Spin correlations in the pyrochlore antiferromagnet Y2Ru2O7 with Curie-Weiss temperature ΘCW* - 1100 K and critical temperature TN = 77 K were examined through neutron scattering. For TN < T < ΘCW / 3 the data show spin relaxation with a rate ℎΓ = 1.17(9)kBT. For T<TN spectral weight moves to higher energies with substantial changes up to 4kBTN. For T << TN there is a Δ = 11(1) meV energy gap and a pronounced spectral maximum at 19.7 meV. Throughout the temperature range examined, the wave vector dependence of inelastic scattering exhibits a broad peak for Qd ≈ 3.8 (d is the Ru-Ru spacing) consistent with dipolar spin correlations

Broholm, C.

Cheong, S.-W.

Huang, Q.Z.

Hur, N.

Perring, T.G.

Qiu, Y.

Taylor, J. W.

van Duijn, J.

JScholarship

From cooperative paramagnetism to Néel order in Y2Ru2O7: Neutron scattering measurementsJ. van Duijn,1,2,3 N. Hur,4 J. W. Taylor,2 Y. Qiu,5 Q. Z. Huang,5 S.-W. Cheong,4 C. Broholm,1,5 and T. G. Perring21Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA2ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom3Departamento Química Inórganica I, Facultad de Ciencias Químicas, Unversidad Complutense de Madrid, Madrid, E-28040, Spain4Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University,Piscataway, New Jersey 08854, USA5NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USAReceived 17 July 2007; revised manuscript received 22 November 2007; published 10 January 2008Spin correlations in the pyrochlore antiferromagnet Y2Ru2O7 with Curie-Weiss temperatureCW*−1100 K and critical temperature TN=77 K were examined through neutron scattering. ForTNTCW /3 the data show spin relaxation with a rate =1.179kBT. For TTN spectral weight movesto higher energies with substantial changes up to 4kBTN. For TTN there is a =111 meV energy gap anda pronounced spectral maximum at 19.7 meV. Throughout the temperature range examined, the wave vectordependence of inelastic scattering exhibits a broad peak for Qd3.8 d is the Ru-Ru spacing consistent withdipolar spin correlations.DOI: 10.1103/PhysRevB.77.020405 PACS numbers: 76.50.g, 75.40.Gb, 75.50.EeIn the pyrochlore structure, with general formula A2B2O7,both the A trivalent rare earth ions and B tetravalent tran-sition metal ions site ions form a lattice of corner-sharingtetrahedra.1 Weakly connected and nonbipartite, this latticeproduces anomalous frustrated magnetism when populatedby spins with near-neighbor antiferromagnetic AFMinteractions.2 For classical spin vectors the lowest-energystates form a manifold characterized by zero magnetizationon every tetrahedron.3 Rather than Néel order for TCW,pyrochlore magnets remain disordered to much lower T,where the collective properties are governed by quantumfluctuations, thermal fluctuations, and subleadinginteractions.4–6 Examples of low-T states that have been re-ported are spin glasses,7 spin liquids,8,9 and magnetoelasti-cally induced Néel order.10,11Y2Ru2O7 is a Mott insulator with S=1 Ru4+ spinand a large negative Curie-Weiss temperature CW−1100 K.12–15 Specific heat and susceptibility data indicatea magnetic phase transition at TN=77 K.13,16,17 Diffractionmeasurements show that the transition is to a long-range-ordered LRO AFM q=0 structure.18 The total spin per tet-rahedron vanishes so this state is indeed a specific member ofthe low-energy AFM pyrochlore manifold. Here we report aneutron scattering experiment probing the anomalous spindynamics of Y2Ru2O7. The measurements reveal that AFMspin correlations are established at temperatures at least ashigh as 300 K and evolve little upon cooling. The spin re-laxation rate, however, decreases linearly in T according to=1.17kBT, consistent with proximity to quantum critical-ity. However, Néel order yields an 111 meV gap in theexcitation spectrum and moves spectral weight to a19.7 meV peak.A powder sample of Y2Ru2O7 was synthesized using thesolid state reaction method. A mixture of Y2O3 and