PHYSICAL REVIEW B, VOLUME 65, 052408

Staggered-field effect on the magnetic-field-induced magnetization of the one-dimensionalantiferromagnet Yb4As3

Kazuaki Iwasa,1 Masahumi Kohgi,1 Arsen Gukasov,2 Jean-Michel Mignot,2 Naokazu Shibata,3 Akira Ochiai,4

Hidekazu Aoki,5,* and Takashi Suzuki6

1Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan2Laboratoire Leon Brillouin, CEA/Saclay, 91191 Gif sur Yvette, France

3Graduate School of Arts and Sciences, University of Tokyo, Tokyo 153-8902, Japan4Center for Low Temperature Science, Tohoku University, Sendai 980-8578, Japan

5Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan6Tsukuba Institute of Science and Technology, Tsukuba, Ibaraki 300-0819, Japan

~Received 29 October 2001; published 8 January 2002!

Magnetic properties in the charge-ordered phase of Yb4As3 have been studied by polarized-neutron diffrac-tion. It is revealed that one-dimensional~1D! chains of magnetic Yb31 ions are formed by charge orderingbelow 290 K. The field-induced magnetic moment on the 1D chain under a field parallel to the chain behavesas that of a spin-1/2 1D Heisenberg antiferromagnet with ag factorgi52.9. In the case of a field perpendicularto the chain, we observed a pronounced enhancement below about 10 K. The observed enhancement of thefield-induced magnetization is reproduced well by a theory which takes into account the staggered-field effectdue to the Dzyaloshinsky-Moriya interaction within the 1D magnetic chain.

DOI: 10.1103/PhysRevB.65.052408 PACS number~s!: 75.10.Jm, 75.25.1z, 75.30.Mb, 75.50.Ee

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Many novel physical properties have been foundf-electron systems: mixed valence, heavy Fermion, nFermi liquid, superconductivity near quantum critical poiand so on. Low-carrier-density systems realized by rare-epnictides also exhibit interesting phenomena owing to etron correlations including 4f states. Cerium monopnictideare typical systems showing various long-period magnstructures which are attributed to strong magnetic polaeffects considered to be a characteristic property of a lcarrier-density system.1 Another attractive low-carrier-density system Yb4As3 shows different phenomena due4 f -electron states: a charge order of Yb ions and a resuunique one-dimensional~1D! magnetism which is focused ithe present study. At the beginning of the study of the eltronic properties of Yb4As3, it was regarded as a heavyelectron material, because the specific heat at the lowestperature obeys a linear function of temperature with a lacoefficient g5205 mJ/mol/K2 and electrical resistivityshows a maximum at around 140 K followed byT2 behaviorwith the coefficientA50.75 mV cm/K2.2 However, the ex-tremely low carrier density of about 1023 per chemical for-mula in the temperature region of these anomalies is oppoto the dense Kondo effect. It is remarkable that Yb4As3 un-dergoes a structural transformation atTC>290 K from ananti-Th3P4 cubic lattice aboveTC to a trigonal one withshrinking along the@111# direction. A previous polarizedneutron diffraction study showed that Yb ions occupyisites aligned along the shrinking@111# (YbI) become nearlytrivalent and the remaining Yb ions (YbII) nearly divalent.3,4

Thus, the charge order gives rise to 1D magnetic chaalong the YbI-ion sites. The inelastic neutron spectra of manetic excitations are well explained by a model for the sp1/2 1D Heisenberg antiferromagnet (S51/2 1D-HAF!.5,6

The exchange coupling constant between neighboYbI-ion spins,J52.2 meV for H1D-HAF5( j JSj•Sj 11, de-

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termined from the spectra gives a largeg value which is veryclose to that obtained by bulk specific-heat measuremThus, the 1D isotropic exchange coupling plays a dominrole in the heavy-electron-like anomalies at low tempetures, while the transport property is still unclear.

In contrast to the clear 1D-HAF behavior of Yb4As3 atzero magnetic field, magnetization under a finite field shoa quite unusual enhancement below about 10 K.2,7 The spe-cific heat is strongly suppressed at lower temperaturesshows a maximum at certain temperatures.8 The specific-heatanomaly suggests the formation of an energy gap in the mnetic excitation, which was clearly detected by inelastic ntron scattering measurements under a magnetic field.9 Theproblem is that these field-induced properties cannot beplained by the model of isotropicS51/2 1D-HAF. Recently,it was proposed that the unusual properties are caused bstaggered field induced by the applied uniform field perpdicular to the 1D magnetic chain.10,11 The Dzyaloshinsky-Moriya ~DM! interaction plays an important role in thmechanism of the induced staggered field.

