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Pomjakushin, Vladimir Yu., [Hase, Masashi](https://orcid.org/0000-0003-2717-461X), Kindo, Koichi, Hester, James R., Matsuo, Akira, Rule, Kirrily C.

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[Reduction of the Ordered Magnetic Moment by Quantum Fluctuation in the Antiferromagnetic Spin-5 2 Dimer Compound FeVMoO7](https://mdr.nims.go.jp/datasets/5de7595d-9b41-4a8e-8c5b-364822f95bf5)

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68988.dviJournal of the Physical Society of JapanReduction of the Ordered Magnetic Moment by QuantumFluctuation in the Antiferromagnetic Spin-52 DimerCompound FeVMoO7Masashi Hase1 ∗, James R. Hester2, Kirrily C. Rule2, Vladimir Yu. Pomjakushin3,Akira Matsuo4, and Koichi Kindo41Research 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, Australia3Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut (PSI),CH-5232 Villigen PSI, Switzerland4The Institute for Solid State Physics (ISSP), The University of Tokyo, 5-1-5Kashiwanoha, Kashiwa-shi, Chiba 277-8581, JapanWe investigated the magnetism of FeVMoO7 by performing magnetization, specificheat, electron spin resonance, and neutron diffraction experiments. We observed anantiferromagnetically ordered state below TN = 10.8 K. We consider that the probablespin model is an interacting antiferromagnetic spin-52dimer model where spin dimers areconnected by interdimer interactions. The intradimer interaction was evaluated to beJ = 10.5±0.5 K. The magnitude of ordered magnetic moments is 4.00(7)μB at 4 K. Themagnitude at 0 K is considered to be smaller than the classical value 4.95μB (g = 1.98).We confirmed a reduction of ordered magnetic moments by quantum fluctuation inhigh-spin (spin-52) clusters as known in high-spin chains.1. IntroductionAntiferromagnetic (AF) XXZ models describe the competition between quantumand classical nature. The Hamiltonian is expressed asH =∑i,jJij(Si+Sj− + Si−Sj+2+ ΔSizSjz). (1)∗HASE.Masashi@nims.go.jp1/16J. Phys. Soc. Jpn.The first term in the parentheses stabilizes spin-singlet pairs, induces quantum fluc-tuation, and destroys magnetic long-range order, whereas the second term stabilizesmagnetic long-range order. In low-spin systems, we know examples where quantumfluctuation prevails over magnetic long-range order such as the spin-Peierls transition(spin-12)1–3) and the Haldane gap (spin-1).4–6) This Hamiltonian is valid regardless ofthe magnitude of the spin. Therefore, quantum nature can exist in high-spin systemssuch as spin-52.A Heisenberg model can explain the magnetism of the AF spin-52trimer compoundSrMn3P4O14 where the Hamiltonian is H = J(S1 · S2 + S2 · S3).7–11) We evaluated amagnetic-field-induced magnetic moment on each Mn2+ site in the 1/3 quantum mag-netization plateau ground state (GS) using neutron diffraction.11) In the GS, quantummechanical values are calculated as S1z = S3z = 157and S2z = −2514, whereas classicalvalues are S1z = S3z = 52and S2z = −52. Experimental values obtained from neutrondiffraction measurements agree well with the quantum mechanical values. Consequently,we have concluded that the spin-52in SrMn3P4O14 can be considered a quantum spin.We can see quantum fluctuation in high-spin chains and clusters. The GS can bea spin-singlet state in these spin systems. For example, in a uniform chain with onlynearest-neighbor AF interactions, the GS is a Tomonaga-Luttinger liquid and a valence-bond-solid state6) for half odd integer and integer spins, respectively. The GS of thespin dimer is also a spin-singlet state. A magnetically ordered state can appear by theintroducing interchain and intercluster interactions. The ordered magnetic moment isexpected to shrink owing