0) Solid State Communications,Vol.31, pp.311—314.Pergamon Press Ltd. 1979. Printed in Great Britain.

EFF~TOF A W~~~ETICFIELD CV T~WREEATI~LE~~IN A a~E-DIME~IaqALPNER~W~T

J.P. ~uther2, L.P. Pegnault,J. Passat-Migncxl,J. Villain

Départeimontde PecthercheFondairentale,Centre d’Etudes Nucldairesde Greixble85X, 38041 Grer~le Cedex - FRNCE

and

J.P. Penard~

Institut d’ Electroniqj.~FondaitentaleUniversité Paris XI - Bat. 220 - 91405 Orsay Ceder FRAICE

(Peceived 12 May 1979 by P.G. c?e Cennes)

New results of quasi-elasticneutron scatteringon the one-dinensional antifer-rceagnetTM’C establish that belcw 5 K Th!’C is actually in an XI state. The ef-fect of a magneticfieifi is describedin termsof crossovertransitions associa-ted with a reductionof the spin dinensionality. TM’C underg3esan XY-Ising tran-sition whenH is applied perpendicular to the chain axis.

During the past decadeconsiderable attention field on the correlation lengths in a 11) antifer-has beenpaid to the study of one-dlirensional(1D) rtsnagnet.As we shall see,l~odifferent correla-magneticsystems.~tre recently it was predicted tion lengths most actually be consideredin thethat the application of an external magneticfield problem, dependingon wether the fluctuations axeH should affect strongly their lc~eten~raturepro- associatedwith the spin ccmponents parallel orperties [i]. As long as the static properties are perpendicular to the direction of H, namely K731

concerned, the relevant quantity to be considered andKJ.’, respectively. It turns out that theirat lcw temperatureis the 1D correlation length field dependences are very different. In order toK’. In ferrosiagnetsthe spins will tend to align study K1(H) (a = II or.L) we performedquasi-elas-in the field direction. An increase of e1 is the.- tic neu~.ronscatteringmeasurementsin presenceofrefore expected,which could explain the narrc7~eing a magnetic field (0~H~4CkCe)on ThTC at lcw tespe-of the spin wavenrx]es observedin C5N1F

3 [2]. In rature (lK6T~lOK).1D antiferronegnetsma direct evidenceof a field We shall mat review the structure andmagma—dependenceof has yet been given. Ha,qeverother tic propertiesof ¶L!’M~which have been studied ex-experimental results let us suspecta strong influ- tensively elsewhere[7]. Hcwever a crimmont is inence of H on K’. For instancean inpertant change order about the value of the exchangecot~lingwas observed on the 3D ordering temperature Tp when J. Assumingthe magnetic interaction to be givena magnetic field was applied to scum quasi-iD anti- by a nearest-neighborNeiserbergexchangeferronegnets [3]. The largest effect was actually -23 ~j ~j+i n~nyexperimentaldeterminationsofseenon (Q)3)4NMrC13(TMC), one of the best 1D an- J have been made in LN~C.All agreewith the Va-tiferranngrets. In this cxmrpound a relative increa- lues J 6.7 ±0.3 K exceptthe evaluationthtai-am of TN of 350% (TN = 0.85 K for H = 0 and TN = ned fran previousquasi-elasticneutron scattering3 K for H = 90 koe) is obtained with H perpendicu- neasureirents,giving a highervalue : J = 7.7 ±0.3Klar to the chain axis [4]. This increase of T with [8]. It must be p,inted out that in this latterH could essentially reproduce the field depen~ence study, the temperaturedependenceof K’ was in-of the 1D correlation length K~ [5]. It has recen- terpretedwithin the Heiserl,erg model in the ten-tly beensh~nthat the same m:xlel, using more pa- perature range 1K <T < 40K. This is questionableranetersand abetter resolution of the transfer since a more recent calculation of D• Hone and A.matrix, reproducesfairly well the pJiase diagram Pires [9] sha~s that when the dilxlar interactionsof several quasi-b anti ferrcunagnets [6]. Hcu~ever bet~en the spins are considered,~1MCshould un-strong discrepancies bet~een theory and experiment dergo a crossover transition fran }~isetherg topersist, especially in ¶I!4C where the large change KY behavior below 20 K. ~I~ICmight thereforecor-in TN is not yet explained. On the other hand, in respondto an XV rather than a Helsethergnxxlel atthe descriptionof ~ the weakly interacting chains lcw temperature.This p.int is quite important inare treated very approximatelyusing the nolecu].ar our problem since the relative change of e

