample, the energy integrated weight ismaximal at the magnetic zone center ( π , π ) as expected[29]; however this zone center enhancement vanishes withthe loss of AF order in the x = 0 .
07 sample.In order to further search for signatures of remnantshort-range order in the metallic regime, REXS measure-ments were collected at 7 K on an x = 0 .
05 crystal. Datacollected at the Ir L edge are plotted in Fig. 4 (b)showing H -scans through the magnetic (0 . , . ,
18) andstructural (0 . , . ,
19) reflections in the σ − π and σ − σ channels respectively. No peak is observed in the σ − π channel at the expected magnetic wave vector; howeverthe weak structural peak apparent in the σ − σ channel at(0 . , . ,
19) gives a sense of the measurement sensitivity.By performing identical measurements on an x = 0 . m AF ≈ . µ B , thisplaces a bound of m AF < . µ B for the metallic x=0.05concentration [25, 28]. Scans along other high symmetrydirections also failed to detect static short-range correla-tions.The absence of static antiferromagnetism in sampleswith x > .
04 is consistent with earlier neutron diffrac-tion measurements [25] and render it distinct from itssingle layer analogue, Sr-214. In electron-doped Sr-214,short-range AF order survives to the highest doping lev-els explored ≈
12% electrons/Ir [26, 30] and can accountfor a magnon dispersion with slightly renormalized mag-netic exchange [31]. In contrast, electron-doping Sr-327reveals gapped spin excitations that persist beyond thedisappearance of AF order. While a slight increase in J c /J from 2.32 to 2.75 accompanies the disappearanceof AF order and is naively consistent with predictions forthe formation of a dimer state beyond a critical ratio of J c /J ≈ . planes creates a nonmagnetic Ir sitewithin a sea of J = moments. For a ground statecomposed of uncorrelated dimers, this nonmagnetic siteshould break a dimer and leave an uncompensated J = moment behind. Hence, doping the dimer state withelectrons should seed nonmagnetic Ir sites and createan increasing fraction of weakly coupled, uncompensatedspins within the sample. An order by disorder transitionshould eventually follow among these unfrustrated localmoments in the T = 0 limit [33–35].Intriguingly, previous magnetization measurementsreported an unusual Curie-Weiss (CW) response inelectron-doped Sr-327 [25]. This fact combined with theabsence of CW behavior in the high temperature sus-ceptibility of the parent system [28] suggests a dopantinduced local moment behavior. To explore this further, magnetization measurements were performed on a seriesof Sr-327 samples with varying levels of La-doping. Thehigh temperature CW susceptibilities for each sample areplotted in Fig. 4 (c) and the local paramagnetic moments( µ eff ) are plotted as a function of La-concentration in Fig.4 (d). The µ eff extracted from CW fits grows with in-creasing doping, and the µ eff induced per La-dopant ap-proaches that of uncompensated J = local moments.The absence of static AF order combined with the growthof local moments in the presence of significant AF ex-change supports the notion of an underlying disordereddimer state in metallic Sr-327.The nearly Q -independent energy-integrated spectralweight of the M -excitations in the metallic regime is alsoconsistent with a dimer state where the intradimer cou-pling ( J c ) approaches the excitation bandwidth. Thesmall increase in the J c /J ratio as doping is increasedfrom x = 0 .
02 and x = 0 .
07 samples is however notthe likely driver for the dimer state’s stabilization, inparticular given that J c /J ≈ . d = 1 . × − [36]) does not change appreciably withelectron doping [25]. Rather, a dimer state is likely sta-bilized by the critical threshold for dimer formation be-ing driven downward via electron-doping similar to t − J models of hole-doping in bilayer cuprates [32, 37, 38].In summary, RIXS data reveal spin excitations in La-doped Sr-327 that persist across the AF insulator to para-magnetic metal transition. Across the insulator-metaltransition, static AF correlations vanish and extendedLSW models fail to describe the surviving spin spectrawith nondegenerate excitations at the two-dimensionalAF zone center and Γ points. Rather a BO-based meanfield approach, reflective of strong interplane dimer inter-actions, captures the observed dispersion and suggests adisordered dimer state in the metallic regime. The pres-ence of a hidden, disordered dimer state is supported bybulk magnetization data which reveal the emergence ofanomalous local moments in electron-doped Sr-327 andare consistent with dopant-induced creation of uncom-pensated spins from broken dimer pairs. Our resultspoint toward an unconventional metallic state realizedbeyond the collapse of spin-orbit Mott state in Sr Ir O .S.D.W. thanks L. Balents for helpful discussions. Thiswork was supported in part by NSF award DMR-1505549(S.D.W.), as well as by the MRSEC Program of theNational Science Foundation under Award No. DMR-1121053 (T.H.). This research used resources of the Ad-vanced Photon Source, a U.S. Department of Energy(DOE) Office of Science User Facility operated for theDOE Office of Science by Argonne National Laboratoryunder Contract No. DE-AC02-06CH11357. CHESS issupported by the NSF and NIH/NIGMS via NSF awardDMR-1332208. 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