Effect of a magnetic field on the correlation length in a one-dimensional antiferromagnet

0)

311—314.

Solid State Communications, Vol.31,in pp. Pergamon Press Ltd. 1979. Printed Great Britain.

EFF~TOF A W~~~ETIC FIELD CV T~WREEATI~LE~~ IN A a~E-DIME~IaqAL PNER~W~T J.P. ~uther2,L.P. Pegnault, J. Passat-Migncxl, J. Villain

Départeimont de Pectherche Fondairentale, Centre d’Etudes Nucldaires de Greixble 85X, 38041 Grer~leCedex - FRNCE and J.P. Penard~

Institut d’ Electroniqj.~ Fondaitentale Université Paris XI - Bat. 220 - 91405 Orsay Ceder FRAICE (Peceived 12 May 1979 by P.G. c?e Cennes) New results of quasi-elastic neutron scattering on the one-dinensional antiferrceagnet TM’C establish that belcw 5 K Th!’C is actually in an XI state. The effect of a magnetic fieifi is described in terms of crossover transitions associated with a reduction of the spin dinensionality. TM’C underg3es an XY-Ising transition when H is applied perpendicular to the chain axis.

During the past decade considerable attention has been paid to the study of one-dlirensional (1D) magnetic systems. ~tre recently it was predicted that the application of an external magnetic field H should affect strongly their lc~eten~rature properties [i].As long as the static properties are concerned, the relevant quantity to be considered at lcw temperature is the 1D correlation length K’. In ferrosiagnets the spins will tend to align in the field direction. An increase of e1 is the.refore expected, which could explain the narrc7~eing of the spin wave nrx]es observed in C5N1F 3 [2]. In 1D antiferronegnets ma direct evidence of a field dependence of has yet been given. Ha,qever other experimental results let us suspect a strong influence of H on K’. For instance an inpertant change was observed on the 3D ordering temperature Tp when a magnetic field was applied to scum quasi-iD antiferronegnets [3].The largest effect was actually seen on (Q)3) 4NMrC13 (TMC), one of the best 1D antiferranngrets. In this cxmrpound a relative increaam of TN of 350% (TN = 0.85 K for H = 0 and TN = 3 K for H = 90 koe) is obtained with H perpendicular to the chain axis [4]. This increase of T with H could essentially reproduce the field depen~ence of the 1D correlation length K~ [5]. It has recently been sh~n that the same m:xlel, using more paraneters and a better resolution of the transfer matrix, reproduces fairly well the pJiase diagram of several quasi-b antiferrcunagnets [6].Hcu~ever strong discrepancies bet~eentheory and experiment persist, especially in ¶I!4C where the large change in TN is not yet explained. On the other hand, in the description of ~ the weakly interacting chains field approximation (WA) whichusing can bethesuspected are treated very approximately nolecu].ar to be inadequate. The variation of TN with H is therefore a rather indirect way of probing the field dependence of e1 which needs to be kzu~n more directly. In this letter we present the first experimental evidence of the effect of a magnetic ~

H~uipede Rediercthe CNRS n°60216

~r Laboratoire associd CN~

311

field on the correlation lengths in a 11) antiferrtsnagnet. As we shall see, l~odifferent correlation lengths most actually be considered in the problem, depending on wether the fluctuations axe associated with the spin ccmponents parallel or perpendicular to the direction of H, namely K731 and KJ.’, respectively. It turns out that their field dependences are very different. In order to study K1(H) (a = II or.L) we performed quasi-elastic neu~.ron scattering measurements in presence of a magnetic field (0~H~4CkCe) on ThTC at lcw tesperature (lK6T~lOK). We shall mat review the structure and magma— tic properties of ¶L!’M~which have been studied extensively elsewhere [7]. Hcwever a crimmont is in order about the value of the exchange cot~ling J. Assuming the magnetic interaction to be given by a nearest-neighbor Neiserberg exchange -23 ~j ~j+i n~nyexperimental determinations of J have been made in LN~C.All agree with the Values J 6.7 ±0.3 K except the evaluation thtained fran previous quasi-elastic neutron scattering neasureirents, giving a higher value : J = 7.7 ±0.3K [8]. It must be p,inted out that in this latter study, the temperature dependence of K’ was interpreted within the Heiserl,erg model in the tenperature range 1K
EFFECT OF A MAGNETIC FIELD ON THE CORRELATION LENGTH