1 withfield approximation(WA) which canbe suspected H crucially dependson the initial (zero field)to be inadequate.The variation of TN with H is state of the spin system.therefore a rather indirect way of probing the It can be shown that at low temperaturefield dependenceof e1 which needs to be kzu~n (kT<<.JS (~fl~)and for small valuesof Hmore directly. In this letter we presentthe first (~‘B’~(S+1)H<<~3S(S+1)) the magneticfield (H//y)experimentalevidenceof the effect of a magnetic acts on an antiferronagnetas an effective arilso-

~ H~uipe de RedierctheCNRS n°60216

~r LaboratoireassocidCN~

311

312 EFFECT OF A MAGNETIC FIELD ON THE CORRELATION LENGTH Vol. 31, No. 5

tropyjeeff = (gt~HS.~)2/8JS(S+1). The direction of Kllh,c(XV) = 1 + [s(s+1)/16] [gu~Wr]2 (2)

H béccuiesa hard aids and consequentlythe spins and for the order parameterswhich enterourwill tend to lie perpendicularto it. If the spin problemmj andrn,

1 wherem~= <S~>/~(S+1)with thesystem was initially in a Heisenbergstate where obvious condition rn1 + rn~, = 1aK(~is) = kT/2JS(S+1) with a the distancebetweenadjacent spins [7], it would be chani~ed into an XI mV,’ / rn(XY) = 1 - [~(S+1)/32] [gp~H/kT]

2 (3)statewhere aic (XI) = k’r/4JS (S+1) [7J. During this with m(XI) = 1/2. asymptoticvalue of K// forHeisenberg-XI transition K would be reducedby a ~ + = can easily be derived fran qualitativefac±ort~o.On the other hand, if ~ is applied in arguments.First we define T~ as the temperaturethe plane of an XV system, a transition towardsan at which the thermalenerc~~ibeixtres ccrtparabletoIsing statewill occur• The change in K canbe n-~ the effective anisotrcw in an initial XV chainofmore important since K (Ising) = emp(—JS(S+1 ) /kT) length ic~(Xf)1 : kT = [aicco(XI)]1 [~] 2,~j.[7]. Very large effects canbe expected evenwith by analo~rw~hthe Heiserberg-XI tram-small valuesof H. A more quantitative evaluation sition ~9], we assumeKI3’ for a given H to “satu-of ic

1 canbe obtainedfran ref [4] whereit is rate” as T + 0 K,/ + cr/4~~(S+1). One easily

shown that, to secondorder in H~r deducesfor Htr + =

K.L/K (XI) = 1 - [s (S+1)/16] Lgii~H/kT]2 (1) K//I K(XI) = ~‘S(S+i)7~ g1.~H/kT (4)Similar expression can be derived for K//(H) E~pressions (1) (2) and 4) are universal functions

of H/P and areplotted on Fig. 1 for the parametersof~1,C:J=6.9KandS=5/2 [bO].~inversecorrelation length ic~can be seento decreasewithI H while K// increases• As a conclusion if ¶I~C isinitially in an XI state, significant changes in

£ 5K / the Ka should be observablefor relatively smallvalues of H/P (H/P = 10 kOe/K).The experimentswere performedon a triple-

2 •4K /~ axis spectrcueterat the Centre d’EtudesNucléai—res de &er~1e Siloé reactor using neutronsofwavelength 2.4 A. The col]J.nation in front of

~ //z) horison~lin s~ a ~ that U~scattering*3K HI, were 30’, 20’ and 30’, respectively. 1~asurementsthe nteochronator, the sampleand the detectorwere performed in the temperaturerange1~’l’6lO0Kusing a crycmagnetwith the magneticfield H//yvertical and 0<11<40kOe• The crystal of abc~it1.5 cm3 was oriented with the chain aids (C axiswave vector Q = (h ; 0 ; 1) couldbe surveyed.Scansin the £ direction were carriedout across

1 the magneticplanes of diffuse scattering, cha-racteristic of the lD short rangeorder ~.8]. Asit has been shown by R.J. Birgtereau et al., there

F~\ ~ is a parasitenuclear scatteringcontribution su—perinçosed to the magnetic scattering [8]. This

i contribution which is temperature ir~per~ant* below 30 K but strongly deper~enton h wasmini-

mum and less than 10% of the full signal at ~ =(1.25 ; 0 ; 1), below 10 K. This nuclear partwas substractedfran the total contribution. The

