Physica B 156 & 157 (1989) 263-265

North-Holland, Amsterdam

MAGNETIC EXCITATIONS IN THE QUASI ONE-DIMENSIONAL SINGLET GROUNDSTATE SYSTEM CsFeBr,

ANTIFERROMAGNETIC

B. DORNER’, D. VISSER’, U. STEIGENBERGER1’4, K. KAKURA13 and M. STEINER3 ‘Institut Laue-Langevin, 156X, F-38042 Grenoble Cedex, France ‘Inorganic Chemistry Laboratory, South Parks Rd., Oxford OX1 3QR, UK ‘Hahn Meitner Institut, Postfach 390128, D-loo0 Berlin 39, Germany 4Permanent address: Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK

The measured dispersion curves of the magnetic excitations in CsFeBr, are very unusual. The observed intensities are

interpreted by a heuristic model including antiferro- as well as ferromagnetic fluctuations. The main dispersion curve with

strong intensity is obtained due to “in-plane” fluctuations. A “mirrored” curve which is not predicted by theory is observed

with weak intensity due to “out-of-plane” fluctuations

All four opmpounds of the AFeX, family (with A = Rb and Cs; X = Cl and Br) have at high temperature the same hexagonal structure with space group P6/3 mmc. Chains of face sharing AX, octahedra running along the c-axis are sepa- rated by the Rb or Cs ions. Thus the magnetic interaction along the chains is stronger than the one between the chains. The Fe*’ ion, with S = 1, has probably in all four compounds a singlet groundstate (SGS). In a series of theoretical and experimental studies it was found that subtle changes in the ratio of anisotropy energy to total exchange energy can result in a magnetic groundstate as in RbFeCl, [l-3] and RbFeBr, [4] or in a true SGS as in CsFeCl, [5-71 and CsFeBr,. A characteristic feature of such SGS systems is the softening of the zone center mode with decreasing T due to correlations in- duced by the exchange interactions. The Cl- compounds show ferromagnetic correlations along the chains while the Br- compounds have antiferromagnetic ones. The Hamiltonian

H = -2J 2 Si * Si+l - J’ c Si . S, + A c (SF)’ I i#j I

(1)

has been used to describe the different materials mentioned above. Here J is the exchange parameter along the chain and J’ the one be-

tween them. If A is positive, it gives the energy gap between m = 0 and m = +l states.

The measured magnetic excitations show a lowest gap at ( $ f 1). The dispersion along the z-direction raises in energy towards the antici- pated Brillouin zone boundary at 1= 1.5. To our astonishment we could follow the excitations with still increasing frequencies all the way to 1 = 2, see fig. 1. The dispersion perpendicular to the chains was studied for 1 = 1 and I= 2, see fig. 2. Along the path [l. 1 1.1 S] we observed two frequencies simultaneously. The low frequency mode at ($ 4 1) showed a strong temperature dependence, but levelled off at low temperatures at a finite gap.

1.5 r;-

2

Fig. 1. Measured dispersion curves of the magnetic excita-

tions versus 5 in [27~/c], where c/2 is the Fe-Fe distance.

0921-4526/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

264 B. Darner et al. I Singlet groundstate system CsFeBr,

T

CsFeBr, T;14K

.!L r [E; 5 ‘I =050

t *I? 5 ‘I w

OL- L_ 1 _~A 0 5-+o25 0333 O5

Fig. 2. Dispersion curves perpendicular to the chain di-

rection.

From the Hamiltonian eq. (1) Lindgard [8,9] derived the following dispersion relation for a

SGS system:

d(q) = A2 - 8A[J cos(nq,) + J’y(2nq,)]R(T)

(2)

Here y(2ng,) is the dispersion relation for a 120” magnetic structure between the chains. R(T) = 1 is the renormalization factor at low

temperature. For details, see ref. [lo]. Note. Eq. (2) holds for positive J as well as for

negative J. The fit of eq. (2) to our data, figs. 1 and 2 gave Alk =29.8+0.5K, Jlk = -3.2-c 0.15 K and J’lk = -0.32 + 0.02 K. All these pa- rameters were found to be temperature in- dependent.

The observation of the dashed (mirrored) dis- persion curves in fig. 1 cannot be explained by the theory for a true SGS [ll, 121.

From the observed signals we determined in- tensities, see figs. 3 and 4. For reasons which will be explained later we corrected the data along the full line dispersion curve in fig. 1 by 2/( 1 + cos’ (Y) and the data along the dashed curve by sin’ (Y. Here cy is the angle between the z-axis

and the neutron momentum transfer Q. A heuristic model [lo] gives eigenvectors of

the modes in the excited state at I = 0, 1,2. . . , shown in fig. 5, for both the low and the high frequency modes. The admixing of ferromag- netic fluctuations to the “basic” antiferromag-

Fig. 3. Measured intensity at different reciprocal lattice

points.

Fig. 4. Measured intensity of the “mirror mode” in the same

scale as fig. 3.

netic ones (for negative J) is determined by f(A) which is zero for A --+ 0 and one for A -+ 35. From the fit to the data, figs. 3 and 4, we found f(A) = 0.71 +- 0.04. To correlate data in fig. 3 to those in fig. 4 we introduced an amplitude ratio between “out-of-plane” (OP) (z-direction) and “in-plane” (IP) (in the x-y plane) components. A fit to the data gave OP/IP = 0.22 k 0.02.

Fig. 5. Eigenvectors for CsFeBr, from a heuristic model for

I = 0, 1,2 The arrows represent the transverse compo-

nents of the fluctuations in projection along the spin direction

(y-axis). e, corresponds to the low frequency and eZ to the high frequency mode.

B. Dower et al. I Singlet groundstate system CsFeBr, 265

These two parameters in the heuristic model provide a very good fit as seen in figs. 3 and 4.

Within this model the full line dispersion cur- ves in fig. 1 are exclusively visible due to IP components with an intensity proportional to (1 + cos2 (Y) 12, while the dashed curves are as well exclusively visible due to OP lluctuations with an intensity proportional to sin2 (Y. As men- tioned above, this was assumed when deriving experimental intensities.

As stated already, the “mirrored” mode, .vis- ible due to OP fluctuations is not predicted by theory, which predicts one doubly degenerate mode for m = kl states. In the SGS system CsFeCl, with positive J this doubly degeneracy could be lifted by applying a magnetic field along the z-axis [5-71. This experiment has to be done in CsFeBr,. In the case of CsFeBr, we believe that the simultaneous observation of two disper- sion branches comes from the fact that the periodicity in real space contains two Fe2+ ions and not one as assumed in the theory.

References

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