312

2/8JS(S+1).The direction of tropyjeeff (gt~HS.~) H béccuies a=hard aids and consequently the spins will tend to lie perpendicular to it. If the spin system was initially in a Heisenberg state where aK(~is)= kT/2JS (S+1) with a the distance between state where aic (XI) [7J. Duringanthis adjacent spins [7], = itk’r/4JS would (S+1) be chani~edinto XI Heisenberg -XI transition K would be reduced by a fac±ort~o. On the other hand, if ~ is applied in the plane of an XV system, a transition towards an Ising state will occur • The change in K can be n-~ more important since K (Ising) = emp (—JS (S+1 ) /kT) [7]. Very large effects can be expected even with small values of H. A more quantitative evaluation

of ic shown1 that, second order in H~r can be toobtained fran ref [4] where it is K.L/K (XI) = 1 - [s (S+1) /16] Lgii~H/kT]2 Similar expression can be derived for K//(H)

(1)

2

*3K

HI,

1 ~

*

\

(IT (K ~ __________________________

Fig. 1 Universality in H/T of the quantities icr/ic (XI). The solid lines corresp~dto als(b, 2 and 4). lIe dotted line is an

interpolation between the two limiting

values of K//Ic (XI) (Ek~s(2 and 4)). ‘lIe dashed line is the apparent li~idth K/K (XI) calculated fran ~s (1-5). The dot-dashed curve is a least sciuare fit of a second order polyr~rd.alexpression in H/P (see text). For creparison, U.~ curve K /K (Heis) corresponding to a ~ also shown (full mated Heis) tern initially in aline Heiserberg stateonisthe Fig.. The position of the scattering wave

vector ~ with respect to H and the chain axis ~ is shown on the Fig. : = (1.25

o

i.

K//I K(XI) = ~‘S(S+i)7~ g1.~H/kT (4) E~pressions (1) (2) and 4) are universal functions of H/P and are plotted on Fig. 1 for the parameters [bO].~inverse

//z) nteochronator, horison~l 30’, 20’ 0<11<40 and in the 30’, s~ respectively. aThe ~ magnetic that range U~ 1~asurements scattering were the using vertical performed a was crycmagnet and in the with kOe temperature sample • the crystal and the field of detector abc~it 1~’l’6lO0K 1.5 cm3 oriented thecould chain (C H//y axis wave (h ; with 0 ; 1) be aids surveyed. Scansvector in theQ £=direction were carried out across

the magnetic planes of diffuse scattering, characteristic of the lD short range order ~.8]. As it has been shown by R.J. Birgtereau et al., there is a parasite nuclear scattering contribution su— perinçosed to the magnetic scattering [8].This contribution which is temperature ir~per~ant below 30 K but strongly deper~enton h was minimum and less than 10% of the full signal at ~ = (1.25 ; 0 ; 1), below 10 K. This nuclear part was substracted fran the total contribution. The remaining sc~ttez~thg~~as ~assuned to be given by

i

0

(3)

the Ka should observable for relatively small values of H/P be (H/P = 10 kOe/K). The experiments were performed on a tripleaxis spectrcueter at the Centre d’Etudes Nucléai— res de &er~1e Siloé reactor using neutrons of wavelength 2.4 A. The col]J.nation in front of

~

F~\

2

with asymptotic value of K// for mV,’ /m(XI) rn(XY) = = 1/2. 1 - [~(S+1)/32] [gp~H/kT] ~ + = can easily be derived fran qualitative arguments. First we define T~ as the temperature at which the thermal enerc~~i beixtres ccrtparable to the effective anisotrcw in an initial XV chain of length ic~(Xf)1 : kT = [aicco (XI)]1 [~] 2,~j. by analo~rw~hthe Heiserberg -XI tramsition ~9], we assume KI3’ for a given H to “satu4~~ (S+1). One easily deduces = rate” as for T +Htr 0 + K,/ + cr/

correlation length ic~can be seen to decrease with initially H while K// inincreases an XI state, • As significant a conclusionchanges if ¶I~Cis in

