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[Hase, Masashi](https://orcid.org/0000-0003-2717-461X), Rule, Kirrily C., Hester, James R., Fernandez-Baca, Jaime A., Masuda, Takatsugu, Matsuo, Yukari

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[A Possible Magnetic Structure of the Cluster-Based Haldane Compound Fedotovite K2Cu3O(SO4)3](https://mdr.nims.go.jp/datasets/574d52ac-c146-44fa-a22f-d33f5b97da48)

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69184.dviJournal of the Physical Society of JapanA Possible Magnetic Structure of the Cluster-Based HaldaneCompound Fedotovite K2Cu3O(SO4)3Masashi Hase1 ∗, Kirrily C. Rule2, James R. Hester2, Jaime A. Fernandez-Baca3,Takatsugu Masuda4, and Yukari Matsuo51Research Center for Advanced Measurement and Characterization, National Institutefor Materials Science (NIMS), 1-2-1 Sengen, Tsukuba-shi, Ibaraki 305-0047, Japan2Australian Nuclear Science and Technology Organisation (ANSTO), Locked Bag2001, Kirrawee DC NSW 2232, Australia3Neutron Scattering Division, Oak Ridge National Laboratory (ORNL), Oak Ridge,Tennessee 37831-6393, USA4The Institute for Solid State Physics (ISSP), The University of Tokyo, 5-1-5Kashiwanoha, Kashiwa-shi, Chiba 277-8581, Japan5Department of Advanced Sciences, Hosei University, 3-7-2 Kajino-cho, Koganei-shi,Tokyo 184-8584, JapanWe carried out neutron powder diffraction experiments on the cluster-based Haldanecompound fedotovite K2Cu3O(SO4)3. Weak magnetic reflections caused by a magneticlong-range order appeared below an antiferromagnetic transition temperature TN =3.1 K. We propose a possible magnetic structure that is consistent with the magneticproperties reported in the literature.1. IntroductionFedotovite K2Cu3O(SO4)3 is attractive in the field of quantum spin systems.1) Thespin system in K2Cu3O(SO4)3 consists of spin hexamers which can be described asfollows. The lines in Figs. 1(a) and (b) show short Cu-Cu pairs and Cu-O-Cu paths,respectively. The Cu-Cu distances are 3.408 Å or shorter at room temperature. Theother Cu-Cu distances are 4.234 Å or longer. From the configuration of Cu2+ and O2−ions, Fujihala et al. considered that six spins (S = 12) on Cu2+ ions form a spin cluster(hexamer). Figure 1(c) shows schematically the spin hexamer proposed by Furrer et∗HASE.Masashi@nims.go.jp1/12J. Phys. Soc. Jpn.Cu2 Cu2Cu3Cu1Cu3Cu1O O(a) (b)JabJacJad JcfJceJcdCu2 Cu3 Cu1Jefabcdef(c) (d)edge spinsinglet pairFig. 1. (Color online) (a) Schematic picture of the Cu2+ hexamer (six-spin cluster) inK2Cu3O(SO4)3. There are three crystallographic Cu sites (Cu1, Cu2, and Cu3) having spin- 12 . Thelines show short Cu-Cu pairs. (b) Schematic picture showing Cu-O-Cu paths. The configurations of Cuand O in (a) and (b) are the same. Details of the Cu-O-Cu paths and expected exchange interactionsare described in the Supplemental Material of the literature.1) (c) Exchange interactions expected inthe spin hexamer. Furrer et al. evaluated the exchange interactions as follows; Jab = −3.4, Jcd = −8,Jef = −3.8, Jac = 7.4, Jce = 8.0, Jad = 19.0, and Jcf = 17.0 meV.2) Fujihala et al. evaluated the ex-change interactions as follows; Jab = Jcd = Jef = −3.0, Jac = Jce = 10.8, and Jad = Jcf = 10.8 meV.1)Here, the exchange interactions are defined in the Hamiltonian H =∑ij JijSi ·Sj . (d) Schematic spinconfiguration of the triple states in the hexamer.1) Two blue circles in a green oval means two Cu sitesconnected by one of the ferromagnetic interactions. The edge spins are denoted by a red arrow. Theline indicates a singlet pair.al.2) As shown in Fig. 1(b) in the literature,2) the ground states (GSs) of each hexamerin zero magnetic field are triplet states (S = 1) and are well separated from the excitedstates (by more than 12 meV). Therefore, it is enough that we consider only the tripletGSs in the energy range of a few meV or less. As shown in Fig. 1(d), it was consideredthat edge spins appeared on Cu1 and Cu2 sites and that spins on Cu3 and Cu1 (orCu2) sites formed singlet pairs.1)A one-dimensional array of the hexamers was considered to be formed by weakantiferromagnetic (AF) intercluster exchange interactions along the b direction.1) Thehexamer corresponds to a Ni2+ ion in Ni-based Haldane compounds and a Haldanesystem of the