PHYSICAL REVIEW B, VOLUME 64, 024419

Magnetic and resonant properties of quasi-one-dimensional antiferromagnet LiCuVO4

A. N. Vasil’ev and L. A. PonomarenkoLow Temperature Physics and Superconductivity Department, Moscow State University, Moscow, 119899, Russia

H. Manaka and I. YamadaDepartment of Physics, Faculty of Science, Chiba University, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

M. Isobe and Y. UedaInstitute for Solid State Physics, University of Tokyo, Roppongi 7-22-1, Tokyo 106, Japan

~Received 27 February 2001; published 20 June 2001!

The electron-spin-resonance~ESR! and dc magnetization measurements of the spinel-type compoundLiCuVO4 in a temperature range 2–300 K are presented. At cooling, the magnetization shows a broad maxi-mum atTM528 K, characteristic of a quasi-one-dimensional magnetic system. Then, the magnetization some-what increases at temperatures below;9 K, shows a second maximum atTN8;4 K, and a subsequent sharpdrop. Both magnetization and ESR data indicate that the three-dimensional antiferromagnetic ordering occursat TN52.3 K. AboveTN the asymmetric ESR spectra of the LiCuVO4 powder sample are in correspondencewith the symmetry of the crystal field on Cu21 ions. Thegi andg' values diverge at cooling as is anticipatedfor a quasi-one-dimensional Heisenberg antiferromagnet. According to the Bonner-Fisher model the interchainexchange interaction isJ1522 K, while the intrachain exchange interaction is estimated to beJ2;1 K.

DOI: 10.1103/PhysRevB.64.024419 PACS number~s!: 75.30.Kz, 75.50.Ee, 75.30.Cr

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I. INTRODUCTION

The discovery of diverse cooperative quantum phenoena in complex metal oxides has stimulated the searchinorganic materials with a low-dimensional magnetic susystem. This search has uncovered a variety of quasi-and quasi-two-dimensional compounds, as well as systof intermediate dimension, i.e., coupled magnetic chainsspin ladders. Such compounds are distinguished by spetemperature dependencies of magnetic properties andcharacterized usually by quite low magnetic ordering teperatures. In certain cases magnetic ordering does not oat all, and one or another interaction mechanism opensspin gap in the magnetic excitation spectrum of a lodimensional magnet.1,2 In the last three decades a large nuber of quasi-one-dimensional antiferromagnets with differvalues of spinS has been discovered. The examples ofmost studied ones3,4 are TMMC and CsMnCl3•2H2O, bothwith S5 5

2 . After first observation of the spin-Peierls transtion in inorganic compounds performed by Hase, Terasand Uchinokura1 on CuGeO3 the attention of researchers hbeen focused on magnetic materials that contain chainions with S5 1

2 . The experimental realization of such manetic ions are Cu21 and V41. That is why in the last yearsmany experimental papers have been devoted to the invgation of magnetic properties of metal-oxide compounwith chainlike arrangements of copper and vanadium atoin a crystal structure.1,2,5–7Rather diverse variations of lowdimensional magnetic structures are encountered in cpounds where these ions coexist with lithium ions Li11.Thus, in the lithium cuprate LiCuO2 the copper ions Cu21

(S5 12 ) in linear CuO4 chains are bound with one another b

a ferromagnetic interaction, while the interaction betwechains is antiferromagnetic.5 Magnetic V41 (S5 1

2 ) and non-magneticV51 (S50) ions are present in the layered stru

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ture of lithium vanadate LiV2O5, and each of the ions formzig-zag chains of vanadium pyramids VO5. A magneticphase transition occurs in this system only at ultraltemperatures.8 Recently, fascinating heavy-fermion behavihas been observed in the LiV2O4 system.6