The purpose of the present polarized-neutron experimis to observe directly the dependence of the induced mnetic moments of the YbI ions on the applied-magnetic-fieldirections. The distinct anisotropy of the induced momewas observed for an applied field parallel and perpendicto the chain, and is explained quantitatively by the staggerfield model, as shown later. A part of this study has begiven in other publications.4,12

The experiments to obtain the induced-moment valwere carried out at the spectrometer 5C1 installed inOrphee reactor of LLB, Saclay. An incident neutron witwavelength of 0.84 Å was polarized by a Heusler monochmator, and a spin flipper was installed after the monochmator. The experiments were performed for a single-domsample in the charge-ordered phase of Yb4As3, which was

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prepared by cooling a single crystal of about 0.6 cm3 withuniaxial stress along the@111# direction by about 50 bars ina cryostat equipped with a Helmholz-type superconducmagnet. The formation of the single-domain sample wconfirmed by the fact that rocking curves of some Brareflections, whose peak positions shift because of the trigodistortion, did not show any distinct broadening or splittinMeasurements were performed under two conditions ofapplied magnetic field oriented parallel (Hi@111#) and per-pendicular (H'@111#) to the 1D chain.

Flipping ratios defined asR5I 1 /I 2 and I 65uFN(Q)6FM(Q)u2 were measured at various Bragg-reflection poiQ, where the subscript6 indicates the direction of theneutron-spin polarization along or opposite to the applmagnetic field. The structure factors for nuclear and mnetic scattering correspond toFN(Q) and FM(Q), respec-tively. SinceFN(Q) is known from the crystal structure, thfield-induced magnetic moment values are determined fan analysis ofR based on a least-squares fitting procedwith calculation ofFM(Q).

Figure 1 showsR measured atH57 T applied in the twodirections and atT>1.5 K. The observed data, shown bsolid circles, were analyzed by least-squares fitting produres with two free parameters for field-induced magnemoments at the YbI- and YbII-ion sites,m I andm II , respec-tively. The fitted results, shown by crosses, agree well wthe experimental data. The magnitudes of induced momat H57 T andT>1.5 K arem I5(0.3560.01)mB and m II5(0.02260.009)mB for Hi@111# m I5(0.3360.01)mB andm II5(0.00960.006)mB for H'@111#. The induced momentsat YbI sites which are much larger than those at YbII sitesindicate that the charge order with the formation of themagnetic chains is almost perfect.

The flipping-ratio measurements were also performedvarious temperatures and applied magnetic fields. The tperature dependence ofm I underHi@111# of 7 T shown bycircles in Fig. 2~a! exhibits a broad maximum around 20 Kwhich is consistent with the Bethe-ansatz results of the mnetic susceptibility for theS51/2 1D-HAF model,13,14 al-though it shows a slight increase at the lowest temperatIn contrast,m I underH'@111# shown by squares in Fig. 2~b!is enhanced below about 10 K and has no pronounced mmum at around 20 K. The same behavior was observedbulk susceptibility measurement.7 The magnetic-field dependence ofm I shows a monotonic increase with increasifields, as in Figs. 2~c! and 2~d!. The value ofm I underHi@111# is almost proportional toH, while the slope ofm IunderH'@111# becomes gentle with increasing field. As dicussed later in detail, the above experimental results supstrongly the theory predicting the staggered-field effect whthe applied magnetic field has a component perpendiculathe 1D chain.

First, since the staggered-field effect is expected onlythe case ofH'@111#, m I underHi@111# was analyzed byassuming that the magnetization induced by the appliedform magnetic field is the sum of those of theS51/2 1D-HAF and Van Vleck–type one. We applied the density matrenormalization group~DMRG! method to calculate magne

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tization for the 1D-HAF model, because we need accurnumerical magnetization data,m i

1D , up to 100 K under finitemagnetic fields parallel to the@111# direction.15 This methodis the only reliable one at present to calculate the magnzation with the staggered-field effect as discussed later.exchange coupling constant ofJ52.2 meV obtained fromthe inelastic neutron scattering result was used for thisculation. The Van Vleck–type magnetization comes fromcrystal-field excited levels, which were determined by ineltic neutron measurements to be located at energies of245, and 335 K.5 Since the excitation energies to these levare quite larger than the temperature region where the cacteristic 1D magnetic behavior appears, the Van Vleck–tmagnetization is almost constant in this temperature ranOnly the contribution of the first excited state was taken inaccount in the evaluation of the Van Vleck–type magnetition, in order to express approximately rather moder

FIG. 1. Solid circles represent the measured flipping ratiospolarized-neutron diffraction at~a! 1.7 K and 7 T (Hi@111#) and at~b! 1.5 K and 7 T (H'@111#). Indices on the horizontal axes represent Bragg reflections. Crosses are the fitted results.

