Abstract
The insulating honeycomb magnet α-RuCl3 exhibits fractionalized excitations that signal its proximity to a Kitaev quantum spin liquid state; however, at T=0, fragile long-range magnetic order arises from non-Kitaev terms in the Hamiltonian. Spin vacancies in the form of Ir3+ substituted for Ru are found to destabilize this long-range order. Neutron diffraction and bulk characterization of Ru1-xIrxCl3 show that the magnetic ordering temperature is suppressed with increasing x, and evidence of zizag magnetic order is absent for x>0.3. Inelastic neutron scattering demonstrates that the signature of fractionalized excitations is maintained over the full range of x investigated. The depleted lattice without magnetic order thus hosts a spin-liquid-like ground state that may indicate the relevance of Kitaev physics in the magnetically dilute limit of RuCl3.
| Original language | English |
|---|---|
| Article number | 237203 |
| Journal | Physical Review Letters |
| Volume | 119 |
| Issue number | 23 |
| DOIs | |
| State | Published - Dec 6 2017 |
Funding
Lampen-Kelley P. 1,2 Banerjee A. 3 Aczel A. A. 3 Cao H. B. 3 Stone M. B. 3 Bridges C. A. 4 Yan J.-Q. 2 Nagler S. E. 3 Mandrus D. 1,2 Department of Materials Science and Engineering, 1 University of Tennessee , Knoxville, Tennessee 37996, USA Materials Science and Technology Division, 2 Oak Ridge National Laboratory , Oak Ridge, Tennessee 37831, USA Neutron Scattering Division, 3 Oak Ridge National Laboratory , Oak Ridge, Tennessee 37831, USA Chemical Sciences Division, 4 Oak Ridge National Laboratory , Oak Ridge, Tennessee 37831, USA 6 December 2017 8 December 2017 119 23 237203 21 December 2016 7 November 2017 © 2017 American Physical Society 2017 American Physical Society The insulating honeycomb magnet α - RuCl 3 exhibits fractionalized excitations that signal its proximity to a Kitaev quantum spin liquid state; however, at T = 0 , fragile long-range magnetic order arises from non-Kitaev terms in the Hamiltonian. Spin vacancies in the form of Ir 3 + substituted for Ru are found to destabilize this long-range order. Neutron diffraction and bulk characterization of Ru 1 − x Ir x Cl 3 show that the magnetic ordering temperature is suppressed with increasing x , and evidence of zizag magnetic order is absent for x > 0.3 . Inelastic neutron scattering demonstrates that the signature of fractionalized excitations is maintained over the full range of x investigated. The depleted lattice without magnetic order thus hosts a spin-liquid-like ground state that may indicate the relevance of Kitaev physics in the magnetically dilute limit of RuCl 3 . Gordon and Betty Moore Foundation http://dx.doi.org/10.13039/100000936 Gordon E. and Betty I. Moore Foundation http://sws.geonames.org/6252001/ GBMF4416 U.S. Department of Energy http://dx.doi.org/10.13039/100000015 DOE http://sws.geonames.org/6252001/ DOE Oak Ridge National Laboratory http://dx.doi.org/10.13039/100006228 ORNL http://sws.geonames.org/6252001/ The quantum spin liquid (QSL) holds particular fascination as a state of matter that exhibits strong quantum entanglement yet is devoid of long-range order [1,2] . These exotic states can possess topologically protected fractionalized excitations, with possible implications for quantum information science [3,4] . A prototypical example is the Kitaev model on a honeycomb lattice [5] , which can be solved exactly and has a QSL ground state. An effective Hamiltonian with Kitaev terms consisting of bond-directional Ising couplings may arise in spin-orbit-assisted Mott insulators with J eff = 1 / 2 moments in an edge-sharing octahedral environment [6] . A strong push for the experimental realization of quasi-2D honeycomb lattices showing Kitaev physics initially focused on iridate materials with the chemical formula A 2 IrO 3 [7–10] and more recently, α - RuCl 3 [11–16] . Each of these compounds orders magnetically at low temperatures in a zigzag or incommensurate phase [17–23] , and the effective low-energy Hamiltonian is believed to be described by a generalized Heisenberg-Kitaev- Γ model [24–35] . Despite the appearance of long-range order, broad scattering continua observed via inelastic neutron