RuO2 inproper molar ratio was prereacted at 850 °C for 15 h in airand then ground and pressed to pellets. The pellets weresintered at 1000–1200 °C in air with intermediate grindingsto improve homogeneity. Powder neutron diffraction datawere collected using the BT1 diffractometer at NIST.Rietveld analysis confirmed the cubic pyrochlore structureabove and below TN with space group Fd3̄m 227 and lat-tice parameter a=10.128 242 Å at T=10 K. The analysisalso revealed 0.0442 wt % unreacted Y2O3. Inelastic neu-tron scattering experiments were performed on the MARIspectrometer at the ISIS Facility and the DCS spectrometerat NIST. On MARI we used an incident energy Ei=150 meV for an elastic energy resolution of 3.5 meV. Thephonon contribution to the neutron scattering was subtractedby scaling the spectrum measured at high wave vectors,where the magnetic response is negligible, using the DISCUSpackage.19 This program uses a Monte Carlo methodto calculate a wave-vector-dependent scaling factor,which showed no significant energy dependence. For theDCS experiment we used 13.09 meV neutrons, which pro-duced an elastic energy resolution of 0.77 meV. For bothexperiments count rates were normalized using Y2Ru2O7Bragg peaks. This produced absolute measurements ofĨQ ,= 	r02  g /2FQ22S̃Q , to an overall scaleaccuracy of 20%. Here 	=−1.913 and g2 are gyromag-netic ratios for the neutron and Ru4+, respectively,r0=2.82 fm is the classical electron radius, and FQ is themagnetic form factor. Lacking specific information for Ru4+,we used the Ru+ form factor for model comparison.20S̃Q , is the spherically averaged dynamical correlationfunction.21The magnetic neutron scattering cross section forY2Ru2O7 powder is shown in Fig. 1 for T=15, 50, and 90 K.For TTN=77 K the spectra indicate short-range AFM cor-relations and a spin relaxation response with a relaxation ratekBT /. Upon cooling below TN, spectral weight movesto higher energies, with modifications up to 4kBTN. Figure 2shows that the wave vector dependence of the inelastic mag-netic scattering is all but unaffected by the comprehensiverearrangement of the excitation spectrum. Indeed the Q de-pendence of scattering changes little below room tempera-ture. These data are consistent with frustrated interactionsPHYSICAL REVIEW B 77, 020405R 2008RAPID COMMUNICATIONS1098-0121/2008/772/0204054 ©2008 The American Physical Society020405-1with an energy scale set by CW  *1100 K that establish alow-energy manifold of near-degenerate states with a char-acteristic interatomic “form factor.”22The Fourier transform of six collinear antiferromagneti-cally correlated spins on the vertexes of a hexagon provide areasonable account of the Q dependence of inelastic scatter-ing in ZnCr2O4 over a wide temperature range.22,23 We havecalculated a spherical average of this function for compari-son with the powder data in Fig. 2h dashed line. Theclose correspondence of the calculated peak width and posi-tion with the data indicates that antiferromagnetically corre-lated hexagons are also prevalent in Y2Ru2O7.A rigorous understanding of spin correlations in the pyro-chlore antiferromagnet is now emerging from theoreticalwork. For classical spins S→  , any spin configuration onthe pyrochlore lattice where all tetrahedra have zero net mo-ment is a ground state. Higher-order spin wave theory 1 /Sexpansion and the Schwinger-boson large-N expansionshow that quantum fluctuations favor states that maximizethe number of flippable spins. Henley argues that this leadsto selection of collinear spin configurations so the low-energy physics can be represented by an effective Isingmodel with a collective spin axis.4 The selected spin configu-rations are further characterized by a zero-divergence condi-tion for a polarization field defined on the dual diamondlattice of bonds. The effective Ising model favors AFMhexagons,24 which may account for their prevalence inZnCr2O4 and Y2Ru2O7. The