\ remaining sc~ttez~thg~~as~assunedto be givenby

(IT M(~) = fffL(Q - S)R(S)d3S

(K ~ whereL (~) represents the magneticscattering__________________________ function andR(~) is the elastic resolution func-0 tion of the inst~ment.Particular attention has

be paid on R(Q). Defining ~ by ~ = + ~ with

= (h , 0 ,21) ore can write R~) asR~ ~Fig. 1 Universality in H/T of the quantities exp [-Ln2 (B,~x + 2B + B~,c1z+icr/ic (XI). The solid lines corresp~d to ite coefficients B~ ~r cz, b= x, y,als(b, 2 and 4). lIe dotted line is an depends explicitely on were determined franinterpolation betweenthe two limiting the Bragg peaks (h, 0, 1) for h = 0, 1, 2 and 3,values of K//Ic (XI) (Ek~s(2 and 4)). ‘lIe In one dimension, integration over qx ~ qy candashed line is the apparentli~idth bemade leading toK/K (XI) calculated fran ~s (1-5). Thedot-dashedcurve is a least sciuare fit M(q~) ‘~ IL (q~ - S~exp(—Ia2C~q~)dqof a second order polyr~rd.al expression with Czz = Bzz - Bj~. One ore seesthatin H/P (see text). For creparison, U.~ C~dependson the three coefficients B

5~,Bxz andcurve K /K (Heis) correspondingto a ~ Bxt. We chedredthat the term B~/BXXgives rise tOtern initially in a Heiserberg state is an important correction to ~ ~-

1Y 30%, whichalso shown (full line matedHeis) on the canmatbe neglected.We also studied the h depei~n—Fig.. The position of the scattering wave on of Czz which is an increasingfunction of h whilevector~ with respect to H and the chain the magneticform factor is a decreasing function ofaxis ~ is shownon the Fig. : = (1.25 h. Fo~~ = (1.25 ; 0 ; C). c~was as large as 8500o i. ±500A2 giving a rather good instrumental resolution,

Vol. 31, No. 5 EFFECT OF A MAGNETICFIELD ON THE CORRELATIONLENGTH 313

~e intensity of the signal was reasonablearid the caneasily be understoodin the medal of the XI-parasitescatteringrelatively small. The function Ising transition. Thee~erinentalposition of theL(q) was assuredto be torentxian scatteringwave vector 0 with respect to the chain

* r 2 2-i aids (c/Is) and to the field aids (11.//y) is irx3ica-L(~) = A/LK + q ~ ± ted on Fig. 1. ‘lIe function L(~)is thereforethewith q = (1 - 4L)i~/a.The dataM(u) were analyzed sunof ~o contributions L(~)= cos’cr LL(q) + LIl(q)througha convolution procedureand the valuesA whereL,,(q) = <~sZ~>andL.L(q) = <S~&c>are thearid c were determinedwith a two-parameterleast fluctha~tionsparafle]1~andperpendicula?t~H,respec-squarefit. The resulting valuesof ic for H = 0 tively. Assumlinga lorentzianshape for L.L(q) andare sl~.inon Fig. 2 as a function of T. The field L I L(~l M;Et be written asdeper*~enceforT=3,4and5Kiss1xwninFig.l //q~where the quantity ic/c(XI) is plotted versusH/T. L(~) = A[cos~tIru~~+ q;~ + m//~~+ q2IIThe value of K(XI) was taken fran the full line 2 2on Fig. 2. with cos cr = 1 - Q~/~I. Howeverthe analysis of

)~‘(A—1) • ~1.25,o,.t)

0 (2.3.0.1).02’ TMMC x (1.3.0.1)

• .o:Lt9v~~1

Fig. 2 Inverse correlation length as a functionof temperaturein zero field~ for diffe-rent scattering wave vector 0 = (h ; 0£). The dot—dashedlines are theoreticalcurves calculated for HeisethergandXInrmdels. The solid line was calculatedby

D. Hone arid A. Fires, taking into accountthe intrachain dipolar interactions [~J.The dashedline correspondsto the Heisen-bergmodelwith J = 7.7 K.