hexamers can be expected. Fujihala et al. considered that gapped spectraat 1.5 K obtained in the inelastic neutron scattering experiments originate from theHaldane gap. The temperature (T ) dependence of the magnetic excitations, however, isslightly different from that of other Haldane compounds. In K2Cu3O(SO4)3 where thevalue of the gap (Δ) at low temperature is 7.1 K, the magnetic excitations seem gapless2/12J. Phys. Soc. Jpn.at 4.0 K.1) On the other hand, magnetic excitations are gapped even at high T in otherHaldane compounds, for example, at 80 K in Y2BaNiO5 (Δ = 99 K )3) and at 30 K inNi(C3H10N2)2N3(ClO4) (NINAZ) (Δ = 42 K ).4) In addition, the energy at which theintensity of the magnetic excitations is maximum is smaller at 4.0 K than that at 1.5 Kin K2Cu3O(SO4)3, whereas the energy increases on heating in Y2BaNiO5 and NINAZ.Fujihala et al. considered that the magnetic behavior above 4.0 K is determinedby the single hexamer (not by the chain of hexamers) and therefore that the spin gapis closed at 4.0 K.1) To understand the T dependence of the magnetic excitations, itis important to investigate further differences in the magnetism below and above 4.0K. The specific heat divided by T shows a maximum around 3 K in zero magneticfield.1) Fujihala et al. considered that the maximum indicates the existence of the spingap. We infer, on the other hand, that the maximum suggests the occurrence of amagnetic long-range order (LRO) around 3 K. Fujihala et al. observed no magneticreflections in the neutron powder diffraction measurement at 1.5 K.1) However, wethink that it is important to reinvestigate whether a magnetic LRO exists or not usinga neutron spectrometer with low background to understand properly the magnetism ofK2Cu3O(SO4)3. Accordingly, we performed neutron powder diffraction experiments onK2Cu3O(SO4)3 using cold-neutron triple-axis spectrometers.2. Experimental MethodsCrystalline K2Cu3O(SO4)3 powder was synthesized by a solid-state reaction. Thestarting materials were K2SO4 (purity 99 %), CuSO4 (99.9 %), and CuO (99.99 %)powder. A stoichiometric mixture of powder was sintered at 783 K in air for 10 h intotal. An X-ray powder diffraction pattern was measured at room temperature usingan X-ray diffractometer (RINT-TTR III, Rigaku). We detected only the allowed reflec-tions of K2Cu3O(SO4)35) which leads us to believe that our sample is a single phase ofK2Cu3O(SO4)3 within experimental accuracy.We performed magnetization measurements using a superconducting quantum in-terference device magnetometer (magnetic property measurement system, QuantumDesign). Preliminary neutron powder diffraction experiments were performed using thecold-neutron triple-axis spectrometer CTAX at the High Flux Isotope Reactor (HFIR)at Oak Ridge National Laboratory (ORNL). Follow-up measurements were performedusing the cold-neutron triple-axis spectrometer, SIKA, at the Open Pool AustralianLightwater (OPAL) reactor at ANSTO. We carried out Rietveld refinements of the3/12J. Phys. Soc. Jpn.0.010.0110.012-0.002-0.00100.0010 2 4 6 8 10χ (emu/mol Cu)dχ/dT (emu/K mol Cu)Temperature (K)Fig. 2. (Color online) Temperature (T ) dependence of the magnetic susceptibility [χ(T )] ofK2Cu3O(SO4)3 in a magnetic field of H = 0.1 T (blue open circles) and T derivative of the mag-netic susceptibility [dχ(T )/dT ] (red solid circles).crystal and magnetic structures using the FULLPROF SUITE program package6) with itsinternal tables for scattering lengths and magnetic form factors.3. ResultsThe blue open circles in Fig. 2 show the T dependence of the magnetic susceptibility[χ(T )] of K2Cu3O(SO4)3 powder in a magnetic field of H = 0.1 T. The broad maximumof χ(T ) around 4.6 K indicates the low-dimensional AF spin system with short-rangecorrelations. The susceptibility obtained in this result is slightly different from thatreported by Fujihala et al.1) Probably the Curie-Weiss term is larger in our samplethan in their sample although we cannot evaluate the Curie constant because of lackof χ(T ) below 2 K. The red solid circles show the T derivative of χ(T ) [dχ(T )/dT ]. Aλ-type peak typical of the second order phase transition was observed in dχ(T )/dT ataround 3.1 K. The peak suggests an AF transition at TN = 3.1 K.We performed preliminary