Persistent low-temperature spin dynamics in the mixed-valence iridate Ba$_{3}$InIr$_{2}$O$_{9}$
Tusharkanti Dey M. Majumder J. C. Orain A. Senyshyn M. Prinz-Zwick S. Bachus Y. Tokiwa F. Bert P. Khuntia N. Büttgen A. A. Tsirlin P. Gegenwart





[Email: ]tusdey@gmail.com
Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232
Villigen PSI, Switzerland


Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), Technische
Universität München, 85747 Garching, Germany


Experimental Physics V, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université
Paris-Saclay, 91405 Orsay Cedex, France


Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université
Paris-Saclay, 91405 Orsay Cedex, France


Experimental Physics V, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


[Email: ]altsirlin@gmail.com
Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany


[Email: ]philipp.gegenwart@physik.uni-augsburg.de
Experimental Physics VI, Center for Electronic Correlations and Magnetism,
University of Augsburg, 86159 Augsburg, Germany



Using thermodynamic measurements, neutron diffraction, nuclear magnetic resonance, and muon spin relaxation, we establish putative quantum spin liquid behavior in Ba_3InIr_2O_9, where unpaired electrons are localized on mixed-valence Ir_2O_9 dimers with Ir^4.5+ ions. Despite the antiferromagnetic Curie-Weiss temperature on the order of 10 K, neither long-range magnetic order nor spin freezing are observed down to at least 20 mK, such that spins are short-range-correlated and dynamic over nearly three decades in temperature. Quadratic power-law behavior of both spin-lattice relaxation rate and specific heat indicates gapless nature of the ground state. We envisage that this exotic behavior may be related to an unprecedented combination of the triangular and buckled honeycomb geometries of nearest-neighbor exchange couplings in the mixed-valence setting.




Persistent low-temperature spin dynamics in mixed-valence iridate Ba_3InIr_2O_9
    P. Gegenwart
    Accepted ???. Received ???; in original form December 30, 2023
===============================================================================



§ INTRODUCTION

Frustrated magnets host multiple exotic states, including quantum spin liquids (QSLs). In a QSL, spins are strongly correlated, but quantum fluctuations prevent them from long-range ordering <cit.>. The initial (and subsequently rebutted) proposal of the QSL resonating-valence-bond state on the triangular lattice of Heisenberg spins <cit.> was followed by similar proposals for several other isotropic (Heisenberg)  models, where the formation of QSLs is now established <cit.>. A few candidate QSL materials proposed over the last decade bear key experimental signatures of this exotic state, including persistent spin dynamics and the absence of long-range order within the experimentally accessible temperature range <cit.>.

More recently, QSL states in anisotropic magnets have been explored. Here, Kitaev model with anisotropic interactions on the honeycomb lattice <cit.> offers an exact solution for the QSL. Real-world manifestations of the Kitaev physics are found in compounds of 4d and 5d transition metals <cit.>, where large spin-orbit coupling triggers strong intersite magnetic anisotropy. However, none of the Kitaev materials reported to date host the QSL ground state in zero field, and long-range order typically sets in at low temperatures, owing to substantial interactions beyond the Kitaev terms <cit.>. 




In this paper, we propose an alternative strategy and search for QSL states in the family of mixed-valence 5d oxides, where unpaired electrons are localized on dimers of the Ir atoms. This should facilitate access to hitherto unexplored local electronic states <cit.> and new regimes of anisotropic exchange interactions. Specifically, we report low-temperature magnetic behavior of the mixed-valence iridate Ba_3InIr_2O_9 as a QSL candidate, and confirm its persistent spin dynamics as well as the absence of long-range magnetic order down to at least 20 mK. We further identify quadratic-like power-law behavior of both specific heat and spin-lattice relaxation rate, and compare these observations to existing theoretical results on QSLs. 

Ba_3InIr_2O_9 belongs to the family of hexagonal perovskites A_3BM_2O_9. Their structures comprise single BO_6 octahedra and M_2O_9 dimers of two face-sharing MO_6 octahedra (Fig. <ref>a). When magnetic ion occupies the B site, triangular interaction geometry is formed, as in Ba_3CoSb_2O_9, which is arguably the best model spin-1/2 antiferromagnet on the triangular lattice <cit.>. Placing a 4d or 5d ion into the B site or into one of the M sites could give rise to a triangular system with leading Kitaev interactions <cit.>, but experimental implementation of this idea is hindered by the strong B/M site mixing that occurs, e.g., in Ba_3IrTi_2O_9 <cit.>. Alternatively, Ir could be introduced into both M sites, while keeping the B site non-magnetic, but for integer valence of M such a spin dimer would simply condense into a non-magnetic singlet <cit.>. Mixed-valence systems with both M sites occupied by a magnetic 5d ion are possible too <cit.>, and seem to be more promising for finding a QSL, because unpaired electrons localized on the dimers appear. Note that such mixed-valence dimers with an unpaired electron delocalized between the two Ir^4.5+ ions are very different from more conventional spin dimers formed by two magnetic ions holding one unpaired electron each.

Guided by this idea, we synthesized polycrystalline samples of Ba_3InIr_2O_9. From our detailed study using  neutron diffraction, magnetization and specific heat measurements, muon spin relaxation (μSR), and nuclear magnetic resonance (NMR) we establish a gapless and, potentially, spin-liquid ground state in Ba_3InIr_2O_9. 



§ EXPERIMENTAL DETAILS


Polycrystalline samples of Ba_3InIr_2O_9 were prepared by a conventional solid-state reaction method  <cit.>. Stoichiometric amounts of high-purity BaCO_3, In_2O_3, and Ir metal powder were mixed thoroughly, pressed into pellets, and calcined at 900 ^∘C for 12 h. Further, the pellet was crushed into powder, mixed well, pelletized, and fired at 1300 ^∘C for 4 days with several intermediate grindings. Neutron diffraction data were collected at the high-resolution instrument SPODI  <cit.> at FRM-II (TU Munich) using the wavelength of 1.55 Å. Jana2006 software  <cit.> was used for structure refinement. 

Magnetization measurements were carried out in a Quantum Design 5 T SQUID magnetometer and in a Quantum Design PPMS 14 T equipped with the vibrating sample magnetometer in the temperature range 2-350 K. Additional high-temperature data extending up to 650 K were collected in the SQUID magnetometer using powder sample enclosed in a thin-walled quartz tube. 

Heat-capacity measurements in the temperature range 0.4-200 K were performed in a Quantum Design PPMS using the ^3He insert. Low-temperature measurements in the 0.08-1 K range were performed using a quasi-adiabatic heat pulse method, adapted to a dilution refrigerator. 





μSR experiments were done on two different spectrometers at the Paul Scherrer Institute (Switzerland), LTF for temperatures from 20 mK up to 750 mK and Dolly for temperatures from 250 mK up to 200 K. For the Dolly experiment, about 300 mg of the polycrystalline sample was mounted on a thin copper plate inside the ^3He cryostat. In order to ensure good thermal contact, we glued the sample with GE varnish. We used the Veto mode, which allowed to get rid of the background signal from the sample holder. Therefore, the acquired signal is due to muons that stopped inside the sample. For the LTF experiment we used the same sample, again glued with GE on a silver plate. By comparing the results obtained between 250 mK and 750 mK on both the spectrometers, we were able to get rid of the experimental background on LTF.

^115In nuclear magnetic resonance (NMR) experiments were carried out with our home-built spectrometer with the dilution-fridge insert. The measurements are performed in the field-sweep mode at a fixed frequency of 70 MHz down to 24 mK. The spin echo intensity was obtained by integrating over the spin echo in the time domain. The final spectrum is constructed by plotting the spin-echo intensity as a function of the applied field. 



