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Matsumoto, Masashige, Sato, Taku J., Kuroe, Haruhiko, Kindo, Koichi, Hester, James R., Yamazaki, Hiroki, [Hase, Masashi](https://orcid.org/0000-0003-2717-461X), Ebukuro, Yuta, Matsuo, Akira

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[Magnetism of the antiferromagnetic spin-3/2 dimer compound CrVMoO7 having an antiferromagnetically ordered state](https://mdr.nims.go.jp/datasets/d9e205be-38fc-4ec8-a6f3-88adad4a5e32)

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PHYSICAL REVIEW B 95, 144429 (2017)Magnetism of the antiferromagnetic spin-32 dimer compound CrVMoO7 havingan antiferromagnetically ordered stateMasashi Hase,1,* Yuta Ebukuro,2 Haruhiko Kuroe,2 Masashige Matsumoto,3 Akira Matsuo,4 Koichi Kindo,4 James R. Hester,5Taku J. Sato,6 and Hiroki Yamazaki71Research Center for Advanced Measurement and Characterization, National Institute for Materials Science (NIMS),1-2-1 Sengen, Tsukuba-shi, Ibaraki 305-0047, Japan2Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan3Department of Physics, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka-shi, Shizuoka 422-8529, Japan4The Institute for Solid State Physics (ISSP), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8581, Japan5Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation (ANSTO),Locked Bag 2001, Kirrawee DC NSW 2232, Australia6Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira,Aoba-ku, Sendai-shi, Miyagi 980-8577, Japan7Nishina Center for Accelerator-Based Science, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan(Received 15 February 2017; published 24 April 2017)We measured magnetization, specific heat, electron spin resonance, neutron diffraction, and inelastic neutronscattering of CrVMoO7 powder. An antiferromagnetically ordered state appears below TN = 26.5 ± 0.8 K. Weconsider that the probable spin model for CrVMoO7 is an interacting antiferromagnetic spin- 32 dimer model.We evaluated the intradimer interaction J to be 25 ± 1 K and the effective interdimer interaction Jeff to be8.8 ± 1 K. CrVMoO7 is a rare spin dimer compound that shows an antiferromagnetically ordered state atatmospheric pressure and zero magnetic field. The magnitude of ordered moments is 0.73(2)μB. It is muchsmaller than a classical value ∼3μB. Longitudinal-mode magnetic excitations may be observable in singlecrystalline CrVMoO7.DOI: 10.1103/PhysRevB.95.144429I. INTRODUCTIONTwo types of magnetic excitations exist in a magneticallyordered state. They are gapless transverse-mode (Nambu-Goldstone mode) [1] and gapped longitudinal-mode (am-plitude Higgs mode) [2–4] excitations corresponding tofluctuations in directions perpendicular and parallel to or-dered moments, respectively. The transverse-mode (T-mode)excitations are well known as spin wave excitations. Thereare a few experimental observations on the longitudinal-mode (L-mode) excitations. The L mode was observed ina pressure-induced magnetically ordered state of the three-dimensional (3D) interacting antiferromagnetic (AF) spin- 12dimer compound TlCuCl3 by inelastic neutron scattering (INS)experiments [5–7]. The ground state (GS) is a spin-singlet stateat atmospheric pressure in this compound. While the L modehas weak intensity and spontaneously decays into a pair ofT modes [8,9], it is well defined in the ordered state in thevicinity of the quantum critical point in 3D systems [10].In low-dimensional systems, it is difficult to observe the Lmode in a longitudinal susceptibility that INS probes [11]because the longitudinal susceptibility exhibits an infraredsingularity, which can obscure an amplitude peak at a finiteenergy. The L mode can be well defined in terms of ascalar susceptibility both in the two- and three-dimensionalsystems, because the scalar susceptibility can display asharp amplitude peak [11]. The L mode was observed in