Neutron scattering studies on powder and single crystals have provided new evidences for unconventional

magnetism in Cu₂Te₂O₅Cl₂. The compound is built from tetrahedral clusters of S = 1/2

Cu²⁺ spins located on a tetragonal lattice. Magnetic ordering, emerging at TN = 18.2 K, leads to a

very complex multi-domain, most likely degenerate, ground state, which is characterized by an incommensurate

(ICM) wave vector k ~ [0.15, 0.42, 1/2]. The Cu²⁺ ions carry a magnetic moment

of 0.67(1) μB/Cu²⁺ at 1.5 K and form a four helices spin arrangement with two canted pairs

within the tetrahedra. A domain redistribution is observed when a magnetic field is applied in the

tetragonal plane (Hc ≈ 0.5 T), but not for H||c up to 4 T. The excitation spectrum is characterized

by two well-defined modes, one completely dispersionless at 6 meV, the other strongly dispersing

to a gap of 2 meV. The reason for such complex ground state and spin excitations may be geometrical

frustration of the Cu²⁺ spins within the tetrahedra, intra- and inter-tetrahedral couplings having

similar strengths and strong Dzyaloshinski–Moriya anisotropy. Candidates for the dominant

intra- and inter-tetrahedral interactions are proposed

Berger, H.

Brown, P.J.

Daoud-Aladine, A.

Juranyi, F.

Mesot, J.

Ronnow, H.M.

Streule, S.