§ RESULTS



 §.§ Crystal structure


Rietveld refinement of room-temperature neutron diffraction data (Fig. <ref>) confirms hexagonal crystal structure (P6_3/mmc). However, at 3.4 K peak splitting of the 203 and 204 reflections, as well as a visible broadening of other peaks, indicated that the symmetry is reduced to monoclinic. The 3.4 K data were refined in the C2/c space group similar to other hexagonal perovskites <cit.>. Both hexagonal and monoclinic structures feature a single crystallographic position of Ir (Tables <ref> and <ref>) suggesting the true intermediate-valence Ir^4.5+ state. This is different from, e.g., Ba_5AlIr_2O_11, where two sites of the dimer belong to two different crystallographic positions, thus making possible charge re-distribution within the dimer <cit.>. 

In contrast to Ba_3IrTi_2O_9 with its 35-40% site mixing <cit.>, our mixed-valence Ba_3InIr_2O_9 shows high degree of structural order. We were able to obtain reasonable atomic displacement parameters in the fully ordered models of both hexagonal and monoclinic structures (Tables <ref> and <ref>). On the other hand, deliberate admixing of In into the Ir position and vice versa leads to a marginal reduction in the refinement residuals and 2.8(5)% site mixing [We introduced the site mixing and constrained the overall composition to Ba_3InIr_2O_9. This leads to R_I=0.038 and R_p=0.050 compared to R_I=0.039 and R_p=0.051 for the fully ordered model (room-temperature data).]. We believe that the diffraction data alone may not distinguish between the fully ordered structure and the weak site mixing scenario. Further studies, such as direct imaging with high-resolution electron microscopy, would be useful to resolve this issue.









The low-temperature monoclinic distortion is primarily related to the tilting of the IrO_6 and InO_6 octahedra. It has nearly no effect on relative positions of the Ir atoms. For example, the Ir–Ir distance within the dimer shrinks from 2.637(2) Å at 300 K to 2.599(4) Å at 3.4 K, presumably due to thermal expansion. The Ir–Ir distances between the dimers do not change at all, compare 5.832(1) Å at 300 K to 5.813(8) Å and 5.815(4) Å at 3.4 K for the nearest-neighbor Ir–Ir distances in the ab plane. Given this negligible structural effect and the absence of any signatures in thermodynamic measurements, we conclude that the hexagonal-to-monoclinic phase transition should be an effect of structural (geometrical) origin and bears no relation to the magnetism of Ba_3InIr_2O_9. Determination of the exact transition temperature requires further dedicated diffraction experiments at intermediate temperatures and lies beyond the scope of our present study.



 §.§ Magnetic susceptibility

Temperature dependence of the magnetic susceptibility (χ=M/H) measured in various applied fields is shown in the inset (i) of Fig. <ref>. Down to 2 K, we did not observe any anomaly or divergence of field-cooled and zero-field-cooled data, suggesting the absence of long-range ordering and spin freezing.

The susceptibility follows the Curie-Weiss (CW) behavior between 10 and 70 K. At higher temperatures (see Fig. <ref>), the data deviate from the CW law due to thermal changes in the mixed-valence Ir_2O_9 dimers that can adopt different electronic configurations  <cit.>. A tentative van Vleck fit with the three-level model 

    χ(T)=    χ_0+N_Aμ_B^2/3k_B(T-θ)×3/4×
       ×g_0^2+5g_1^2 e^-Δ_1/k_BT+5g_2^2 e^-Δ_2/k_BT/1+e^-Δ_1/k_BT+e^-Δ_2/k_BT,

where N_A is Avogadro's number, g_0 is electronic g-factor for the ground state, and g_1 and g_2 are g-factors for the excited states, which are separated from the ground state by energy gaps of Δ_1 and Δ_2, respectively, yields decent description of the magnetic susceptibility up to at least 650 K. This fitting function can be understood as follows. In the absence of electronic correlations and spin-orbit coupling, 9 electrons occupying 6 t_2g orbitals of two Ir atoms give rise to S=1/2 and S=3/2 states depending on the filling of the molecular orbitals of the dimer <cit.>. The effect of spin-orbit coupling is taken into account by introducing electronic g-factors as fitting parameters. Additionally, we assumed that the S=3/2 state splits into two, because fitting with one excited state was not successful, whereas two distinct excited states provide a good description of the susceptibility in the broad temperature range.

Fitting the susceptibility with Eq. (<ref>) yields χ_0=-6.8× 10^-5 cm^3/mol, θ=-6.8 K, Δ_1=107 K, Δ_2=472 K, g_0=0.872, g_1=0.678, and g_2=1.810. The relatively low value of Δ_1 explains the deviation from the Curie-Weiss behavior already above 70 K. The obtained Δ_1 and Δ_2 are of the same order of magnitude as in the mixed-valence ruthenates isostructural to Ba_3InIr_2O_9 <cit.>. The paramagnetic effective moments are μ_ eff=0.76 μ_B in the ground state, μ_ eff,1=1.31 μ_B in the first excited state, and μ_ eff,2=3.51 μ_B in the second excited state. 





For the rest of this paper, we focus on the low-temperature regime below 70 K with the paramagnetic effective moment of μ_=0.76 μ_B/dimer, which is comparable to the values reported for mixed-valence iridates earlier <cit.>. Antiferromagnetic couplings between magnetic moments localized on the mixed-valent dimers are confirmed by the negative Curie-Weiss temperature θ_χ=-7 K. Isothermal magnetization curve at 2 K (see inset (ii) of Fig. <ref>) does not show any sign of saturation up to 14 T. This weak sensitivity to the field may be due to the strongly reduced g-factor (only 44% of its spin-only value) that lessens the effect of the external field.







 §.§ Specific heat

First insight into the low-temperature magnetism is obtained from the specific-heat data. A broad peak in C_p/T is observed around 1.6 K (Fig. <ref>a) indicative of a crossover between the paramagnetic (thermally disordered) and spin-liquid (quantum disordered) regimes <cit.>, further confirmed by the increase in the muon zero-field relaxation rate around the same temperature (Sec. <ref>). The peak shifts toward lower temperatures in the applied field, although the changes are relatively small even at 14 T, and no transition anomaly is observed.

Heat capacity was further measured at temperatures well below the broad maximum. For an insulating material, total heat capacity is a sum of the magnetic, lattice, and nuclear contributions, C_p=C_m+C_ lat+C_ nuc. To extract the magnetic specific heat of the material, we need to subtract the lattice part and nuclear part from the total specific heat C_p. In the absence of a suitable non-magnetic analog, we fitted the measured specific heat with C_p=β T^3 in the range 14-20 K <cit.>. The fitting of the lattice part yields β=1.45 mJ mol^-1 K^-4 and the Debye temperature Θ_D=272 K. The fitted curve is extrapolated to low temperatures and taken as the lattice part (C_ lat) that was subtracted from the experimental data. 

At low temperatures, the nuclear contribution becomes prominent. To extract the magnetic heat capacity, we adopted the following procedure:

(1) We fitted the C_p data for each field (B) from lowest T up to 300-400 mK with C_p = α/T^2 + C_0 T^γ <cit.>, where α/T^2 stands for C_ nuc, and power-law behavior of C_ mag is assumed.

(2) For each field, the magnetic heat capacity C_m is obtained as C_m=C_p-C_ nuc, whereas C_ lat is negligible in this temperature range.

(3) Reliability of the α values is verified by plotting the field dependence α(B^2), which was linear, as expected <cit.>.