atwo-dimensional ultracold atomic gas near the superfluid toMott-insulator transition [12]. In magnetic systems, Raman*HASE.Masashi@nims.go.jpspectra can measure the scalar susceptibility. The L modewas actually observed by Raman scattering experiments in thepressure-induced ordered state of KCuCl3 [13,14] and in themagnetic-field-induced ordered state of TlCuCl3 [15].According to results of theoretical investigations, the L-mode excitations may be observed in an antiferromagneticallyordered state appearing on cooling at atmospheric pressureand zero magnetic field in interacting AF spin-cluster com-pounds [16]. A shrinkage of ordered magnetic moments byquantum fluctuations leads to a large intensity of the L-modeexcitations. If the GS of the corresponding isolated spin clusteris a spin-singlet state, the shrinkage of ordered moments canbe expected in an ordered state generated by the introductionof intercluster interactions.In interacting spin clusters, the ordered state may appearunder the condition that the value of an effective interclusterinteraction is not so small compared with that of � [16]. Herethe effective intercluster interaction is given by the sum of theproducts of the absolute value of each intercluster interaction(|Jint,i |) and the corresponding number of interactions perspin (zi) as Jeff = ∑i zi |Jint,i |. � is the energy difference(spin gap) between the singlet GS and first excited tripletstates. It is advantageous for the appearance of the orderedstate that � is much smaller than the dominant intraclusterinteractions. In a spin- 12 tetramer of which the HamiltonianH = J1S2·S3 + J2(S1·S2 + S3·S4) with J1 > 0 and J2 < 0,the GS is a spin-singlet state and �/J1 can be sufficientlysmall [17–19]. The values of J1, J2, Jeff , and � are 317,−162, 42, and 19 K, respectively, in Cu2CdB2O6 [20] and240, −142, 30, and 17 K, respectively, in CuInVO5 [19].The ordered state appears in Cu2CdB2O6 [18,20,21] andCuInVO5 [19] below the transition temperature TN = 9.8 and2469-9950/2017/95(14)/144429(7) 144429-1 ©2017 American Physical Societyhttps://doi.org/10.1103/PhysRevB.95.144429MASASHI HASE et al. PHYSICAL REVIEW B 95, 144429 (2017)FIG. 1. (a) The unit cell of CrVMoO7 [25,26]. An AF spin-32 dimer is formed by two neighboring Cr3+ ions (3d3 electronconfiguration) with the distance of 3.01 Å. (b) Interacting spin dimermodel used to calculate magnetization using a mean-field theorybased on the dimer unit (dimer mean-field theory).2.7 K, respectively. Magnetic excitations in Cu1142 Cd11B2O6were studied by inelastic neutron scattering experiments on itspowder [20]. The results suggest the existence of the L-modeexcitations. Magnetic excitations in CuInVO5 have not beeninvestigated.Spin dimer compounds are also attractive for investigationof the L-mode excitations at atmospheric pressure and zeromagnetic field. In contrast with the small �/J1 in the spin- 12tetramer, the value of �/J is 1 in the isolated AF spin dimergiven by JS1·S2 irrespective of the spin value. It is rare thatspin dimer compounds show a magnetically ordered state atatmospheric pressure and zero magnetic field. An example isthe AF spin- 12 dimer compound NH4CuCl3 [22–24].We can expect an interacting AF spin- 32 dimer modelin CrVMoO7 from its crystal structure as shown inFig. 1(a) [25,26]. Only the Cr3+ ion (3d3) has a localizedspin- 32 . The shortest distance between two Cr3+ ions is 3.01 Åat 153 K, whereas the other Cr-Cr distances are 4.97 Åor longer [25]. We found an antiferromagnetically orderedstate below TN = 26.5 ± 0.8 K. We investigated magnetismof CrVMoO7 using magnetization, specific heat, electron spinresonance, neutron diffraction, and inelastic neutron scatteringexperiments. In this paper, we report the results.II. EXPERIMENTAL AND CALCULATION METHODSCrystalline CrVMoO7 powder was synthesized by a solid-state reaction. Starting materials are