Journal of Magnetism and Magnetic Materials 104-107 (1992) 857-858

North-Holland

Magnetic correlations in the quasi one-dimensional antiferromagnetic ABX, systems

K. Kakurai ‘, K. Nakajima b, Y. Endoh b, K. Iio ‘, H. Tanaka d and M. Steiner e

’ ISSP, University of Tokyo, Roppongi 7-22-1, Tokyo 106, Japan h Dep. of Physics, Tohoku lJnil,ersity, Sendai 980, Japan ’ Dep. of Physics, Tokyo Institute of Technology, Tokyo 152, Japan d Dep. of General Education, Nagoya Uniclersity, Nagoya 464, Japan ’ Inst. fiir Physik, Uniclersitiit Maim, Postfach 3980, W-6500 Mainz, Germany

We report the results of quasi-elastic neutron scattering experiments on quasi one-dimensional antiferromagnets of

hexagonal ABX, type. In the S = 1 near-Heisenberg systems finite correlation lengths for T = 0 are extrapolated from the

quasi one-dimensional temperature regime. This observation is in accordance with the Haldane conjecture for integer spin

value systems, but the experimentally determined correlation lengths are larger than expected from the valence bond solid picture.

The quasi one-dimensional (1D) antiferromagnets (AFs) of hexagonal ABX, type with different spin values (S) and different exchange constants offer an excellent test field to study the interesting AF ground- state problem. Inelastic neutron scattering using unpo- larized and polarized neutrons have been performed on the S = 1 system to look for the evidence of the Haldane gap [I]. It was indeed found that even the dispersion relation in the 3D ordered state could not be properly described by the classical spin wave (SW) theory when the polarization of the spin fluctuations observed by polarized neutron scattering experiments was taken into account [2,3]. .The recent theory for quasi lD, S = 1 AF system by Affleck [4] including the Haldane effect can account for the experimental re- sults. Hence the S = 1 ABX,-type systems can be re- garded as weakly coupled chains with the Haldane groundstate. A single AF chain with integer spin value does not order even at T = 0. The spin correlation in the groundstate decays exponentially and not with a powerlaw as for systems with half integer spins. One of the physical pictures of the Haldane groundstate, the valence bond solid (VBS) picture [5], predicts a very short range correlation at T = 0 of lo = 1 spin. The numerical calculations [6] however yield ia = 5 spins. It is therefore important for our physical understanding of this novel groundstate to determine the correlation length experimentally.

Using neutron diffractometer with an incident neu- tron energy of 30.5 meV, energy-integrating quasi-elas- tic experiments are performed on different AF ABX, systems, CsNiCl,, RbNiCl, (both S = 1) and CsMnI, (S = 2). For all three systems the classical exchange constants are known from the inelastic neutron scatter- ing experiments by determining the zone boundary energies (J = - 16.6, -23.8 and - 9.5 K for the three systems respectively). It is also known that in all three

systems the anisotropy is very small (D/J 5 0.0025 in all cases). Single crystals of - l-2 ems are oriented with their (110) and (001) axis in the scattering plane. The 1D AF correlations show up in the diffuse scatter- ing planes perpendicular to the (001) direction inter- cepting the (001) axis at odd integer 1.

Fig. 1 shows typical spectra at different tempera- tures scanning across the 1D diffuse plane. The solid

‘*O” I 1000 _

600 - .4

d u 600 -

400 -

1000

600 - e E 3 600 -

400 -

1000 -

600 - .c E

3 600 -

400-

T=35K

T=51K

200' I 0.0 0.5 1.0 1.5 2.0

I

Fig. 1. The temperature evolution of the 1D diffuse scattering

at Q = (0.42, 0.42, I) in RbNiCl,.

0312-8853/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

8.58 Mugnefic correlations in ABX., K. Kakurui et ul.

0.3

CsMnl3

CsNiC13

0.4 -

b)

RbNiCl ,

Fig. 2. The temperature dependence of the HWHM corre-

sponding to the inverse correlation length K in (a) CsMnI,,

(b) CsNiCl i and (c) RbNiCl,.

lines indicate fits with resolution-convoluted Lorentzian line shape. The half widths at half maximum (HWHM), corresponding to the inverse correlation lengths K, obtained from these fits are plotted in fig. 2 for the three different materials.

For CsMnI,, an S = s case, the measured K(T) in the 1D temperature regime can be well described by the Fisher formula for classical AF Hcisenberg chain consistent with the known exchange constant J (solid line in fig. 2a). This implies that the correlation length diverges at T= 0. The upward turning of the inverse correlation length below 12 K is caused by the 3D ordering at T, = 11.4 K.

In contrast to this the inverse correlation lengths of CsNiCl, and RbNiCl, in the 1D temperature regime above T, (T, = 4.8 and 12 K respectively) cannot be

explained using the exchange constants detcrmincd by the inelastic neutron scattering experiments, It is note- worthy that the slopes of the inverse correlation lengths in both cases seem to agree with the slope predicted by Fisher’s formula, if the renormalized form for finite S (S(.S + 1) instead of S*) is applied (see dashed lines in fig. 2b and 2~). Hence a reasonable description can be achieved if a finite inverse correlation length Kg at T = 0 is introduced. The fits with this additional pa- rameter (solid lines in fig. 2b and 2c) yield J = -(IS.7 f 3.3) K, K,, = (0.060 f 0.008) rlu and J = -(25.5 f 2.6) K, K,, = (0.026 5 0.011) rlu, for CsNiCl, and RbNiCI, respectively. The agreement with the cxchangc con- stants determined by the inelastic neutron scattering experiments is good.

We conclude that there is a clear experimental evidence for the finite correlation length at T = 0 in the S = 1 chains in contrast to the half-integer spin chains. This is in qualitative agreement with the theo- retical expectation for the integer-spin Haldane groundstate. But the experimentally extrapolated T = 0 correlation lengths, <,, = 5.3 and lo = 12.2 spins for CsNiCI, and RbNiCl, respectively, arc much larger than expected from the VBS picture and more compat- ible with the numerical calculations. (‘(, also seems to depend on system parameters, in contrast to the VBS picture where <,, = 1 is expected for all VBS systems.

It seems that in reality the quantum fluctuations in S = I chains are more suppressed than the VBS pic- ture predicts. Whether this is caused by the weak but still existing interchain exchange (3D effect) or is con- nected to the fundamental nature of the chain with integer spin value is yet an open question.

References

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[3] Z. Tun, W.J.L. Buyers, R.L. Armstrong, E.D. Hallman

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[4] J. Affleck, Phys. Rev. Lett. 62 (1989) 474, 65 (1990)

2477(E), 2385(E). [5] 1. Affleck, T. Kennedy, E.H. Lieb and H. Tasaki, Phys.

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