E Kermarrec

P Mendels

F Bert

R H Colman

A S Wills

P Strobel

P Bonville

A Hillier

A Amato

LPS

Keywords: numbers: 75.10.Kt, 76.75.+i, 75.30.Hx

We report µSR experiments on MgxCu4-x(OH)6Cl2 with x ∼ 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of S = 1 2 ions (Cu 2+ ), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (∼ J/10 4 ). This report presents a detailed investigation of the spin dynamics on well characterized samples in zero and applied longitudinal fields and a defect-based interpretation is proposed to explain the unconventional dynamics observed in the quantum spin liquid phase.

Quantum magnetism in frustrated networks has been acknowledged for a long time as the ideal playground to stabilize new quantum phases. Since the proposal of an RVB state by P.W. Anderson [1], advances in theory has led to the emergence of a rich variety of spin liquid phases, including algebraic and gapped spin liquids [2,[START_REF] Lacroix | Introduction to Frustrated Magnetism[END_REF]. On the experimental side, Herbertsmithite, ZnCu 3 (OH) 6 Cl 2 , is among the best materials to explore such quantum states, as it combines the highly frustrated two-dimensional kagome lattice and quantum spins 1 2 of Cu 2+ [4]. No magnetic freezing has been detected down to 50 mK ∼ J/4000 [5,6] and spin-spin correlations are found to be short-ranged as expected for a liquid state [7].

Nevertheless, this material deviates from the "perfect" image since it has sizable level of Cu-Zn intersite mixing. The replacement of non-magnetic Zn 2+ ions at the interlayer position by magnetic Cu 2+ causes almost free S = 1 2 defects that correspond to 5 -10 % of the total Cu content, as determined from various techniques (see [8] for a review). The exact amount of the complementary defect, where a non-magnetic Zn 2+ impurity induces a spin vacancy in the kagome plane, remains difficult to evaluate quantitatively, due to the similar x-ray scattering factors of Cu and Zn, and the absence of a straightforward magnetic response. As a result, this value has been found to vary with samples and experimental techniques, from 1 % [9] (from anomalous x-ray scattering) to 5 % [10,11] (from NMR).

Very recently, a new series, the "Mg-paratacamites" Mg x Cu 4-x (OH) 6 Cl 2 isostructural to the Zn-based paracatamite, has been successfully synthesized. The similar ionic radii of the diamagnetic Mg 2+ and Zn 2+ ions leads to a minimal difference of the crystal structure and hence exchange pathway, resulting in comparable coupling J ∼ 190 K [12][13][14]. If Cu/Mg mixing is still expected, the difference in their x-ray scattering factors now enables reliable x-ray structure analysis. Chu et al. [15] succeeded in synthesizing materials for x < 0.75 where they found a ferromagnetic component in macroscopic susceptibility under T C = 4 K, attributed to a 3D coupling via interlayer Cu 2+ , similar to the Zn case. A minimal Mg 2+ substitution within the kagome planes (≤ 3 %) was determined through x-ray diffraction. A different synthesis was recently reported which led to samples with 0.93 ≤ x ≤ 0.98 [13], these correspond to the Herbertsmithite analogues and correspondingly to model quantum kagome antiferromagnets. A small ferromagnetic fraction at T c ≃ 4 -5 K was tentatively ascribed to an impurity phase on the basis of susceptibility data.

In this Communication, we first report the µSR local probe investigation down to 20 mK in the Mg x Cu 4-x (OH) 6 Cl 2 "Mg-Herbertsmithites" with x ∼ 1 which evidences a ground state with no sign of spin freezing, hence a spin liquid character. We also study the sub-Kelvin unconventional spin dynamics of both paratacamites (Mg, Zn) characterized by an x-dependent plateau of 1/T 1 . We argue that this relaxation is driven by interlayer Cu 2+ ions.

The experiments were carried out on "Mgparatacamites" powder samples close to the Herbertsmithite structure, x = 0.84, 0.92, and 1.21, synthesized following a hydrothermal route described elsewhere [13], as well as on the Zn Herbertsmithite (x = 1) sample from [16]. The ratios of Cu/Mg and Cu/Zn were determined by ICP-AES (Table I). Refinements of x-ray diffraction data for the Mg compounds give separately the Cu (n) and Mg (p) occupancies of the interlayer and the kagome sites corresponding to the formula (Cu

1-p M p ) 3 (M 1-n Cu n )(OH) 6 Cl 2 (M=Mg, Zn).
The M total amount is x = 3p -n + 1 (Table I). A visible reduction in the quality of the fit, and a corresponding increase in goodness-of-fit statistic (χ 2 = 1.37 to 1.42 for x = 0.92), was found when attempting to fix p = 0 as reported in [9], evidencing the ability of x-ray diffraction to determine the metal site occupancies of the kagome and triangular sites [13]. µSR experiments were performed at the ISIS and PSI facilities in zero and longitudinal applied field configurations down to 20 mK. The DC magnetic susceptibility was also measured on a Quantum Design SQUID magnetometer in the 1.8 -300 K T -range and magnetization data were taken at 1.75 K in fields up to 14 T with a Cryogenic Vibrating Sample Magnetometer.

In order to reveal the magnetic response of the interplane defects, we measured the magnetization of the Mg (x = 0.92 and x = 1.21) and Zn (x = 1) samples at low T = 1.75 K and up to 14 T. Following the analysis in Ref. [13,16], we divide the total magnetization into two contributions, a Brillouin-like component M def arising from the weakly coupled interlayer Cu 2+ and a linear term arising from the strongly coupled Cu 2+ of the kagome planes (Fig. 1). By subtraction of the latter, we have access to the saturated magnetization, nM sat , of the interlayer Cu 2+ [17]. Taking g = 2.2 from Ref. [18], this analysis provides an independent determination of n, which agrees well with the x-ray refinements for the Mg samples and provides a value for the Zn sample otherwise inaccessible by structural studies (Table I). These results confirm quantitatively the existence of the weakly coupled S = 1 2 interplane defects in the Mg and Zn paratacamites with x ∼ 1.

We now turn to the local µSR investigations. µSR very sensitive to any small magnetic field (down to ∼ 0.1 G) and is therefore a powerful tool to detect any frozen moment. The muon is implanted inside the volume and, as a positive charged particle, will stop in the vicinity of a negative environment, i.e. either near OH - or Cl - [5]. The polarizations from 0 (ZF) to 2500 G longitudinal applied field (LF) are reported in Fig. 2. Our experiments demonstrate a similar magnetic behavior of the Mg and Zn compounds, as expected due to their crystallographic similarities. Following the former work of Ref. [5], the ZF polarization is fitted on a high statistics run at 50 mK by P (t) = P nucl (t)e -(λt) β . P nucl (t) depends only on static fields from surrounding nuclei, see [17], and λ stands for a small dynamical relaxation. The well-defined oscillation of P nucl (t) due to the formation of a µ-O-H complex [19], and from the field experienced by the muon, H µ-OH = 7.8 G, one estimates a distance of 1.5 Å to hydrogen [20]. The ZF polarization is found largely unchanging in the extended T -range 0.05 -20 K, except for a slight variation of λ. Therefore, we conclude that there is no magnetic ordering of the electronic spins down to T = 20 mK (∼ J/10 4 ) for x ∼ 1, as in the Zn counterpart.

The spin dynamics is revealed by experiments under longitudinal fields. From 10 to 100 G, the static relaxation of nuclear origin is progressively decoupled as expected (Fig. 2). Above 100 G (> 10H µ-OH ), P nucl (t) = 1 and a single stretched exponential fit of P (t) yields the relaxation rate λ = 1/T µ 1 of electronic origin. λ = 1/T µ 1 is linked to the spin autocorrelation function by 1/T µ 1 ∼ +∞ 0 S(t)S(0) cos(γ µ H LF t)dt, where H LF is the longitudinal applied magnetic field. Starting from a high-T value ∼ 0.005 µs -1 , λ increases upon cooling below 1 K and saturates at lower temperature at a value which differs from sample to sample (Fig. 3). This increase of λ indicates a dynamical slowing down [? ].