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BRIEF REPORTS PHYSICAL REVIEW B 65 052408

variations at higher temperatures due to the thermal exction to these excited levels. This approximation is reliabbecause the error caused by disregarding the contributionthe higher-energy levels is estimated to be comparable toerror of the measured magnetization. Then, we used amula m i

V5AiH(12e2E/kBT)/Z(T), where E5160 K andAi corresponds to a squared matrix element of angularmentum. The termZ(T) is the partition function. TakingAiand the effectiveg factorgi in the DMRG calculation as freeparameters, we performed a least-squares fitting ofm i

1D

1m iV to the data of temperature dependence above 5 K.

result with gi52.960.1 andAi50.04160.008 reproducesthe data well, as shown in Fig. 2~a! by a solid line. Using the

FIG. 2. Circles and squares represent magnetic-field-indumomentsm I , measured withHi@111# @~a! and ~c!# and H'@111#@~b! and~d!#. Solid lines in~a! and~b! are results of fitting based osum of magnetizations due to 1D magnetic interactions andVleck–type contributions. The latter magnitudes are representedotted lines. Those in~c! and~d! are calculated results of magnetifield dependences based on the obtained fitting parameters fotemperature dependences.

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DMRG method with these resultant parameters, we calated the magnetic-field dependence ofm i

1D1m iV at 1.7 K,16

as shown in Fig. 2~c!. It also reproduces well the measuredata which increase almost linearly with increasing field. Tobtained Van Vleck–type contribution is also shown by dted lines in these figures. Thus, the datam I underHi@111#are explained well by the simple 1D-HAF model.

Before analyzing the data ofm I underH'@111#, we dis-cuss here the anisotropy of theg value of Yb4As3. The factthat m I shows no pronounced peak around 20 K undH'@111# suggests thatg' is smaller thangi . The inelasticmagnetic response of the 1D spin excitation also exhibitsanisotropic property. Figure 3 shows the measured neutscattering intensity along theq5p/d ridge in the reciprocalspace at 1.5 K and zero field with fixed excitation energy0.5 meV, whereq is the 1D wave number andd is the inter-atomic distance between Yb ions on the 1D chain. This dwere taken by cold-neutron scattering performed at the Hspectrometer installed in the JRR-3M reactor of JAERI, Tkai. The scattering intensity can be expressed as

I} f 2~Q!$gi2~sin2a!1g'

2 ~11cos2a!%, ~1!

wherea is an angle betweenQ and the direction of the 1Dchain andf (Q) is a magnetic form factor of a Yb31 ion. Theobserved intensity shows a local minimum atQ5(2/3,2/3,2/3) which is parallel to the 1D-chain directioThis fact means thatg' is smaller thangi . From a least-squares fitting of Eq.~1! to the observed intensity distribution, the ratiogi /g' is evaluated to be 2.360.2. Thus, weobtainedg'51.360.1, since we have already evaluatedgi52.9 as shown before.

Here, for analyzing the present experimental datam I un-der H'@111#, we will summarize the essence of the theoon the effective magnetic Hamiltonian for the ground-stdoublet of Yb4As3.10,11 Oshikawaet al. pointed out that astaggered field is induced in the 1D Yb31 chains by an ap-plied uniform magnetic field perpendicular to the chains. T

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FIG. 3. Circles are inelastic scattering intensities due to sexcitation with energy of 0.5 meV at 1.5 K and zero field, whiwere corrected for neutron absorption by the sample. Horizoaxis z is a coordinate of the scattering vector,Q5(z,z,222z),corresponding to the 1D-HAF ridge. The mark@111# represents thecondition thatQ be parallel to the 1D magnetic chain. The solid linis a result of fitting based on the anisotropicg factors.

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BRIEF REPORTS PHYSICAL REVIEW B 65 052408

magnitude of the staggered field is expressed asH sinu,where H is the magnitude ofH'@111# and u is a factordepending on the DM interaction. Then, the effective Hamtonian was derived in Ref. 11 as

H5H1D-HAF2gi(j

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$~cosu!Sjx1

~21! j~sinu!Sjy%Hx . ~2!