II. EXPERIMENT AND RESULTS

The orthorhombic metal-oxide compound LiCuVO4,where all of the ions listed above are present, is geneticrelated with the spinel structure, where the lithium ions Li11

and magnetic copper ions Cu21 (S5 12 ) are located in an

octahedral environment, while the nonmagnetic vanadiions V51 (S50) are located in a tetrahedral environmeconsisting of oxygen ions O22.9 As shown in Fig. 1, thechains of copper-oxygen octahedra CuO6, which are coupledalong an edge in the basal plane, extend along theb axis, andthey form almost regular triangles in thea-c plane. Chains oflithium-oxygen octahedra LiO6 extend along thea axis, andthe vanadium-oxygen tetrahedra VO4 are isolated from oneanother. The room-temperature lattice constants area50.5652 nm,b50.5810 nm, andc50.8750 nm,9 so thatcopper-oxygen octahedra are characterized by a strongtragonal distortion, the long axis of the CuO6 octahedra be-ing oriented along thec axis. In nonstoichiometric sampleof Li12xCuVO4 (0,x,0.2) a structural phase transition othe cooperative Jahn-Teller effect type has been obseabove room temperature.10

The LiCuVO4 samples were prepared by solid-phase sthesis from a stoichiometric mixture of lithium carbonaLi2CO3, copper oxide CuO, and vanadium pentoxide V2O5.Synthesis had been conducted at 530 °C for one weekthen synthesis continued after additional repeated mixifor one month. The final product—a light-yellow powder—consisted of a monophase sample, as was verified by x

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A. N. VASIL’EV et al. PHYSICAL REVIEW B 64 024419

diffraction. Magnetic measurements were performed oQuantum Design superconducting quantum interferencevice magnetometer in fields up to 5 T in the temperaturerange 2–300 K. The electron-spin resonance~ESR! spectrawere taken over 1.3–300 K using a 100-kHz field-modulaspectrometer operated at 24.5 GHz, so that the derivativethe absorption signals were recordered.

The temperature dependence of the magnetic suscepity of LiCuVO4 taken atH 5 0.1 T is presented in Fig. 2The solid line represents the best fit according to a Bonn

FIG. 1. The crystal structure of LiCuVO4. The copper ions aresituated within edge-sharing oxygen octahedra.

FIG. 2. The temperature dependence of the magnetic suscbility of LiCuVO4. The solid line is a fit corresponding to a BonneFisher model. The inset represents the temperature dependensusceptibility and the first derivative of susceptibility in the lowtemperature region.

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Fisher model for a quasi-one-dimentional magnetic system11

As temperature decreases, the magnetic susceptibilitxpasses through a wide peak atTM528 K, then increasessomewhat at;9 K, and once again sharply decreasesTN8;4 K. The magnetizationM as a function of the fieldHis linear aboveTN8 ; below these temperatures the depedenceM (H) shows weak nonlinearity. In contrast to thwide peak in x(T) at TM , the position of the low-temperature peak inx at TN8;4 K depends nonmonotonously on the magnetic field. In weak fields the peak fishifts somewhat to higher temperatures and then rapshifts to lower temperatures as the field increases furtThis dependence is shown in Fig. 3, where the solid lconnecting the experimental points is drawn only for visuclarity.

All experimental data presented are characteristic oquasi-one-dimensional magnet, which, as the temperadecreases, first exhibits short-range magnetic correlatwithin the chains and then undergoes three-dimensionaltiferromagnetic ordering at low temperatures. The antifermagnetic ordering temperatureTN is somewhat differentfrom TN8 , and it can be determined according to the positof the peak in the temperature dependence of the deriva]x/]T ~see the inset to Fig. 2!. In weak fieldsTN52.3 K,and it decreases to 2 K at H55 T.

At high temperatures (T>150 K) the magnetic susceptbility of LiCuVO4 can be approximated by the Curie-Weilaw

x5C

T2Q, ~1!

with Q5215 K and the effectiveg factor is 2.26. However,in a wide temperature range the best fit for the temperadependence of magnetic susceptibility is given by a polymial corresponding to the Bonner-Fisher curve.11 The latteris a numerical calculation ofx(T) for an ideal one-dimensional Heisenberg chain of spinsS5 1

2 .12

The ESR measurements were performed over 1.3–30using a 100-kHz field-modulatedK-band spectrometer operated at 24 GHz. Examples of the spectra observed at sevtemperatures are shown in Fig. 4. When we see the spe

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FIG. 3. The position of the low-temperature maximumTN8 atvarious magnetic fields.