Zaharko, O.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

Fizika Nizkikh Temperatur, 2005, v. 31, Nos. 8/9, p. 1068–1072Incommensurate magnetism in the coupled spintetrahedra system Cu2Te2O5Cl2O. Zaharko1,H.M. Ronnow1, A. Daoud-Aladine1, S. Streule1, F. Juranyi1,J. Mesot1, H. Berger2, and P.J. Brown31Laboratory for Neutron Scattering, ETHZ & PSI, CH-5232 Villigen PSI, SwitzerlandE-mail: oksana.zaharko@pci.ch2Institute de Physique de la Matire Complexe, EPFL, CH-1015 Lausanne, Switzerland3Institute Laue-Langevin, 156X, F-38042 Grenoble Cedex, FranceReceived January 25, 2005Neutron scattering studies on powder and single crystals have provided new evidences for uncon-ventional magnetism in Cu2Te2O5Cl2. The compound is built from tetrahedral clusters of S = 1/2Cu2+ spins located on a tetragonal lattice. Magnetic ordering, emerging at TN = 18.2 K, leads to avery complex multi-domain, most likely degenerate, ground state, which is characterized by an in-commensurate (ICM) wave vector k  [0.15, 0.42, 1/2]. The Cu2+ ions carry a magnetic momentof 0.67(1) B/Cu2+ at 1.5 K and form a four helices spin arrangement with two canted pairswithin the tetrahedra. A domain redistribution is observed when a magnetic field is applied in thetetragonal plane (Hc  0.5 T), but not for H||c up to 4 T. The excitation spectrum is characterizedby two well-defined modes, one completely dispersionless at 6 meV, the other strongly dispersingto a gap of 2 meV. The reason for such complex ground state and spin excitations may be geometri-cal frustration of the Cu2+ spins within the tetrahedra, intra- and inter-tetrahedral couplings hav-ing similar strengths and strong Dzyaloshinski–Moriya anisotropy. Candidates for the dominantintra- and inter-tetrahedral interactions are proposed.PACS: 75.30.–m, 61.12.Ld, 75.10.JmIntroductionReduced dimensionality, geometrical frustrationand low spin values lead to quantum fluctuations of-ten resulting in interesting new ground states and spindynamics [1]. The most famous examples are based ontriangular units (triangular and kagome lattices [2])in two dimensions (2D) and tetrahedral clusters(FCC and pyrochlore lattices [3]) in 3D. The natureof the ground state in such systems is a subject of cur-rent strong interest, especially for the extreme quan-tum mechanical case S = 1/2.The copper tellurate Cu2Te2O5X2 (X = Cl, Br,space group P-4) [4] belong to a new family of suchcompounds. Their structure can be viewed as a stackingof layers of Cu4O8Cl4 clusters along c. The four Cu2+ions within such a cluster, Cu1 (x, y, z), Cu2 (1–x,1–y, z), Cu3 (y, 1–x, –z), and Cu4 (1–y, x, –z), forman irregular tetrahedron with two longer (Cu1–Cu2,Cu3–Cu4) and four shorter edges. The tetrahedrahave a 2D square arrangement within the ab-layers.The Cu2Te2O5Cl2 system attracted much attentionas the first magnetic susceptibility data fitted well amodel of isolated tetrahedra [4]. The observed broadmaximum between 20–30 K and a rapid drop at lowertemperatures indicated a strength of the intra-tetrahe-dral coupling J  38.5 K. Raman spectroscopy, how-ever, indicated a substantial inter-tetrahedral cou-pling along the c-axis [5,6] and the data analysis havebeen performed [7] in terms of a dimerized model withthe two pairs of Cu2+ spins: Cu1–Cu2 and Cu3–Cu4.Further magnetic susceptibility and specific heat mea-surements [5] indicated an onset of antiferromagnetic(AF) order at TN = 18.2 K, thus confirming the impor-tance of inter-tetrahedral couplings. Recent neutrondiffraction studies [8] revealed the details of the mag-netic order: it is incommensurate and very complex.© O. Zaharko, H.M. Ronnow, A. Daoud-Aladine, S. Streule, F. Juranyi, J. Mesot, H. Berger, and P.J. Brown, 2005In spite of considerable progress in experimentalstudies, the relevant intra- and inter-tetrahedral mag-netic interactions in Cu2Te2O5Cl2 remain a puzzle dueto the rather complex 3D exchange topology (Fig. 1).The intra-tetrahedral spin interactions are mediatedvia the superexchange paths Cu–O–Cu and can be de-scribed by J1 and J2 exchange constants. It was sug-gested [9] according to the Goodenough rules, that theJ2 interaction should be weakly antiferromagnetic if notferromagnetic, while J1 is antiferromagnetic and ratherweak [9]. From the band structure calculations [10] it isexpected that within the ab-layers the Ja and Jdinter-tetrahedral couplings are substantial (see Fig. 1)and mediated by the halogen p orbitals. Between theadjacent layers the tetrahedra interact through thesuper-superexchange paths Cu–O…O–Cu and thecorresponding inter-tetrahedral couplings are as wellimportant.The nature of the magnetic ordering transition isalso still unclear. A strong spin-lattice coupling nearTN has been suggested from magnetic susceptibilityand