We now argue that the muon is dominantly coupled to the interlayer Cu 2+ moments from the following experimental observations: (i) The low-T muon shift K µ was shown to track the intersite defect susceptibility [21]. This is in fair agreement with recent 2 D NMR study [22] but contrasts with NMR results on 17 O which is strongly coupled to the planes. (ii) From Fig. 3 (b) and the inspection of Table I, λ is found to increase linearly with n, the concentration of intersite defects, but is anticor- related with the level of in plane defects, p. Since the distance between Zn sites is large (d = 6.12 Å), the linearity in n can be easily explained by an "all or nothing" model: some muons (n) sit next to an interlayer Cu 2+ defect with a relaxation rate λ 1 whereas the others (1 -n) stay far from a defect with a relaxation rate λ 2 → 0. Under the valid condition λ 1,2 t ≪ 1, the total polarization becomes P (t) = n exp(-λ 1 t) + (1 -n) exp(-λ 2 t) ∼ exp(-nλ 1 t), which explains the linear n-dependence of λ. (iii) From the scaling of K µ versus χ bulk , one can extract the coupling constant A µ = 0.08 T/µ B [21], consistent with a dipolar interaction. From 17 O NMR T 17 1 , the contribution of the kagome planes Cu 2+ to the muon relaxation can then be estimated using:

1/T µ 1 = 1/T 17 1 ×(γ µ A µ /γ 17 n A 17 hf ) 2 ∼ 3×10 -5 µs -1
. This leads at high-T to a value 150 times smaller than the measured one, which therefore requires a different source of relaxation. (iv ) Finally in the high-T Moriya paramagnetic limit [23], 1/T µ 1 is given by 1/T µ 1 = 2γ 2 n H 2 µ n/ν with ν = 4J ′2 zS(S + 1)/3π 2 and H µ = gA µ S(S + 1)/3 = 880 G. From the high-T constant value 1/T µ 1 ∼ 5 × 10 -3 µs -1 , an average value n ∼ 0.22 and a number of nearest neighbors z = 6, one obtains the coupling between an interlayer Cu 2+ and a kagome Cu 2+ J ′ ∼ 3 K, in rough agreement with the temperature of the magnetic ordering T C = 6 K in the clinoatacamite, Cu 2 (OH) 3 Cl, parent compound [24][25][26].

In this context, the slowing down below 1 K of intersite defects can be attributed either to the strengthening of the correlations with the two nearby kagome planes or to a coupling between two intersite defects mediated by the kagome plane to which they are coupled. The energy scale of 1 K for the interaction between defects was also evidenced in magnetization measurements [16].

We now discuss the T → 0 value of the relaxation rate. In order to reveal the dynamics of the correlated regime under 1 K, we probe the excitation spectrum S(ω) in the low energy range by applying a longitudinal field H LF = ω/γ µ , H LF < 0.25 T. Two scenarios can be considered based on different correlation functions S(t) = S(t)S(0) for the interplane spins. Exponential correlation function S(t) = e -νt combined with field induced polarization of the interlayer defects. Such correlation leads to the usual Lorentzian spectral density S(ω) and

λ 1 = 2γ 2 µ H 2 fluct ν ν 2 + γ 2 µ H 2 LF (1)
where H fluct is the fluctuating component of the field at the muon site perpendicular to its initial polarization, ν is the fluctuation frequency, and γ µ = 851.6 Mrad/s/T is the muon gyromagnetic factor. However, not only is the expected H 2 LF dependence of λ not convincing (Fig. 4), but a forced fit results in an unphysical H fluct ∼ 20 G, while the lowest possible dipolar field value is 200 G which corresponds to a maximal distance of the µ + to intersite Cu 2+ . We therefore propose that the fluctuating field is reduced when the interlayer S = 1 2 defect starts to be polarized in the external applied field H LF . In a mean field Brillouin approach, the fluctuating moment is m fluct = µ B (1 -tanh(gµ B SH LF /k B (T + θ))) where θ is introduced to account for interactions. The reduced value of H fluct = m fluct H µ /µ B can be injected in Eq.1 and leads to only two shared fit parameters to account for the T µ 1 (H LF ) variation for all x samples. Although the obtained fits are not perfect, this approach yields ν = 100 ± 20 GHz, a typical frequency of fluctuations in a paramagnetic regime, and θ = 0.7 ± 0.2 K, consistent with both magnetization measurements and the 1 K Tscale where the slowing down occurs. Power law correlation function S(t) = (1/t) 1-α The corresponding spectral density S(ω) yields a power law relation T µ 1 ∝ ω α . This more exotic approach is at play (α = 0.35) in the spin liquid case of the S = 1 2 antiferromagnetic chain [27], where a spinon continuum of excitations is well established. Such a spectral density (α = 1) was also invoked for the spin liquid pyrochlore TbTi 2 O 7 [START_REF] Yaouanc | Muon Spin Rotation, Relaxation, and Resonance; Applications to Condensed Matter[END_REF][START_REF] Keren | [END_REF]. A perfect fit of our data can be found with 1/λ 1 = T 0 1 (x) + Aω 0.63 , which would point to an exotic relaxation channel for the intersite defect. Using the scaling of χ ′′ T α ∼ (T /ω) α tanh(ω/βT ) from neutron experiments [30], one gets 1/T 1 ∼ k B T χ ′′ /ω ∼ ω -α by means of the fluctuation dissipation theorem. The reported value α = 0.66 [30] agrees well with that deduced from our data. This points to a common origin and following [31] one could invoke a distribution of couplings between intersite defects as a source of the power law. Another possibility could be that the kagome dynamics drives that of the intersite defects. The inconsistency between the T -plateau of the relaxation rate measured at low fields and the T -0.7 dependence of T 17 1 at 7 T [10] would then require that the field impacts on the kagome plane dynamics.

In conclusion, the spin liquid behavior of the new kagome antiferromagnet Mg x Cu 4-x (OH) 6 Cl 2 for x > 0.84 is clearly established by our µSR experiments. Our data show that the measured interlayer site dynamics differs from those of the kagome plane at 7 T. This calls for a careful inspection of probes which integrate both responses and/or the field impact on relaxation. Whether

a

  FIG. 1. Interlayer Cu 2+ contribution M def extracted from magnetization measurements and normalized by Msat = NAgµBS = 6143 emu. The saturation value gives n, the amount of interlayer Cu 2+ per formula unit. The lines reproduce a Brillouin fit with an interacting scale of θ = 0.8 K. Inset: Normalized magnetization at T = 1.75 K up to 14 T. Lines are fits for the linear component.

FIG. 2 .

 2 FIG. 2. Upper panel: Polarization in zero field (ZF, black circles) and under longitudinal applied fields (LF) from 10 to 2500 G. The black line is a fit (see text). Bottom panel: The relaxation is faster at low temperatures and when n increases. Lines are stretched exponential fits.

FIG. 3 .

 3 FIG. 3. (a) T -dependence of relaxation rates λ for different samples. (b) Plot of the plateau value of λ = 1/T1 versus n. The black line is a linear fit. The error bars on n account for the discrepancy between values derived from M (H) and x-ray characterization.

FIG. 4 .

 4 FIG. 4. The T1 dependence with external field HLF underlines the unconventional spin dynamics at T = 50 mK. The lines refer to different models (see text).

TABLE I .

 I Chemical composition determined through ICP, x-ray refinements and saturated magnetization for


Edwin Kermarrec

C A Marjerrison

C M Thompson

D D Maharaj

K Levin

S Kroeker

G E Granroth

R Flacau

Z Yamani

J E Greedan

B D Gaulin

The frustrated FCC antiferromagnet Ba 2 YOsO 6 : structural characterization, magnetic properties and neutron scattering studies

Keywords: numbers: 75, 25, -j 75, 40, Gb 75, 70, Tj

I. INTRODUCTION

Geometrical frustration in magnetic materials has proven to be extraordinary fertile ground for the discovery of new exotic quantum states of matter. [START_REF]Introduction to Frustrated Magnetism[END_REF] Studies of materials with geometrically frustrated geometries such as the triangular, 2-4 kagomé, 5-7 hyperkagomé 8,9 or pyrochlore 10,11 lattices have yielded a host of topical disordered and ordered states, among them spin ice, spin liquid, and spin glass states for example. However, much less attention has been devoted to the face-centered-cubic lattice, comprised of edge sharing tetrahedra, which is also frustrated in the presence of antiferromagnetic interactions.

Such a lattice can be conveniently realized in the double perovskite structure, with chemical formula A 2 BB ′ O 6 . If the two ions B and B ′ order over the octahedral sites, two interpenetrating FCC lattices are formed and, if only B ′ is magnetic, an FCC magnetic lattice results, as shown in Fig. 1. Such a lattice is stabilized when the size and charge of the two cations B ′ and B are sufficiently different. 12 In general such materials can be prepared with very low levels of B/B ′ intersite mixing. For example in the series Ba 2 YM O 6 where M = Mo, Re and Ru, site mixing levels as determined by 89 Y NMR were reported as 3%, < 0.5% and 1%, respectively. [13][14][15] Despite possessing a relatively common structure, frustrated magnetic materials with FCC lattices have yet to be widely explored. The study of the double perovskite family is therefore a promising avenue in this regard, as shown by recent measurements underlining the diversity of stabilized states. [16][17][18][19] The flexibility of the cubic double perovskite structure allows systematic investigation of a large fraction of the transition elements in the periodic table, going from those possessing rather large, classical, spin-only moments such as S = 3 2 to the extreme quantum case of S = 1 2 . Of particular interest is the Ba 2 YB ′ O 6 family, where B ′ is a magnetic 4d or 5d transition-metal element in its 5+ oxidation state. These materials tend to retain the ideal cubic F m3m structure to the lowest temperatures studied. Examples include Ba 2 YRuO 6 (4d 3 ), 13,17 which enters a long-range ordered antiferromagnetic state at T N = 36 K, well below its Curie-Weiss temperature θ CW = -571 K, Ba 2 YReO 6 (5d 2 ) which shows anomalous spin freezing behaviour below T ∼ 35 K, 15 and Ba 2 YMoO 6 (4d 1 ) which possesses a collective spin-singlet ground state. 16,[20][21][22][23] The double perovskite structure also allows for the study of magnetism of heavier 5d elements, where the spin-orbit coupling and the crystal field energy are known to become of comparable value. The originality of 5d in-sulating systems has been recently highlighted in the 5d 5 iridate compounds, where a strong SOC induces a Mott instability leading to an effective total angular momentum J eff = 1 2 state, 24 very different from the well-known spin S = 1 2 localized state of conventional Mott insulators.