to the effect of the singlet GS. Table I shows results of spin-chain and spin-cluster compounds having spin-52. Reduced moments were observed inthese compounds, indicating that quantum fluctuation exists.There are not many experimental results that show quantum fluctuations resultingin a reduced magnetic moment in high-spin clusters. Further experimental confirmationof quantum fluctuations is therefore important. In this work, we focus our attention onthe spin-52compound FeVMoO7.19,20) Figure 1 shows the unit cell of the crystal structureof FeVMoO7. Fe3+ ions (3d5) possess a localized spin-52. The shortest distance betweentwo Fe3+ ions is 3.11 Å at 153 K, whereas the other Fe-Fe distances are 5.01 Å orlonger.20) If the exchange interaction in the shortest Fe-Fe pair is dominant and AF,the spin system in FeVMoO7 consists of AF spin dimers. We studied the magnetism ofFeVMoO7 powder by performing magnetization, specific heat, electron spin resonance,and neutron diffraction experiments. We report the results in this paper.2/16J. Phys. Soc. Jpn.Table I. Magnitude of ordered magnetic moments (m) in spin-chain and spin-cluster compoundshaving spin- 52 . This table also shows the temperature at which the magnitude of ordered magneticmoments was determined (Tmea), the AF transition temperature (TN), and the temperature at whichthe magnetic susceptibility shows a maximum (Tmax). In Cu2Fe2Ge4O13, Fe3+ and Cu2+ ions havespin- 52 and spin- 12 , respectively. The spin tetramers Fe-Cu-Cu-Fe are formed. The probable spin modelin FeVMoO7 is an interacting AF spin- 52 dimer model where spin dimers are connected by interdimerinteractions.m (μB) Tmea (K) TN (K) Tmax (K) Ref.classical value ∼ 5chainSrMn(VO4)(OH) 3.4(1) 4 30 80 12)BaMn2Si2O7 3.9 4 26 55 13)SrMn2V2O8 3.99(1) 1.5 42.2(2) 170 14)NaFeGe2O6 4.09(4) 2.5 11.2 33.8 15)LiFeGe2O6 4.48(5) 5 20.2(2) 24.4(2) 16)clusterCu2Fe2Ge4O13 3.62(3) Fe 1.5 39 100 17, 18)0.38(4) CuFeVMoO7 4.00(7) 4 10.8 16 this work2. Experimental and Calculation MethodsCrystalline FeVMoO7 powder was synthesized by a solid-state reaction. The startingmaterials were Fe2O3 (purity 99.9%), V2O5 (99.99%), and MoO3 (99.99%) powders. Astoichiometric mixture of the powders was sintered at 903 K in air for 88 h in total. AnX-ray powder diffraction pattern was measured at room temperature using an X-raydiffractometer (RINT-TTR III, Rigaku). We detected only reflections of FeVMoO7. Thisleads us to believe that our sample is a single phase of FeVMoO7 within experimentalaccuracy.Electron spin resonance (ESR) measurements were carried out using an X-bandspectrometer (JES-FE2XG, JEOL) at room temperature. We performed specific heatmeasurements and magnetization measurements in magnetic fields of up to 5 T usinga physical property measurement system (Quantum Design) and a superconductingquantum interference device magnetometer (magnetic property measurement system,Quantum Design), respectively. High-field magnetization measurements were carriedout using an induction method with a multilayer pulsed field magnet at the Institutefor Solid State Physics (ISSP), The University of Tokyo.3/16J. Phys. Soc. Jpn.(a)(b)Fig. 1. (Color online) (a) Unit cell of FeVMoO7.19, 20) The brown line indicates the shortest Fe-Fepair (3.11 Å at 153 K).20) (b) Schematic figure showing Fe positions. The brown, green, and blue linesindicate the shortest pairs, the second shortest pairs (5.01 Å), and the third shortest pairs (5.32 Å),respectively.Neutron powder diffraction experiments were performed using the high-resolutionpowder diffractometer ECHIDNA (Proposal ID MI7075) at the Open Pool AustralianLightwater (OPAL) reactor at Australian Nuclear Science and Technology Organisation(ANSTO). We carried out Rietveld refinements of the crystal and magnetic structuresusing the FULLPROF SUITE program package21) with its internal tables for scatteringlengths and magnetic form factors.4/16J. Phys. Soc. Jpn.