thermal conductivity studies [11]. However, theinfrared spectroscopy study [12], as well as high-reso-lution neutron diffraction study [8] gave no evidenceof any lattice distortion.We present neutron diffraction and inelastic scat-tering results, which supply new information on themagnetic ground state, spin-orbit coupling and spindynamics. We hope this will provide a better startingpoint for theoretical modeling [13–17].ExperimentalHigh-purity powder and single crystals ofCu2Te2O5Cl2 were prepared by the halogen vaportransport technique, using TeCl4 and Cl2 as transportagents. Neutron powder diffraction (NPD) patternswere collected in the temperature range 1.5–30 K onthe DMC instrument, with a neutron wavelength of = 4.2  and on the high-resolution HRPT instru-ment ( = 1.889 ) at SINQ, Villigen, Switzerland.The neutron single crystal diffraction (NSCD) experi-ments on two crystals of dimensions 2.535 mm and23.56 mm were carried out using the diffractometersTriCS at SINQ ( = 1.18 ) and D15 ( = 1.17 ) atthe high-flux ILL reactor, France. The NSCD with ap-plied magnetic field were performed on a larger 1 cm3crystal on TriCS ( = 1.18 and 2.4 ) for three fielddirections H||a, b and c.The inelastic neutron scattering experiment wascarried out on 15 g powder on neutron time-of-flightspectrometer FOCUS ( = 2.8 and 4 ) at SINQ andon a large 1.5 cm3 crystal on the IN8 thermal neutronthree-axis spectrometer at ILL. IN8 was configuredwith doubly focusing monochromator and analyzerwith a 5 cm graphite filter in kf and fixed final neu-tron energy of 14.7 meV.ResultsDiffractionBelow TN = 18 K tiny magnetic peaks appeared(Fig. 2) in DMC neutron diffraction patterns ofCu2Te2O5Cl2, as already reported in [8]. Moreover,the onset of magnetic order at TN can be followedfrom the structural peaks in the HRPT data. The latticeconstant a(b) significantly decreases with temperatureabove TN and changes very little below TN (Fig. 2, in-set). This implies that the spin-lattice coupling is sub-stantial, but no changes of the crystal structure couldbe determined from the neutron patterns.To determine correctly the magnetic ground state itis very important to elucidate the magnetic symmetry.The [001] projection of neutron diffraction pattern ofa typical Cu2Te2O5Cl2 single crystal is presented inFig. 3. Up to 16 magnetic satellites of the (0,0,0)reflection have been observed. The reflection setdenoted by black circles arises from four arms of thestar of the incommensurate (ICM) wave vectork[0.150, 0.422, 1/2]. The reflections denoted bydotted circles correspond to the star of another wavevector k’[–0.150, 0.422, 1/2]. The k and k’ vectorsare not related by the symmetry elements of the groupP-4, and could belong to growth crystallographictwins. Since for several studied crystals the k’ reflec-Incommensurate magnetism in the coupled spin tetrahedra system Cu2Te2O5Cl2Fizika Nizkikh Temperatur, 2005, v. 31, Nos. 8/9 1069Fig. 1. The xy-projection of the Cu2Te2O5Cl2 crystalstructure (z = – 1/21/2) with the J1, J2 and possibleintertetrahedral exchange paths [10]. The double-line seg-ment is normal to the incommensurate component of thewave vector k’ [8].tions are absent, we conclude that the k and k’ sets areindependent. Interestingly, the intensity ratio be-tween the two first magnetic reflections for the k andk’ sets is different, implying that the magnetic struc-tures associated with these two stars are different.We further tried to clarify if the magnetic structureis single-k or multi-k. In the case of a single-k mag-netic structure the k(k’) set contains contributions offour configuration domains. The configuration do-mains must all have the same structure but possiblydifferent populations. Each of them could have two180 deg domains and two chiral domains. In the caseof multi-k structure, the four arms of the star buildone magnetic structure.It is possible to distinguish the single-k or multi-kcases by studying the variation of magnetic intensitiesas a function of an applied magnetic field H. We per-formed such study for fields along a, b, and c crystaldirections. For H along c the intensities of the mag-netic reflections hkl with l > 0 increase and for l < 0they decrease, but all reflections persist up to 4 T.This implies a change of the spin arrangement with re-spect to the zero-field magnetic structure, but withoutdomain redistribution and/or meta-magnetic transi-tion. For H||a a transition occurs at Hc  0.5 T: inten-sities of the (±,±,±l/2) reflections vanish, whilethe magnetic reflections of the type (±,±,±l/2)change their intensities smoothly (Fig. 4). Flippingthe field to –a results in the same behavior. Switchingoff the field restores partly the vanished peaks. A si-milar picture is observed for H||b, but now