Cr2O3, V2O5, and MoO3powder. Their purity is 99.99%. A stoichiometric mixture ofpowder was sintered at 923 K in air for 268 h with intermediategrindings. We measured an x-ray powder diffraction pattern atroom temperature using an x-ray diffractometer (RINT-TTRIII, Rigaku). We confirmed that our sample was a nearly singlephase of CrVMoO7.Electron spin resonance (ESR) measurements were per-formed using an X-band spectrometer (JES-RE3X, JEOL)at room temperature. We measured the specific heat usinga physical property measurement system (Quantum Design).We measured the magnetization in magnetic fields of up to5 T using a superconducting quantum interference devicemagnetometer magnetic property measurement system (Quan-tum Design). High-field magnetization measurements wereconducted using an induction method with a multilayer pulsedfield magnet installed at the Institute for Solid State Physics(ISSP), the University of Tokyo.We carried out neutron powder diffraction experimentsusing the high-intensity powder diffractometer Wombat (Pro-posal ID P5174) at Australia’s Open Pool Australian Lightwa-ter (OPAL) reactor in Australian Centre for Neutron Scatteringin Australian Nuclear Science and Technology Organisation(ANSTO). We performed Rietveld refinements of the crystaland magnetic structures using the FULLPROF SUITE programpackage [27] with its internal tables for scattering lengthsand magnetic form factors. We performed inelastic neutronscattering measurements using the inverted geometry time-of-flight spectrometer LAM-40 in High Energy AcceleratorResearch Organization (KEK).We obtained the eigenenergies of isolated spin- 32 dimersusing an exact diagonalization method. We calculated thetemperature T dependence of the magnetic susceptibility χ (T )and the magnetic-field H dependence of the magnetizationM(H ) using the eigenenergies.We calculated M(H ) for the model shown in Fig. 1(b) usinga mean-field theory based on the dimer unit (dimer mean-field theory). Finite magnetic moments were initially assumedon the Cr sites in the dimer. The mean-field Hamiltonian wasthen expressed by a 16 × 16 matrix form under considerationof the external magnetic field and the molecular field fromthe nearest-neighbor sites. The eigenstates of the mean-fieldHamiltonian were used to calculate the expectation value of theordered moments on the Cr sites. We continued this procedureuntil the values of the magnetic moments converged. We finallyobtained a self-consistently determined solution for M(H ).III. RESULTS AND DISCUSSIONFigure 2 shows the H derivative of the intensity of electronparamagnetic resonance (EPR) of a CrVMoO7 pellet at roomtemperature. The frequency of the incident microwave is9.455 GHz. A clear resonance appeared. We evaluated theg value to be 1.92 ± 0.02.Figure 3(a) shows the T dependence of the specific heatC(T ) of CrVMoO7 in zero magnetic field and the T derivativeof the magnetic susceptibility χ (T ) of CrVMoO7 in H = 0.1T.The sample was a pressed pellet and powder for C(T ) andχ (T ), respectively. We can see a peak around 26.5 K in C(T )and around 25.5 K in dχ (T )/dT . As described later, weobserved an antiferromagnetically ordered state at low T inneutron powder diffraction experiments. The peak in C(T ) isconsistent with the λ-type peak typical of the second-order144429-2MAGNETISM OF THE ANTIFERROMAGNETIC SPIN- . . . PHYSICAL REVIEW B 95, 144429 (2017)FIG. 2. The electron paramagnetic resonance (EPR) spectrum ofa CrVMoO7 pellet at room temperature measured using an X-bandelectron spin resonance (ESR).phase transition. We determined the transition temperatureTN = 26.5 ± 0.8 K mainly from the specific heat result.The red circles in Fig. 3(b) show the T dependence ofχ (T ) of CrVMoO7 powder in H = 0.1T. The broad maximumof χ (T ) around 35 K indicates a low-dimensional AF spinsystem. The susceptibility seems to approach a