-1000-500050010000 0.1 0.2 0.3 0.4 0.5 0.6dI/dH (arb. unit)H (T)Fig. 2. (Color online) Electron paramagnetic resonance (EPR) spectrum of FeVMoO7 powder atroom temperature measured using an X-band electron spin resonance (ESR).The eigenenergies of an isolated spin-52dimer were calculated using an exact di-agonalization method. We calculated the temperature T dependence of the magneticsusceptibility χ(T ) and the magnetic-field H dependence of the magnetization M(H)using the eigenenergies.3. Results3.1 Results obtained by bulk methodsWe show the H derivative of the intensity of the electron paramagnetic resonance(EPR) of the FeVMoO7 powder at room temperature in Fig. 2. The frequency (f) ofthe incident microwave is 9.442 GHz. We observed a clear resonance. The intensity (I)shows a maximum at around Hr = 0.341 T where dI/dH = 0. From the relationg = hfμBHr, the g value was evaluated to be 1.98 ± 0.02.We show the T dependence of the specific heat divided by T [C(T )/T ] of anFeVMoO7 pellet in zero magnetic field and the T derivative of the magnetic susceptibil-ity [dχ(T )/dT ] of FeVMoO7 powder in H = 0.1 T in Fig. 3(a). A λ-type peak typical ofthe second-order phase transition was observed in both measurements at around 10.8K. The peak indicates an AF transition. As described later, an antiferromagneticallyordered state was observed at low T in neutron powder diffraction experiments.We show the T dependence of χ(T ) of the FeVMoO7 powder in H = 0.1 T by thered circles in Fig. 3(b). The broad maximum of χ(T ) around 16 K indicates a low-dimensional AF spin system with short-range correlations. The susceptibility appearsto approach a finite value (∼ 0.04 emu/mol Fe) at 0 K. The magnetic order generates5/16J. Phys. Soc. Jpn.00.511.5200.0010.0020.0030 5 10 15 20C(T)/T (J/mol Fe K2)dχ/(T)dT (emu/K mol Fe)T (K)(a)⟹⟸H = 0.1 T00.020.040.060 100 200 300χ(T) (emu/mol Fe)T (K)(b)Exp.J = 10.0 KJ = 10.5 KJ = 11.0 KFig. 3. (Color online) (a) Temperature (T ) dependence of the specific heat divided by T [C(T )/T ]of FeVMoO7 in zero magnetic field and T derivative of the magnetic susceptibility [dχ(T )/dT ] ofFeVMoO7 in a magnetic field of H = 0.1 T. (b) T dependence of χ(T ) of FeVMoO7 in H = 0.1 T (redcircles). The lines indicate χ(T ) calculated for the isolated AF spin- 52 dimers with J = 10.0 K (green),10.5 K (blue), and 11.0 K (lightblue). We used g = 1.98 determined in the EPR measurement.finite susceptibility at 0 K. We fitted the formula CT+TW+ χ0 to the susceptibility. Weused C = 4.29 (emu K/mol Fe) obtained from the spin value S = 52and g = 1.98. Weevaluated TW = 47 K and χ0 = 5.0 × 10−5 (emu/mol Fe) from the susceptibility above200 K. The values are nearly independent of the T range of the fitting. The value of TWis close to 5120) and 49 K.22,23) The susceptibility obtained in this result is close to thatreported for the supporting material in the literature.20) Groń et al.22) and Kurzawa23)reported the T dependence of 1/χ(T ) above 77 K and the magnetization above 4.2 K,respectively. Wang et al.20) and we observed the broad maximum around 16 K in χ(T )in 0.1 T, whereas Kurzawa observed a peak at 14 K in the magnetization in 10 T. Thedifferent T dependences are probably caused by the different magnetic fields.We show the H dependence of the magnetization [M(H)] of the FeVMoO7 powdermeasured at 4.2 and 1.3 K by the red and pink lines, respectively, in Fig. 4. As the mag-netic field increases, the magnetizations increase monotonically and seem to approachsaturation above 