After subtracting the nuclear contribution <cit.>, we arrive at the robust power-law behavior C_m=C_0T^γ with C_0=832 mJ mol^-1 K^-2.83 and γ=1.83 (Fig. <ref>b). This behavior gives first indication of a gapless ground state, because otherwise low-energy excitations over a spin gap would give rise to the exponential decay of C_m at low temperatures. The power-law behavior persists up to at least 14 T, but above 9 T the exponent γ is slightly reduced <cit.>.





By integrating C_m/T in zero field (see Fig. <ref>c) within the temperature range from 0.08 to 20 K, we estimated magnetic entropy change of 3.4 J mol^-1 K^-1 (see Fig. <ref>d), which is about 60% of the entropy expected for spin-1/2. Part of the magnetic entropy should be then released at higher temperatures, where the magnetic contribution is concealed behind a much larger lattice term. We note here that a two-step release of the magnetic entropy (and, consequently, two well-separated peaks of the magnetic specific heat C_m) are not uncommon in frustrated magnets <cit.>.



 §.§ μSR


Whereas thermodynamic measurements provide first hints towards the absence of long-range magnetic order in Ba_3InIr_2O_9, experimental evidence for the QSL formation is not complete without a local probe. To this end, we use muon spin relaxation (μSR), which is a very sensitive technique to detect static local fields arising from weak long-range order or spin freezing. 

The relaxation curves of the muon polarization in zero field (ZF) are shown in Fig. <ref>. The absence of oscillations in the zero-field (ZF) signal and the lack of the polarization recovery to 1/3 indicate the absence of any frozen moments in Ba_3InIr_2O_9 in the temperature range from 200 K down to 20 mK. The polarization curves can be fitted with Eq. <ref> which is a combination of the depolarization due to the muon coupled to the In nuclear magnetism (Kubo-Toyabe Gaussian function) and depolarization due to the electronic magnetism evolving with temperature.

    P(t)=fe^-(λ_ F t)^β+(1-f)(1/3+2/3(1-(σ t)^2) e^-(σ t)^2/2)
 
Here, f=0.786(2) is the fraction of muons coupled to the electronic magnetism, σ=0.094(2) μs^-1 is the nuclear depolarization rate, β=1.308(7) is the stretched exponent, and λ is the electronic depolarization rate. The stretched exponent β is independent of field and temperature. The small deviation from unity could be due to a small distribution of the muon sites close to the In ions.

The ZF μ^+ relaxation rate (λ_ ZF) obtained from fitting the ZF muon depolarization curves is shown as function of temperature in Fig. <ref>b. At high temperatures (20 K to 3 K), λ_ ZF remains constant at ∼0.12μs^-1, which is consistent with the paramagnetic fluctuations of Ir moments
according to the Bloembergen Purcell, and Pound theory <cit.>.

From 3 K down to 1 K, λ_ ZF increases with decreasing temperature. The enhancement of λ_ ZF in a narrow temperature window indicates a slowing down of Ir spin fluctuations due to the development of strong short-range correlations, a common feature seen in other QSL candidates <cit.>. Upon further cooling, λ_ ZF shows temperature-independent plateau-like behavior between 1 K and 20 mK. The plateau-like behavior in λ_ ZF vs T (see Fig. <ref>b) has also been observed in several other QSL compounds. 

To verify if the plateau-like behavior is originating from the muons directly coupled to the frustrated spins <cit.> or the muons coupled to defects <cit.>, we have performed μSR experiments under transverse field (TF) of 0.4 T and estimated the μSR line shift (K^μ) as a function of temperature  <cit.> as shown in Fig. <ref>a. K^μ increases with decreasing temperature and saturates below 3 K, from where λ (see Fig. <ref>b) starts increasing. This indicates that antiferromagnetic (AFM) spin fluctuations are dominating at low temperature in Ba_3InIr_2O_9. The similarity between the temperature dependence of K^μ and NMR shift (K_ NMR) (see Fig. <ref>a) proves that the muons are directly coupled to the Ir moments. 





In order to identify the origin of the depolarization rate being static or dynamic, we performed decoupling experiments at 250 mK (shown in Fig. <ref>a) applying longitudinal fields (LF) from 5 mT up to 100 mT. Should the low-temperature plateau in λ_ ZF arise from a static field, the size of this field can be estimated as B_ loc=λ/γ_μ≈1.4 mT, where γ_μ=135.5×2π s^-1μT^-1 is the gyromagnetic ratio for muons. The static field can then be decoupled by applying an external magnetic field ≃14 mT, which is one order of magnitude higher than B_ loc. The polarization curve under a field of 100 mT does not show the signs of a full polarization,
suggesting that the plateau does not originate from a static internal field and the spins are dynamic in nature even at the lowest temperature of 20 mK, as expected in a QSL. The plateau-like behavior of λ_ ZF toward lowest temperature indicates much slower spin dynamics of the material compared to the μSR time window. It is another characteristics of QSL candidates <cit.>.








 §.§ NMR

Nuclear magnetic resonance (NMR) is a concurrent probe for local magnetic fields and spin dynamics. ^115In NMR spectra measured at 70 MHz in the temperature range 0.024-138 K are shown in Fig. <ref>(a). At high temperatures (for example, at 138 K), the spectra exhibit one single isotropic line which indicates the unique crystallographic site for indium, consistent with our structural analysis. The spectra can be described satisfactorily assuming the I=9/2 nuclei with the 380 kHz quadrupolar coupling constant (ν_Q). 

Below about 100 K, we observed a second line, which remained unshifted within the entire temperature range. This second line presumably originates from trace amounts (0.9 %) of a non-magnetic impurity phase present in the sample. For estimating the impurity contribution in the spectral line shape, we measured the spectra at several temperatures with τ=50 μs and τ=200 μs, where τ is the pulse separation between the spin-echo sequence π/2-τ-π. The intrinsic line has much shorter spin-lattice relaxation time T_1 as well as the spin-spin relaxation time T_2 compared to the impurity line <cit.>. Hence it is expected that with longer τ the intrinsic part of the spectra is already relaxed, whereas the impurity contribution sustains. The comparison of the spectra corresponding to different τ measured at T=25 K is shown in Fig. <ref>c.

The spectra are described at all temperatures below 100 K with two Gaussian lines, one for magnetic (intrinsic) and the other one for a non-magnetic (impurity) contribution as shown in Fig. <ref>(a)). At low temperatures, the two lines (intrinsic line and the impurity line) merge together. For estimating the Knight shift of the intrinsic line, we have used the peak of the intrinsic contribution marked with the green arrows in Fig. <ref>a. This peak shifts towards higher fields with decreasing temperature yielding the local spin susceptibility K. In general,


    K=K_0+(A_ hf/N_Aμ_B) χ(T),

where K_0 is the temperature-independent part of the line shift K, and N_A is the Avogadro's number. The hyperfine coupling constant is estimated at A_ hf=-1.675 T/μ_B <cit.>. The temperature dependence of the ^115In line shift (K) is shown in Fig. <ref>a. A continuous increase in the line shift K(T) with decreasing temperature from 100 K down to ∼4 K indicates the development of spin correlations. The inverse of the temperature-dependent part of the line shift 1/(K-K_0) is shown as a function of temperature in the inset of Fig. <ref>a. A CW fit of the data yields the CW temperature θ_ NMR=-14 K. This value should be more reliable than θ_χ=-7 K estimated from the bulk susceptibility, since the NMR line shift does not contain any impurity contributions.

At low temperature the total spectra remain unchanged as shown in Fig  <ref>b. This indicates that both the line shift K and line width Δ H of the spectra remain constant down to the base temperature of 25 mK. Saturation of both these quantities suggests saturation of spin correlations below ∼4 K. The finite and temperature-independent value of K below 4 K gives strong evidence for the gapless behavior. From Δ H, we estimated the saturated magnetic moment μ_s=0.89 μ_B/f.u. close to 1 μ_B expected for one unpaired electron per the Ir_2O_9 dimer.