/ /~

•4K

Kllh,c(XV) = 1 + [s(s+1)/16] [gu~Wr]2 (2) and for the order parameters which enter our problem mj and rn, 1 where m~= /~(S+1) with the obvious condition rn1 + rn~,= 1

of~1,C:J=6.9KandS=5/2

I

£ 5K

Vol. 31, No. 5

M(~) = fffL(Q

-

S)R(S)d3S

where L (~)represents theelastic magnetic scatteringfuncfunction and R(~) is the resolution tion of the inst~ment. Particular attention has be paid on R(Q). Defining ~ by ~ = + ~ with (h ,(B,~x 0 ,21)+ ore R~)asR~ ~ exp =[-Ln2 2B can write + B~,c1z+ ite coefficients B~ ~r cz, b= x, y, depends explicitely on were determined fran the Bragg peaks (h, 0, 1) for h = 0, 1, 2 and 3, In one dimension, integration over qx ~ be made leading to

qy can

M(q~) ‘~ IL (q~- S~exp(—Ia2C~q~)dq with Czz = Bzz - Bj~. One ore sees that C~ depends on the three coefficients B 5~, Bxz and 1Y 30%, which Bxt. We chedred that the term B~/BXXgives rise tO canmat be neglected. We also an important correction to ~ studied ~-the h depei~n— on of Czz which is an increasing function of h while the magnetic form factor is a decreasing function of

h. Fo~~

=

(1.25 ; 0 ; C).

c~was

as large as 8500

±500A2 giving a rather good instrumental resolution,

Vol. 31, No. 5

EFFECT OF A MAGNETIC FIELD ON THE CORRELATION LENGTH

~e intensity of the signal was reasonable arid the parasite scattering relatively small. The function L(q) was assured to be torentxian * r2 2-i L(~) = A/LK + q ~ ± with q = (1 - 4L)i~/a.The data M(u) were analyzed through a convolution procedure and the values A arid c were determined with a two-parameter least square fit. The resulting values of ic for H = 0 are sl~.inon Fig. 2 as a function of T. The field deper*~enceforT=3,4and5Kiss1xwninFig.l where the quantity ic/c(XI) is plotted versus H/T. The value of K(XI) was taken fran the full line on Fig. 2.

)~‘(A—1)

.02’

•

TMMC

313

can easily be understood in the medal of the XIIsing transition. The e~erinental position of the scattering wave vector 0 with respect to the chain aids (c/Is) and to the field aids (11.//y) is irx3icated on Fig. 1. ‘lIe function L(~)is therefore the sun of ~o contributions L(~) = cos’cr LL(q) + LIl(q) where L,,(q) = <~sZ~> and L.L(q) = are the fluctha~tionsparafle]1~andperpendicula? t~H, respectively. Assumling a lorentzian shape for L.L(q) and L I L(~l M;Et be written as //q~

L(~) = A[cos~tIru~~ + q;~+ m//~~ + q2II 2 with cos cr

2 =

1

-

Q~/~I. However the

analysis of

• ~1.25,o,.t) 0 (2.3.0.1) x (1.3.0.1)

.o:Lt9v~~1

Fig. 2 Inverse correlation length as a function of temperature in zero field~for different scattering wave vector 0 = (h ; 0 £). The dot—dashed lines are theoretical

curves calculated for Heisetherg and XI nrmdels. The solid line was calculated by D. Hone arid A. Fires, taking into account the intrachain dipolar interactions The dashed line corresponds to the Heisenberg model with J = 7.7 K.

[~J.