40 T.6/16J. Phys. Soc. Jpn.Exp. at 4.2 KJ = 10.0 KJ = 10.5 KJ = 11.0 K0123456780 10 20 30 40 50 60M(H) (μB/Fe)H (T)Exp. at 1.3 KJ = 10.5 KFig. 4. (Color online) Magnetic-field H dependence of the magnetization [M(H)]. The red and pinklines indicate M(H) of the FeVMoO7 powder at 4.2 and 1.3 K, respectively. The three red lines are thesame. The green, blue, and lightblue lines indicate M(H) calculated for the isolated AF spin- 52 dimermodel at 4.2 K with J = 10.0, 10.5, and 11.0 K, respectively. The purple line indicates M(H) calculatedfor the same model at 1.3 K with J = 10.5 K. In the calculation, we used g = 1.98 determined inthe EPR measurement. The three calculated lines at 4.2 K overlap with one another without verticalshifts. Therefore, the vertical positions of the pairs of experimental and calculated magnetizations areshifted by a step of 1μB/Fe.3.2 Neutron diffraction resultsThe red circles in Fig. 5 indicate the neutron powder diffraction pattern of FeVMoO7at 15 K above TN = 10.8 K. The wavelength λ is 2.439 Å. We carried out Rietveldrefinements using the space group P1 (No. 2) to evaluate crystal structure parameters.The blue line on the experimental pattern portrays the result of Rietveld refinementsand agrees well with the experimental pattern. We show the refined crystal structureparameters in Table II. The atomic positions obtained in this result are similar to thosein the literature.19,20)Figure 6(a) shows the neutron powder diffraction pattern of FeVMoO7 at 4 K withthe pattern at 15 K from Fig. 5. The two patterns almost overlap each other except for7/16J. Phys. Soc. Jpn.�  ���-5 x 10305 x 1031 x 1041.5 x 1042 x 1040 1 2 3 4 5Intensity (arb. unit)Fig. 5. (Color online) Neutron powder diffraction pattern (red circles) of FeVMoO7 at 15 K. Thewavelength λ is 2.439 Å. The blue line on the measured pattern indicates a Rietveld refined patternobtained using the crystal structure with P1 (No. 2). The black line at the bottom indicates thedifference between the measured and Rietveld refined patterns. The hash marks show the positions ofnuclear reflections.below Q = 1 Å−1. We show the difference pattern obtained by subtracting the neutronpowder diffraction pattern at 15 K from that at 4 K in Fig. 6(b). We observed severalmagnetic reflections at 4 K. We can index all the reflections with the propagation vector(12, 12, 12).We show the T dependence of the integrated intensity of the magnetic reflection at1212− 12(Q = 0.88 Å−1) in the inset in Fig. 6(b). As T decreases, the intensity increases.We fitted the formula A(1 − T10.8)2β to the experimental data above 8 K. We obtainedA = 701(90) and β = 0.28(3).According to the magnetic space groups in P1,24) the allowed magnetic structuresare collinear. We carried out Rietveld refinements for the difference pattern using twomodels. Two ordered moments in each shortest Fe-Fe pair are parallel in one modeland antiparallel in the other one. Only the antiparallel model can explain the magneticreflections as shown in Fig. 6(b).We show the magnetic structure of FeVMoO7 in Fig. 7(a). An ordered momentvector is [3.32(5),−0.21(5), 2.15(6)]μB lying nearly in the ac plane. Its magnitude is4.00(7)μB at 4 K. Two ordered moments are antiparallel to each other in the shortestFe-Fe pairs indicated by brown lines, whereas two ordered moments are parallel to eachother in the second and third shortest Fe-Fe pairs indicated by green and blue lines,respectively.8/16J. Phys. Soc. Jpn.Table II. Structural parameters of FeVMoO7 evaluated from Rietveld refinements of the neutronpowder diffraction pattern at 15 K. The space group is triclinic P1 (No. 2). The lattice constants area = 5.563(1) Å, b = 6.666(1) Å, c = 7.911(1) Å, α = 96.31(1)◦, β = 90.33(1)◦, and γ = 101.28(1)◦. It isdifficult to determine the V position by neutron diffraction experiments because of the small scatteringlength. We used the position determined by X-ray diffraction .20) The estimated standard deviationsare shown in parentheses. The reliability indexes of the refinement are Rp = 3.81%, Rwp = 4.82%, andRexp = 1.83%.Atom Site x y z Biso Å2Fe 2i 0.3265(5) 0.3065(5) 0.4040(3) 0.72(7)V 2i 0.1888 0.7573 0.3342 0.4Mo 2i 0.7959(6) 0.2127(5) 0.1079(4) 0.88(10)O1 2i 0.2957(7) 0.0091(7) 0.3888(5) 0.85(11)O2 2i 0.3936(7) 0.6240(6) 0.4267(5) 0.42(11)O3 2i 0.1660(9) 0.7065(6) 0.1045(5) 0.58(9)O4 2i 0.0860(6) 0.3143(6) 0.5881(4) 0.19(8)O5 2i 0.5643(8) 0.3116(6) 0.2172(5) 1.22(11)O6 2i 0.0690(7) 0.2998(6) 0.2321(4) 0.38(11)O7 2i 0.2775(7) 0.0539(6) 0.9062(5) 0.83(11)4. DiscussionWe consider a probable spin model for FeVMoO7. As described, if the exchangeinteraction in the shortest Fe-Fe pair is dominant and AF, the spin system consists ofAF spin dimers. The spin-52on Fe3+ ions is usually a Heisenberg spin. Six oxygen ionscoordinate octahedrally the Fe3+ ion. The symmetries of the crystal fields influencingthe Fe3+ ions are almost cubic. We infer that the single ion anisotropy of the Fe3+ ionsis small. Accordingly, we consider the isolated AF Heisenberg spin-52dimer model as afirst approximation. The Hamiltonian isH = JS1 · S2. (2)Figures 3(b) and 4 show χ(T ) and M(H), respectively, calculated for isolated AFspin-52dimers. The calculated M(H) with J = 10.5 K is close to the experimentalM(H) at 4.2 K. When J = 10.0 or 11.0 K, a discrepancy between the calculated andexperimental values of M(H) becomes apparent above about 25 T. The calculated χ(T )with J = 10.5 K is also close to the experimental χ(T ) above about 50 K. Consequently,we evaluated J to be 10.5 ± 0.5 K.We can see, however, a clear difference between the experimental and calculated9/16J. Phys. Soc. Jpn.�  ���(b)-2 x 103-1 x 10301 x 1032 x 1033 x 1034 x 1035 x 1030 1 2 3 4Intensity (arb. unit)02004006000 5 10I (arb. unit)T (K)(a)4 K15 K�  ���05 x 1031 x 1041.5 x 1042 x 1040 1 2 3 4Intensity (arb. unit)Fig. 6. (Color online) (a) Neutron powder diffraction patterns of FeVMoO7 at 4 and 15 K. Thewavelength λ is 2.439 Å. (b) Difference pattern obtained by subtracting the neutron powder diffractionpattern at 15 K from that at 4 K (red circles). The blue line on the measured pattern indicates a Rietveldrefined pattern of the magnetic structure only. The black line at the bottom indicates the differencebetween the measured and Rietveld refined patterns. The hash marks show positions of magneticreflections. The reliability indexes of the refinement are Rp = 10.3%, Rwp = 12.5%, and Rexp = 5.56%.The inset represents the T dependence of the integrated intensity of the magnetic reflection at 1212 − 12(Q = 0.88 Å−1). The blue line shows A(1 − TTN)2β with A = 701, TN = 10.8 K, and β = 0.28.χ(T ) at low T . The experimental magnetization at 1.3 K increases monotonically,whereas the calculated one at 1.3 K has magnetization plateaus. We cannot perfectlyreproduce M(H) at 4.2 K using the isolated AF spin-52dimer model. The discrepanciesare probably caused by interdimer interactions that must exist in FeVMoO7 to stabilizethe ordered state. Intercluster interactions show a greater effect at lower T in spin clus-ter compounds.25–28) Thus, the discrepancies between the experimental and calculatedresults are apparent at low T .As described, the isolated AF spin-52dimer model can explain the magnetization ofFeVMoO7 at 4.2 K but it cannot explain that at 1.3 K. Therefore, we infer that the10/16J. Phys. Soc. Jpn.