To probe the low-energy spin dynamics, we have studied the NMR spin-lattice relaxation rate (1/T_1) at various temperatures. (1/T_1) was measured at the peak position of the intrinsic line using long pulses to avoid any interference from the impurity line. 1/T_1 at different temperatures are obtained by fitting (shown in the inset of Fig. <ref>b) the longitudinal nuclear magnetization recovery curves with the equation

    1-M_t/M_∞ =    C ( 0.006 e^-(2Wt)^β+0.0335 e^-(12Wt)^β+ 
       +0.0925 e^-(30Wt)^β+0.215 e^-(56Wt)^β
       +0.653 e^-(90Wt)^β),

where 1/T_1=2W. Here, M is the nuclear magnetization, β is a stretched exponent, which accounts for a distribution of the T_1 values due to disorder, and C is a pre-factor. 

In general,

    (1/T_1T)∼∑_qA_ hf(q)^2×χ^''(q,ω→0),
 where χ^''(q,ω) is the imaginary part of the dynamical spin susceptibility. The temperature dependence of 1/T_1 is shown in Fig. <ref>b. Between 30 K and 4 K, 1/T_1 is almost temperature-independent, indicating the paramagnetic behavior. A weak hump-like feature is seen around 1.6 K, which coincides with the hump in the C_p/T data (Fig. <ref>a) and with the rapid increase in λ_ ZF (Fig. <ref>b). No long-range order occurs in Ba_3InIr_2O_9. Therefore, this hump is not a broadened signature of a magnetic transition. Instead, it may indicate some intrinsic physics, as recently proposed for the honeycomb iridates <cit.>. The applicability of this scenario to Ba_3InIr_2O_9 may be an interesting venue for future research.

Below 0.3 K, (1/T_1) follows the ∼ T^2.2 power law similar to the ∼ T^1.83 behavior of C_m(T).



§ DISCUSSION AND SUMMARY

Our results establish gapless ground state and persistent spin dynamics down to at least 20 mK, rendering Ba_3InIr_2O_9 a potential QSL material. However, its low-temperature behavior is rather different from theoretical expectations for a gapless QSL, where magnetic excitations are usually described in terms of a spinon Fermi surface and should give rise to the linear behavior of both NMR spin-lattice relaxation rate and magnetic specific heat <cit.> at low temperatures. Our data for Ba_3InIr_2O_9 clearly deviate from this scenario.

Microscopically, we expect two superexchange pathways. The mixed-valence Ir_2O_9 dimers may interact in the ab plane via the coupling J_T (the Ir–Ir distance of 5.83 Å) and along the c direction via the coupling J_H (the Ir–Ir distance of 5.71 Å), see Fig. <ref>. Note that we consider Ir–Ir distances, because magnetic electrons are expected to occupy a molecular orbital of the dimer with equal contributions of both Ir sites <cit.>. While the coupling J_T forms a triangular lattice in the ab plane, as already anticipated in Ba_3IrTi_2O_9 <cit.>, the coupling J_H leads to a buckled honeycomb geometry. Depending on the ratio between J_T and J_H, the system can interpolate between the purely two-dimensional regime (|J_T|≫ |J_H|, or vice versa) and a 3D behavior when both |J_H| and |J_T| are of the same size.

On the phenomenological level, quadratic behavior of the zero-field specific heat is expected in an algebraic spin liquid on the kagome lattice <cit.>. Another manifestation of the T^2 behavior was proposed for a spin model combining the triangular and honeycomb geometries <cit.>, as in Ba_3InIr_2O_9, but its applicability to our system is obscured by the large single-ion anisotropy term that is central to the model but seems unlikely in iridates <cit.>. Intriguingly, the robust quadratic behavior of the zero-field specific heat has been reported in frustrated magnets with slow dynamics <cit.> and interpreted in the framework of Halperin-Saslow modes for two-dimensional spin glasses <cit.>. It was also observed in Li_2RhO_3, the Kitaev antiferromagnet, where spins freeze below 6 K <cit.>. To what extent these scenarios apply to Ba_3InIr_2O_9 with its clear signatures of persistent spin dynamics should be a subject of future investigations.

Mixed-valence dimers are also reported in ruthenates with the hexagonal perovskite structure. However, these compounds show long-range magnetic order or disordered static magnetism at low temperatures <cit.>. This is different from our case, where persistent spin dynamics is observed. From magnetism point of view, mixed-valence hexagonal perovskites remain a largely uncharted territory. The nature of local moments within the mixed-valence dimers requires further investigation, and peculiarities of magnetic interactions between the dimers remain to be explored. Experiments reveal instances of non-trivial magnetic states, including the potential QSL state in Ba_3InIr_2O_9, and call for a better understanding from theoretical and microscopic perspectives.

Altogether, we demonstrated that Ba_3InIr_2O_9 is a structurally well-ordered QSL candidate showing the  behavior of zero-field specific heat and the ∼ T^2.2 power-law for the spin-lattice relaxation rate at low temperatures. Not only would it be interesting for further experimental (probe of the spin excitations) and theoretical (microscopic analysis of the magnetic model) research, it also puts forward mixed-valence iridates as a promising playground for finding new QSL materials. The unique combination of the triangular and buckled honeycomb geometries bears strong connections to current theoretical models of frustrated magnetism <cit.>, and may lead to novel manifestations of the QSL physics when different lattice geometries concur.

We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center TRR 80 (Augsburg/Munich). TD, MM, and AT were funded by the Federal Ministry for Education and Research through the Sofja Kovalevskaya Award of Alexander von Humboldt Foundation. FB acknowledges financial support from the project SOCRATE (ANR-15-CE30-0009-01) of the ANR French agency. PK acknowledges support from the European Commission through Marie Curie International Incoming Fellowship (PIIF-GA-2013-627322). Part of the work was performed at the LTF and DOLLY spectrometers of the Swiss Muon Source (Paul Scherrer Institute, Villigen, Switzerland). We thank C. Baines for his support on LTF, and Dana Vieweg for her help with high-temperature susceptibility measurements.