The role of SOC for t 3 2g ions with d 3 configurations, such as Ru 5+ and Os 5+ , is less clear, as L = 0 in L -S coupling. The ordered moment for a number of Ru 5+ double perovskites is found to be ∼ 2 µ B rather than the spin only value of 3 µ B . 13,25 While SOC can contribute to such an effect, other factors may also be important as will be discussed later. However, seemingly unequivocal experimental evidence for the effects of SOC is provided by inelastic neutron scattering studies of the 4d 3 material Ba 2 YRuO 6 17 . A clear ∼ 5 meV gap in the spin excitation spectrum, centered at the (100) magnetic reflection position is observed to develop below T N . Such a gap is not expected for a pure L = 0 magnetic ground state, and we are very interested in whether a related spin gap occurs for 5d 3 Ba 2 YOsO 6 .

One further unusual feature of some Ru 5+ double perovskites is the observation of at least two cases of two ordering temperatures, T N1 and T N2 . For cubic Ba 2 YRuO 6 these are 36 K and 47 K while for monoclinic Sr 2 YRuO 6 , 24 K and 32 K. 18 Ba 2 YRuO 6 shows a spin gap that is fully formed only below T N1 = 36 K and elastic magnetic Bragg peaks with a resolution-limited, symmetric, Gaussian line shape indicative of 3D correlations that persist up to T N2 = 47 K. For Sr 2 YRuO 6 , it has been argued that the region between T N1 and T N2 represents a mixed short range/long range ordering between AFM layers. 18 . Are multiple ordered states a characteristic of antiferromagnetic d 3 configurations on the FCC lattice and therefore also expected in 5d 3 Ba 2 YOsO 6 ?

In this paper we report structural and phase characterization including 89 Y NMR, bulk magnetic measurements, and elastic magnetic neutron diffraction, as well as spin dynamical characterization using time-offlight neutron experiments on polycrystalline samples of Ba 2 YOsO 6 . This study shows obvious long range antiferromagnetic order below T N ∼ 69 K, with magnetic Bragg peaks appearing at the [100] and [110] positions, consistent with a Type I antiferromagnetic structure with a reduced ordered moment on the Os 5+ site. Neutron measurements of the order parameter show evidence for a second, weakly first-order transition just below T N , at T c,2 = 67.45 K. The inelastic neutron data reveal a surprisingly large spin gap of ∆ ∼ 17 meV develops below T N . These results are discussed in light of recent measurements performed on the related 4d 3 double perovskite system Ba 2 YRuO 6 .

II. EXPERIMENTAL DETAILS AND SAMPLE CHARACTERIZATION

Ba 2 YOsO 6 was prepared by a solid state reaction according to the equation:

Ba 4 Y 2 O 7 + 2Os(10% excess) + 5 2 O 2 = 2Ba 2 YOsO 6 (1)
The reaction was carried out in air at 1400 Magnetization measurements were performed using a Quantum Design MPMS magnetometer from 2 K to 300 K at various applied fields µ 0 H < 5 T.

Neutron diffraction data were collected over the temperature range 3.5 K to 290 K using the C2 diffractometer at the Canadian Neutron Beam Centre, Chalk River, Ontario, Canada, using neutron wavelengths of 1.33 Å and 2.37 Å with no energy analysis. The sample, ∼ 2g, was enclosed in a vanadium can in the presence of a He exchange gas. Crystal and magnetic structure refinements were performed using the FULLPROF analysis suite. Elastic neutron scattering experiments were also conducted on a ∼ 8 g powder sample using the N5 triple-axis spectrometer at the Canadian Neutron Beam Centre, employing pyrolitic graphite (PG) as both monochromator and analyser, as well as a PG filter. These measurements with a neutron wavelength of 2.37 Å had a corresponding energy resolution of 1 meV (FWHM). The sample temperature was monitored using two sensors placed on either end of the sample can, show-ing a temperature difference of less than 0.1 K across top and bottom of the sample can between T = 65 K and T = 70 K.

89 Y NMR was carried out at the University of Manitoba on a Bruker Avance III 500 (B 0 = 11.7 T) spectrometer operating at a Larmor frequency of 24.493 MHz. A 280 mg powder sample of Ba 2 YOsO 6 was packed into a 4 mm (outer diameter) zirconia rotor and spun at 13.5 kHz. A set of 100k transients were averaged with a pulse repetition rate of 1.66 Hz. A rotor-synchronized Hahn-echo acquisition was used to eliminate probe ringing, with π 2 and π pulses of 9 and 18 µs, respectively. Frequency shifts are referenced to 2M Y(NO 3 ) 3 (aq) at 0 ppm. Due to the extreme temperature dependence of the paramagnetically shifted peaks, the sample temperature and its associated temperature gradient were calibrated using the 207 Pb signal of solid Pb(NO 3 ) 2 . 27 Inelastic neutron scattering measurements were performed at the Spallation Neutron Source (SNS, Oak Ridge National Laboratory), on the SEQUOIA Fine Resolution Fermi Chopper Spectrometer. 28 Incident neutron energies of 40 and 120 meV were employed, giving an energy resolution (FWHM) of 2.4 and 7 meV, respectively. The incident energies were chosen by Fermi chopper No.1 spinning at 180 Hz (40 meV) or at 300 Hz (120 meV). Background from the prompt pulse was removed by the T 0 chopper spinning at 90 Hz (40 meV) or 180 Hz (120 meV). The sample was enclosed in a planar aluminium cell with dimensions 5.0 × 5.0 × 0.1 cm, under a He exchange gas atmosphere, and then loaded into an Orange 4 He-flow cryostat, capable to achieve a temperature range of 1.5 to 300 K. An identical empty can was measured under the same experimental conditions and used for background subtraction. A boron nitride mask was used to reduce background scattering and normalization to a white-beam vanadium run was performed to correct for the detector efficiency differences.

A. Crystal structure and limits on B/B ′ site disorder determined from 89 Y NMR

The neutron powder diffraction data shown in Fig. 2 was refined in space group F m3m, indicating a fully Bsite ordered double perovskite structure at both 290 K and 3.5 K, indicating no change in symmetry over this range. The structural parameters resulting from these fits are summarized in Table I. There is no evidence of B/B ′ anti-site disorder from the neutron diffraction data.

The extent of B/B ′ anti-site disorder can be measured more accurately using magic angle spinning (MAS) NMR as demonstrated previously. 13 The results are displayed in Fig. 3 which shows a single peak in the NMR signal intensity as a function of frequency (B 0 = 11.7 T), centred near -4740 ppm. The low frequency shoulder is due to a thermal gradient associated with the sample spinning rotor as shown by the 207 Pb reference signal of the in- set. Any feature due to anti-site disorder would appear shifted by ∼ +800 ppm from the main peak as found to be the case in Ba 2 YRuO 6 . 13 We therefore conclude that any B/B ′ anti-site disorder in Ba 2 YOsO 6 is below the level of the noise. An upper limit on the possible extent of B/B ′ site disorder in our samples of Ba 2 YOsO 6 is 0.5 %, assessed as described in Ref. 13.

B. Magnetization

Figure 4a shows χ(T ) -1 (main panel) and χ(T ) as measured in a magnetic field of 0.05 T. We observe a clear anomaly in χ(T ) at T N ∼ 69 K, indicative of antiferromagnetic order. In this χ(T ) data there is no obvious evidence for multiple ordering temperatures, in contrast to the cases of 4d 3 antiferromagnetic Ba 2 YRuO 6 and Sr 2 YRuO 6 . A Curie-Weiss fit was attempted over the temperature range 150-300 K with the resulting parameters θ cw = -717(5) K and a Curie constant C = 1.93(1) emu.K/mol, equivalent to an effective moment µ eff = 3.93(1) µ B . These parameters are close to the spin-only values relative to the Os 5+ moment, C = 1.87 emu.K/mol and µ eff = 3.87 µ B , but remains suspicious due to the large Curie-Weiss temperature which indicates that the true paramagnetic regime is not found below 300 K. Nonetheless, such large negative θ cw reflects the presence of strong antiferromagnetic interactions in this system and a frustration index |θ cw |/T N ∼ 11. No significant divergence between the zero field-cooled (ZFC) and field-cooled (FC) χ(T ) curves is found for the entire temperature range measured. Furthermore, the field dependence of the magnetization at 2 K indicates no hysteresis and slight non-linearity for the dominant Ba 2 YOsO 6 phase, implying that the ordered structure possesses no ferromagnetic component to it. A plot of d(χT )/dT , the so-called Fisher heat capacity, 29 Fig. 4b, shows a sharp lambda-like peak at 68.5 K.