finite value(∼0.012 emu/mol Cr) at 0 K. The magnetic order results inthe probable finite susceptibility at 0 K. The susceptibilityobtained by us is close to that reported in literature [25,28].We considered the simple isolated AF spin- 32 dimer modelas a first approximation because of the following reasons. Thespin- 32 on Cr3+ ions is usually a Heisenberg spin. The Cr3+ ionis coordinated octahedrally by six oxygen ions. Symmetriesof crystal fields affecting the Cr3+ ions are nearly cubic. It isinferred that single ion anisotropy of the Cr3+ ions is small.FIG. 3. (a) Temperature T dependence of the specific heat C(T )of CrVMoO7 in zero magnetic field and T derivative of the magneticsusceptibility χ (T ) of CrVMoO7 in a magnetic field of H = 0.1 T.(b) T dependence of χ (T ) of CrVMoO7 in H = 0.1T (red circles).A green line with several circles indicates χ (T ) calculated for anisolated AF spin- 32 dimer with J = 25 K and g = 1.92.FIG. 4. Magnetic-field H dependence of the magnetizationM(H ) of CrVMoO7 powder (red lines). Blue and green lines indicateM(H ) calculated for the interacting spin- 32 dimer model in Fig. 1(b)labeled by “w/ Jeff” and for an isolated spin- 32 dimer labeled by“w/o Jeff”, respectively. The values of the parameters are J = 25 K,Jeff = 8.8 K, and g = 1.92. (a) M(H ) at 1.3 K. (b) M(H ) at 30 K.The green line in Fig. 3(b) shows χ (T ) calculated for theisolated AF spin- 32 dimer with J = 25 K and g = 1.92 that wasdetermined in EPR. The experimental and calculated χ (T ) areclose to each other at high T . We evaluated J to be 25 ± 1 K.According to Fig. 9 in Ref. [29], the magnitude of theexchange interaction J3d3 is mainly determined by the distanceR between two magnetic ions. There is an empirical relationJ3d3 = a exp(−R/b) with a = 8.7 × 107 K and b = 0.21Å forcompounds including Cr3+ ions (3d3). The value of J3d3 wascalculated to be 53 K for R = 3.01Å. The values of J and J3d3are the same in order.The red lines in Fig. 4 show the H dependence of themagnetization M(H ) of CrVMoO7 powder measured at 1.3and 30 K. The magnetization increases monotonically withincrease in H . The green lines in Fig. 4 indicate M(H )calculated for the isolated AF spin- 32 dimer with J = 25 K andg = 1.92. The calculated M(H ) is close to the experimentalM(H ) at 30 K, whereas the isolated spin dimer model failsto reproduce the experimental M(H ) at 1.3 K. There are 13and 23 quantum magnetization plateaus in the calculated line,whereas no plateau exists in the experimental line. The 13 and23 magnetization-plateau phases are polarized paramagneticphases in which ST = 1 and 2, respectively. Here ST representsthe size of the total spin of the two S = 32 spins. We couldnot find the J value of the isolated spin dimer model thatreproduced the experimental M(H ) at 1.3 K.144429-3MASASHI HASE et al. PHYSICAL REVIEW B 95, 144429 (2017)FIG. 5. A neutron powder diffraction pattern (circles) ofCrVMoO7 at 35 K. The wavelength λ is 2.955 Å. A blue line on themeasured pattern portrays a Rietveld refined pattern obtained usingthe crystal structure with P 1̄ (No. 2). A line at the bottom portrays thedifference between the measured and the Rietveld refined patterns.Hash marks represent positions of nuclear reflections.According to the results in CuInVO5 [19], the discrepancybetween experimental and calculated M(H ) is probablycaused by interdimer interactions. Interdimer interactions mustexist in CrVMoO7 to stabilize the ordered state. Interdimerinteractions have a greater effect on the magnetization at lowerT . Therefore, the discrepancy between the experimental resultsand those calculated for the isolated spin dimer appears at lowT . We assumed the simple model shown in Fig. 1(b) as inthe case of CuInVO5 [19] and calculated M(H ) using thedimer mean-field theory. The blue lines in Fig. 4 indicateM(H ) calculated for the interacting spin