(a)bacbac(b)Fig. 7. (Color online) (a) Magnetic structure of FeVMoO7. The brown lines connecting two arrowsindicate the shortest Fe-Fe pairs. The green and blue lines indicate the second and third shortest Fe-Fepairs, respectively. (b) Magnetic structure of CrVMoO7. The lightblue lines connecting two arrowsindicate the shortest Cr-Cr pairs.value of the effective interdimer interaction is close to 4.2 K according to our previousresults.26–28) Here, the effective interdimer interaction is given by the sum of the productsof the absolute value of each interdimer interaction (|Jint,i|) and the correspondingnumber of interactions per spin (zi) as Jeff =∑i zi|Jint,i|. Each |Jint,i| must be smallerthan 4.2 K. Consequently, we consider that the intradimer interaction (10.5± 0.5 K) is11/16J. Phys. Soc. Jpn.dominant and that the probable spin model is an interacting AF spin-52dimer modelwhere spin dimers are connected by interdimer interactions.On the basis of the following results, we infer that the dominant interdimer in-teractions are ferromagnetic (F). The experimental χ(T ) is larger than the calculatedone at low T . The saturation field is unchanged by the introduction of ferromagneticinterdimer interactions.29) The neutron-diffraction results indicate that the exchangeinteractions in the second and third shortest Fe-Fe pairs are ferromagnetic.In the molecular field theory, TW is given as S(S +1)zJ/3, where z is the number ofinteractions per spin. TW can be larger than J in S = 52systems. When J = 10.5 K andz = 1 (dimer), TW is 30.6 K, which is slightly smaller than the experimental value. Bytaking interdimer interactions into account, the calculated value of TW may be largerthan 30.6 K. Similarly, we speculate that TN is close to J because of the large S despitethe low-dimensional spin system.We comment on the β value of FeVMoO7. The β values are 0.36, 0.33, and 1/8for three-dimensional Heisenberg, three-dimensional Ising, and two-dimensional Isingmodels, respectively. In the Ising models, β is smaller in the lower dimension. The spinmodel in FeVMoO7 is an interacting AF spin dimer model (zero-dimensional). Thus, theβ value of FeVMoO7 is smaller than that of the three-dimensional Heisenberg models.The pink circle at 0 K in the inset of Fig. 6(b) indicates the intensity in the case thatthe magnitude of the moment is the classical value 4.95μB (g = 1.98). The intensity ofFeVMoO7 at 0 K cannot reach the intensity indicated by the pink circle. Accordingly,the magnitude of the ordered moment at 0 K is smaller than the classical value 4.95μB(g = 1.98). Since the magnetic Bragg reflections were well reproduced by the collinearspin structure, magnetic frustration on the spin system should be weak. The GS of theisolated spin dimer is a spin-singlet state. Therefore, the ordered moment is reduced byquantum fluctuation.We have not investigated whether the other possible spin models can explain theexperimental results. As shown in Fig. 1(b), an AF-F alternating chain is formed bythe exchange interactions in the shortest and second (or third) shortest Fe-Fe pairs. Atwo-dimensional spin model is formed by the three types of exchange interactions. Wedo not have susceptibility and magnetization results calculated for the spin models. Infuture, if we can make large single crystals and investigate magnetic excitations usinginelastic neutron scattering, we can precisely estimate the spin model for FeVMoO7.Then we will compare the experimental results with those calculated for the estimated12/16J. Phys. Soc. Jpn.spin model.We compare the magnetic structure of FeVMoO7 with that of isostructuralCrVMoO7 shown in Fig. 7(b). The magnetic structure shown here is the same as thatreported in the literature.27) The propagation vector is (12, 0, 12), which is different fromthe propagation