III. NEUTRON SCATTERING RESULTS

A. Magnetic Neutron Diffraction

Figure 5 shows a comparison of neutron diffraction data for Ba 2 YOsO 6 at 75 K and 3 K taken with the C2 powder diffractometer. Four magnetic reflections are identified as they appear at low temperatures only. These peaks are indexed as indicated and are consistent with a Type I FCC magnetic structure (see inset of Fig. 5) as found for several 4d 3 Ru 5+ based double perovskites, including Ba 2 YRuO 6 . 13,25 The refined magnetic moment at the 5d 3 Os 5+ site is 1.65(6) µ B , significantly smaller than for Ru 5+ in Ba 2 YRuO 6 , 2.2(1) µ B , 13,25 and for a number of other Ru 5+ -based double perovskites which also show an ordered moment of 2 µ B . The 5d 3 Os 5+ ordered moment is also much reduced compared with the spin-only value of near 3 µ B expected for the t 3 2g electronic configuration. 30 A comparison between ordered moments found in perovskites with 4d 3 , 5d 3 and 3d 3 electronic configurations is clearly of interest. 3d 3 Cr 3+ , also t 3 2g , in the perovskite La 0.5 Pr 0.5 CrO 3 shows an or- dered moment of 2.50(5) µ B , 31 confirming a progression to smaller ordered moments as SO coupling becomes progressively stronger.

What is the origin of the ordered moment reduction, of order 33 -45 % between 4d 3 Ba 2 YRuO 6 and 5d 3 Ba 2 YOsO 6 ? Among effects which can reduce the ordered moment are both SO coupling as well as covalency between the d and ligand orbitals, which removes some fraction of the ordered moment from the transition metal ion site and transfers it to the ligand sites. Fluctuations induced by either geometrical frustration or quantum effects can also reduce the relevant ordered moments. However, given that Ba 2 YRuO 6 and Ba 2 YOsO 6 share the same frustrated FCC lattice and d 3 configuration, it is likely that SO coupling and covalency are more important effects.

The role of SO coupling is thought to be least important in the case where B ′ has the t 3 2g configuration, as to first order, L = 0, assuming L -S coupling. The main effect is in second order which results in a reduction of The broad peak at the (100) magnetic reflection position indicates short-range magnetic correlations at 75 K. Red line is a structural and magnetic refinements of the diffraction pattern observed at 3.5 K (grey circles). The overfitting of the ( 120) and (211) magnetic reflections is ascribed to inaccuracies in the Os 5+ form factor.

the electronic g-factor by a term ∼ 8λ/10Dq, where λ is the SO coupling constant and 10Dq is the overall cubic crystal field splitting between the t 2g and e g states. [START_REF] Abragam | Electron Paramagnetic Resonance of Transition Ions[END_REF] In such a scenario, one expects that the ordered moment for t 3 2g ions, µ = gS, with S = 3 2 , will be somewhat reduced from the expected spin only value of 3 µ B . For Ba 2 YRuO 6 and Ba 2 YOsO 6 , the SO coupling parameters for Ru 5+ and Os 5+ estimated as λ = 55 meV and 186 meV, respectively. [START_REF] Ma | Values extrapolated from[END_REF] Taking 10Dq in the range 2eV-3eV, the moments should fall between 2.7 -2.8 µ B for Ru 5+ and 1.9 -2.3 µ B for Os 5+ . Thus, SO coupling alone appears to be insufficient to fully explain the reduced ordered moments.

A similarly reduced ordered moment, 1.9 µ B , was found for the simple perovskite SrTcO 3 which involves the Tc 4+ ion, also 4d-t 3 2g . 34 In this case, it was argued from a first principles calculation that most of the moment reduction arises from 4d/ligand covalency. 35,36 Nonetheless, very recently, it has been argued that SO coupling does play a major role in the magnetism of 4d 3 and 5d 3 perovskites in that a coupling scheme intermediate between L -S and j -j is required for a description of such a configuration. 37 So, the role of SO coupling in 4d 3 and 5d 3 perovskite magnetic materials appears to be unsettled, at least regarding ordered moment reduction, at present.

B. Neutron Order Parameter Measurements

We first discuss our elastic neutron scattering results derived from time-of-flight measurements, as shown in Fig. 6. Measurements on Ba 2 YOsO 6 with the incident energy E i = 40 meV, and integrated over the elastic position [-1,1] meV, show magnetic Bragg peaks at |Q| = 0.75 Å-1 and |Q| = 1.06 Å-1 , corresponding to the [100] and [110] magnetic Bragg reflections, respectively (Fig. 6). Their temperature-independent and resolutionlimited widths in |Q| stands as a clear signature of a 3D long range magnetic order, consistent with the type-I ordering of the FCC lattice near T N ∼ 69 K, as observed from the C2 powder diffraction data presented above.

Additional elastic scattering measurements at the [100] position, with enhanced temperature stability and muchfiner temperature steps, were performed with the N5 triple-axis spectrometer at the CNBC, as shown in Fig. 7. The temperature of the sample was carefully equilibrated and stabilized to ± 0.005 K, and these measurements focused on the temperature dependence of the elastic magnetic intensity at the [100] position. The resulting order parameter, taken on both warming and cooling, for Ba 2 YOsO 6 is shown in Fig. 7a. These measurements show a small but clear discontinuity in the temperature dependence of the order parameter at T c,2 = 67.45 K, both on warming and cooling, indicative of a weak firstorder transition below T N . The same data is plotted on a log-log scale in the reduced temperature, (1 -T /T N ) with T N =69.65 K, in Fig. 7b. A weak discontinuity in the shape of the order parameter manifests itself as a small change in the critical exponent β estimated using data above and below T c,2 . This is in contrast with Fisher heat capacity and neutron data reported above, which could only single out a unique transition around T ∼ 69 K, but this could be due to the proximity of the two transition temperatures and the relative smallness of the discontinuity.

The critical behaviour of the order parameter was fit using data above and below T c,2 , within the temperature ranges [59.4 K, 67.4 K] and [67.5 K, 69.2 K], to a standard power-law function:

I = A T N -T T N 2βi + I b ( 2
)
with T N = 69.65 K and I b = 240 as determined from a linear fit to the background intensity between 80 and 90 K, where the contribution from critical fluctuations is minimal. The two critical exponents are found to be β 1 = 0.30(3) for T N > T > T c,2 and β 2 = 0.327(9) for T < T c,2 .

Both of these are consistent with 3D universality, and only β 1 = 0.30(3) for T N > T > T c,2 is meaningful as a critical exponent. Nonetheless, all of this critical and critical-like behaviour is consistent with a weakly first order transition at T c,2 = 67.45 K, just below T N , and the presence of two different, ordered magnetic phases.

C. Time-of-flight neutron spectroscopy and spin gap determination

We now turn to the description of our inelastic time-offlight neutron measurements. The temperature variation of the neutron scattering intensity S(|Q|, E) is shown in Fig. 8. The incident energy employed in these measurements, 120 meV, is high enough to allow an accessible region of (|Q|, E) space sufficient for the observation of the full spin bandwidth, while being low enough such that the energy resolution of the measurement is suitable to access the inelastic gap. For T ≥ 70 K, the spins are a paramagnetic regime and we observe a quasi-elastic scattering mainly located at the [100] position (Fig. 8,ab). As the temperature drops below T N , a clear gap of ∼ 17 meV opens and separates the elastic (off-scale) intensity from the inelastic magnetic scattering, with a bandwidth presumably arising from the dispersion of the spin waves (c-f) within the ordered state.

In order to better characterize the formation of the spin gap, we take different energy and wave-vector integrated cuts through both this dataset and the corresponding inelastic scattering dataset performed using E i = 40 meV. The energy dependence of the low |Q|integrated scattering (|Q| = [0.5, 1.5] Å-1 ), mainly of magnetic origin, is shown in Fig. 9a for different temperatures. Upon cooling below 70 K, intensity within the gap region 7 < E < 12 meV is depleted and transferred , at least in part, to higher energies where it contributes to the gapped and dispersive inelastic spin excitation. To quantify this, we fit the inelastic scattering at T = 1.8 K in Fig. 9a to two Gaussians functions, one centered at each of the elastic and inelastic positions, along with a linear background to account for any weak inelastic background scattering, originating from, for example, phonons. The inelastic excitation is characterized by a spin gap ∆ = 18(2) meV and a bandwidth of 15(5) meV, respectively defined by the center and the FWHM of the appropriate Gaussian. The temperature evolution of the spin gap can also be followed from the |Q| dependence of the E-integrated scattering within the gap (E = [6, 8] meV), measured with E i = 40 meV in order to obtain higher energy-resolution (∆E = 2.4 meV) (Fig. 9b). The low-T dataset at 1.8 K offers an appropriate background subtraction, since minimal scattering is expected inside the gap. As the temperature is increased, we observed the progressive filling of the gap a build-up of intensity near the [100] region. The broad and asymmetrical lineshape observed in (Fig. 9b) is attributed to the presence of scattering coming up from the [110] position, less intense than that near [100] due to the appropriate structure factor and to its higher |Q| value.