dimer model withJ = 25 K, Jeff = 8.8 K, and g = 1.92. The experimental andcalculated M(H ) are in agreement with each other. The Jeffvalue is not so small compared with the J value. Therefore,the antiferromagnetically ordered state appears.We can explain qualitatively M(H ) of CrVMoO7. In aweakly interacting spin dimer model, magnetization plateausexist at low T . Magnetization-plateau phases are polarizedparamagnetic phases without a spontaneous magnetic order.An ordered phase can appear in a magnetic-field range, whereM(H ) increases, between two magnetization-plateau phases.In the case of spin- 32 , there are three types of ordered phases,phase 1, 2, and 3 at 0 � H < H1s , H1f < H < H2s , andH2f < H < H3s , respectively. Here, His and Hif indicatemagnetic fields at which the i3 plateau starts and finishes,respectively. The phase 1 is mainly formed by ST = 0 andST = 1 states of isolated AF spin dimers. The phase 2 is mainlyformed by ST = 1 and ST = 2 states. The phase 3 is mainlyformed by ST = 2 and ST = 3 states. As interdimer interac-tions increase, magnetic-field ranges of ordered phases arespread. When interdimer interactions are strong, the orderedphases are connected with each other. A single ordered phaseis formed until the saturation of the magnetization. Therefore,the magnetization increases monotonically with increase in H .The circles in Fig. 5 show a neutron powder diffractionpattern of CrVMoO7 at 35 K above TN = 26.5 ± 0.8 K. Thewavelength λ is 2.955 Å. We performed Rietveld refinementsusing the space group P 1̄ (No. 2) to evaluate crystal structureparameters. The line on the experimental pattern indicatesthe result of Rietveld refinements. The line agrees with theTABLE I. Structural parameters of CrVMoO7 derived fromRietveld refinements of the neutron powder diffraction patternat 35 K. We used triclinic P 1̄ (No. 2). The lattice constantsare a = 5.521(1)Å, b = 6.575(1)Å, c = 7.859(1)Å, α = 96.24(1)◦,β = 89.91(1)◦, and γ = 101.99(1)◦. Estimated standard deviationsare shown in parentheses. The reliability indexes of the refinementare Rp = 3.16%, Rwp = 4.14%, and Rexp = 0.21%.Atom Site x y z Biso Å2Cr 2i 0.826(3) 0.310(3) 0.408(2) 0.30(4)V 2i 0.311(3) 0.242(3) 0.665(3) 0.31(5)Mo 2i 0.301(2) 0.209(1) 0.109(1) 0.24(5)O1 2i 0.203(2) 0.981(1) 0.616(1) 0.33(5)O2 2i 0.108(3) 0.375(1) 0.574(1) 0.33(5)O3 2i 0.336(2) 0.295(2) 0.891(1) 0.33(5)O4 2i 0.597(2) 0.314(1) 0.580(1) 0.33(5)O5 2i 0.057(2) 0.319(1) 0.222(1) 0.33(5)O6 2i 0.564(2) 0.292(1) 0.233(1) 0.33(5)O7 2i 0.213(2) 0.948(2) 0.098(1) 0.33(5)experimental pattern. The refined crystal structure parametersare presented in Table I. The atomic positions in our resultsare similar to those in the literature [25,26].Figure 6(a) shows neutron powder diffraction patterns ofCrVMoO7 at 5 and 35 K. The two patterns nearly overlapeach other except for around 2θ = 20◦. Figure 6(b) shows thedifference pattern made by subtracting the neutron powderdiffraction pattern at 35 K from that at 5 K. Several magneticreflections are apparent at 5 K. All the reflections can beindexed with the propagation vector k = ( 12 ,0, 12 ).The inset in Fig. 6(b) shows the T dependence of theintegrated intensity between 17 and 22◦ including − 12 0 12 and12 0 12 reflections. The intensity increases with decrease in Tand is nearly constant below 14 K. The blue line indicatesA(1 − TTN)2β with A = 1.98, TN = 27.3 K, and β = 0.29.These values were obtained from the data above 20 K. Weevaluated β to be 0.26 in the spin- 12 tetramer compoundCu2CdB2O6 from the inset figure in Fig. 4 in Ref. [18]. The twovalues of the critical exponent are close to each other. The βvalue is 0.36, 0.33, and 1/8 for three-dimensional Heisenberg,three-dimensional Ising, and two-dimensional Ising models,respectively. In the Ising models, β is smaller in the lowerdimension. The spin models in CrVMoO7 and Cu2CdB2O6are low-dimensional