Magnetic excitations in cerium antimonide

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Magnetic excitations in cerium antimonide

A. Furrer, W. Haelg, H. Heer, O. Vogt

To cite this version:

A. Furrer, W. Haelg, H. Heer, O. Vogt. Magnetic excitations in cerium antimonide. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-122-C5-123. �10.1051/jphyscol:1979543�. �jpa-00218960�

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JOURNAL DE PHYSIQUE Colloque C5, supplément au ri> 5, Tome 40, Mai 1979, page C5-122

Magnetic excitations in cerium antimonide

A. Furrer, W. Haelg and H. Heer

Institut ftir Reaktortechnik, Eidg. Technische Hochschule Zurich, CH-5303 Wiirenlingen, Switzerland

and O. Vogt

Laboratorium fur Festkorperphysik, Eidg. Technische Hochschule Zurich, CH-8093 Zurich, Switzerland

Résumé. — Nous avons mesuré la dispersion des excitations magnétiques dans CeSb ferromagnétique à 4,2 K au moyen de la diffusion inélastique des neutrons. Les expériences sont bien décrites par un champ cristallin cubique et par un échange fortement anisotrope.

Abstract. — By means of neutron inelastic scattering we measured the dispersion of magnetic excitations in ferro- magnetic CeSb at 4.2 K. The experiments are well described in terms of a cubic crystal field and a strongly anisotropic exchange interaction.

The low-temperature magnetic behaviour of CeSb shows a variety of interesting effects. CeSb crystallizes in the rocksalt structure and is tetragonally distorted below the magnetic ordering temperature [1]. The magnetic structures of the numerous antiferroma- gnetic phases below TN — 16 K were determined by means of neutron diffraction [2, 3]. The ordered magnetic moments are confined to the < 001 > easy directions. This led Cooper and Vogt [4] to suspect the presence of strongly anisotropic exchange favour- ing the < 001 > alignment and overcoming the ten- dency of the crystal field to favour < 111 > alignment as found experimentally upon diluting the Ce with Y or La. It is the purpose of the present work to provide detailed information on the exchange interactions by studying the magnetic excitations of CeSb by means of neutron inelastic scattering.

— ( j - , . )— _ — — j ]

6- 4 f\ '

o L I \

CD > \ • / / T

1 - 7 7^x1° -

• • . -^

~5 t 3 2 1 0

fico [meVI

Fig. 1. — Energy spectrum of neutrons scattered from ferromagne- tic CeSb at 4.2 K for q = 2 n/a (0.5,0, 0). The curve is drawn as a guide to the eye.

The experiments were performed on a multi-angle- reflecting-crystal (MARC) spectrometer at the reactor Diorit at Wurenlingen. The CeSb sample was a single crystal of 0.15 cm3 volume aligned so as to have a [001] axis normal to the scattering plane. The measurements were done at 4.2 K. In order to avoid the pro- blems arising from the different domain orientations, the measurements were carried out in an external magnetic field of 42 kOe applied along the [001] axis which is sufficiently strong to cause ferromagnetic ordering below 10 K [2, 5]. A typical energy spectrum is shown in figure 1 for q = 2 nja (0.5, 0, 0). Besides the elastic line the spectrum exhibits a well defined peak of magnetic origin at fia> = 4 meV. The disper- sion of the magnetic excitations of ferromagnetic CeSb is shown in figure 2. The interesting feature of the dispersion curves is the large difference between the zone-boundary energies at the reciprocal-lattice points (100) and (110). This directly proves the pre-

5-

3 2- 1-

1 08 06 0U 0.2 0 02 0 4 0.6 08 1

Fig. 2. — Dispersion of magnetic excitations of ferromagnetic CeSb at 4.2 K. The line is the result of the least-squares fitting procedure as described in the text.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979543

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MAGNETIC EXCITATIONS IN CERIUM ANTIMONIDE C5-123

sence of strongly anisotropic exchange in CeSb, since for isotropic exchange the excitation energies at (100) and (1 10) are identical by symmetry.

We describe the Hamiltonian of the spin system of CeSb as the sum of crystal-field and Heisenberg exchange interaction terms :

where B, is a crystal-field parameter and

6,"

are Stevens operator equivalents [6]. Directional exchange anisotropy is introduced in the sense that the exchange parameters depend on the z-component (z-axis = polar axis) of the vector Rij = Iti -

Rj

interconnect- ing the spins J(Ri) and J(Rj).

A mean-field analysis of Eq. (1) for CeSb [7] suggests that nearly all the excitation strength resides in the transition to the first excited state corresponding to a transverse transition within the exchange-split doublet ground-state of the Ce3+ ion. Thus we attribute the observed excitation energies of figure 2 to this transition.

A least-squares fitting procedure based on Eq. (1) including nearest-neighbour and next-nearest neighbour exchange parameters

a,

and

a,

and keeping the crystal-field parameter constant at B4= 9.1 x meV [7] yields

The external field was taken into account in the single-ion part of Eq. (1). The dominant contribution

to the exchange results from next-nearest neighbour exchange along ( 001 ), whereas the exchange parameter

a,

perpendicular to the polar axis as well as the exchange parameters

a,

are at least an order of magnitude smaller.

The excitation energies calculated from these model parameters are shown as solid lines in figure 2. The calculated zero-field moment is 2.05 p,, in excellent agreement with the experimental value

- - -

In order to study the nature of the large quasi- elastic contribution in the observed energy spectra (see figure I), we recently performed a measurement with increased energy resolution. As a result we were able to resolve a peak of magnetic origin at tio x 2 meV. Obviously the magnetic excitation spectrum of CeSb is split into two branches. Such a splitting may be explained by an anisotropic exchange interaction whenever the crystal-field Hamiltonian

contains terms with m = 2 [8].

Recently, Cooper [9] studied the qualitative nature of the anisotropic effects in cerium and actinide intermetallics. The idea was introduced that magneto- elastic effects involving internal rearrangement modes may play a key role in the occurrence of highly anisotropic magnetic structures. While no attempt has been made so far to observe such a static lattice mode in CeSb by X-ray or neutron diffraction, the present results may be indicative of internal rearrangement modes : static lattice modes having the appro- priate symmetry may give rise to crystal-field terms with m = 2 which in turn are necessary to produce the observed splitting of the transverse mode.

References

HULLIGER, F., LANDOLT, M., OTT, H. R. and SCHMELCZER, R., [5] MEDER, G., FISCHER, P., HAELG, W., LEBECH, B., RAINFORD, B. D.

J. Low Temp. Phys. 20 (1975) 269. and VOGT, O., J. Phys. C 11 (1978) 1173.

ROSSAT-MIGNOD, J., BURLET, P., VILLAIN, J., BARTHOLIN, H., [6] STEVENS, K. W. H., Proc. Phys. Soc. A 65 (1952) 209.

TCHENG-SI, W., FLORENCE, D. and VOGT, O., Phys. [71 HEER, H . , Thesis (Eidg. Technische Hochschule Ziirich) 1978.

Rev. B 16 (1977) 440. [8] LINDGARD, P. A., Rare Earths and Actinides, Durham 1977 [3] FISCHER, P., LEBECH, B., MEIER, G., RAINFORD, B. D . and (The Institute of Physics, London) 1977.

VOGT, O., J. Phys. C 11 (1978) 345. [9] COOPER, B. R., Phys. Rev. B 17 (1978) 293.

[4] COOPER, B. R. and VOGT, O., J. Physique Colloq. 32 (1971) C1-1026.