With the background within the spin gap estimated us- ing our base temperature data at T = 1.8 K, we now examine the dynamical susceptibility χ ′′ (|Q|, E), and eliminate the effect of the thermal Bose factor in the temperature dependence of the spin dynamics within the gap. We then obtain ∆S(|Q|, E), which is related to χ ′′ (|Q|, E) through:

∆S(|Q|, E) = χ ′′ (|Q|, E) 1 -e -E/kBT . (3)
The temperature behaviour of χ ′′ (|Q|, E) can then be extracted from the E and Q integration of the scattering intensity of panels (a) and (b) in Fig. 9. The results, shown in panel (c), are in very good agreement and attest of the consistency of the measurements performed at two different incident energies. Below T N , the dynamic susceptibility shows an exponential behaviour, χ ′′ (T ) ∝ exp(-∆/k B T ), consistent with a thermally activated excitation (red line, Fig. 9c). The spin gap extracted from this temperature dependence, ∆ = 16(2) meV, is in good agreement with that previously estimated from the energy cut of panel (a).

IV. SUMMARY AND CONCLUSIONS

The 5d 3 based double perovskite, Ba 2 YOsO 6 , has been prepared and characterized using a variety of methods including neutron and x-ray diffraction, 89 Y NMR, magnetization and inelastic neutron scattering. To within the resolution of the elastic neutron diffraction data, the F m3m space group is found for the entire temperature range to 3.5 K. The level of B/B ′ anti-site disorder is below the level of detection from 89 Y NMR studies (< 0.5 %). The material exhibits a strong antiferromagnetic Curie-Weiss constant, and magnetic frustration as characterized by a large frustration index, f ∼ 11. Nonetheless, it displays at least one, and likely two phase transitions to ordered states resembling a Type I FCC antiferromagnetic ordered state below 70 K. While there is no obvious evidence from the Fisher heat capacity of two ordering temperatures, high resolution triple-axis elastic neutron scattering shows evidence for two transitions; a continuous one at T N = 69.65 K and a weakly first-order one at T c,2 = 67.45 K. Superficially, this appears to resemble the situation reported for two other d 3 double perovskites, Ba 2 YRuO 6 17 and Sr 2 YRuO 6 , 18 for which two ordering temperature scales were also observed at 36K and 47K and 24K and 32K, respectively. However, in the case of Ba 2 YRuO 6 evidence for a continuous transition and a heat capacity anomaly were seen only at the lower temperature, 36K. For Sr 2 YRuO 6 , while two heat capacity anomalies are reported, a continuous transition is claimed only for 24K while the region up to 36K is dominated by short range spin correlations. Thus, the observations presented here for Ba 2 YOsO 6 are unique to this material.

The low temperature ordered moment at the 5d 3 Os 5+ site is 1.65(5) µ B , much smaller than the spin only value of ∼ 3 µ B . It can be compared with low temperature ordered moments found in other d 3 configuration ions in perovskite structures, such as La 0.5 Pr 0.5 CrO 3 (2.50(5) µ B ) and Ba 2 YRuO 6 (2.2 µ B ). Such a sequence of ordered moment reduction from 3d 3 to 4d 3 to 5d 3 configuration suggests a strong quenching of the ordered moment from a combination of SO coupling and transition metal-ligand covalency. Additional measurements, such as X-ray magnetic circular dichroism (XMCD) experiments, 39 could confirm the importance of SO interaction in the double perovskites systems Ba 2 YRuO 6 and Ba 2 YOsO 6 . Moreover, oxygen K-edge XMCD could bring further information on the hybridization between Os-5d and O-2p electrons.

A large spin gap, ∼ 17 meV, is observed in the inelastic neutron scattering in 5d 3 Ba 2 YOsO 6 which can be compared with a spin gap of ∼ 5 meV in 4d 3 Ba 2 YRuO 6 . As no spin gap is expected for the orbitally quenched t 3 2g configuration, it is attributed to the effects of SO coupling. Indeed the ratio of the spin gaps for the 5d 3 osmate and the 4d 3 ruthanate is 17/5 = 3.4, essentially the same as the ratio of the free ion SO coupling constants for Os 5+ and Ru 5+ , 186/55 ∼ 3.4, 33 making a strong case for attributing the origin and magnitude of the spin gap to spin-orbit coupling.

Recently, the low temperature properties of 5d 3 distorted (monoclinic) double perovskite La 2 NaOsO 6 was investigated with inelastic neutron scattering and µSR. 40 This system fails to display long range magnetic order at any temperature, presumably a consequence of its lowerthan-cubic symmetry. Below a spin freezing temperature of T f = 6 K, the spins of this system enter into a static short-range incommensurate order and a spin gap never fully develops. These results bear some similarities with the orthorhombic 5d 3 double perovskite Li 3 Mg 2 OsO 6 , 41 which also shows a frozen, short-range ordered groundstate, whereas the Ru analog orders at 17 K. 42 It would seem that the highly symmetrical FCC structure is a requirement for long-range magnetic order which in turn is key to the formation of the spin gap, perhaps via anisotropic exchange. Both Ba 2 YOsO 6 and Ba 2 YRuO 6 display a spin gap which forms as their magnetically or-dered states form, below their appropriate T N .

The combination of geometric frustration and SO coupling is a relatively unexplored arena in correlated electron physics. 5d magnetism based on iridates has been of recent interest, but other 4 and 5d systems involving osmates and ruthanates offer complex and exotic ground states, and are better suited to techniques such as neutron scattering. Many related double perovskite structures can be stabilized, at least a subset of which display undistorted FCC lattices at low temperatures. We anticipate that further basic and advanced characterization of these ground states will yield exciting new physics, as has already been predicted, for example, in 5d 1 and 5d 2 systems. 43,44

FIG. 1 .

 1 FIG. 1. (Color online) Left: Representation of the double perovskite structure of Ba2YOsO6 emphasizing the octahedral environment of Os 5+ . Right: The magnetic Os 5+ ions form a frustrated FCC sublattice made of edge-sharing tetrahedra.

FIG. 2 .

 2 FIG. 2. (Color online) Room temperature powder neutron diffraction patterns of Ba2YOsO6 recorded at 2.37 Å (a) and 1.33 Å (b). The 3.5 K neutron diffraction patterns at 2.37 Å (c) and at 1.33 Å (d) which shows that there is no structural change from 290 K. Tick marks represent Ba2YOsO6, Y2O3 (∼ 1% in mass), Ba11Os4O24 (∼ 5% in mass), and the magnetic phase of Ba2YOsO6 (c) respectively.

FIG. 4 .

 4 FIG. 4. (Color online) (a)The temperature dependence of the inverse magnetic susceptibility of Ba2YOsO6 at 0.05 T and the field dependence of magnetization at 2 K (inset). The red line is a Curie-Weiss fit, performed for 150 < T < 300 K. (b) Fisher heat capacity of Ba2YOsO6. A single peak is observable at 68.5 K, unlike the case of Ba2YRuO6. The inset is a zoom near the transition.

FIG. 5 .

 5 FIG. 5. (Color online) Neutron diffraction patterns onBa2YOsO6 collected at 3.5 and 75 K and type I fcc antiferromagnetic magnetic structure (inset). The magnetic reflections are indexed with a propagation vector k = (1, 0, 0). The broad peak at the (100) magnetic reflection position indicates short-range magnetic correlations at 75 K. Red line is a structural and magnetic refinements of the diffraction pattern observed at 3.5 K (grey circles). The overfitting of the (120) and (211) magnetic reflections is ascribed to inaccuracies in the Os 5+ form factor.

FIG. 6 .

 6 FIG. 6. (Color online) Temperature dependence of the elastic neutron scattering intensity in Ba2YOsO6, for Ei = 40 meV, integrated over the energy range [-1, 1] meV. A long range order is observed below 70 K, with magnetic Bragg peaks at the [100] (|Q| = 0.75 Å-1 ) and [110] (|Q| = 1.06 Å-1 ) positions. A high temperature background dataset (150 K) has been subtracted from each data to isolate the magnetic contribution.

FIG. 7 .

 7 FIG. 7. (Color online) (a) Temperature dependence of the [100] intensity from the N5 data (upon warming and upon cooling), showing a discontinuity at Tc,2 = 67.45 K. Inset: zoom near Tc,2 (red arrow). (b) Blue and orange lines are fits to standard power-law to extract the critical behaviour (see text).

FIG. 8 .

 8 FIG. 8. (Color online) (a)-(f) Evolution of the neutron scattering intensity S(|Q|, E) across the magnetic transition at TN ∼ 69 K. The background intensity of the sample cell has been subtracted off. Below 70 K, a spin gap ∆ is progressively opening, finally reaching a ∼ 17 meV value at 20 K and below. The upper intensity scale refers to (a) and (b) only, while the lower intensity scale refers to (c) to (f), highlighting the opening of the gap.

1 FIG. 9 .

 19 FIG. 9. (Color online) (a) Energy cuts of Fig.8, integrated over Q = [0.5, 1.5] Å-1 , and showing the formation of the spin gap ∆. The red line is a fit of the 1.8 K data to two-Gaussians centered on elastic and inelastic positions, resulting in a spin gap value of ∆ = 18(2) meV and a spin wave bandwidth above the gap of 15(5) meV. (b) Q cuts of the scattered intensity measured with an incident energy Ei = 40 meV, integrated over E = [6, 8] meV, i.e. in the inelastic regime, within the gap. The low T dataset (1.8 K) has been subtracted as a background, and the plot shows the magnetic spectral weight filling the gap as the temperature is increased. Tick marks show the [100] and [110] positions. (c) T -evolution of χ ′′ (|Q|, E), extracted from the data of panels (a) and (b) (see text), normalized by their respective plateau value above T = 70 K. Below 70 K, the intensity decreases exponentially (red line), allowing us to estimate ∆ = 16(2) meV from this activated temperature dependence.