corresponding spin correlationfunction SQ is, however, not the Fourier transform of afinite-size object as it has infinitely sharp features pinchpoints associated with the divergence-free condition.4,5 Isa-kov et al. derive an analytic expression for SQ from thelarge-N approximation, which accurately reproduces resultsfrom Monte Carlo simulations of the classical spin Heissen-berg model.5 The solid line in Figs. 2e–2h is the sphericalaverage of this expression multiplied by the squared Ru+form factor.20 The discrepancy at high Q may result fromresidual phonon contributions to the experimental dataand/or the ruthenium magnetic form factor employed in themodel calculation. With the overall amplitude as the soleadjustable parameter the large N result provides an excellentaccount of the data. Note though that the spherical averaginginherent to powder neutron scattering precludes insight onfiner details such as the predicted pinch points. Indeed, thereare substantial differences between SQ from the large-Nexpansion and SQ for antiferromagnetic hexagons. Single-crystal data will be needed to determine which is more ap-propriate for Y2Ru2O7. At elevated temperatures defectsshould appear in the form of monopoles4 that give rise to afinite divergence of the polarization field and broadening of504030201004030201004030201000.5 1 1.5 201020Ĩ(Q,ħω) (mb/Sr/meV/f.u.)ħω(meV)Q (Å )-150 K90 K15 KFIG. 1. Color online Normalized magnetic neutron scatteringintensity ĨQ , for a Y2Ru2O7 powder sample at T=90 top, 50middle, and 15 K bottom. Phonon scattering was subtracted asdescribed in the text. The elastic intensity is dominated by nuclearscattering.0 10 20 30 40010200 1 2 3ħω (meV)Ĩ(ħω)(mb/meV/f.u.)Q (Å )-1Ĩ(Q)(mb/Sr/f.u.)a eb fgQ [0.8, 1.4] Å-190 Kħω [12 ,22] meV01020450 Kc01020200 Khd0102001020010200102001020∈∈15 KFIG. 2. Color online Q integrated a–d and  integratede–h inelastic neutron scattering intensity of Y2Ru2O7 taken atT=200, 90, 50, and 15 K. Ranges of integration are indicated ineach column. The solid and dashed lines show fits to the datadescribed in the text. Lines in a and b account for the finitesampling of Q- space and partially resolved elastic scattering.Solid squares in h are normalized energy-integrated data fromDCS covering the energy range from 2 to 8 meV.VAN DUIJN et al. PHYSICAL REVIEW B 77, 020405R 2008RAPID COMMUNICATIONS020405-2pinch points,25 which again may not be detectable in powderdata. While the theory is not relevant for the ordered state,the close correspondence with the measurements here indi-cate similarities in local dynamic correlations across thephase transition.Although the Q dependence of the data does not changeappreciably below room temperatures Fig. 2 shows substan-tial changes in the fluctuation spectrum. Above TN the spec-tra are well described solid line in Figs. 2a and 2b bythe response function =0 / 2+2, which is re-lated to the neutron scattering spectrum through the fluctua-tion dissipation theorem.28 Factorization of the Q and  de-pendence of the cross section was assumed so characterizes the local response. The T dependence of therelaxation rate Fig. 3 is described by =CkBT whereC=1.179, allowing for a constant-0 term gives0=31 meV and C=0.81. Linear-in-T dependence of was previously found in simulation of classical Heisenbergspins with AFM interactions on a pyrochlore lattice.3 A spinfluctuation rate close to kBT was also observed in the frus-trated spinel systems ZnCr2O4 and LiV2O4.10,26For TTN a gap appears in the excitation spectra as spec-tral weight moves to higher energy Figs. 2c and 2d. AtT=15 K the neutron data indicate an energy gap=111 meV. This is significantly less than the 23 meVgap inferred from specific heat data, which may be domi-nated by activation of the modes associated with the19.7 meV peak.17 A gapped spectrum was confirmed by thenormalized higher-resolution DCS data which, integratedover energies from 2 to 8 meV, show