On Fig. 2 the experimental temperaturedepen- tIe data reportedon Fig. 2 was madewithonlyoielo-dance of K in zero field is crzrpared to different rentzian according to flj. (5). The experimentalpa-thexoretical curves• The dot-dashedlines corres- raneterK therefore plays the role ot an apparentpond to the Heisermbergarid to the XV models, the width. It caneasily be evaluatedfran the theore-full line is the curve calculatedby Hone arid Pi- tical values of K//, cL, mi, andxn~given by Ek~s(1-res [9], which takes into accountthe dipDlar in— 4). We chtain the dashed lire on Fig. I, in good agree—teractiorms.For crmparison, the curve for the Hei- sent with the experimentaldata for all three tern-serberg modelwith J = 7.7 K, which fits the expe— peratures.We cthedcedthat, whateverset of pointsrinental results of ref[8], is s1~n on Fig. 2 (T = 3, 4 and 5K) is cxzrsidereda least square fit(dashedlire). Our data (especially for = (1.25 ; with a second order polynanial expression gives theO ; ~) do not agreewith this model. The excellent sane resultwithin the statistical standarddavia-agreement betweenthe theory of Hone andPires [9] tion. Sucha polyrxznial expression is shown as thearid the experimental data definitely establishes dot-dashedcurve The role of universality in H/Pthat below 5 K ‘lM~C is in an XV state. The spins are given by F1~(1-4) is thereforequantitatively em-expectedto be perpendicular to the chain axis. ‘l~ tablished. ‘l~ rernarts are in order : i) for H/I’negretic tield it being alongy is applied in the = 10 k0e/K, K which representsessentially K.l. hasplane of the spins arid the data of Fig. 1 should beenreducedby more than a factor two ; this factcorrespondto an XI-Ising transition. Whateverthe corrthoratesthe previousresult : ‘II*C is initial~-temperature(T = 3, 4 and 5 K) a plateauis first ly (H = 0) in an XI statebelow 5 K ; ii) the dif-cbservedin low field followed by a rapid drop of ference between the dot-dashedcurve arid the curvec for higher valuesof H. This surprising behavior for c.i canbe explainedby the fact that EkI. (1) is

314 EFFECT OF A MAGNETICFIELD ON THE CORRELATIONLENGTH Vol. 31, No. 5

a pertuthation expansionvalid only for small va- effective anisotropy which inducesa crossoverlues of H/I’. Higher order terne would have to be transition associatedwith a reductionof the spintaken into accxxrnt. dimensionality. If the spin system is initially in

Generalconclusions can be drm~nfran this an Heisenbergstate it will be changedinto an XIwork. The isotropic characterof any Heiserberg statewith the spins perpendicular to I~.If theantiferraragnetic chainwill alwaysbe lost at spins are initially in anXI state, the applica-low temperaturebecauseof the intrachaindipolar tion of ~ in the plane of the spins will driveinteractions. Our results establish that ~1MCis the systantowardsan Ising state. We showthatactually in an XI state at low temperature(T .~ 5K) ~C displays the latter behavior.We have experin~ntallyshownthat the effect of amagneticfield 11 Ce an antiferratagnetic chain at Acknowl~dg~mentThis work was supportedin partlow temperaturecanbe describedin terra of an by twio grant n°1044.

References

Lii A.R. ~Gurn, P.A. Mcitano aridD.I. Scalapino 16] J.P.A.M. Hijinans, K. Kcpinga, F. BoersmaandSol. Stat. Carnun., 15, 1463 (1974). W.J.M. do Jonge, Phys. ~ev. Iett., 40, 1108

[2] M. Steiner and J.K. KjeiTs, j. ~iys. c. : (1978).Solid State Phys. 10 (1977). [7] M. Steiner, J. Villain and C.G. Windsor, I½dv.

[3] C. Dupesarid J.P. Penard,Sol. ~ Cat~., in Phys., 25, 87 (1976).20, 581 (1976) ; W.J.M. de Jonge, J.P.A.M. [8] R.J. Birgeneau, R. Dingle, M.T. Hutchings, G.Hijmas, F. Boersma, J.G. Shoutenarid K. Shiraneand S.L. Holt, Phys. Rev. Lett., 26,Kcpinga, Phys. Rev., B17, 2922 (1978). 718 (1971).

[4] F. Borsa, j.P. Boucherand J. Villain, J. Appl. [9] D. Hone and A. Pires, Phys. Rev., HiS, 323Phys., 49, 1326 (1978). (1977).

[5] J. Villain andJ.M. I~veludc,Journal do Phy- [io] The value J = 6.9 K wasusedby D. Hone andsique, 38, l,-77 (1977). A. Fires 19]. It agreeswith the nest prththle

experimentalevaluationJ = 6.7 ±0.3 K.