or Raman scattering in α - RuCl 3 [13,36–38] and the iridates [39] match the predicted signatures of itinerant Majorana fermions in pure Kitaev calculations [40–42] , suggesting that these materials are proximate to the QSL state and that Kitaev interactions play an important role. In this Letter, we report the evolution of the magnetic ground state in α - RuCl 3 with magnetic Ru 3 + substituted by nonmagnetic Ir 3 + and determine a phase diagram as a function of temperature and dilution. The motivation is twofold: to understand the role of defects in Kitaev-candidate materials and to explore avenues towards suppression of long-range order. Numerous theoretical studies predict the emergence of novel superconductivity with hole doping in the strong Kitaev limit [43–49] , while bond disorder [50] , dislocations [51] , magnetic impurities [52] , and spin vacancies [53–60] have also received theoretical attention. Experimentally, substitution of both magnetic and nonmagnetic cations for Ir rapidly led to spin glass freezing in Na 2 IrO 3 and Li 2 IrO 3 [61,62] . Isoelectronic substitution within the solid solution ( Na , Li ) 2 IrO 3 decreased the magnetic ordering temperature, although phase separation has hampered efforts to completely suppress long-range order [63–65] . The chemically simpler binary compound α - RuCl 3 provides an excellent framework to explore the effects of various perturbations on the relevant physics. Low-spin 5 d 6 Ir 3 + ( S = 0 ) represents a nonmagnetic impurity in the J eff = 1 / 2 Ru 3 + magnetic sublattice, while the identical ionic radii (0.68 Å) of Ru 3 + and Ir 3 + preserve a regular MCl 6 environment ( M = Ru , Ir) [66] . The van der Waals bonded honeycomb layers in α - RuCl 3 are susceptible to stacking faults that are known to affect the magnetic ordering properties. Single crystals without stacking faults show zigzag order with T N ≃ 7 K and a threefold ( ABC ) out-of-plane periodicity. With stacking faults, a phase with twofold periodicity ( ABAB ) also appears at T N ≃ 14 K [13–16,22,23] . Polycrystalline material shows only the 14 K transition. Our present study of Ru 1 − x Ir x Cl 3 reveals the suppression of the ABC and ABAB magnetic phases with critical concentrations of x ≃ 0.1 and x ≃ 0.3 , respectively, demonstrating that site dilution represents a viable approach to destabilizing long-range magnetic order. Spectroscopic examination of the magnetically disordered limit reveals a dynamic ground state with indications of persistent fractionalization of spin excitations. Figure 1(a) shows the magnetic susceptibility of a series of Ru 1 − x Ir x Cl 3 single crystals with the magnetic field applied in the honeycomb a b plane. In addition to the T N 1 = 7 K zigzag transition of the parent compound, a second feature at T N 2 ≤ 14 K for x > 0 [black arrow, Fig. 1(a) inset] indicates that substituted crystals obtained from the current growth process are not completely free of stacking faults. The sharp cusp in the susceptibility at T N 1 is rapidly shifted toward lower temperatures at nonzero x (red arrow), denoting a suppression of the ordering temperatures with dilution. As x increases, the minority phase contribution ( T N 2 ) gains prominence and is the only transition evident above 2 K by x = 0.09 . Further Ir substitution leads to a rounding of the cusp at T N 2 , which decreases continuously with x and disappears near the percolation limit of the honeycomb lattice x ∼ 0.3 [67] . Notably, field-cooled and zero-field-cooled measurements are identical for all values of x , in contrast to the spin-glass-like characteristics reported in the honeycomb iridates with nonmagnetic substitution [64] . In fact, muon spin relaxation ( μ SR ) experiments rule out a glassy state and point to fast dynamics on the μ SR time scale ( 1 0 4 - 10 12 Hz ) in the magnetically disordered limit (see Supplemental Material [68] Figs. S4 and S9 and discussion, including Refs. [69,70] ). 