neutron powder diffraction experiments onK2Cu3O(SO4)3 using the CTAX spectrometer at ORNL. Diffraction patterns at1.6 K and 4.2 K suggest the appearance of magnetic reflections.7)We performed follow-up neutron powder diffraction experiments using the SIKAspectrometer at ANSTO. The horizontal collimator sequence was open-20’-sample-20’-60’. The red circles with error bars in Fig. 3(a) indicate a neutron powder diffractionpattern of K2Cu3O(SO4)3 at 2.2 K. The blue line on the experimental pattern portraysthe result of Rietveld refinements and agrees well with the experimental pattern. Weevaluated the scale coefficient for refinements of the magnetic structure from the resultsof the refinements of the crystal structure.4/12J. Phys. Soc. Jpn.The red circles with error bars in Fig. 3(b) indicate a difference pattern ofK2Cu3O(SO4)3 made by subtracting a neutron powder diffraction pattern at 5 K fromthat at 1.7 K obtained using the SIKA spectrometer. From the results of the CTAXmeasurements,7) we inferred that magnetic reflections were observable in the three Qranges in Fig. 3(b). We measured high-statistics data at 1.7 and 5 K only in the threeQ ranges. We observed a magnetic reflection at Q = 1.41 Å−1as in the CTAX results.7)The magnetic reflection is weak but well-defined within experimental accuracy and isas sharp as the nuclear reflection at Q = 1.37 Å−1. Therefore, the magnetic reflection isresolution-limited and indicates the appearance of a magnetic LRO. In addition, otherweak magnetic reflections may exist around Q = 0.75 and 1.0 Å−1.4. DiscussionWe looked for magnetic structures that were consistent with the magnetic propertiesreported in the literature such as an absence of magnetic frustration, an absence of spon-taneous magnetization, and the signs of the exchange interactions in the hexamer.1,2)From the positions of the magnetic reflections, we inferred that the propagation vectorof the magnetic structures was k = (0, 0, 0). This propagation vector implies that mag-netic frustration, which can generate incommensurate magnetic structures, does notexist. We simply considered a common irreducible representation for all the Cu sitesdue to the absence of magnetic frustration. We have four possible Shubnikov groups aslisted in Table I.8) Spontaneous magnetizations [ferromagnetic (F) components] werenot observed. If the Shubnikov group for K2Cu3O(SO4)3 is C2/c, the v componentshould be negligible. If the Shubnikov group is C2′/c′, both the u and w componentsshould be negligible. Here, u, v, and w are components of an ordered magnetic momentin the a, b, and c coordinates, respectively. As shown in Fig. 1, the Jab, Jcd, and Jefinteractions are ferromagnetic. Magnetic moments of sites (1) and (2) in Table I arecoupled by these interactions. Therefore, the signs of dominant components of magneticmoments of sites (1) and (2) should be the same. In C2/c, the signs of the u and wcomponents of site (1) are opposite those of site (2). In C2′/c′, the sign of the v com-ponent of site (1) is opposite that of site (2). Consequently, magnetic structures basedon C2/c and C2′/c′ are not consistent with the reported magnetic properties.1,2)Let us consider C2/c′ and C2′/c. As described, the signs of dominant components ofmagnetic moments of sites (1) and (2) should be the same. The v component is probablydominant in C2/c′. Similarly, the u and w components are probably dominant in C2′/c.5/12J. Phys. Soc. Jpn.Table I. Four possible Shubnikov groups (first row) in monoclinic C2/c for the magnetic structurewith the propagation vector k = (0, 0, 0). The most left line shows symmetry operations of 8f sites.Components of an ordered magnetic moment in the a, b, and c coordinates are indicated by u, v, andw, respectively.C2/c C2′/c C2/c′ C2′/c′(1) x, y, z u, v, w u, v, w u, v, w u, v, w(2) x̄, y, z̄ + 1/2 ū, v, w̄ u, v̄, w ū, v, w̄ u, v̄, w(3) x̄, ȳ, z̄ u, v, w ū, v̄, w̄ ū, v̄, w̄ u, v, w(4) x, ȳ, z + 1/2 ū, v, w̄ ū, v, w̄ u, v̄, w u, v̄, w(5) x + 1/2, y + 1/2, z u, v, w u, v, w u, v, w u, v, w(6) x̄ + 1/2, y + 1/2, z̄ + 1/2 ū, v, w̄ u, v̄, w ū, v, w̄ u, v̄, w(7) x̄ + 1/2, ȳ + 1/2, z̄ u, v, w ū, v̄, w̄ ū, v̄, w̄ u, v, w(8) x + 1/2, ȳ + 1/2, z + 1/2 ū, v, w̄ ū, v, w̄ u, v̄, w u, v̄, wAs shown in Fig. 1(d), spins