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MAGNETIC AND RESONANT PROPERTIES OF QUASI- . . . PHYSICAL REVIEW B 64 024419

obtained at 100 K, 20 K, and 3.3 K, it seems as if thconsist of two derivative lines, but that is not correct. Sinthe sample was a powder, the observed ESR spectra shbe a superposition of those of many single crystals,therefore the spectra should be a asymmetric, as can bein Fig. 4. The spectrum obtained at 1.9 K is different frothose obtained at higher temperatures, which indicatesthe magnetic state at 1.9 K is not paramagnetic.

The electron-paramagnetic-resonance~EPR! line of one-dimensional Heisenberg magnets is not necessaLorentzian.13 At present, however, we assume a Lorentzline shape to elucidate approximate characteristics ofEPR in the present compound.

Assuming a derivative Lorentzian line for a single crystwe analyze the observed spectra. The observed line prI 8(H) corresponds to the expression given by

I 8~H !}2Ep

02@G~u!#2•@H2Hr~u!#sinu

$@G~u!#21@H2Hr~u!#2%2du, ~2!

whereH is the external field,G(u) andHr(u) are the half-width at the maximum and the resonance field, respectivwhile u is an angle betweenH and the crystal axis alongwhich gi is determined. The derivative peak-to-peak linwidth DHpp is 2G/A3. In LiCuVO4, gi and g' are thegcomponents parallel and perpendicular to thec axis.

Treating G(u) and Hr(u) as adjustable parameters, wtried to get the best fit of Eq.~2! on each experimentallyobserved spectrum. In the simulation over the higtemperature region where no magnetic short-range orderists, we used a relation14

G~u!5G0~11cos2u!, ~3!

whereG0 is the minimum.The g(u) in S5 1

2 compounds with a uniaxial symmetriligand is given by

g~u!5Ag'2 sin2u1gi

2cos2u. ~4!

Then theu dependence ofHr is given by

FIG. 4. The ESR spectra of LiCuVO4 taken in a wide temperature range. AtT,TN the spectrum observed exhibits a qualitatitransformation.

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where v is a fixed microwave frequency. Equation~3! isestablished in one-dimensional Heisenberg magnets, whave no effect on spin diffusion and therefore have a Lorezian line shape in their ESR spectra.

Over the temperature region where the magnetic shrange order develops, spin correlations act as an effecinternal field and therefore cause a shift of the resonafield Hr from that at high temperatures where no magneshort-range order exists.15 The shiftdHr(u) has the angulardependence as

dHr~u!}~3 cos2u21!. ~6!

Taking these assumption and conditions, we tried to obthe best fit of Eq.~2! on each observed spectrum.

As a result, we obtain the temperature dependence oHrandDHpp for u 5 0 andp/2, which are shown in Figs. 5 an6. Instead ofHr(T), we plot g(T), which we obtain usingequation

FIG. 5. The temperature dependencies of theg factors observedin asymmetric ESR spectra of LiCuVO4.

FIG. 6. The temperature dependencies of the peak-to-pwidths of ESR signalsDHpp.

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A. N. VASIL’EV et al. PHYSICAL REVIEW B 64 024419

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III. DISCUSSION

The temperature dependence of the magnetic suscepity observed in LiCuVO4 is somewhat different from thaexpected of a quasi-one-dimensional antiferromagnetexperiences a three-dimensional magnetic ordering attemperatures. As is well known, an ideal Heisenberg chdoes not undergo long-range ordering at any temperatHowever, the short-range ordering, which does not imphase transition, results in the smooth increase of the colation length. Three-dimensional ordering is possible at ltemperatures when the interchain interaction becomes cparable with the thermal energykT. For example, this behavior has recently been observed in another quasi-odimensional inorganic compound CuV2O6.7 In thiscompound the broad maximum at thex(T) dependence habeen accompanied by the decrease of magnetic susceptiat the Neel point. No upturn ofx when approaching the Neepoint has been detected in CuV2O6.