1 10.1103/PhysRevLett.119.237203.f1 FIG. 1. (a) Magnetic susceptibility curves of Ru 1 − x Ir x Cl 3 single crystals ( x values indicated in legend) with a magnetic field of B = 1 T applied in the a b plane. Inset: magnification of low-temperature range. Red arrow and black/grey arrows mark the evolution of T N 1 and T N 2 , respectively. (b) Field-dependent magnetization at 2 K. The data of (a) and (b) with normalization to Ru content are shown in Supplemental Material [68] , Fig. S7. (c) Heat capacity curves of crystals with small Ir concentration. Solid lines are an estimate of the lattice contribution. Dotted lines are a guide to the eye. The low-temperature susceptibility does not decrease monotonically with x , but instead increases over the range 0.07 < x < 0.16 . This behavior might arise from uncompensated moments introduced by nonmagnetic impurities in the ordered antiferromagnetic ground state of the parent compound. We also note that vacancies in a site-diluted Kitaev model are predicted to increase the local susceptibility [53,54,58] . In the parent compound, the field-dependent magnetization at 2 K shows an upward curvature approaching the suppression of the zigzag phase near 7.5 T [14,22] . For x > 0.09 , the field-dependent magnetization curves in Fig. 1(b) develop opposite concavity from the clean limit. Interestingly, this coincides with the region of increase in the low-temperature susceptibility mentioned above. The downward trend in T N 1 and T N 2 with x is also reflected in specific heat measurements [Fig. 1(c) ]. The lattice contribution in all cases can be described by C p ∝ T 2 , an approximation of the 2D Debye law characteristic of the parent compound [13] and other van der Waals bonded materials [71] . The 2D character of the materials is thus not strongly affected by Ir substitution. Weak low-temperature features with a magnetic origin (evidenced by magnetic field dependence) are observed at larger x of 0.2 and 0.3 [see Supplemental Material [68] , Fig. S11]; however, the absence of a λ -like anomaly indicates no long-range ordering transition above 2 K. The magnetic ground state of lightly substituted crystals with x ≤ 0.06 was characterized by neutron diffraction using the HB-1A and HB-3A beam lines at the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. Similar to the parent compound with stacking faults, Ir-substituted crystals show transitions at T N 1 with (trigonal notation) Q 1 = ( 1 / 2 0 1 ) and T N 2 with Q 2 = ( 1 / 2 0 3 / 2 ) [13,36] , corresponding, respectively, to ABC and ABAB magnetic layer stacking. For x = 0.035 [Figs. 2(a) and 2(b) ], the relative peak intensities I ( Q 1 ) / I Q 2 ) ≃ 6 at 1.5 K show that the majority of the sample adopts the ABC -type phase. The observed T N 1 of ≃ 5.5 K is consistent with χ and C p for similarly doped samples. Measurements using the four-circle diffractometer at HB-3A were refined to yield an ordered moment of 0.32 ( 2 ) μ B / Ru in the ABC zigzag phase, corresponding to two thirds of the ordered moment at x = 0 [23] . An extensive survey of reciprocal space did not reveal additional peaks associated with alternative magnetically ordered states in the H - K - Γ phase diagram [24] . 2 10.1103/PhysRevLett.119.237203.f2 FIG. 2. (a) Scan at 1.5 K collected at HB-1A along [1/2 0 L] through characteristic magnetic reflections Q 1 = ( 1 / 2 0 1 ) and Q 2 = ( 1 / 2 0 3 / 2 ) for a 50-mg single crystal with x = 0.035 . 20 K ( T > T N ) data are subtracted as a background. (b) Temperature scans of the scattering intensity at Q 1 and Q 2 . Scans along [1/2 0 L] at (c) 4 K and (d) 0.3 K in a 20-mg single crystal with x = 0.06 . 50 K data are subtracted as a background. Increasing the Ir content to x = 0.06 [Figs. 2(c) and 2(d) ] strongly affects T N as well as the relative intensities at the two magnetic wave vectors. The ( 1 / 2 0 1) peak is absent at 4 K [Fig. 2(c) ] and acquires significant intensity only below 1.6 K. The relative amount of the ABC phase is greatly reduced, leading to I ( Q 1 ) / I Q 2 ) ≃ 0.7 at 0.3 K. No additional peaks characteristic of other candidate magnetic structures were observed in the ( H 0 L ) scattering plane. There is thus no evidence for the emergence of a new magnetically ordered phase as the ABC -type zigzag order is suppressed in the dilute system. A phase diagram of the Ru 1 − x Ir x Cl 3 system is summarized in Fig. 3 . Linear fits to the normalized critical