  YOsO 6 since the Ba 11 Os 4 O 24 impurity orders magnetically at temperatures lower than, and distinct from, those relevant to ordering in Ba 2 YOsO 6 , i.e. 6.8 K.26

	• C for 1.5
	hours in a Pt crucible with one regrinding after 30 min-
	utes. The precursor material, Ba 4 Y 2 O 7 , was prepared
	from stoichiometric amounts of BaCO 3 and Y 2 O 3 fired
	at 1000 • C in air for 24 hrs. Characterization by x-
	ray powder diffraction indicated a single phase sam-
	ple, whereas powder neutron diffraction revealed small
	amounts of the weak ferromagnetic impurity Ba 11 Os 4 O 24
	(∼ 5% in mass) and of the non-magnetic Y 2 O 3 (∼ 1% in
	mass). This does not interfere with our measurements on
	Ba 2

TABLE I .

 I Neutron diffraction refinement results of Ba2YOsO6 at 290 K. The refinement was done simultaneously with two wavelengths, 2.37 Å and 1.33 Å. The results provided for the 1.33 Å are reported in { } beside the 2.37 Å results and the 3.5 K refinement results are reported in [ ] below the 290 K data. RBragg = 1.93 {3.26}; RF = 1.41 {1.97}; χ 2 = 6.32 {10.0} RBragg = 2.06 {2.63}; RF = 1.30 {1.66}; χ 2 = 7.04 {14.1}

	Atoms	x	y	z	Biso ( Å2 )
	Ba	0.25	0.25	0.25	0.40(5)
					[0.01(5)]
	Y	0.50	0.50	0.50	0.38(9)
					[0.12(8)]
	Os	0	0	0	0.20
					[0.15]
	O	0.235(2)	0	0	0.64(4)
		[0.235(2)]			[0.29(4)]
			a0 = 8.3541(4) Å a0 = 8.3435(4) Å

V. ACKNOWLEDGEMENTS

We acknowledge useful discussions with J. P. Clancy and thank J. P. Carlo for sharing information on ex-perimental setup. SEQUOIA data were reduced using Mantid 45 and the DAVE software package 46 was used for data analysis. Research at Oak Ridge National Laboratory's Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. S.K. acknowledges the Canada Foundation for Innovation and Manitoba Research Innovation Fund for infrastructure support. S.K., J.E.G. and B.D.G. thanks the NSERC of Canada for operating funds via a Discovery Grant.


L Clark

G J Nilsen

E Kermarrec

G Ehlers

K S Knight

A Harrison

J P Attfield

B D Gaulin

From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores

Keywords: numbers: 75.10.Kt, 75.40.Cx, 75.50.Lk

We present new magnetic heat capacity and neutron scattering results for two magnetically frustrated molybdate pyrochlores: S = 1 oxide Lu2Mo2O7 and S = 1 2 oxynitride Lu2Mo2O5N2. Lu2Mo2O7 undergoes a transition to an unconventional spin glass ground state at T f ∼ 16 K. However, the preparation of the corresponding oxynitride tunes the nature of the ground state from spin glass to quantum spin liquid. The comparison of the static and dynamic spin correlations within the oxide and oxynitride phases presented here reveals the crucial role played by quantum fluctuations in the selection of a ground state. Furthermore, we estimate an upper limit for a gap in the spin excitation spectrum of the quantum spin liquid state of the oxynitride of ∆ ∼ 0.05 meV or ∆ |θ| ∼ 0.004, in units of its antiferromagnetic Weiss constant θ ∼ -121 K.

Geometric magnetic frustration arises when the arrangement of magnetic moments on an ordered lattice prevents the simultaneous satisfaction of each pair-wise magnetic exchange interaction [1]. This can generate a macroscopic ground state degeneracy, whereby the the spins on the vertices of the frustrated lattice fluctuate within a manifold of non-ordered states. In materials that possess both strong geometric frustration and quantum (S = 1 2 ) magnetic moments, quantum fluctuations can induce a quantum spin liquid (QSL) ground state [2], [3] and allow the system to remain dynamic and avoid any symmetry breaking phase transition, even in the thermodynamic limit of T = 0 K. There are now several promising experimental realisations of materials that host this exotic QSL state in two-dimensional frustrated lattices [4], [5], [6], [7], [8]. However, examples of three-dimensional QSL candidates, such as a S = 1 2 pyrochlore antiferromagnet that possesses a frustrated magnetic lattice of corner sharing tetrahedra, remain scarce [9]. There is some uncertainty regarding the exact nature of the spin liquid ground state of a S = 1 2 pyrochlore antiferromagnet [10], [11], [12] and the synthesis and study of such new materials remain important tasks [13].

Magnetic frustration in the rare earth molybdate pyrochlores, R 2 Mo 2 O 7 , arises from exchange interactions between Mo 4+ 4d 1 S = 1 spins residing on a network of vertex sharing tetrahedra. Among the phenomena observed in these materials [14], the spin glass state in the apparently disorder free Y 2 Mo 2 O 7 is of particular interest [15], [16], [17], [18], [19]. As this state -a spin glass in the absence of any significant chemical or bond disorder -is very unusual, its realisation in a similarly simple material may be revealing. Lu 2 Mo 2 O 7 is a sister compound to Y 2 Mo 2 O 7 and exhibits strong antiferromagnetic exchange, with the Weiss constant θ = -160 K, as well as a spin freezing transition at T f ∼ 16 K [20]. These parameters are remarkably close to the θ ∼ -200 K and

T f ∼ 22 K displayed by Y 2 Mo 2 O 7 .
A group of materials related to the R 2 Mo 2 O 7 pyrochlores are the corresponding oxynitride phases. Oxynitrides are mixed anion materials that are often prepared by a direct nitridation of an oxide precursor. In the case of the molybdate pyrochlores, this means that the cubic pyrochlore structure is retained. The incorporation of the nitride (N 3-) anion into the oxide (O Polycrystalline Lu 2 Mo 2 O 7 was synthesised as described elsewhere [20]. An oxynitride phase with a composition close to the ideal S = 1 2 Lu 2 Mo 2 O 5 N 2 stoichiometry was prepared by thermal ammonolysis of a Lu 2 Mo 2 O 7 precursor. As shown in the Supplemental Material (SM), Rietveld refinement of the F d 3m cubic pyrochlore model to powder neutron diffraction data confirms that the oxynitride adopts this structure with oxide and nitride anions disordered over the two available anion sites. Magnetic susceptibility data for the oxynitride (see SM) reveal an absence of long range order or spin freezing transitions down to 2 K despite the large antiferromagnetic θ = -121(1) K. The small effective 2 ). The 64 % reduction of the observed µ ef f from the expected spin-only value for S = 1 2 is consistent with the 67 % reduction from the expected S = 1 spin-only moment displayed by Lu 2 Mo 2 O 7 [20]. This suggests that the spin-orbit coupling interaction is significant in both of these 4d systems.

The heat capacity of Lu 2 Mo 2 O 7 was measured on a 9.0 mg pressed powder pellet in a Quantum Design PPMS. In an attempt to estimate the lattice contribution to the total heat capacity, the high temperature data were modelled by the Debye equation. The fit to the data, which gave a Debye temperature θ D = 540 K, is shown in Fig. 1(a). Upon subtraction of the estimated lattice contribution, a broad hump centred ∼ 50 K is observed in the magnetic heat capacity C mag , typical of a spin glass system. The heat capacity of the oxynitride was measured on a 8.9 mg sample over the range 0.5 -30 K using a 3 He insert. Given the similar structure and formula weight of the oxide and oxynitride phases, the lattice contribution estimated for Lu 2 Mo 2 O 7 was also used to extract the magnetic heat capacity of the oxynitride. A comparison of the low temperature magnetic heat capacities of the oxide and oxynitride are shown in Fig. 1(b). The temperature dependencies are markedly different with C mag ∝ T 2 for the oxide and C mag ∝ T for the oxynitride.