vector (12, 12, 12) in FeVMoO7. An ordered moment vector in CrVMoO7 is[0.10(5), 2.41(4),−1.42(6)]μB lying nearly in the bc plane.30) Its magnitude is 2.92(7)μB.The ordered moment vector is 4 times larger than that reported in the literature27) be-cause of a mistake in the scale factor. Two ordered moments are aligned in paralleland antiparallel in the shortest Cr-Cr and Fe-Fe pairs indicated by lines, respectively.The report of the antiparallel alignment of two ordered moments in the shortest Cr-Crpair27) is incorrect. The ellipse in Fig. 7 in the literature27) indicates the second short-est Cr-Cr pair. The magnetism of CrVMoO7 can be explained well by the interactingantiferromagnetic spin-32dimer model. The dominant AF interaction may exist in thesecond shortest Cr-Cr pairs (4.97 Å) or in the third shortest pairs (5.24 Å).We consider the origin of the sign of the exchange interactions. The exchange in-teractions are AF (F), F (AF), and F (AF) in the shortest, second shortest, and thirdshortest Fe-Fe (Cr-Cr) pairs, respectively. An exchange interaction is the sum of di-rect exchange and superexchange interactions. The midpoint of two Fe (or Cr) ions inthe shortest pair is an inversion center of the crystal structure. 3d orbits of the twoFe (or Cr) ions are expected to overlap each other. The direct exchange interactionsare probably AF. The Fe-O-Fe and Cr-O-Cr angles in the shortest pair are 100◦ and99◦, respectively. The superexchange interactions are probably F. We speculate thatthe sum of the AF and F interactions results in the weak AF and F interactions in theshortest pairs of FeVMoO7 and CrVMoO7, respectively. We do not know which pathsare dominant for the interactions in the second and third shortest pairs. Therefore, wedo not know the origin of the signs of the interactions.5. ConclusionWe studied the magnetism of FeVMoO7 by performing magnetization, specific heat,electron spin resonance (ESR), and neutron diffraction experiments. We observed an an-tiferromagnetically ordered state below TN = 10.8 K. The broad maximum of magneticsusceptibility around 16 K indicates a low-dimensional AF spin system with short-rangecorrelations. The magnetization increases monotonically with increasing magnetic fieldand seems to approach saturation above 40 T. We consider that the probable spin13/16J. Phys. Soc. Jpn.model is an interacting antiferromagnetic spin-52dimer model where spin dimers areconnected by interdimer interactions. We evaluated the intradimer interaction J to be10.5 ± 0.5 K. We determined the magnetic structure. Two ordered magnetic momentsare antiparallel in each dimer (shortest Fe-Fe pair). The magnitude of the moments is4.00(7)μB at 4 K. The magnitude at 0 K is considered to be smaller than the classi-cal value 4.95μB (g = 1.98 determined in the ESR measurements). We confirmed thereduction of ordered magnetic moments by quantum fluctuation in high-spin (spin-52)clusters as known in high-spin chains.AcknowledgmentsThis work was financially supported by Japan Society for the Promotion of Science(JSPS) KAKENHI (Grant Nos. 15K05150 and 18K03551), grants from National Insti-tute for Materials Science (NIMS), and Development of advanced hydrogen liquefac-tion system by using magnetic refrigeration technology, Japan Science and TechnologyAgency (JST). The high-field magnetization experiments were conducted under theVisiting Researcher’s Program of the Institute for Solid State Physics (ISSP), The Uni-versity of Tokyo. The neutron powder diffraction experiments were performed by usingthe ECHIDNA diffractometer at Australian Nuclear Science and Technology Organisa-tion (ANSTO), Australia (proposal ID. MI7075). 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