temperatures give initial suppression rates [72] - d [ T N i / T N i ( 0 ) ] / d x = 8.1 ( 7 ) for T N 1 and 4.4(3) for T N 2 . The more sensitive response to magnetic site dilution in the ABC phase may be related to a higher degree of frustration in magnetic interactions for three-layer magnetic stacking than for two-layer stacking, as evidenced by the different T N values for the two phases in the parent compound. Extrapolating linearly from small x , the suppression of T N 1 and T N 2 to T = 0 occurs at x ≃ 0.11 and x ≃ 0.22 , respectively. Above x ≃ 0.2 , T N 2 falls below the base temperature of 2 K for susceptibility measurements. However, extrapolation of d χ / d T to zero indicates that T N 2 may not vanish until the percolation threshold is crossed (grey symbols, Fig. 3 ). 3 10.1103/PhysRevLett.119.237203.f3 FIG. 3. Phase diagram of Ru 1 − x Ir x Cl 3 . Transition temperatures T N 1 (red symbols) and T N 2 (blue symbols) determined from magnetic susceptibility, heat capacity, and neutron diffraction mark the boundaries of the ABC -stacked (ZZ1) and ABAB -stacked (ZZ2) zigzag phases in multiphase single crystals. Linear fitting to T N ( x ) (dotted lines) gives a critical dilution level for T N 1 → 0 of x ∼ 0.11 . The cusp at T N 2 is driven below the experimental base temperature of 2 K (indicated by hashmarks) by x ≃ 0.2 ; at larger x , T N 2 is estimated by extrapolation to d χ / d T = 0 (grey symbols). The nature of the magnetic ground state in Ru 1 − x Ir x Cl 3 can be further revealed via examination of the excitation spectrum using inelastic neutron scattering (INS). The existing Ir-substituted single crystals are too small for INS experiments and have coexisting magnetic ground states. On the other hand, powders exhibit only the ABAB -type ordering [13] . The 14 K ( T N 2 -type) transition in polycrystalline RuCl 3 becomes suppressed by x ≃ 0.3 , similar to the trend in T N 2 for the single crystals (Supplemental Material [68] , Fig. S3). The SEQUOIA time-of-flight spectrometer at the Spallation Neutron Source (SNS) was used to measure the response of powders with x = 0 , 0.05, and 0.35 (Fig. 4 ). The INS spectrum of RuCl 3 ( x = 0 ) shows two magnetic features [13] [Fig. 4(a) ]. The lower feature M 1 arises from zigzag-ordered state spin waves and vanishes above T N 2 . In contrast, the temperature dependence and energy width of the upper feature M 2 ≃ 6 meV are incompatible with spin-wave theory but resemble the calculated spectrum for fractionalized excitations of the pure Kitaev QSL model [13,36,40] . 4 10.1103/PhysRevLett.119.237203.f4 FIG. 4. Powder inelastic scattering of Ru 1 − x Ir x Cl 3 measured at SEQUOIA with Ei = 25 meV . The background from Al sample cans is subtracted from all data, and a correction for the increasing absorption cross section with Ir content is applied to allow direct comparison of intensities. (a)–(c) 2D spectra at 5 K ( x values indicated). Constant- Q cuts integrated over Q = [ 0.5 , 1 ] Å − 1 are shown at (d) 5 K and (e) 15 K. Solid lines are a guide to the eye. The data in (d),(e) are normalized by sample mass; see Supplemental Material [68] , Sec. V for a discussion of the data normalized per Ru ion. (f) Constant- Q cuts at 5 K for x = 0 and x = 0.35 after subtraction of a linear background. The x = 0.35 data have been scaled by a factor of 1.6 to match the height of the x = 0 data. Solid blue and red lines represent the calculated scattering of the upper mode of the Kitaev model convoluted with experimental resolution (grey bar) for x = 0 and x = 0.35 , respectively. At low energies, the scattering in the magnetically ordered parent compound departs from the model (open symbols, dashed line). (g) Constant-energy cuts at the M 2 peak position of [6,7] meV for x = 0.35 normalized by n ( ω ) + 1 to account for the temperature dependence of phonon contamination at low Q . Solid lines are a guide to the eye. Ir substitution affects M 1 most strongly as seen in Figs. 4(a)–4(c) . The energy dependence of the scattering intensity normalized by sample mass and integrated over the Q range [ 0.5 , 1 ] Å − 1 is shown at T = 5 K [Fig. 4(d) ] and T = 15 K [Fig. 4(e) ]. At 5 K, the modes M 1 and