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@bib@innerbibempty

[Balents(2010)]balents2010
  author author L. Balents, title title Spin liquids in
  frustrated magnets, 10.1038/nature08917 journal journal Nature volume 464,  pages 199–208 (year 2010)NoStop
[Savary and Balents(2017)]savary2017
  author author L. Savary and author L. Balents, title title Quantum spin
  liquids: a review, 10.1088/0034-4885/80/1/016502
  journal journal Rep. Prog. Phys. volume 80, pages 016502 (year
  2017)NoStop
[Anderson(1973)]anderson1973
  author author P .W. Anderson, title title Resonating
  valence bonds: A new kind of insulator? 10.1016/0025-5408(73)90167-0 journal journal
  Mater. Res. Bull. volume 8, pages
  153–160 (year 1973)NoStop
[Yan et al.(2011)Yan,
  Huse, and White]yan2011
  author author S. Yan, author D. A. Huse,   and author S. R. White,  title title Spin-liquid ground state of
  the S=1/2 kagome Heisenberg antiferromagnet, 10.1126/science.1201080 journal journal
  Science volume 332, pages 1173–1176
  (year 2011)NoStop
[Mishmash et al.(2013)Mishmash, Garrison, Bieri, and  Xu]mishmash2013
  author author R. V. Mishmash, author J. R. Garrison, author S. Bieri,   and author C. Xu, title title Theory of a competitive spin liquid
  state for weak Mott insulators on the triangular lattice, 10.1103/PhysRevLett.111.157203 journal journal Phys. Rev. Lett. volume 111, pages 157203 (year 2013)NoStop
[Kaneko et al.(2014)Kaneko,
  Morita, and Imada]kaneko2014
  author author R. Kaneko, author S. Morita,   and author M. Imada, title title Gapless spin-liquid phase in an
  extended spin-1/2 triangular Heisenberg model, 10.7566/JPSJ.83.093707 journal journal J. Phys.
  Soc. Jpn. volume 83, pages 093707
  (year 2014)NoStop
[Hu et al.(2015)Hu,
  Gong, Zhu, and Sheng]hu2015
  author author W.-J. Hu, author S.-S. Gong,
  author W. Zhu,  and author D. N. Sheng, title
  title Competing spin-liquid states in the
  spin-1/2 Heisenberg model on the triangular lattice, 10.1103/PhysRevB.92.140403 journal journal Phys. Rev. B volume 92, pages 140403(R) (year 2015)NoStop
[Iqbal et al.(2016)Iqbal,
  Hu, Thomale, Poilblanc, and  Becca]iqbal2016
  author author Y. Iqbal, author W.-J. Hu,
  author R. Thomale, author D. Poilblanc,  and author F. Becca, title
  title Spin liquid nature in the Heisenberg
  J_1-J_2 triangular antiferromagnet, 10.1103/PhysRevB.93.144411 journal journal Phys.
  Rev. B volume 93, pages 144411
  (year 2016)NoStop
[Norman(2016)]norman2016
  author author M. R. Norman, title title Colloquium:
  Herbertsmithite and the search for the quantum spin liquid, 10.1103/RevModPhys.88.041002 journal journal Rev. Mod. Phys. volume 88, pages 041002 (year 2016)NoStop
[Fåk et al.(2012)Fåk, Kermarrec, Messio, Bernu, Lhuillier, Bert, Mendels, Koteswararao, Bouquet,
  Ollivier, Hillier, Amato,
  Colman, and Wills]fak2012
  author author B. Fåk, author E. Kermarrec,
  author L. Messio, author B. Bernu, author
  C. Lhuillier, author
  F. Bert, author P. Mendels, author B. Koteswararao, author F. Bouquet, author J. Ollivier, author A. D.  Hillier, author A. Amato, author R. H. Colman,   and author A. S. Wills,  title title Kapellasite: A kagome
  quantum spin liquid with competing interactions, 10.1103/PhysRevLett.109.037208 journal journal
  Phys. Rev. Lett. volume 109, pages
  037208 (year 2012)NoStop
[Clark et al.(2013)Clark,
  Orain, Bert, De Vries,
  Aidoudi, Morris, Lightfoot,
  Lord, Telling, Bonville,
  Attfield, Mendels, and Harrison]clark2013
  author author L. Clark, author J. C. Orain,
  author F. Bert, author
  M. A. De Vries, author
  F. H. Aidoudi, author
  R. E. Morris, author
  P. Lightfoot, author
  J. S. Lord, author
  M. T. F. Telling, author
  P. Bonville, author
  J. P. Attfield, author
  P. Mendels,  and author
  A. Harrison, title title Gapless spin liquid ground state in the S=1/2
  vanadium oxyfluoride kagome antiferromagnet
  [NH_4]_2[C_7H_14N][V_7O_6F_18], 10.1103/PhysRevLett.110.207208 journal journal
  Phys. Rev. Lett. volume 110, pages
  207208 (year 2013)NoStop
[Balz et al.(2016)Balz,
  Lake, Reuther, Luetkens,
  Schönemann, Herrmannsdörfer,
  Singh, Nazmul Islam, Wheeler, Rodriguez-Rivera, Guidi,
  Simeoni, Baines, and Ryll]balz2016
  author author C. Balz, author B. Lake, author J. Reuther, author
  H. Luetkens, author
  R. Schönemann, author
  T. Herrmannsdörfer, author
  Y. Singh, author A. T. M. Nazmul Islam, author E. M. Wheeler, author J. A.  Rodriguez-Rivera, author T. Guidi, author G. G.  Simeoni, author C. Baines,  and author H. Ryll, title title Physical
  realization of a quantum spin liquid based on a complex frustration
  mechanism, 10.1038/nphys3826 journal
  journal Nature Phys. volume 12,  pages 942–949 (year 2016)NoStop
[Kitaev(2006)]kitaev2006
  author author A. Kitaev, title title Anyons in an
  exactly solved model and beyond, 10.1016/j.aop.2005.10.005 journal journal Ann.
  Phys. volume 321, pages 2–111
  (year 2006)NoStop
[Jackeli and Khaliullin(2009)]jackeli2009
  author author G. Jackeli and author G. Khaliullin, title title Mott
  insulators in the strong spin-orbit coupling limit: From Heisenberg to a
  quantum compass and Kitaev models, 10.1103/PhysRevLett.102.017205 journal journal
  Phys. Rev. Lett. volume 102, pages
  017205 (year 2009)NoStop
[Winter et al.(2016)Winter,
  Li, Jeschke, and Valentí]winter2016
  author author S. M. Winter, author Y. Li, author H. O. Jeschke,  and author R. Valentí, title title Challenges in design of Kitaev
  materials: Magnetic interactions from competing energy scales, 10.1103/PhysRevB.93.214431 journal journal Phys. Rev. B volume 93, pages 214431 (year 2016)NoStop
[Winter et al.()Winter,
  Tsirlin, Daghofer, van den
  Brink, Singh, Gegenwart, and  Valentí]winter2017
  author author S. M. Winter, author A. A. Tsirlin,
  author M. Daghofer, author J. van den Brink, author Y. Singh, author
  P. Gegenwart,  and author
  R. Valentí, @noop  title Models and materials for generalized Kitaev
  magnetism, note arXiv:1706.06113NoStop
[Streltsov and Khomskii(2016)]streltsov2016
  author author S. V. Streltsov and author D. I. Khomskii, title title Covalent bonds
  against magnetism in transition metal compounds, 10.1073/pnas.1606367113 journal journal Proc.
  Nat. Acd. Sci. volume 113, pages
  10491–10496 (year 2016)NoStop
[Shirata et al.(2012)Shirata, Tanaka, Matsuo, and  Kindo]shirata2012
  author author Y. Shirata, author H. Tanaka,
  author A. Matsuo,  and author K. Kindo, title
  title Experimental realization of a spin-1/2