on the Cu3 sites are nearly zero.1) Therefore, we take themoments on Cu1 and Cu2 sites into account. In C2/c′, when the v components of Cu1and Cu2 sites are refined, the calculated magnetic reflection around Q = 1.41 Å−1isnot largest in all the calculated ones. We consider that C2/c′ is not applicable to themagnetic structure of K2Cu3O(SO4)3.In C2′/c, when the u and w components of the Cu1 and Cu2 sites are refinedsimultaneously, values of these components do not converge which is probably due tothe limited number of magnetic reflections. When only the w components of Cu1 andCu2 sites are refined, the calculated magnetic reflection around Q = 1.41 Å−1is notlargest in all the calculated ones. When only the u components of Cu1 and Cu2 sitesare refined, the calculated magnetic reflection around Q = 1.41 Å−1is largest in all thecalculated ones as indicated by the blue line in Fig. 3 (b). Consequently, we infer thatC2′/c is most applicable to describe the magnetic structure of K2Cu3O(SO4)3.We consider the reason why only the magnetic reflection at 021 around Q = 1.41 Å−1is statistically relevant. Table II shows calculated intensities of major magnetic reflec-tions and nuclear reflections near the magnetic reflections. The intensities of the mag-netic reflections at 110, 111, −203, and 003 are smaller by one order of magnitude thanthe intensity of the magnetic reflection at 021. Large nuclear reflections overlap withthe magnetic reflections at −201, 111, 201, and −203. Therefore, it is difficult to extractproperly the magnetic reflections at these indices. Accordingly, only the magnetic re-flection at 021 was clearly observed. Intensities of magnetic reflections were calculated6/12J. Phys. Soc. Jpn.Table II. Calculated intensities of major magnetic reflections and nuclear reflections near the mag-netic reflections. The symbol ”F” means a forbidden reflection. We consider only the u components.Therefore, the intensities of several allowed magnetic reflections are 0.Q (Å−1) Index Imagn (arb. unit) Inucl (arb. unit)0.701 −201 101 F0.709 200 0 85,2240.752 110 41 160.950 002 0 8,9880.954 111 34 4,9940.965 −202 0 9,7100.982 201 223 F1.350 −203 34 F1.370 202 0 13,3801.402 −402 0 11,2321.409 021 409 4661.425 003 47 Ffrom Q = 0.70 to 1.45 Å−1in the Rietveld refinements. The maximum intensity betweenthe three Q ranges in Fig. 3(b) is 8. Therefore, we think that we were not able to detectmagnetic reflections between the three Q ranges in the CTAX measurements.7)Figure 4 shows the ”possible” magnetic structure. The values of u are 0.5(2)μBand −1.0(2)μB at 1.7 K on the site (1) of Cu1 and that of Cu2, respectively. The wcomponents of Cu1 and Cu2 sites may not be negligible. As described, however, we werenot able to evaluate them in Rietveld refinements. The ratio of the Cu1 and Cu2 atomsto the total atoms is 2 : 21. Since the concentration of Cu sites having the orderedmoments is small, the magnetic reflections are very weak as the magnitudes of theordered moments. The ordered moments are parallel to one another in each hexamer.This alignment is consistent with the signs of the intracluster interactions. The magneticstructure indicates that intercluster interactions are F, F, and AF in the a, b, and cdirections, respectively, whereas the AF chains were considered to be formed parallelto the b direction.1) We have to reconsider the direction of the AF chains.The results reported in the literature1,2) and our results indicate totally that the spingap remains even when the magnetic LRO appears in a unique state. Similar results havebeen reported in impurity-doped spin-Peierls CuGeO39) and AF spin-cluster compoundssuch as Cu2CdB2O610) and CrVMoO7.11,12) The GS of the spin system in CuGeO3 isspin singlet.13–15) In the AF spin-cluster compounds, if each cluster were isolated, the7/12J. Phys. Soc. Jpn.GS of each cluster would be spin singlet. The GS can be magnetic in impurity-dopedCuGeO3 due to the appearance of unpaired spins and in the AF spin-cluster compoundsdue to intercluster interactions.10) Therefore, the magnetic LRO is possible by interchainor intercluster interactions. The origin of the spin gap is essentially singlet pairs thatcan remain in the above-mentioned magnetic GS. Therefore, the spin-gap