M 2 are clearly visible for x = 0 , and M 1 is gapped. For x = 0.05 , with T N 2 ≃ 10 K , both modes are also observed, although M 1 is broadened and renormalized downwards, and no M 1 gap is visible as significantly more scattering is observed at low frequencies. In contrast, the x = 0.35 sample, which is magnetically disordered, shows only one broad feature peaked near M 2 . At 15 K, above T N 2 for both x = 0 and x = 0.05 , the M 1 peak disappears as expected since it arises from spin waves associated with zigzag order. On the other hand, for all three concentrations, the M 2 feature remains robust, with very little temperature dependence. Figure 4(f) shows the constant- Q cuts for x = 0 and x = 0.35 at 5 K after the subtraction of a linear background. The width of the M 2 scattering feature is very broad compared with instrumental resolution. It was shown previously that the scattering on the high-energy side of the M 2 mode for x = 0 [13] bears a strong resemblance to that calculated for the isotropic antiferromagnetic Kitaev model at Q = 0 [40] [blue line, Fig. 4(f) ]. The red line in Fig. 4(f) is a fit of the x = 0.35 data to this model over the full energy range of the M 2 feature, showing very good agreement with a value of the Kitaev energy scale K = 5.3 ( 2 ) meV . The Q dependence of the scattering in the vicinity of the M 2 mode in the x = 0.35 system is illustrated in Fig. 4(g) , with the data normalized by ( 1 - e - E / k B T ) - 1 . The signal exhibits little change up to moderate temperatures, consistent with expectations for a QSL with the energy scale set by K [73] . However, for higher temperatures, the scattering shows a stronger temperature dependence than the pure material [13,36] , suggesting that the excitations in the dilute system are more fragile. The energy, temperature, and wave-vector dependence of the spectrum at x = 0.35 are all consistent with expectations for fractionalized excitations, suggesting that the T = 0 ground state is effectively a QSL. In the pure Kitaev model, spin-spin correlations do not extend beyond nearest neighbors and thus are relatively insensitive to nonmagnetic dilution. Therefore, it is reasonable that these correlations and their associated excitations exist beyond the percolation threshold for long-range order. Excitations in Kitaev systems with mobile holes have been predicted to form bound states [59,60] , which one might expect to manifest as sharp peaks in the magnetic response function. No such peaks are observed in the present experiment; however, this is not surprising as the nonmagnetic Ir 3 + impurities here are completely static and do not introduce any change in charge neutrality to the system. In summary, incorporating Ir 3 + into Ru 1 − x Ir x Cl 3 decreases the Néel temperatures of the ordered magnetic phases while leaving intact the broad upper excitation mode associated with fractionalized excitations in the x = 0.05 and x = 0.35 compositions investigated by INS. Above the percolation threshold where long-range order is absent, the fractionalized excitations dominate the spectrum, and the low-temperature region may effectively be a dilute QSL. The robust nature of such QSL physics in RuCl 3 with respect to chemical substitution strongly motivates further investigation of dopants, in particular, those that would introduce mobile charge carriers, an avenue which is predicted to bring about exotic superconductivity [43–49] . P. L. K and D. M. were supported by the Gordon and Betty Moore Foundations EPiQS Initiative Grant No. GBMF4416. J. -Q. Y. and C. A. B. acknowledge support from the U.S. DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The work at ORNL HFIR and SNS was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. DOE. We thank I. McKenzie for support at TRIUMF, B. Chakoumakos and F. Ye for assistance with XRD, and B. Sales, M. McGuire, and A. 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| Funders | Funder number |
|---|---|
| Office of Basic Energy Sciences | |
| Scientific User Facilities Division | |
| U.S. DOE | |
| Gordon and Betty Moore Foundation | |
| Office of Science | |
| Basic Energy Sciences | |
| Oak Ridge National Laboratory |