AF interacting spin clusters. Therefore,the β values in these compounds are smaller than that ofthree-dimensional Heisenberg models.According to magnetic space groups in P 1̄ [30], onlya collinear magnetic structure is possible. We performedRietveld refinements for the difference pattern using twomodels. Two ordered moments in each dimer are parallel inone model and antiparallel in the other one. As expected, onlythe antiparallel model can explain the magnetic reflections asshown in Fig. 6(b).The magnetic structure is shown in Fig. 7 [31]. An orderedmoment vector is [0.02(2),0.60(1),−0.36(2)]μB lying nearlyin the bc plane. Its magnitude is 0.73(2)μB. It is much smallerthan a classical value ∼3μB. The GS of the spin dimer is aspin-singlet state [32–34]. Therefore, the ordered moment isshrunk.144429-4MAGNETISM OF THE ANTIFERROMAGNETIC SPIN- . . . PHYSICAL REVIEW B 95, 144429 (2017)FIG. 6. (a) Neutron powder diffraction patterns of CrVMoO7 at 5and 35 K. The wavelength λ is 2.955 Å. (b) A difference pattern madeby subtracting a neutron powder diffraction pattern at 35 K from that at5 K. A line on the measured pattern portrays a Rietveld refined patternof the magnetic structure. A line at the bottom portrays the differencebetween the measured and the Rietveld refined patterns. Hash marksrepresent positions of magnetic reflections. The reliability indexes ofthe refinement are Rp = 4.37%, Rwp = 6.17%, and Rexp = 0.46%.Indexes of major magnetic reflections labeled by 1, 2, 3, 4, and 5are − 12 0 12 , 12 0 12 , 12 − 1 12 , − 12 1 12 , and − 12 0 32 , respectively. The insetshows T dependence of the integrated intensity between 17 and 22◦.A blue line indicates A(1 − TTN)2β with A = 1.98, TN = 27.3 K, andβ = 0.29.Figure 8 shows INS intensity I (Q,ω) maps of CrVMoO7powder at 1.5 and 30 K. Here, Q and ω are the magnitude ofthe scattering vector and the energy transfer, respectively. Theenergy of final neutrons Ef is 4.59 meV. We can see excitationsFIG. 7. The magnetic structure of CrVMoO7. An ellipse indicatesan AF dimer.FIG. 8. INS intensity I (Q,ω) maps in the Q-ω plane forCrVMoO7 powder at 1.5 K (a) and 30 K (b) measured using theLAM-40 spectrometer. The energy of final neutrons Ef is 4.59 meV.The right vertical key shows the INS intensity in arbitrary units.between 2 and 7 meV at 1.5 K. The intensity of the excitationsis suppressed at higher Q. Excitations at 1.5 K also exist below2 meV around Q = 0.7 Å−1. Excitations at 30 K exist in lowerenergies in comparison with those at 1.5 K. The intensity isstrong at low ω around Q = 0.7 Å−1.Figure 9(a) shows the ω dependence of I (Q,ω) in the Qrange of 0.95–1.05 Å−1. The intensity at 1.5 K is the strongestaround 4.5 meV. The intensity at 30 K decreases with increasein ω. The red circles in Fig. 9(b) show the Q dependence ofI (Q,ω) at 1.5 K summed in the ω range of 4–5 meV. Theintensity shows a peak around Q = 1.0 Å−1.Considering the INS results of Cu2CdB2O6 [20], we canexplain qualitatively the INS results of CrVMoO7 using theinteracting AF spin- 32 dimer model. The blue line in Fig. 9(b)indicates the Q dependence of the intensity calculated for theisolated spin dimer model with the Cr-Cr distance of 3.01 Å.The experimental and calculated results are similar to eachother. The first excited spin-triplet states exist at 2.2 meV(=25 K) in the isolated AF spin- 32 dimer. Interdimer inter-actions change discrete levels of excited states to excitationbands with finite widths. The excitations between 2 and 7 meVindicate the existence of the excitation bands [35].The magnetic reflection is the strongest at − 12 0 12 . Themagnetic zone center of the spin configuration shown inFIG. 