  triangular-lattice Heisenberg antiferromagnet, 10.1103/PhysRevLett.108.057205 journal journal
  Phys. Rev. Lett. volume 108, pages
  057205 (year 2012)NoStop
[Zhou et al.(2012)Zhou,
  Xu, Hallas, Silverstein,
  Wiebe, Umegaki, Yan,
  Murphy, Park, Qiu,
  Copley, Gardner, and Takano]zhou2012
  author author H. D. Zhou, author C. Xu, author A. M. Hallas, author
  H. J. Silverstein, author
  C. R. Wiebe, author
  I. Umegaki, author J. Q. Yan, author T. P.  Murphy, author J.-H.  Park, author Y. Qiu, author J. R. D. Copley,
  author J. S. Gardner,  and  author Y. Takano, title title Successive phase transitions and
  extended spin-excitation continuum in the S=1/2 triangular-lattice
  antiferromagnet Ba_3CoSb_2O_9, 10.1103/PhysRevLett.109.267206 journal journal
  Phys. Rev. Lett. volume 109, pages
  267206 (year 2012)NoStop
[Ma et al.(2016)Ma,
  Kamiya, Hong, Cao,
  Ehlers, Tian, Batista,
  Dun, Zhou, and Matsuda]ma2016
  author author J. Ma, author Y. Kamiya, author T. Hong, author
  H. B. Cao, author G. Ehlers, author W. Tian, author C. D.  Batista, author Z. L.  Dun, author H. D. Zhou,  and author M. Matsuda, title title Static and
  dynamical properties of the spin-1/2 equilateral triangular-lattice
  antiferromagnet Ba_3CoSb_2O_9, 10.1103/PhysRevLett.116.087201 journal journal
  Phys. Rev. Lett. volume 116, pages
  087201 (year 2016)NoStop
[Becker et al.(2015)Becker,
  Hermanns, Bauer, Garst, and  Trebst]becker2015
  author author M. Becker, author M. Hermanns,
  author B. Bauer, author M. Garst,  and author
  S. Trebst, title title Spin-orbit physics of j=1/2 Mott insulators on the
  triangular lattice, 10.1103/PhysRevB.91.155135
  journal journal Phys. Rev. B volume 91, pages 155135 (year
  2015)NoStop
[Catuneanu et al.(2015)Catuneanu, Rau, Kim, and Kee]catuneanu2015
  author author A. Catuneanu, author J. G. Rau,
  author H.-S. Kim,  and  author H.-Y. Kee, title title Magnetic orders proximal to the Kitaev
  limit in frustrated triangular systems: Application to
  Ba_3IrTi_2O_9, 10.1103/PhysRevB.92.165108
  journal journal Phys. Rev. B volume 92, pages 165108 (year
  2015)NoStop
[Dey et al.(2012)Dey,
  Mahajan, Khuntia, Baenitz,
  Koteswararao, and Chou]dey2012
  author author T. Dey, author A. V. Mahajan,
  author P. Khuntia, author M. Baenitz, author
  B. Koteswararao,  and author
  F. C. Chou, title title Spin-liquid behavior in J_ eff=1/2 triangular
  lattice compound Ba_3IrTi_2O_9, 10.1103/PhysRevB.86.140405 journal journal Phys.
  Rev. B volume 86, pages 140405(R)
  (year 2012)NoStop
[Kumar et al.(2016)Kumar,
  Sheptyakov, Khuntia, Rolfs,
  Freeman, Rønnow, Dey,
  Baenitz, and Mahajan]kumar2016
  author author R. Kumar, author D. Sheptyakov,
  author P. Khuntia, author K. Rolfs, author
  P. G. Freeman, author
  H. M. Rønnow, author
  T. Dey, author M. Baenitz,  and author A. V. Mahajan, title title Ba_3M_xTi_3-xO_9 (M = Ir, Rh): A family of
  5d/4d-based diluted quantum spin liquids, 10.1103/PhysRevB.94.174410 journal journal Phys.
  Rev. B volume 94, pages 174410
  (year 2016)NoStop
[Lee et al.(2017)Lee,
  Do, Yoon, Lee, Choi, Jang, Brando, Lee,
  Choi, Ji, Jang, Suh, and Choi]lee2017
  author author W.-J. Lee, author S.-H. Do,
  author S. Yoon, author
  S. Lee, author Y. S. Choi, author D. J.  Jang, author M. Brando, author M. Lee,
  author E. S. Choi, author S. Ji, author
  Z. H. Jang, author
  B. J. Suh,  and author
  K.-Y. Choi, title title Putative spin liquid in the triangle-based iridate
  Ba_3IrTi_2O_9, 10.1103/PhysRevB.96.014432
  journal journal Phys. Rev. B volume 96, pages 014432 (year
  2017)NoStop
[Darriet et al.(1976)Darriet, Drillon, Villeneuve, and  Hagenmuller]darriet1976
  author author J. Darriet, author M. Drillon,
  author G. Villeneuve,  and  author P. Hagenmuller,  title title Interactions magnétiques
  dans des groupements binucléaires du Ruthénium +V, 10.1016/0022-4596(76)90170-5 journal journal J. Solid State Chem. volume 19,  pages 213–220 (year 1976)NoStop
[Darriet et al.(1983)Darriet, Soubeyroux, and Murani]darriet1983
  author author J. Darriet, author J.L. Soubeyroux,  and author A.P. Murani, title title Neutron
  inelastic scattering study of exchange interactions in a ruthenium(V) dimer
  Ba_3CaRu_2O_9, 10.1016/0022-3697(83)90062-8
  journal journal J. Phys. Chem. Solids volume 44, pages 269–272 (year
  1983)NoStop
[Doi and Hinatsu(2004)]doi2004
  author author Y. Doi and author Y. Hinatsu,  title title The structural and magnetic
  characterization of 6H-perovskite-type oxides Ba_3LnIr_2O_9 (Ln =
  Y, lanthanides), 10.1088/0953-8984/16/16/009 journal journal J. Phys.: Condens. Matter volume 16, pages 2849–2860 (year
  2004)NoStop
[Sakamoto et al.(2006)Sakamoto, Doi, and Hinatsu]sakamoto2006
  author author T. Sakamoto, author Y. Doi,   and author Y. Hinatsu,  title title Crystal structures and
  magnetic properties of 6H-perovskite-type oxides Ba_3MIr_2O_9 (M =
  Mg, Ca, Sc, Ti, Zn, Sr, Zr, Cd and In), 10.1016/j.jssc.2006.04.055 journal journal J.
  Solid State Chem. volume 179, pages
  2595–2601 (year 2006)NoStop
[Dey et al.(2013)Dey,
  Mahajan, Kumar, Koteswararao,
  Chou, Omrani, and Ronnow]dey2013
  author author T. Dey, author A. V. Mahajan,
  author R. Kumar, author B. Koteswararao, author
  F. C. Chou, author
  A. A. Omrani,  and author
  H. M. Ronnow, title
  title Possible spin-orbit driven spin-liquid ground
  state in the double perovskite phase of Ba_3YIr_2O_9, 10.1103/PhysRevB.88.134425 journal journal Phys. Rev. B volume 88, pages 134425 (year 2013)NoStop
[Dey et al.(2014)Dey,
  Kumar, Mahajan, Kaushik,  and Siruguri]dey2014
  author author T. Dey, author R. Kumar, author A. V. Mahajan, author
  S. D. Kaushik,  and author
  V. Siruguri, title title Unconventional magnetism in the spin-orbit-driven Mott
  insulators Ba_3MIr_2O_9 (M = Sc, Y), 10.1103/PhysRevB.89.205101 journal journal Phys.
  Rev. B volume 89, pages 205101
  (year 2014)NoStop
[Hoelzel et al.(2012)Hoelzel, Senyshyn, Juenke, Boysen, Schmahl, and Fuess]spodi
  author author M. Hoelzel, author A. Senyshyn,
  author N. Juenke, author H. Boysen, author
  W. Schmahl,  and author
  H. Fuess, title title High-resolution neutron powder diffractometer SPODI at
  research reactor FRM II, @noop  journal journal Nuclear Instruments & Methods in Physics Research, Section A:
  Accelerators, Spectrometers, Detectors, and Associated Equipment volume 667, pages 32–37 (year
  2012)NoStop
[Petr̆íc̆ek et al.(2014)Petr̆íc̆ek, Dus̆ek, and Palatinus]jana2006