Diffuse magnetic neutron diffraction was measured for the oxide and oxynitride pyrochlores on the D7 Diffuse Scattering Spectrometer at the Institut Laue-Langevin, France [22]. xyz polarisation analysis was used separate the components of total neutron scattering [23], [24]. In this way, the magnetic diffuse scattering that arises from disordered spin systems can be isolated from the strong nuclear Bragg scattering that dominates a typical neutron diffraction pattern [25]. Data were collected for both samples with an incident neutron wavelength λ = 4.8 Å, at which final neutron energies are integrated up to E ∼ 3.5 meV. A detailed experimental account, including a description of the absorption correction applied to the data is given in the SM. Fig. 2 shows the magnetic scattering cross sections (dσ/dΩ) mag of the oxide and oxynitride at 1.5 K, well below T f ∼ 16 K. The magnetic diffuse scattering from the oxide displays a broad peak centred around 0.6 Å-1 that indicates the presence of static short ranged molybdenum spin correlations. The data were modelled according to the expression [26],

dσ dΩ mag = 2 3 (γ n r 0 ) 2 1 2 gF (Q) 2 × S(S + 1) + i Z i S 0 •S i sinQr i Qr i (1)
where S 0 •S i gives the correlation between a spin and its Z i nearest neighbours at a distance r i . γ n is the neutron gyromagnetic ratio, r 0 is the classical radius of the electron, g is the g-factor and F (Q) is the molybdenum form factor [START_REF] Brown | International tables for crystallography[END_REF]. The best fit to the data, shown as a black solid line in Fig. 2, was obtained by allowing for nearest-(r 1 = 3.581 Å, Z 1 = 6) and nextnearest-neighbour (r 2 = 6.203 Å, Z 2 = 12) correlations S 0 •S 1 = -0.029 (6) and S 0 •S 2 = -0.056 (7), respectively. Adding further exchange correlations did not improve the quality of the fit significantly. The negative sign of the spin correlations confirms their antiferromagnetic nature. In contrast, the magnetic diffuse scattering of the oxynitride at 1.5 K is much weaker than that of the oxide and appears to follow F (Q) 2 . These data were thus modelled using Equation 1 with S 0 •S i = 0 for all i [START_REF] Wills | [END_REF]. The fit is shown as the solid line against the oxynitride data in Fig. 2. The effective magnetic moment extracted from the fit to the data, 0.11(1) µ B , corresponds to only 6 % of the expected S = 1 2 spin-only value, suggesting that most of the scattering from the oxynitride is inelastic and thus outside the energy range over which D7 integrates scattered neutron energies [25].

In order to probe their full static and dynamic behaviour, both the oxide and oxynitride pyrochlores were studied on the Cold Neutron Chopper Spectrometer (CNCS) [29] at the Spallation Neutron Source of the Oak Ridge National Laboratory. Measurements on both samples were performed on cooling to 1.5 K with an incident neutron energy E i = 3.3 meV. The inset of Fig. 2 shows the Q-dependence of the elastic scattering from the oxide and oxynitride at 1.5 K, obtained by integrating the inelastic spectra over the energy of the elastic line, E = [-0.1, 0.1] meV. A broad peak at low Q is observed for the oxide, which can again be modelled by FIG. 2. The magnetic scattering cross sections of the oxide and oxynitride obtained from xyz polarization analysis of data measured on the D7 spectrometer at 1.5 K. The solid lines are fits to the data described in the text. For comparison, the inset shows the Q-dependence of elastic magnetic scattering measured on CNCS at the same temperature. A scaled version of the spin correlation model fitted to the CNCS oxide data is shown on top of the D7 magnetic scattering cross section (dashed line).

Equation 1. To confirm the consistency of the analyses of the CNCS and D7 data sets, a scaled version of the fit to the CNCS data is plotted with the D7 fit in the main panel of Fig. 2; agreement is excellent. Remarkably, the scattering collected for the oxynitride at 1.5 K within the narrowly defined elastic window on CNCS is consistent with no elastic magnetic scattering, as shown in the inset to Fig. 2.

The temperature dependencies of the background corrected, normalised and Q-integrated (Q = [0.5, 2.0] Å-1 ) inelastic scattering for the oxide and oxynitride are shown in the top panels of Figs. 3(a) and 3(b), respectively. The oxide (Fig. 3(a)) presents a rather broad frequency spectrum at higher temperatures, T > 50 K, well above the spin freezing transition. Upon cooling, low energy spin fluctuations develop and sharpen in frequency approaching the spin freezing transition. The transition is clearly marked by a collapse of inelastic scattering intensity into the elastic line as short range spin correlations build up and give rise to elastic intensity in the diffuse magnetic scattering peak at 0.6 Å-1 . In order to obtain a more quantitative understanding of the inelastic scattering data, energy cuts were fitted to the general form of the scattering function [17],

S(E) = 1 π χ (E)[1 + n(E)] (2)
where n(E) is the Bose-Einstein thermal population factor and χ is the imaginary part of the dynamic suscepti-bility. A good phenomenological description of the data was obtained with,

χ (E) = χ 0 arctan E Γ ( 3
)
where Γ is related to the frequency width of the inelastic spectrum. Fits to the data are shown in the SM. The bottom panel of Fig. 3(a) shows the temperature dependence of Γ for the oxide, which goes to zero at or near T f ∼ 16 K, consistent with spin glass freezing. The overall dynamic behavior of Lu 2 Mo 2 O 7 is thus very similar to that of its sister "disorder free" spin glass pyrochlore Y 2 Mo 2 O 7 [17]. Again in rather stark contrast, the oxynitride displays a temperature-independent energy width of Γ ∼ 0.08 meV, consistent with that of Lu 2 Mo 2 O 7 near 30 K, almost twice T f (Fig. 3(b)). Therefore the temperature dependence observed in S(E) for the oxynitride originates entirely from the Bose-Einstein factor in Equation 2. Fig. 4 directly compares the inelastic scattering integrated over Q = [0.5, 2.0] Å-1 from the oxide and oxynitride samples at 1.5 K. Given that the inelastic scattering from Lu 2 Mo 2 O 7 is strongly suppressed below the spin freezing transition, the scattering from the oxide at 1.5 K is a good measure of the background. The oxynitride sample thus clearly shows an enhanced inelastic signal on either side of the elastic line. The persistence of inelastic scattering, particularly on the neutron energy gain side where the incident neutron destroys a spin fluctuation, directly demonstrates that the oxynitride remains strongly fluctuating at 1.5 ∼ |θ|/100 K. By subtracting the 1.5 K oxide data from the oxynitride data and integrating in energy (E = [0.2, 1.5] meV) the Q-dependence of the inelastic scattering from the oxynitride is obtained (see Fig. 4, inset). The form of this inelastic scattering reveals the nature of dynamical spin correlations within the oxynitride. The Q-dependence is well described by the magnetic form factor, F (Q) 2 . Taken together, the inelastic magnetic scattering from Lu 2 Mo 2 O 5 N 2 strongly suggests a gapless QSL state at 1.5 K, with few or no structured spatial correlations between the S = 1 2 spins. Our study of Lu 2 Mo 2 O 7 and Lu 2 Mo 2 O 5 N 2 present both interesting similarities and contrasts. They share the same cubic pyrochlore structure and their magnetic interactions are antiferromagnetic and of similar strength. Yet the S = 1 Lu 2 Mo 2 O 7 displays an unconventional spin glass state below T f ∼ 16 K, while the S = the oxides and C mag ∝ T for the oxynitride. Quadratic temperature dependencies of heat capacity have been reported in a number of quasi-two-dimensional geometrically frustrated magnets with spin glass ground states, such as SCGO [30] and the jarosites [31]. For Y 2 Mo 2 O 7 [19] it was argued that this unusual temperature dependence arises from the coupling between spin and orbital degrees of freedom [32]. Linear temperature dependencies have been observed in a number of QSL candidate materials [7], [33], [34], where it provides an upper limit for any gap, ∆, in the spin excitation spectrum. In the case of the oxynitride, Lu 2 Mo 2 O 5 N 2 , this is ∆ ∼ 0.5 K ∼ 0.05 meV. Neutron spectroscopic data for the oxynitride (Figs. 3(b) and4) set the upper limit for a gap at ∼ 0.1 meV.

We finally turn to the relationship between the ground states of Lu 2 Mo 2 O 7 and Y 2 Mo 2 O 7 . The ionic radius of Lu 3+ is ∼ 4 % smaller than that of Y 3+ [35], yet both oxides are"disorder free" spin glasses with similar T f , 16 K and 22 K, respectively. It is intriguing that a second pyrochlore antiferromagnet with a single magnetic site displays such a similar spin glass ground state. If weak disorder is responsible for this state, it would imply that this disorder is very similar in the two materials -a conclusion which is not obvious based on their ionic radii. Short range spin correlations within these two spin glass ground states are similar but distinct: Y 2 Mo 2 O 7 To conclude, we observe a new realisation of an unconventional spin glass state in the S = 1 molybdate oxide, Lu 2 Mo 2 O 7 with T f ∼ 16 K. This state is similar to that shown by its sister compound Y 2 Mo 2 O 7 , although with shorter range static correlations peaked at Q = 0.6 Å-1 in the magnetic scattering cross section. The incorporation of the nitride anion into the oxide precursor tunes

S = 1 to S = 1 2 in Lu 2 Mo 2 O 5 N 2 .
In contrast to the oxide, no evidence for any transition to a frozen or ordered state is observed to ∼ 0.5 K and no elastic magnetic scattering is observed at temperatures as low as 1.5 K. The strength of the quantum fluctuations induced by the the reduction of S in the oxynitride overcomes any competition with disorder in the selection of a ground state and gives rise to a QSL, with an upper bound on a gap in the spin excitation spectrum of ∆ ∼ 0.05 meV ∼ 0.5 K or ∆ |θ| ∼ 0.004. This study also demonstrates the potential of nitriding oxide precursors as a means of tuning the oxidation state on magnetic ions, and therefore the spin degree of freedom and strength of quantum fluctuations. This is a relatively unexplored route to exotic magnetic ground states, but one with the potential to be very rewarding.