9. (a) ω dependence of the INS intensity for CrVMoO7powder in the Q range of 0.95–1.05 Å−1 at 1.5 and 30 K. (b) TheQ dependence of the INS intensity of CrVMoO7 powder summedin the ω range of 4–5 meV at 1.5 K (circles). A line indicates theintensity calculated for an isolated AF spin- 32 dimer. The formulais Af (Q)2[1 − sin(3.01Q)/(3.01Q)] where A and f (Q) represent ascaling factor and an atomic magnetic form factor, respectively.144429-5MASASHI HASE et al. PHYSICAL REVIEW B 95, 144429 (2017)Fig. 7 is − 12 0 12 . The Q value is 0.70 Å−1. Therefore, theexcitations at 1.5 K below 2 meV around Q = 0.7 Å−1 areT-mode (Nambu-Goldstone mode) excitations in the vicinityof the gapless point.The magnetic excitations are gapless below TN. The tem-perature 30 K is slightly higher than TN = 26.5 ± 0.8 K. Thebandwidths are large and the excitation gap is small. Therefore,magnetic excitations appear in low energies. Excitations fromthermally excited states in the excitation bands also generatethe continuous low-energy intensities at 30 K.We could not confirm L-mode excitations because ofthe powder sample. We intend to make single crystalsof CrVMoO7 and to perform INS and Raman scatteringexperiments on them to investigate L-mode excitations. Weexpect that L-mode excitations are observable because of thesmall ordered moment. In the weakly ordered spin- 12 chainantiferromagnet Sr2CuO3, unusual magnetic excitations wererecently observed by ESR experiments [36]. It is reportedthat the excitations can be attributed to the Nambu-Goldstonemode renormalized due to its interaction with the high-energy L mode. We also pursue such unusual excitations inCrVMoO7.IV. CONCLUSIONWe investigated magnetism of CrVMoO7 using magnetiza-tion, specific heat, electron spin resonance, neutron diffraction,and inelastic neutron scattering experiments. An antiferro-magnetically ordered state appears below TN = 26.5 ± 0.8 K.The magnetic susceptibility of CrVMoO7 powder at highT is close to that calculated for the isolated AF spin- 32dimer with the intradimer interaction value J = 25 ± 1 K andg = 1.92 ± 0.02. We were able to explain the magnetizationcurves using the interacting AF spin- 32 dimer model with the ef-fective interdimer interaction Jeff = 8.8 ± 1 K. We determinedthe magnetic structure of CrVMoO7. The magnitude of orderedmoments is 0.73(2)μB. It is much smaller than a classicalvalue ∼3μB. Two ordered moments are antiparallel in eachdimer. We observed magnetic excitations in inelastic neutronscattering experiments. We can explain qualitatively the resultsusing the interacting AF spin- 32 dimer model. CrVMoO7 is arare spin dimer compound that shows an antiferromagneticallyordered state at atmospheric pressure and zero magnetic field.Longitudinal-mode magnetic excitations may be observable insingle crystalline CrVMoO7.ACKNOWLEDGMENTSThis work was financially supported by Japan Societyfor the Promotion of Science (JSPS) KAKENHI (Grant No.15K05150) and grants from National Institute for MaterialsScience (NIMS). M.M. was supported by JSPS KAKENHI(Grant No. 26400332). The high-field magnetization ex-periments were conducted under the Visiting Researcher’sProgram of the Institute for Solid State Physics (ISSP), theUniversity of Tokyo. The neutron powder diffraction exper-iments were performed by using the Wombat diffractometerat Australian Nuclear Science and Technology Organisation(ANSTO), Australia (Proposal ID. P5174). We are gratefulto S. Matsumoto for sample syntheses and x-ray diffractionmeasurements.[1] J. Goldstone, A. Salam, and S. Weinberg, Broken symmetries,Phys. Rev. 127, 965 (1962).[2] S. Sachdev, Quantum Phase Transitions, 2nd ed. (CambridgeUniversity Press, Cambridge, 2011).[3] S. Sachdev and B. Keimer, Quantum criticality, Phys. Today 64,29 (2011).[4] D. Pekker and C. M. Varma, Amplitude/Higgs modes incondensed matter physics, Annu. Rev. Condens. Matter Phys. 6,269 (2015).[5] Ch. Rüegg, B. Normand, M. Matsumoto, A. Furrer, D. F.McMorrow, K. W. Krämer, H.-U. Güdel, S. N. Gvasaliya, H.Mutka, and M. 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