  author author V. Petr̆íc̆ek, author M. Dus̆ek,  and author L. Palatinus, title title Crystallographic computing system JANA2006: General features,  @noop  journal journal Z. Krist.  volume 229, pages 345–352 (year 2014)NoStop
[Ling et al.(2010)Ling,
  Kennedy, Zhou, Spencer, and  Avdeev]ling2010
  author author C. D. Ling, author B. J. Kennedy,
  author Q. Zhou, author
  J. R. Spencer,  and author
  M. Avdeev, title title Synthesis, structures, and phase transitions of barium
  bismuth iridium oxide perovskites Ba_2BiIrO_6 and
  Ba_3BiIr_2O_9, 10.1016/j.jssc.2010.01.017
  journal journal J. Solid State Chem. volume 183, pages 727–735 (year
  2010)NoStop
[Terzic et al.(2015)Terzic,
  Wang, Ye, Song, Yuan, Aswartham, DeLong, Streltsov, Khomskii, and Cao]terzic2015
  author author J. Terzic, author J. C. Wang,
  author F. Ye, author
  W. H. Song, author
  S. J. Yuan, author
  S. Aswartham, author
  L. E. DeLong, author
  S. V. Streltsov, author
  D. I. Khomskii,  and author
  G. Cao, title title Coexisting charge and magnetic orders in the dimer-chain
  iridate Ba_5AlIr_2O_11, 10.1103/PhysRevB.91.235147 journal journal Phys.
  Rev. B volume 91, pages 235147
  (year 2015)NoStop
[Note1()]Note1
  note We introduced the site mixing and constrained the overall
  composition to Ba_3InIr_2O_9. This leads to R_I=0.038 and R_p=0.050
  compared to R_I=0.039 and R_p=0.051 for the fully ordered model
  (room-temperature data).Stop
[Ziat et al.(2017)Ziat,
  Aczel, Sinclair, Chen,
  Zhou, Williams, Stone,
  Verrier, and Quilliam]ziat2017
  author author D. Ziat, author A. A. Aczel,
  author R. Sinclair, author Q. Chen, author
  H. D. Zhou, author
  T. J. Williams, author
  M. B. Stone, author
  A. Verrier,  and author
  J. A. Quilliam, title
  title Frustrated spin-1/2 molecular magnetism in
  the mixed-valence antiferromagnets Ba_3MRu_2O_9 (M = In, Y, Lu),  10.1103/PhysRevB.95.184424 journal journal Phys. Rev. B volume 95, pages 184424 (year 2017)NoStop
[Miiller et al.(2012)Miiller, Avdeev, Zhou, Kennedy, Sharma, Kutteh, Kearley, Schmid, Knight, Blanchard, and Ling]miiller2012
  author author W. Miiller, author M. Avdeev,
  author Q. Zhou, author
  B. J. Kennedy, author
  N. Sharma, author R. Kutteh, author G. J.  Kearley, author S. Schmid, author K. S. Knight,
  author P. E. R. Blanchard,   and author C. D. Ling,  title title Giant magnetoelastic effect
  at the opening of a spin-gap in Ba_3BiIr_2O_9, 10.1021/ja211517h journal journal J. Amer. Chem.
  Soc. volume 134, pages 3265–3270
  (year 2012)NoStop
[Li et al.(2015a)Li, Liao, Zhang, Li,
  Jin, Ling, Zhang,
  Zou, Pi, Yang, Wang, Wu, and Zhang]li2015
  author author Y. Li, author H. Liao, author Z. Zhang, author
  S. Li, author F. Jin, author L. Ling, author L. Zhang,
  author Y. Zou, author
  L. Pi, author Z. Yang, author J. Wang, author Z. Wu,  and  author Q. Zhang, title title Gapless quantum spin liquid ground state
  in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO_4,  10.1038/srep16419 journal journal Sci. Reports volume 5, pages
  16419 (year 2015a)NoStop
[Li et al.(2016)Li,
  Adroja, Biswas, Baker,
  Zhang, Liu, Tsirlin,
  Gegenwart, and Zhang]li2016
  author author Y. Li, author D. Adroja, author P. K. Biswas, author
  P. J. Baker, author
  Q. Zhang, author J. Liu, author A. A.  Tsirlin, author P. Gegenwart,  and author Q. Zhang, title title Muon spin
  relaxation evidence for the U(1) quantum spin-liquid ground state in the
  triangular antiferromagnet YbMgGaO_4, 10.1103/PhysRevLett.117.097201 journal journal
  Phys. Rev. Lett. volume 117, pages
  097201 (year 2016)NoStop
[sup()]supplement
  @noop  note See Supplemental Material for details of
  synthesis, structure refinement, thermodynamic measurements, NMR, and μSR
  data.Stop
[Sindzingre et al.(2000)Sindzingre, Misguich, Lhuillier,
  Bernu, Pierre, Waldtmann,  and Everts]sindzingre2000
  author author P. Sindzingre, author G. Misguich, author C. Lhuillier,
  author B. Bernu, author L. Pierre, author
  Ch. Waldtmann,  and author
  H.-U. Everts, title
  title Magnetothermodynamics of the spin-1/2 kagomé
  antiferromagnet, 10.1103/PhysRevLett.84.2953 journal journal Phys. Rev. Lett. volume 84, pages 2953–2956 (year
  2000)NoStop
[Nasu et al.(2015)Nasu,
  Udagawa, and Motome]nasu2015
  author author J. Nasu, author M. Udagawa,   and author Y. Motome,  title title Thermal fractionalization of
  quantum spins in a Kitaev model: Temperature-linear specific heat and
  coherent transport of Majorana fermions, 10.1103/PhysRevB.92.115122 journal journal Phys.
  Rev. B volume 92, pages 115122
  (year 2015)NoStop
[Bloembergen et al.(1948)Bloembergen, Purcell, and Pound]pound1948
  author author N. Bloembergen, author E. M. Purcell,  and author R. V. Pound, title title Relaxation
  effects in nuclear magnetic resonance absorption, @noop 
  journal journal Phys. Rev. volume 73, pages 679 (year 1948)NoStop
[Colman et al.(2011)Colman,
  Bert, Boldrin, Hillier,
  Manuel, Mendels, and Wills]colman2011
  author author R. H. Colman, author F. Bert,
  author D. Boldrin, author A. D. Hillier, author
  P. Manuel, author P. Mendels,  and author A. S. Wills, title title Spin dynamics in the S=1/2 quantum kagome compound vesignieite,
  Cu_3Ba(VO_5H)_2, 10.1103/PhysRevB.83.180416
  journal journal Phys. Rev. B volume 83, pages 180416(R) (year
  2011)NoStop
[Kermarrec et al.(2011)Kermarrec, Mendels, Bert, Colman, Wills, Strobel, Bonville, Hillier, and Amato]kermarrec2011
  author author E. Kermarrec, author P. Mendels,
  author F. Bert, author
  R. H. Colman, author
  A. S. Wills, author
  P. Strobel, author P. Bonville, author A. Hillier,  and author A. Amato, title title
  Spin-liquid ground state in the frustrated kagome antiferromagnet
  MgCu_3(OH)_6Cl_2, 10.1103/PhysRevB.84.100401
  journal journal Phys. Rev. B volume 84, pages 100401(R) (year
  2011)NoStop
[Gomils̆ek et al.(2016)Gomils̆ek, Klanjs̆ek, Pregelj,
  Coomer, Luetkens, Zaharko,
  Fennell, Li, Zhang, and  Zorko]gomilsek2016
  author author M. Gomils̆ek, author M. Klanjs̆ek, author M. Pregelj, author F. C. Coomer,
  author H. Luetkens, author O. Zaharko, author
  T. Fennell, author Y. Li, author Q. M.  Zhang,  and author A. Zorko, title title
  Instabilities of spin-liquid states in a quantum kagome antiferromagnet,  10.1103/PhysRevB.93.060405 journal journal Phys. Rev. B volume 93, pages 060405(R) (year 2016)NoStop
[Orain et al.(2014)Orain,
  Clark, Bert, Mendels,
  Attfield, Aidoudi, Morris,
  Lightfoot, Amato, and Baines]orain2014
  author author J. C. Orain, author L. Clark,
  author F. Bert, author