the(±,±,±l/2) reflections vanish at  0.5 T. Our re-sults imply that 0.5 T applied in the tetragonal plane isenough to depopulate the domains with the propaga-tion vector nearly normal (90 ± 10 deg) to the field di-rection. This supports the idea that the magnetic struc-ture is a single-k and not a multi-k structure.The model for the k’ magnetic structure has beenrecently elaborated in [8]. The only symmetry con-straint is imposed by the commensurate component ofthe wave vector. It implies that the ab-layers of tetra-hedra alternating along c carry oppositely orientedspins. The magnetic moments of the four Cu2+ ions inthe unit cell can be independent and a generalizedhelix characterizing spin arrangement of each of themin the crystal is expressed asSj= A cos(k·rj+ ) + B sin(k·rj+ ).The spin components are modulated by the wave vec-tor k, rj is the radius vector to the origin of the j-th1070 Fizika Nizkikh Temperatur, 2005, v. 31, Nos. 8/9O. Zaharko et al.Neutronintensity, arb. units250020001500100050020 30 40 50 60 702 , deg4 K18 K7.59157.59256.31806.31846.31880 5 10 15 20 25 30T, KTNa,Åb,ÅFig. 2. The 18 and 4 K DMC NPD patterns of Cu2Te2O5Cl2 ( = 4.2 ), arrows point to magnetic reflections. Inset:temperature evolution of the lattice constants from HRPT NPD data ( = 1.889 ).baFig. 3. The [001] projection of the reciprocal space of aCu2Te2O5Cl2 single crystal. The black circles correspondto the k magnetic reflections and the dotted circles – tothe k’ set;  = 0.15,  = 0.422.unit cell. A and B are orthogonal vectors, which de-fine the magnitude and direction of the axes of the he-lix, whilst  defines its phase. For the most generalcase 27 independent parameters should be considered.Since the available number of experimental observa-tions does not allow to refine with confidence all ofthem, we imposed physically sound constraints: iden-tical moment value for all four independent Cu2+ ionsand a circular envelope of the helices. This loweredthe number of independent parameters to 12.Very good fits were obtained for a model (Fig. 5)in which the 4 Cu2+ moments in each tetrahedron formtwo canted pairs: Cu1–Cu2 and Cu3–Cu4. The twospins of the pair share a common (A, B) plane, but theassociated helices have different phases . The differ-ence between the phases defines the canting anglebetween spins of the pair . The canting angle for thefirst pair is 12 = 38(6) deg and for the second pair34 = 111(14) deg. The amplitude of the magnetic mo-ment carried by each Cu2+ ion is 0.67(1) B at 1.5 K.It is interesting that the vector sum of the spins of onepair is the same for all tetrahedra in the crystal(m12 = 1.27(6) B, m34 = 0.76(14) B), whilst the lo-cal magnetic moment of the tetrahedra is not zero andchanges from one unit cell to another. For an isotropicexchange the spin state of the tetrahedra would bezero, so our model might suggest that the two intra-tet-rahedral couplings J1 and J2 are different and that theJ2 interaction is stronger.Such a particular magnetic ground state might be aconsequence of one dominant interaction or result fromcontributions of several inter-tetrahedral couplings ofsimilar strengths. We tried to attribute the observed re-ciprocal wave vector k’ = (–0.15,0.42,1/2) to somespecific exchange inter-tetrahedral path in the struc-ture and found a simple correlation not to k’, but tothe (–0.15,–0.58,0) vector. As this vector is relateby alattice translation to the (–0.15,0.42,0), the twoIncommensurate magnetism in the coupled spin tetrahedra system Cu2Te2O5Cl2Fizika Nizkikh Temperatur, 2005, v. 31, Nos. 8/9 1071(–0.15, –0.42, –1/2) 0.5 T0 Ta( –0.15, –1/2)–0.42,0.5 T0 Tb0 5 10 15 20 25 30 350 5 10 15 20 25Step, Step, 90080070060050040030020030002500200015001000500Neutroncounts,arb. unitsNeutroncounts, arb. unitsFig. 4. The TriCS -scans of the (–0.15,–0.42,–1/2) (a)and (0.42,–0.15,1/2) (b) magnetic reflections ( = 2.4 )at H = 0 T and H = 0.5 T along a.Fig. 5. The xy-projection of the Cu2Te2O5Cl2 magneticstructure with the spin tetrahedra at the z = 0 layer.051020253035401 2 3 4 5 6 7 8Energy, meVIntensity1.5 K14 K18 K30 KFig. 6. Inelastic powder neutron scattering of Cu2Te2O5Cl2integrated between 0.8 –1 and 3.3 –1 for four tempera-tures between 2 and 30 K. With incident energy Ei = 10.4meV inelastic focusing was adjusted to provide optimal res-olution at 5 meV of 0.45 meV (full-width-half-maximum).vectors mean a different choice of the unit cell of thesame magnetic structure. The ICM component is or-thogonal to a specific set of planes containing the Cu2+ions. One of these planes, presented by a double-linesegment in Fig. 1, passes through the Cu2–Cu4 ions ofthe adjacent tetrahedra. This corresponds to the Jacoupling, which according to Ref. 10 is substantialand is mediated by the halogen