excitationsare observable even in the ordered state. As shown in Fig. 1 (d), two edge spins wereconsidered to appear in each hexamer of K2Cu3O(SO4)3 like two S = 12spins on a Ni2+ion in the valence bond solid picture.16) Therefore, the origin of the spin gap is singletpairs formed by AF intercluster interactions. If interactions between chains of hexamersalso exist, the magnetic LRO is possible like in CsNiCl3.17)Nambu-Goldstone (NG) mode excitations must exist in the ordered state but werenot observed in K2Cu3O(SO4)3. We consider the reasons as follows. The magnetic re-flections are very weak. Therefore, NG mode excitations are also very weak. In addition,nuclear reflections seem generate signals up to 0.5 meV in Fig. 3(a) of the literature.1)The signals may hide NG mode excitations.5. SummaryWe performed neutron powder diffraction experiments on the cluster-based Haldanecompound fedotovite K2Cu3O(SO4)3 of which space group is monoclinic C2/c (No. 15).We observed weak magnetic reflections caused by a magnetic long-range order belowTN = 3.1 K. We looked for magnetic structures that were consistent with the magneticproperties reported in the literature. Probably, the Shubnikov group C2′/c with thepropagation vector k = (0, 0, 0) is applicable to describe the magnetic structure ofK2Cu3O(SO4)3. Among the three crystallographic Cu sites (Cu1, Cu2, and Cu3) havingspin-12, the edge sites (Cu1 and Cu2) in the hexamer have ordered magnetic moments.The a components of the magnetic moments are dominant.AcknowledgmentThis work was supported by Japan Society for the Promotion of Science (JSPS)KAKENHI Grant Number 18K03551, the grant for advanced measurement and char-acterization technologies accelerating the materials innovation at National Institutefor Materials Science (NIMS), and JST-Mirai Program Grant Number JPMJMI18A3,Japan. Preliminary neutron powder diffraction measurements at the CTAX spectrom-eter used resources at the High Flux Isotope Reactor, a DOE Office of Science User8/12J. Phys. Soc. Jpn.Facility operated by the Oak Ridge National Laboratory (ORNL), USA (proposal ID.2018-06). Follow-up neutron powder diffraction experiments were performed by usingthe SIKA spectrometer at Australian Nuclear Science and Technology Organisation(ANSTO), Australia (proposal ID. P6939). Business travel expense for the CTAX ex-periments was supported by the US-Japan cooperative program for neutron scattering.We are grateful to T. Hong, M. Matsuda, H. Mamiya, M. Nishino, N. Terada, N. Tsujii,M. Fujihala, and T. Sugimoto for fruitful discussion and to S. Matsumoto for the samplesyntheses and X-ray diffraction measurements.9/12J. Phys. Soc. Jpn.�  ���Intensity (count/70s)(a)-5.0 x 1030.05.0 x 1031.0 x 1041.5 x 1042.0 x 1040.7 0.8 0.9 1 1.1 1.2 1.3 1.4�  ���Intensity (count/600s)(b)-1000-5000500100015000.7 0.8 0.9 1 1.1 1.2 1.3 1.4Fig. 3. (Color online) Neutron powder diffraction patterns of K2Cu3O(SO4)3 obtained using theSIKA spectrometer. The wavelength is 4.04 Å. (a) A neutron powder diffraction pattern at 2.2 K(red circles with error bars). A blue line on the measured pattern indicates a Rietveld refined patternobtained using the crystal structure with monoclinic C2/c (No. 15). In the refinements, we used thefractional atomic coordinates and isotropic displacement factor listed in the Supplemental Material forthe paper.2) The lattice constants were evaluated as a = 18.944(6) Å, b = 9.472(3) Å, c = 14.131(2) Å,and β = 110.56(1)◦. A black line at the bottom indicates the difference between the measured and theRietveld refined patterns. Hash marks show positions of nuclear reflections. (b) A difference patternmade by subtracting a neutron powder diffraction pattern at 5 K from that at 1.7 K (red circles witherror bars). A blue line on the measured pattern indicates a Rietveld refined pattern of the magneticstructure only. The measured and refined patterns are shifted 600 in the vertical direction to decreaseoverlap with the black line, indicating the difference between the measured and the Rietveld refinedpatterns. Hash marks show positions of magnetic reflections.10/12J. Phys. Soc. Jpn.bacFig. 4. (Color online) The possible magnetic structure of K2Cu3O(SO4)3. 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