Physica B 180 & 181 (1992) 197-198 North-Holland PHYSICA El

Magnetic correlations in the S = 1 quasi-one-dimensional HeGenberg antiferromagnet AgVP,S,

H. Mutka”, C. Payenb, P. Molinikb, J.L. Soubeyroux’, P. Colombetb and A.D. Taylor’ “lnstitut Laue-Langevin, 156X, 38402 Grenoble Cedex, France hlnstitut des Mat&au de Nantes, 2 rue de la Houssinitre, 44072 Names Cedex 03, France ‘Neutron Division, Rutherford Appleton Laboratory, Chilton. Didcot, Oxon OX11 OQX, UK

AgVP$, has a gap of E, = 26 meV at the point 9 = n. The excitations are well described with spin-wave velocity

C = 150 meV and a correlation length 5 = 5.5 = C/E,, in quantitative agreement with the predictions and numerical results

on the Haldane state.

After the first clues to the existence of the Haldane gap by neutron inelastic scattering [l, 21, only a few new systems, presenting the particular properties of the S = 1 spin chains, have been found. AgVP,S,, the S = 1 chain compound with well separated V3’ chains embedded in a layer matrix, was listed as a candidate right from the beginning [3]. The gap in its excitation spectrum was confirmed in a preliminary inelastic neutron scattering study [4], in spite of the drawback that it can be prepared in sufficient quantity only in polycrystal form. A second difficulty was recognised in the elevated energy scale (confirmed by inelastic neu- tron scattering) J/k, 7’~ 700 K. However, the powder averaged data, obtained on the time-of-flight spec- trometers IN4 at ILL and HET at RAL, were shown to be adequate for analysing the dynamic spin correla- tions [5]. Furthermore, static susceptibility and de- tailed powder diffraction (DIB) examination of AgVPzSh and its isostructural S = 3/2 companion AgCrP,S,, gave further evidence of the spin depen- dent difference between these two systems [6,7]. The magnetic parameters of AgVP,S, are summarized in table 1. In the following we shall give a short overview on the analysis of the inelastic powder data.

The powder average S( Q, W) of the dynamic spin- spin correlation function S(Q, W) of the isotropic 1D magnet is (see fig. 1)

Table I

Magnetic parameters of AgVPS, (H = J C (S,S,+, + (DIJ)S;:), J >O).

rid p J’IJh’ D/J 5 [Am’1 [meVl

1.07 5814 ~10~’ 2x10.’ 26 150 2 10 5.5 r 1

” Calculated from C = 2.65. h, Taking the broadening A = 1.4 meV at E, as transverse

dispersion, i.e. equal to 8(JJ’)“‘.

S(Q, w> = & ~(w)lF(Q)l' j- S(Q> w) dQ , Q=9+9, (1)

where the temperature factor is T(w) = (1 - exp(-hwl k,T))-’ for our neutron energy loss spectra and F(Q)

\______

5‘ 160

g

10

0.5 1 1.5 2 2.5 3 3.5

Reduced wave-vector

Fig. 1. (a) The inelastic scattering measurement on a 1D

system probes the intensity found on intersection of a re-

ciprocal plane and the Ewald sphere with radius Q, i.e. the

circle with radius 9, that is perpendicular to the ID wave

vector 9. For a powder sample this intensity is distributed

over the surface of the Q-sphere and energy conservation

decides which value of 9 is selected for a given Q, note that

along q,, there is no energy dispersion. (b) At a constant angle all (9, w)-points with 191 < Q and hw CC E, will contrib-

ute in the energy transfer spectrum. The angle and incident

energy define cut-offs that can be used to follow the disper- sion of the mode.

0921.4526/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

198 H. Mutka et al. / S = 1 ID-HAF AgVPJS,

I! 20 25 30

Energy transfer (meV)

35

Fig. 2. The singularity at E, is only broadened by d = 1.4 meV (IN4, E, = 45 meV, 5 < H < 26”). The instrumental

resolution is 1 meV. The fitted line is as described in the text.

is the ionic form factor. Supposing a 1D scattering law

S(q, w) = S(q) S(w ~ w(q)) 1 (2)

S( Q, w) becomes proportional to the density-of-states function g(w) of the dispersion relation w(q) of eq. (2), weighted by the instantaneous spin-spin correla-

tion S(q)

.VQ. 0) = (4~Q2L)~‘S(q)S(0)T(w)lF(Q)I~. (3) This is the information available in a powder experi- ment on an ideal 1D sample. The experimental Q- averaging samples S( Q, w) along constant angle

s(e. w) = S(Q> w)<,~cw, c,.wj (4)

and will show characteristic features due to the disper- sive nature of the excitations. Intensity discontinuities are produced whenever the experimental (Q. w)-trace cuts the dispersion surface. The problem is fully tract- able because of the unique (q, o)-relation of the 1D system, i.e. any intensity at a given 0 can only come from a limited number of points in q for which o = w(q) and (41 < Q. A dispersion with a gap E,,

h’w’( q) = Ez + C’ sin’( q - r) , (5)

produces a density of states that has singularity both at EE and at the upper limit of the excitation band. We have observed both of these and the figs. 2 and 3 illustrate the data obtained at extreme conditions with incident energy of 4.5 and 650 meV, respectively. These figures include the fitted curves with a square-root of Lorentzian-type S(q) [8]. The agreement of the above model with our data is very good using the set of parameters listed in table 1. Note, that with E, = 220 meV it was possible to confirm that the gap singu- larity is located at q = 7~ [5].

The results on AgVP?S, are representative of the low T one-dimensional behaviour, because of the strong coupling compared to the temperature (k, T = Ji 100) and because of the absence of magnetic order. We have a satisfactory agreement between the correla- tion length deduced from the model fit and the in-

L I / 1 I ,

0 50 100 150 200 Energy Transfer (meV)

Fig. 3. On HET, E, = 6SOmeV. the observed spectrum is

almost directly the density of states. In the angular range

3 < 0 < 7” the Q-cutoff occurs in the low-intensity valley at

2rr, with close to constant Q. The high incident energy favors

the observation of high energy transfer contributions because

of small value of Q. Accordingly, the band edge around

hw = C = IS0 meV becomes visible. The litted continuous

line suggests a broadening of the order of A = 3OmeV

(FWHM) in this energy range.

dependently obtained CIEp ratio, that are equal ac- cording to the theory.

In this paper we have demonstrated how the time- of-flight inelastic spectra on a polycrystal sample can be used for an analysis of quasi-1D magnetic excita- tions in a Heisenberg system. The success of such a study is partly connected to the rather simple structure of the ideal 1D scattering law and by consequence to the existence of samples that obey this simple law. Another important factor is the availability of an extensive range of incident energies for scanning in the (Q. w)-space, with good resolution and small enough wave vector transfer.

PI

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