orbitals. Based onthese considerations we suggest that Ja is the domi-nant inter-tetrahedral coupling.Inelastic scatteringSeveral inelastic neutron scattering studies havebeen performed to investigate the excitation spectrumof the Cu2Te2O5Cl2 system. Spectra from powder re-vealed in the ordered phase below TN a sphericallyaveraged density of states extending to a maximum at6 meV, above which no significant scattering was de-tected up to 15 meV (Fig. 6). Raising the temperatureabove TN, spectral weight shifted downwards to abroad quasi-elastic peak.For single crystal neutron spectroscopy a singlecrystal was aligned with (3,1,0) and (0,0,1) in thehorizontal scattering plane, such that (0.42,0.15,1/2)and the equivalent magnetic Bragg peaks were accessi-ble given the wide ( 5 deg) vertical resolution. Scansperformed along the Q = (h,h/3,3/2), (0.45,0.15,l)and (0,0,l) directions revealed two well defined exci-tation modes. One mode is completely dispersionlessat 6.0 meV and shows no variation in intensity as afunction of Q. The other mode displays strong disper-sion along both accessible directions from a maximumenergy close to the flat mode down to a minimum en-ergy gap of 2.1 meV at the same positions in Q as theICM magnetic Bragg peaks.While more detailed modeling of the excitationspectrum is under way, several important conclusionscan be read directly off the figure. If the system wouldbe a collection of very weakly coupled tetramers, onewould expect a series of essentially dispersionlessmodes. The strong dispersion observed in our measure-ments imply strong inter-tetrahedral coupling bothwithin the ab-plane and along the c-axis. Secondly, aclassical ordered magnetic structure with continuoussymmetry of the order parameter should have gaplessspin waves emerging from the magnetic Bragg peaks.The rather large energy gap must involve strong aniso-tropy terms in the Hamiltonian, whose origin remainsto be determined.SummaryThe presented results of neutron diffraction and in-elastic neutron scattering evidence new details of themagnetic ordering in the Cu2Te2O5Cl2 compound.The idea of a single-k magnetic structure is stronglysupported by the observed magnetic domains redistri-bution in an applied magnetic field. The presence oftwo different k and k’ structures suggests that a num-ber of ground states with equal or close energies mightexist. The discovered relation between the incommen-surate component of the wave vector and the inter-tet-rahedral coupling Ja invites for a theoretical revisionof the Cu2Te2O5X2 system. The peculiar features ofthe spin excitation spectrum deserve further study.The work was performed at SINQ, Paul Scherrer In-stitute, Villigen, Switzerland, at ILL reactor, Grenoble,France. We thank Prof. F. Mila, Dr. M. Prester, andProf. A. Furrer for fruitful discussions and SwissNCCR research pool MANEP of the Swiss NSF forfinancial support.1. Quantum magnetism, Lect. Notes Phys. 645,Springer-Verlag, Berlin, Heidelberg (2004).2. F. Mila, Eur. J. Phys. 21, 499 (2000).3. A.P. Ramirez, Geometrical Frustration, in: Handbookof Magnetic Materials 13, Elsevier Science (2001).4. M. Johnsson, K.W. Tornroos, F. Mila, and P. Millet,Chem. Mater. 12, 2853 (2000).5. P. Lemmens, K.-Y. Choi, E.E. Kaul, C. Geibel, K.Becker, W. Brenig, R. Valenti, C. Gross, M. Johnsson,P. Millet, and F. Mila, Phys. Rev. Lett. 87, 227201(2001).6. C. Gross, P. Lemmens, M. Vojta, R. Valenti, K.-Y.Choi, H. Kageyama, Z. Hiroi, N.M. Mushnikov, T.Goto, M. Johnsson, and P. Millet, Phys. Rev. B67,174405 (2003).7. J. Jensen, P. Lemmens, and C. Gross, Europhys. Lett.64, 689(2003).8. O. Zaharko, A. Daoud-Aladine, S. Streule, J. Mesot,P.-J. Brown, and H. Berger, Phys. Rev. Lett. 93,217206 (2004).9. M.H. Whangbo, H.J. Koo, and D. Dai, J. Solid StateChem. 176, 417 (2003).10. R. Valenti, T. Saha-Dasgupta, C. Gros, and H. Rosner,Phys. Rev. B67, 245110 (2003).11. M. Prester, A. Smontara, I. Zivkovi’c, A. Bilusi’c, D.Drobac, H. Berger, and F. Bussy, Phys. Rev. B69,180401R (2004).12. A. Perucchi, L. Deiorgi, H. Berger, and P. Millet,Eur. Phys. J. B38, 65(2004).13. W. Brenig and K.W. Becker, Phys. Rev. B64, 214413(2001).14. W. Brenig, Phys. Rev. B67, 64402 (2003).15. K. Totsuka and H.-J. Mikeska, Phys. Rev. B66, 54435(2002).16. V.N. Kotov, M.E. Zhitomirsky, M. Elhajal, and F.Mila, Phys. Rev. B70, 214401 (2004).17. V.N. Kotov, M.E. Zhitomirsky, M. Elhajal, and F.Mila, J. Phys.: Condens. Matter 16, S905 (2004).1072 Fizika Nizkikh Temperatur, 2005, v. 31, Nos. 8/9O. Zaharko et al.

Incommensurate magnetism in the coupled spin tetrahedra system Cu₂Te₂O₅Cl₂

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Incommensurate magnetism in the coupled spin tetrahedra system Cu₂Te₂O₅Cl₂

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