The z axis corresponds to the direction of the 1D chain.pseudospinSj at the j th YbI site is defined by rotating thespinSj in thex-y plane by an angleu in a staggered way. Wepicked up only the term includingHx for the field perpen-dicular to the 1D chains. As shown in Ref. 11, the magnezation is modified by the induced staggered field expresas the last term of this equation. Based on this Hamiltontemperature- and field-dependent magnetizations of thechain,m'

1D , with the HAF interaction and staggered-field efect were calculated by the DMRG method in the presstudy.15 The Van Vleck–type magnetization was also icluded in the analysis of the data of theH'@111# case. Theform of Van Vleck–type magnetization is assumed tom'

V5A'H(12e2E/kBT)/Z(T), as was used in the analysfor theHi@111# case. A least-squares fitting of the sum of t1D magnetization based on the DMRG and the Van Vletype one,m'

1D1m'V , to the observedm I was carried out with

free parameters ofu and A' . The result is shown in Fig2~b!, and the obtained parameters are tanu50.1960.02 andA'50.06960.001. Using the fitted parameters, we can aevaluate the 1D magnetization based on the DMRG methThe result is shown in Fig. 2~d!, which contains the esti-mated Van Vleck–type contributions shown by the dashline. In order to show the staggered-field effect more cleawe replotted the magnetization data after subtraction ofVan Vleck–type component in Fig. 4. The dot-dashed lincorrespond to the calculated magnetization for the pureHAF system without the staggered-field effect. The agrment between the observation and the present analysis bon the Hamiltonian, Eq.~2!, is satisfactory. The errors of thfit parameters are caused dominantly by the statistics of ntron counts, so that the fitted resultm'

1D has an accuracy

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corresponding to the error bars of the measurement, whicsmaller than the increase ofm I below 10 K. Thus, thestaggered-field effect is necessary to explain the behaviom I .

In conclusion, the magnetic moments induced byfields applied parallel and perpendicular to the YbI chains areexplained well by the DMRG calculation applied for the efective Hamiltonian including the staggered field. As dscribed in Ref. 9, the inelastic neutron measurement unH'@111# revealed a magnetic excitation gap whose magtude obeysH2/3, which agrees with the theoretical result bthe bosonization method applied for the staggered-fimodel. Both neutron scattering experiments support stronthe staggered-field model based on the DM interactionthe 1D magnetism of Yb4As3.

Professor K. Ueda is acknowledged for his valuable dcussions. The authors thank Dr. H. Kadowaki for allowinguse the focusing-type analyzer mirror which he developfor the experiment at HER. The present study is supportedGrant-in-Aids No. 09044097 from the Ministry of EducatioCulture, Sports, Science and Technology of Japan and11694093 from Japan Society for Promotion of Science,the Inoue Foundation for Science.

FIG. 4. Solid circles represent the experimental datatemperature- and magnetic-field-dependent magnetization aftertracting the Van Vleck–type contribution. Calculated magnetitions for tanu50.19 by the DMRG method are solid lines. Dodashed lines represent the calculated magnetization for the1D-HAF model withJ52.2 meV andg'51.3.

a-l-re-the

*Present address: Max-Planck Institute for Chemical PhysicSolids, D-01187 Dresden, Germany.

1See, for example, M. Kohgiet al., Physica B281&282, 417~2000!.

2A. Ochiai et al., J. Phys. Soc. Jpn.59, 4129~1990!.3M. Kohgi et al., Physica B230-232, 638 ~1997!.4K. Iwasaet al., Physica B281&282, 460 ~2000!.5M. Kohgi et al., Phys. Rev. B56, R11 388~1997!.6M. Kohgi et al., Physica B259-261, 269 ~1999!.7H. Aoki and A. Ochiai, Physica B281&282, 465 ~2000!.8M. Koppenet al., Phys. Rev. Lett.82, 4548~1999!.9M. Kohgi et al., Phys. Rev. Lett.86, 2439~2001!.

of10M. Oshikawaet al., J. Phys. Soc. Jpn.68, 3181~1999!.11H. Shibaet al., J. Phys. Soc. Jpn.69, 1493~2000!.12K. Iwasa and T. Suzuki, J. Magn. Magn. Mater.226-230, 441

~2001!.13S. Eggertet al., Phys. Rev. Lett.73, 332 ~1994!.14J. C. Bonner and M. E. Fisher, Phys. Rev.135, A640 ~1964!.15N. Shibata and K. Ueda, J. Phys. Soc. Jpn.76, 3690~2001!.16In the previous paper~Ref. 12!, we assumed that the magnetiz

tion underHi@111# is proportional to the calculated susceptibiity for the pure 1D-HAF model based on the Bethe ansatzported in Refs. 13 and 14. Thus, the previous result ofanalysis is slightly different from the present one.

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