no evidence of spinwaves emanating from the AFM Bragg peaks solid squaresin Fig. 2h as in ZnCr2O4.10 When a phase transition breaksa continuous symmetry, Goldstone’s theorem assures gaplessexcitations. The observation of a spin gap in Y2Ru2O7 is,however, consistent with both easy-plane and easy-axis an-isotropy. This is because easy planes in the pyrochlore struc-ture by symmetry are not parallel. Hence no global rotationcan maintain spins in easy planes.27Having examined both the high-T critical state and thelow-T ordered state, we focus on the transition between thesephases. Figure 4 compares the T dependence of the inelasticpeak position to the integrated intensity of the 111 Braggreflection. Apart from probing the staggered magnetizationsquared, the 111 reflection has a small nuclear componentand therefore does not vanish for TTN.18 The inelastic peakposition was obtained by fitting a damped harmonic oscilla-tor response28 to the 0.8Q1.4 Å−1 integrated part of theexcitation spectra. While the inelastic peak moves to lowerenergies upon heating see Fig. 4 it is important to note thata finite-energy peak persists for T=TN. This indicates thatshort-range dynamic correlations at TN are sufficient to main-tain a distinct spectral maximum in the excitation spectrum.The shift of spectral weight from a relaxation responsetowards higher energies implies that the energy of the spinsystem, Hs	, is reduced through the phase transition. Thiscan be quantified using normalized inelastic magnetic neu-tron scattering data and the first moment sum rule10,29Hs	 = −32201 − e−SQ,d1 − sin Qd/Qd. 1Here we consider only the isotropic nearest-neighbor inter-action between spins separated by a distance d. A more com-plete expression that includes anisotropy terms can readilybe derived28 but the quality of the present data do not war-rant the added complexity. Limiting the integral to 5 to30 meV and averaging data for 0.8Q1.4 Å−1, the tem-perature variation of the spin energy Hs	 relative to thevalue at T=90 K is shown as open circles in Fig. 4b. Thedata can be compared to the overall change in energyobtained from the magnetic specific heat,17 ET=0TCmTdT−0TmaxCmTdT, shown as a solid line inFig. 4b. While most of the variation in the thermal energyis accounted for by Hs	 and no structural changes haveħΓ(meV)T (K)0 100 200 300010203040FIG. 3. T dependence of the spin relaxation rate derived fromthe global fitting analysis described in the text. The solid line showsthe best straight line fit, =CkBT with C=1.179.integratedBraggint.(arb.units)T (K)0 20 40 60 80 100510152005101520-4-3-2-10energychange(meV/f.u.)○ ∆<H >− ∆E(T)abinelasticpeakposition(meV)sFIG. 4. a T dependence of the integrated intensity of the 111Bragg peak  which has nuclear and magnetic contributions. Indicates the position of the inelastic peak in the spectrum, derivedby fits described in the text. b Results of the first moment analysisdescribed in the text.  indicates the change in spin exchangeenergy, while the solid line denotes the overall change in energyobtained by integrating specific heat data Ref. 17.FROM COOPERATIVE PARAMAGNETISM TO NÉEL ORDER IN… PHYSICAL REVIEW B 77, 020405R 2008RAPID COMMUNICATIONS020405-3been observed at the transition, the relatively large error barsleave room for an increase in the lattice energy below TN byup to 1.55 meV / f.u. Note also that spin-phonon couplingwas detected through an anomaly in the temperature depen-dence of a Raman-active mode frequency at TN.30While all known pyrochlore antiferromagnets show someform of intrinsic or extrinsic static correlations for suffi-ciently low T, only Y2Ru2O7 and its derivatives featuresecond-order phase transitions to long-range Néel order. Theapparent lack of involvement of lattice degrees of freedomindicates that this is a true magnetic instability the under-standing of which may require a different frame work thanfor ZnCr2O4. The apparent gap in the