SUPPLEMENTAL MATERIAL SAMPLE PREPARATION AND CHARACTERISATION

The oxynitride pyrochlore phase presented here was prepared by heat treatment of Lu 2 Mo 2 O 7 in ammonia gas at 600 • C for 24 hours with a gas flow rate of 250 cm 3 min -1 . 3 g of oxide was nitrided per run spread over a surface area of 15 cm 2 in an alumina crucible to give a single phase oxynitride product. Thermogravimetric and elemental analyses gave an average composition of Lu 2 Mo 2 O 4.8 N 1.7 . Powder neutron diffraction data were collected for the oxynitride sample on the High Resolution Powder Diffractometer (HRPD) at the ISIS spallation neutron source, Rutherford Appleton Laboratory, UK. 3 g of sample was packed into a 6 mm outer-diameter vanadium can and loaded into a He cryostat. Diffraction data were collected at 4 K with a data collection time of 20 hours. The cubic F d 3m model was refined to the data collected on the backscattering and 90 • detector banks simultaneously using the GSAS software package [START_REF] Larson | Los Alamos National Laboratory Report No[END_REF]. The total anion content was constrained to the analytically determined values whilst allowing the oxide and nitride occupancies to refine over both anion sites. Isotropic thermal parameters were constrained together for cations and anions in order to minimise correlation effects. A plot of the fit to the 90 • data set is shown in Fig. 5 and the results of the refinement are summarised in Table I. The DC magnetic susceptibility of the oxynitride was measured in an applied field of 1 T from 2 K to 300 K in a zero field cooled (ZFC) field cooled (FC) cycle in a Quantum Design SQUID magnetometer. The magnetic and inverse susceptibilities of the oxynitride are shown in Fig. 6. The effective magnetic moment and Weiss constant extracted from the Curie Weiss fit depend on the temperature range over which the fit is applied. A similar temperature dependence is observed for the Curie Weiss fit to the inverse magnetic susceptibility of Lu 2 Mo 2 O 7 [20]. These results are summarised in Table II. There is no evidence of the spin freezing transition in the magnetic susceptibility that is observed for the oxide precursor at 16 K [20].

D7 MEASUREMENTS

The oxide and oxynitride samples, both with a mass of 18 g, were packed individually into 2 cm outer-diameter aluminium cans with an annular geometry, in order to minimise beam attenuation from the samples. Calibration measurements of quartz, cadmium and vanadium standards allowed for the determination of the magnetic scattering cross sections of the samples in absolute units of barns st. -1 per formula unit. The transmission of the oxide sample at λ = 4.8 Å was determined by measuring the monitor counts of the direct beam through the sam-FIG. 7. The transmission factor for an annular cylindrical powder sample as a function of scattering angle taken from ref. [37], which was fitted by a third order polynomial function in sin 2 θ (red solid line).

ple (C S ) with the monitor counts of the beam through the empty can (C E ), normalised by the counts measured for a cadmium standard (C Cd ), which account for any neutrons that do not pass through the sample. Each of these monitor count measurements were taken for a total of 120 s, such that the sample transmission is given by,

T = C S -C Cd C E -C Cd = 5015 -70 10224 -70 = 0.49 (4)
which reveals a significant attenuation of the neutron beam. As a result, the magnetic scattering cross sections of the oxide and oxynitride have been corrected for absorption. For a powder sample in an annular cylindrical geometry the attenuation of the incident neutron depends on two factors, µR and ρ, where µ is the linear attenuation coefficient, R is the outer radius of the annulus and ρ is the ratio between the radii of the inner and outer cylinders in the annulus. For Lu 2 Mo 2 O 7 , µ ∼ 0.8 due to the large absorption cross section of lutetium [38], and with inner and outer annulus radii of approximately 0.5 cm and 1.0 cm, respectively, µR ∼ 0.8 and ρ ∼ 0.5. The transmission factors for an annular cylindrical sample have been calculated elsewhere [37] and are plotted in Fig. 7 as a function of sin 2 θ for µR and ρ values consistent with our experiment. The angular dependence of the transmission factor follows a third order polynomial function in sin 2 θ [39]. A fit of this form to the calculated sample transmission (Fig. 7) was performed to extract this angular dependence and was used to correct the data as a function of Q. A comparison of the magnetic scattering cross section of Lu 2 Mo 2 O 7 before and after the absorption correction is shown in Fig. 8.

CNCS MEASUREMENTS

For the collection of inelastic neutron spectra on the Cold Neutron Chopper Spectrometer (CNCS) the same 18 g samples used in the D7 experiment were loaded into annular aluminium sample cans, in the same fashion that was employed in the diffuse scattering experiment. Individual cuts in Q and E were taken using the DAVE software package [40]. E-cuts were taken by integrating background corrected data over the Q-range [0.5,2.0] Å-1 , which were modelled according to Equation 3 given in the main manuscript. Fig. 9 shows the fits to the data collected for the oxide and oxynitride at various temperatures.

FIG. 1 .

 1 FIG. 1. (a) The total heat capacity C of Lu2Mo2O7 as a function of temperature (open circles) with an estimation of the lattice contribution from a Debye fit to the high temperature data (dashed line). The magnetic heat capacity Cmag (closed circles) was obtained by substraction of this fit from the measured total. (b) The magnetic heat capacities of the oxide and oxynitride phases follow strikingly different behaviour at low temperatures.

1 2 2

 12 FIG. 3. The temperature dependence of background subtracted, normalised inelastic neutron scattering intensity integrated over Q = [0.5, 2.0] Å-1 (top) and the frequency width of the inelastic spectra, Γ, (bottom) for the (a) oxide and (b) oxynitride, respectively.

[ 17 ]

 17 displays a broad magnetic diffuse elastic scattering peak centred at 0.4 Å-1 , as compared with the peak at 0.6 Å-1 reported here for Lu 2 Mo 2 O 7 . The lower Q position of the peak of Y 2 Mo 2 O 7 indicates that its magnetic correlations have a longer ranged spatial extent. Indeed, those in Y 2 Mo 2 O 7 were found to form domains extending over an entire conventional unit cell, whereas the static magnetic correlations in Lu 2 Mo 2 O 7 are confined to a next-nearest-neighbour length scale, roughly half a unit cell.

FIG. 4 .

 4 FIG. 4. The energy cuts of the oxide and oxynitride neutron scattering spectra at 1.5 K, obtained by integrating over a range of Q = [0.5, 2.0] Å-1 . The inset shows the Qdependence of the background subtracted inelastic scattering from the oxynitride sample at the same temperature, to which an F (Q) 2 form was fitted (red solid line).

  Work at McMaster University was supported by NSERC of Canada. Work at the University of Edinburgh was supported by EPSRC and STFC. Research at Oak Ridge National Laboratory's Spallation Neutron Source was supported by the Scientific User Facilities Division, Office of Basic Energy Sciences, U. S. Department of Energy. LC gratefully acknowledges useful discussions with J. R. Stewart, C. Stock and M. A. de Vries and support from the University of Edinburgh.

FIG. 5 .

 5 FIG. 5. Rietveld refinement of the cubic F d 3m model to 4 K HRPD data. Bottom tick marks show the reflections for the oxynitride pyrochlore phase and top ticks mark a MoO2 impurity phase (∼4 %) that was present in the oxide precursor.

FIG. 6 .

 6 FIG.6. The magnetic and inverse susceptibility data of Lu2Mo2O5N2 with a Curie-Weiss fit to the high temperature inverse susceptibility shown by the white solid line. The inset shows the FC and ZFC magnetic susceptibilities in the low temperature region.

FIG. 8 .

 8 FIG.8. The magnetic scattering cross section of Lu2Mo2O7 measured at 1.5 K with an incident neutron wavelength λ = 4.8 Å before and after the angular dependent absorption correction for an annular cylindrical sample geometry.

  2-) framework is accompanied by oxidation of the molybdenum cations to maintain overall charge neutrality. Oxynitrides of composition R 2 Mo 2 O 5 N 2 possess S = 1 2 spins due to the Mo 5+ 4d 1 oxidation state and are thus excellent candidates for the study of QSL phenomena [21]. Here we present a comparison of Lu 2 Mo 2 O 7 and Lu 2 Mo 2 O 5 N 2 by way of low temperature heat capacity and neutron scattering studies.

TABLE I

 I

	. Refined atomic coordinates and occupancies for
	Lu2Mo2O4.8N1.7 (a = 10.1428(2) Å). Isotropic thermal pa-
	rameters were 0.0337(6) Å2 for metal cations and 0.0398(6)
	Å2 for anion sites. Total Rwp = 2.21 %, χ 2 = 14.58 for 64
	variables.
	Atom Site	x	y z Occupancy
	Lu 16d

TABLE II .

 II Results from the Curie Weiss fit to magnetic susceptibilities of the oxide and oxynitride pyrochlores.

	Sample	Fit region / K -θ / K µ ef f / µB
		150 -300	158(1) 1.89(1)
	Lu2Mo2O7	200 -300	171(1) 1.92(1)
		250 -300	184(2) 1.85(1)
		150 -300	121(1) 1.11(1)
	Lu2Mo2O5N2	200 -300	135(1) 1.13(1)
		250 -300	152(2) 1.16(1)