In principle, the upturn ofx below 9 K could be attributedto paramagnetic impurity. However, the subsequent abdrop of x at TN8 contradicts this assumption, besides tESR data in this temperature range do not reveal any ational paramagnetic signal.

The increase of magnetic susceptibility in LiCuVO4 be-low 9 K can be attributed to the strengthening of the roleinterchain interaction, which is frustrated due to the almregular triangular arrangement of the Cu21 ions in thea-cplane. This frustration competes with the tendency to foshort-range ordering within the chains. In fact, within tCu21 triangle the distance between Cu21 ions along theaaxis is 5.652 Å, while two other distances are 5.209 Å. Acordingly, the exchange integrals within the Cu21 trianglesomewhat differ. At a further lowering of temperature thdifference becomes significant and the frustration is lifoff. As a result, a three-dimensional magnetic orderingfinally established.

To establish the nature of the decrease ofx at TN8 thetemperature dependencies of magnetization in various mnetic fields were measured. As can be seen from Fig. 3position of the low-temperature maximum is a nonmononous function of a magnetic field. This behavior is charteristic of the low-dimensional antiferromagnets.16 The ini-tial increase in the antiferromagnetic ordering temperaturdue to the fact that the external field efficiently decreasesnumbern of degrees of freedom in the magnetic subsystetransferring a Heisenberg magnet (n53) into an XY-typemagnet (n52). The subsequent decrease of theTN8 is due tothe Zeeman splitting of the levels in a magnetic field.

The ESR data appear to be in accordance with the mnetization measurements. The deviation ofg factors fromconstant values is related to the short-range antiferromnetic correlations within the chains. Above the Ne´el point the

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with the axial model for the Heisenberg chain15 in which thedipole-dipole and~or! the anisotropic exchange interactionare the main perturbation terms. The rapid decrease ofESR signal linewidths in the range of well-developed shorange correlations is not clear. Usually, the linewidthsESR signals that accompany the deviation ofg factors di-verge when approaching the Ne´el point. At lowest tempera-ture the ESR spectrum observed undergoes qualitachange and transforms into an antiferromagnetic resonaspectrum.

Comparing the Bonner-Fisher curve with experimegives the appreciably large value 2.39 for theg factor aver-aged over the crystallographic directions, and from the potion of the wide peak along the temperature scale,

TM51.282J1 , ~8!

it follows11 that the exchange integral in the chains isJ1522 K. The interchain exchange interactionJ2 can beestimated17 from the three-dimensional antiferromagnetic odering temperatureTN as

J25TN

1.28Aln 5.8J1 /TN

. ~9!

In order of magnitudeJ2;1 K.

IV. CONCLUSION

The electron-spin-resonance~ESR! and dc magnetizationmeasurements have revealed a complicated interplay offerent exchange interactions in the spinel-type compoLiCuVO4. At cooling, short-range correlations are estalished in the chains of edge-sharing CuO6 octahedra and themagnetization shows a broad maximum atTM528 K. Then,the magnetization somewhat increases below;9 K, showsa second maximum atTN8;4 K, and a subsequent shardrop. Above TN the asymmetric ESR spectra of thLiCuVO4 powder sample are in correspondence withsymmetry of the crystal field on Cu21 ions. Thegi andg'

values diverge at cooling as is anticipated of a quasi-odimensional Heisenberg antiferromagnet. Both magnettion and ESR data indicate that the three-dimensional aferromagnetic ordering occurs atTN52.3 K.

Further information about quasi-one-dimensional antifromagnetic ordering in LiCuVO4 can be apparently obtainethrough neutron-diffraction investigations. Specifically, tvalue estimated for the interchain exchange integral maytoo low because of frustrations of the exchange interactioa triangular arrangement of chains, if the interaction betwthe copper ions in thea-c plane is antiferromagnetic.

ACKNOWLEDGMENTS

This work was supported by the RFBR 99-02-17828,INTAS 99-0155, and the NWO 047-008-012 grants.

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MAGNETIC AND RESONANT PROPERTIES OF QUASI- . . . PHYSICAL REVIEW B 64 024419

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