excitation spectrumindicates that spin space anisotropy may be significant.While we detect the magnitude of the gap there is no directinformation about the magnitude or nature of any spin spaceanisotropic terms in the Hamiltonian. The fact that the gapmode is relatively sharp in energy for a powder sample indi-cates that the corresponding excitations are weakly disper-sive and this points to local soft modes pushed to a finiteenergy on account of quantum fluctuations. Indeed the firstmoment analysis of S̃Q , shows that the energy gain as-sociated with ordering is intimately related to the develop-ment of the 19.7 meV peak. The principal challenge posedby our experiment is thus to understand the interplay be-tween quantum fluctuations and anisotropy terms in estab-lishing the Néel state spin gap and spin resonance in thefrustrated pyrochlore AFM.We gratefully acknowledge discussions with L. Balents,M. Gingras, and O. Tchernyshyov. Work at JHU and ISISwas supported by DOE through Grant No. DE-FG02-02ER45983 and NSF through Grant No. DMR-0306940.Work at Rutgers was supported by NSF through Grant No.DMR-0405682.1 J. E. Greedan, J. Mater. Chem. 11, 37 2001.2 P. W. Anderson, Phys. Rev. 102, 1008 1956.3 R. Moessner and J. T. Chalker, Phys. Rev. Lett. 80, 2929 1998.4 C. L. Henley, Phys. Rev. B 71, 014424 2005.5 S. V. Isakov, K. Gregor, R. Moessner, and S. L. Sondhi, Phys.Rev. Lett. 93, 167204 20046 O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Europhys. Lett.73, 278 2006.7 J. S. Gardner, B. D. Gaulin, S.-H. Lee, C. Broholm, N. P. Raju,and J. E. Greedan, Phys. Rev. Lett. 83, 211 1999.8 J. S. Gardner, A. Keren, G. Ehlers, C. Stock, E. Segal, J. M.Roper, B. Fåk, M. B. Stone, P. R. Hammar, D. H. Reich, and B.D. Gaulin, Phys. Rev. B 68, 180401R 2003.9 Y. Machida, S. Nakatsuji, Y. Maeno, T. Tayama, T. Sakakibara,and S. Onoda, Phys. Rev. Lett. 98, 057203 2007.10 S.-H. Lee, C. Broholm, T. H. Kim, W. Ratcliff, II, and S.-W.Cheong, Phys. Rev. Lett. 84, 3718 2000.11 O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Phys. Rev. B66, 064403 2002.12 R. Kanno, Y. Takeda, T. Yamamoto, Y. Kawamoto, and O. Yama-moto, J. Solid State Chem. 102, 106 1993.13 S. Yoshii and M. Sato, J. Phys. Soc. Jpn. 68, 3034 1999.14 J. Park, K. H. Kim, H.-J. Noh, S.-J. Oh, J.-H. Park, H.-J. Lin, andC.-T. Chen, Phys. Rev. B 69, 165120 2004.15 H. Sakai, H. Kato, S. Kambe, R. E. Walstedt, H. Ohno, M. Kato,K. Yoshimura, and H. Matsuhata, Phys. Rev. B 66, 100509R2002.16 N. Tiara, M. Wakeshima, and Y. Hinatsu, J. Solid State Chem.152, 441 2000.17 M. Tachibana, H. Kawaji, and T. Atake, Phys. Rev. B 71,060402R 2005.18 M. Ito, Y. Yasui, M. Kanada, H. Harashina, S. Yoshii, K. Murata,M. Sato, H. Okumura, and K. Kakurai, J. Phys. Soc. Jpn. 69,888 2000; M. Ito, Y. Yasui, M. Kanadaa, H. Harashinaa, S.Yoshii, K. Murata, M. Sato, H. Okumura, and K. Kakurai, J.Phys. Chem. Solids 62, 337 2001.19 M. W. Johnson, Harwell Report No. AERE-R7682, 1974 unpub-lished.20 P. J. Brown, in International Tables for Crystallography, editedby A. J. C. Wilson Kluwer, London, 1995, Vol. C.21 S. W. Lovesey, Theory of Neutron Scattering from CondensedMatter Clarendon Press, Oxford, 1984.22 S.-H. Lee, C. Broholm, W. Ratcliff, G. Gasparovic, Q. Huang, T.H. Kim, and S.-W. Cheong, Nature London 418, 856 2002.23 O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett.88, 067203 2002.24 U. Hizi and C. L. Henley, J. Phys.: Condens. Matter 19, 1452682007.25 S. Yoshida, K. Nemoto, and K. Wada, J. Phys. Soc. Jpn. 71, 9482002.26 S.-H. Lee, Y. Qiu, C. Broholm, Y. Ueda, and J. J. Rush, Phys.Rev. Lett. 86, 5554 2001.27 L. 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From cooperative paramagnetism to Neel order in Y2Ru2O7: neutron scattering measurements

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From cooperative paramagnetism to Neel order in Y2Ru2O7: neutron scattering measurements

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