  P. Mendels, author P. Attfield, author F. H.  Aidoudi, author R. E.  Morris, author P. Lightfoot, author A. Amato,   and author C. Baines,  title title μSR study of a quantum
  spin liquid candidate: the S=1/2 vanadium oxyfluoride kagome
  antiferromagnet, 10.1088/1742-6596/551/1/012004
  journal journal J. Phys.: Conference Series  volume 551, pages 012004 (year 2014)NoStop
[Yoshitake et al.(2016)Yoshitake, Nasu, and Motome]yoshitake2016
  author author J. Yoshitake, author J. Nasu,   and author Y. Motome,  title title Fractional spin fluctuations
  as a precursor of quantum spin liquids: Majorana dynamical mean-field study
  for the Kitaev model, 10.1103/PhysRevLett.117.157203
  journal journal Phys. Rev. Lett. volume 117, pages 157203 (year
  2016)NoStop
[Lawler et al.(2008)Lawler,
  Paramekanti, Kim, and Balents]lawler2008
  author author M. J. Lawler, author A. Paramekanti,
  author Y. B. Kim,  and  author L. Balents, title title Gapless spin liquids on the
  three-dimensional hyperkagome lattice of Na_4Ir_3O_8, 10.1103/PhysRevLett.101.197202 journal journal Phys. Rev. Lett. volume 101, pages 197202 (year 2008)NoStop
[Yamashita et al.(2008)Yamashita, Nakazawa, Oguni, Oshima, Nojiri, Shimizu, Miyagawa, and Kanoda]yamashita2008
  author author S. Yamashita, author Y. Nakazawa,
  author M. Oguni, author Y. Oshima, author
  H. Nojiri, author Y. Shimizu, author K. Miyagawa,  and author K. Kanoda, title title
  Thermodynamic properties of a spin-1/2 spin-liquid state in a kappa-type
  organic salt, 10.1038/nphys942 journal
  journal Nature Phys. volume 4,  pages 459–462 (year 2008)NoStop
[Yamashita et al.(2011)Yamashita, Yamamoto, Nakazawa,
  Tamura, and Kato]yamashita2011
  author author S. Yamashita, author T. Yamamoto,
  author Y. Nakazawa, author M. Tamura,  and author
  R. Kato, title title Gapless spin liquid of an organic triangular compound
  evidenced by thermodynamic measurements, 10.1038/ncomms1274 journal journal Nature
  Comm. volume 2, pages 275 (year 2011)NoStop
[Ran et al.(2007)Ran,
  Hermele, Lee, and Wen]ran2007
  author author Y. Ran, author M. Hermele,
  author P. A. Lee,  and  author X.-G. Wen, title title Projected-wave-function study of the
  spin-1/2 heisenberg model on the kagomè lattice, 10.1103/PhysRevLett.98.117205 journal journal
  Phys. Rev. Lett. volume 98, pages
  117205 (year 2007)NoStop
[Hermele et al.(2008)Hermele, Ran, Lee, and Wen]hermele2008
  author author M. Hermele, author Y. Ran,
  author P. A. Lee,  and  author X.-G. Wen, title title Properties of an algebraic spin liquid
  on the kagome lattice, 10.1103/PhysRevB.77.224413
  journal journal Phys. Rev. B volume 77, pages 224413 (year
  2008)NoStop
[Chen et al.(2012)Chen,
  Hermele, and Radzihovsky]chen2012
  author author G. Chen, author M. Hermele,   and author L. Radzihovsky,  title title Frustrated quantum critical
  theory of putative spin-liquid phenomenology in
  6H-B-Ba_3NiSb_2O_9, 10.1103/PhysRevLett.109.016402 journal journal
  Phys. Rev. Lett. volume 109, pages
  016402 (year 2012)NoStop
[Ramirez et al.(1992)Ramirez, Espinosa, and Cooper]ramirez1992
  author author A. P. Ramirez, author G. P. Espinosa,  and author A. S. Cooper, title title Elementary
  excitations in a diluted antiferromagnetic kagomé lattice, 10.1103/PhysRevB.45.2505 journal journal Phys. Rev. B volume 45, pages 2505–2508 (year 1992)NoStop
[Nakatsuji et al.(2005)Nakatsuji, Nambu, Tonomura, Sakai, Jonas, Broholm, Tsunetsugu, Qiu, and Maeno]nakatsuji2005
  author author S. Nakatsuji, author Y. Nambu,
  author H. Tonomura, author O. Sakai, author
  S. Jonas, author C. Broholm, author H. Tsunetsugu, author Y. Qiu,  and author Y. Maeno, title title
  Spin disorder on a triangular lattice, 10.1126/science.1114727 journal journal
  Science volume 309, pages 1697–1700
  (year 2005)NoStop
[Sachdev(1992)]sachdev1992
  author author S. Sachdev, title title Kagomé- and
  triangular-lattice Heisenberg antiferromagnets: Ordering from quantum
  fluctuations and quantum-disordered ground states with unconfined bosonic
  spinons, 10.1103/PhysRevB.45.12377 journal
  journal Phys. Rev. B volume 45,  pages 12377–12396 (year 1992)NoStop
[Podolsky and Kim(2009)]podolsky2009
  author author D. Podolsky and author Y. B. Kim, title title Halperin-Saslow
  modes as the origin of the low-temperature anomaly in NiGa_2S_4,  10.1103/PhysRevB.79.140402 journal journal Phys. Rev. B volume 79, pages 140402(R) (year 2009)NoStop
[Khuntia et al.(2017)Khuntia, Manni, Foronda, Lancaster, Blundell, Gegenwart, and  Baenitz]khuntia2015
  author author P. Khuntia, author S. Manni,
  author F. R. Foronda, author T. Lancaster, author
  S. J. Blundell, author
  P. Gegenwart,  and author
  M. Baenitz, title title Local magnetism and spin dynamics of the frustrated
  honeycomb rhodate Li_2RhO_3, 10.1103/PhysRevB.96.094432 journal journal Phys.
  Rev. B volume 96, pages 094432
  (year 2017)NoStop
[Rousochatzakis et al.(2015)Rousochatzakis, Reuther, Thomale,
  Rachel, and Perkins]rousochatzakis2015
  author author I. Rousochatzakis, author J. Reuther, author R. Thomale,
  author S. Rachel,  and author N. B. Perkins, title title Phase diagram and quantum order by
  disorder in the Kitaev K_1-K_2 honeycomb magnet, 10.1103/PhysRevX.5.041035 journal journal Phys.
  Rev. X volume 5, pages 041035
  (year 2015)NoStop
[Jackeli and Avella(2015)]jackeli2015
  author author G. Jackeli and author A. Avella, title title Quantum order by
  disorder in the Kitaev model on a triangular lattice, 10.1103/PhysRevB.92.184416 journal journal Phys.
  Rev. B volume 92, pages 184416
  (year 2015)NoStop
[Li et al.(2015b)Li, Yu, and Li]li2015b
  author author K. Li, author S.-L. Yu,  and  author J.-X. Li, title title Global phase diagram, possible chiral
  spin liquid, and topological superconductivity in the triangular
  Kitaev-Heisenberg model, 10.1088/1367-2630/17/4/043032
  journal journal New J. Phys. volume 17, pages 043032 (year
  2015b)NoStop
[Rousochatzakis et al.(2016)Rousochatzakis, Rössler, van den
  Brink, and Daghofer]rousochatzakis2016
  author author I. Rousochatzakis, author U. K. Rössler, author J. van den
  Brink,  and author M. Daghofer, title title Kitaev
  anisotropy induces mesoscopic ℤ_2 vortex crystals in frustrated
  hexagonal antiferromagnets, 10.1103/PhysRevB.93.104417
  journal journal Phys. Rev. B volume 93, pages 104417 (year
  2016)NoStop





Supplemental Material
 Persistent low-temperature spin dynamics in mixed-valence iridate Ba_3InIr_2O_9

