On Fig. 2 the experimental temperature dependance of K in zero field is crzrpared to different

tIe data reported on Fig. 2 was made withonlyoielorentzian according to flj. (5). The experimental pathexoretical curves • The dot-dashed lines corresraneter K therefore plays the role ot an apparent pond to the Heisermberg arid to the XV models, the width. It can easily be evaluated fran the theorefull line is the curve calculated by Hone arid Pitical values of K//, cL, mi, and xn~given by Ek~s(1res [9], which takes into account the dipDlar in— 4). We chtain the dashed lire on Fig. I, in good agree— teractiorms. For crmparison, the curve for the Heisent with the experimental data for all three ternserberg model with J = 7.7 K, which fits the expe— peratures. We cthedced that, whatever set of points rinental results of ref[8], is s1~non Fig. 2 (T = 3, 4 and 5K) is cxzrsidered a least square fit (dashed lire). Our data (especially for = (1.25 ; with a second order polynanial expression gives the O ; ~) do not agree with this model. The excellent sane result within the statistical standard daviaagreement between the theory of Hone and Pires [9] tion. Such a polyrxznial expression is shown as the arid the experimental data definitely establishes dot-dashed curve The role of universality in H/P that below 5 K ‘lM~Cis in an XV state. The spins are given by F1~(1-4) is therefore quantitatively emexpected to be perpendicular to the chain axis. ‘l~ tablished. ‘l~ rernarts are in order : i) for H/I’ negretic tield it being along y is applied in the = 10 k0e/K, K which represents essentially K.l. has plane of the spins arid the data of Fig. 1 should been reduced by more than a factor two ; this fact correspond to an XI-Ising transition. Whatever the corrthorates the previous result : ‘II*C is initial~temperature (T = 3, 4 and 5 K) a plateau is first ly (H = 0) in an XI state below 5 K ; ii) the difcbserved in low field followed by a rapid drop of ference between the dot-dashed curve arid the curve c for higher values of H. This surprising behavior for c.i can be explained by the fact that EkI. (1) is

EFFECT OF A MAGNETIC FIELD ON THE CORRELATION LENGTH

314

a pertuthation expansion valid only for small values of H/I’. Higher order terne would have to be taken into accxxrnt.

General conclusions can be drm~nfran this work. The isotropic character of any Heiserberg antiferraragnetic chain will always be lost at low temperature because of the intrachain dipolar interactions. Our results establish that ~1MCis actually in an XI state at low temperature (T .~ 5K) We have experin~ntally shown that the effect of a magnetic field 11 Ce an anti ferratagnetic chain at low temperature can be described in terra of an

Vol. 31, No. 5

effective anisotropy which induces a crossover transition associated with a reduction of the spin dimensionality. If the spin system is initially in an Heisenberg state it will be changed into an XI state with the spins perpendicular to I~.If the

spins are initially in an XI state, the application of ~ in the plane of the spins will drive the systan towards an Ising state. We show that ~C displays the latter behavior. Acknowl~dg~ment This work was supported in part

by

twio grant n° 1044.

References

Lii

A.R. ~Gurn, P.A. Mcitano arid D.I. Scalapino Sol. Stat. Carnun., 15, 1463 (1974).

16] J.P.A.M. Hijinans, K. Kcpinga, F. Boersma and W.J.M. do Jonge, Phys. ~ev. Iett., 40, 1108

Steiner and J.K. KjeiTs, j. ~iys. c. : Solid State Phys. 10 (1977). C. Dupes arid J.P. Penard, Sol. ~ Cat~., 20, 581 (1976) ; W.J.M. de Jonge, J.P.A.M. Hijmas, F. Boersma, J.G. Shouten arid K. Kcpinga, Phys. Rev., B17, 2922 (1978).

(1978). [7] M. Steiner, J. Villain and C.G. Windsor, I½dv.

[2] M. [3]

in Phys., 25, 87 (1976). [8] R.J. Birgeneau, R. Dingle, M.T. Hutchings, G. Shirane and S.L. Holt, Phys. Rev. Lett., 26, 718

(1971).

[4]F. Borsa, j.P. Boucher and J. Villain, J. Appl. Phys., 49, 1326 (1978).

[9] D. Hone and A. Pires, Phys. Rev., HiS, 323 (1977).

[5]J. Villain and J.M. I~veludc, Journal do Phy-

[io] The value J

sique, 38, l,-77 (1977).

= 6.9 K was used by D. Hone and A. Fires 19]. It agrees with the nest prththle experimental evaluation J = 6.7 ±0.3 K.