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Magnetoelastic effects and the anomalous anisotropic magnetic behavior of cerium monopnictides
B. Cooper, R. Siemann
To cite this version:
B. Cooper, R. Siemann. Magnetoelastic effects and the anomalous anisotropic magnetic behav- ior of cerium monopnictides. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-126-C5-127.
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JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-126
Magnetoelastic effects and the anomalous anisotropic magnetic behavior of cerium monopnictides
B. R. Cooper and R. Siemann
Dept. of Physics, West Virginia University (*), Morgantown, West Virginia 26506, U.S.A.
Résumé. — Une anisotropie magnétique < 100 > extrêmement forte est observée dans les composés CeBi et CeSb.
Cette anisotropie < 100 > est accompagnée d'une distortion tétragonale et est due à la forte sensibilité de l'inter- action du champ cristallin aux changements du paramètre de la maille cristalline dans les monopnictides de Ce.
Le changement de phase magnétique entre le type I (up-down-up-down) et le type IA (up-up-down-down) dans CeBi suggère la présence d'un type spécial d'interaction d'échange d'ordre supérieur.
Abstract. — Extremely strong < 100 > magnetic anisotropy occurs in CeBi and CeSb. The occurrence of this
< 100 > anisotropy, together with a tetragonal distortion, is associated with the remarkable sensitivity of the crystal-field interaction to lattice spacing in the cerium monopnictides. We find that the type I (up-down-up- down) to IA (up-up-down-down) magnetic structural transition in CeBi calls for the additional presence of a special type of higher order exchange interaction.
CeBi and CeSb display extraordinary magnetic behavior through their highly anisotropic and unusual magnetic ordering structures [1-3]. A central feature of this anomalous behavior is the presence and strength of < 100 > magnetic anisotropy in contrast with the theoretical crystal-field-only < 111 > easy direction as found experimentally [4] upon diluting the Ce with Y or La.
A key question is the source of this strong < 100 >
anisotropy. There are two possible origins to be considered for such effects. One is distortional effects on the single-ion crystal-field in conjunction with magnetic ordering arising from isotropic exchange, i.e., the only anisotropic interaction present is single- ion. The other possibility is the effect of anisotropic exchange, i.e., macroscopic anisotropy via a two-ion anisotropic interaction. Despite the apparent simi- larity of the cerium and light actinide monopnictides [5], e.g., qualitative similarities in magnetic behavior of CeBi and UAs, the relative importance of these two possibilities may be quite different for the two classes of compounds. This is indicated by the presence of significant tetragonal distortion [6] in conjunction with magnetic ordering for CeBi and CeSb, and the absence [7] of any distortion at all, within experimental accuracy, for actinide monopnictides such as UAs and USb.
From neutron scattering [8] and other measurements we know that the crystal-field for the cerium mono- pnictides differs from that of the heaver rare earth monopnictides in having a variation with lattice parameter extraordinarily stronger than that expected on the basis of the point charge model. We find that
(*) Supported in part by NSF Grant No. DMR 77-06721.
the extraordinarily strong < 100 > anisotropy in CeBi follows as a direct consequence of the extreme sen- sitivity of the crystal-field to lattice displacement.
The < 100 > tetragonal state is relatively less favorable than the < 111 > trigonal state for the crystal-field energy : but, on the other hand, the < 100 > tetragonal state is relatively less unfavorable for the elastic energy, and the latter effect leads to the < 100 >
tetragonal state winning out in the overall energy balance.
We introduce the enhancement of the change in crystal-field interaction with lattice displacement, relative to that expected on the basis of the point charge model, through an enhancement factor, p.
Since this is equivalent to assuming an enhancement with distortion of the effective charge, we refer to p as the crystal-field gradient charge enhancement factor. Our self-consistent calculations for CeBi use the experimental crystal-field splitting, T
N, and elasticconstants. A comparison of the free energy for < 111 >
ordering, with trigonal expansion, compared to < 100 >
ordering, with tetragonal compression, is shown in figure 1. The fact, found in our detailed calculations, that for a given p, the < 100 > equilibrium distortion is always larger than the < 111 > distortion gives the
< 100 > ordering an advantage with regard to lowering the crystal-field energy that becomes of increasing importance with increasing p. For p « 10, the < 100 >
energy crosses below the < 111 > energy. At T = 0, the predicted distortion is 5 = — 0.6 % compared to the experimental — 0.1 %.
Thus despite the crudeness of our way of parame- trizing the enhancement of the crystal-field gradient, our model calculations using isotropic exchange predict a < 100 > anisotropy, with an associated distortion
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979545
MAGNETOELASTIC EFFECTS AND THE ANOMALOUS ANISOTROPIC MAGNETIC C5-127
0 2 4 6 8 1 0 1 2
p (GRADIENT CHARGE ENHANCEMENT)
Fig. 1. - Comparison of the free energy as a function of p for the two directions of magnetic ordering. The relative distortion 6 is tetragonal ( E ( c
-
a)/a) for ( 100 ) orderings and is trigonal for ( I 1 1 ) ordering.of both the type and order of magnitude observed experimentally in CeBi. However, the existence of the I to IA magnetic structural transition at T close to TN/2 with an observed lack ofassociated distortional effects, internal or external, above a rather small limit set by experimental accuracy, indicates the need for additional higher order, possibly anisotropic, exchange interaction. We have arrived at this conclu- sion by investigating three possible mechanisms for the transition
:(1) a lattice structural transition involving the + + -
-internal rearrangement (see Fig. 1 of Ref. [9])
:(2) a dependence of the exchange integrals on the size of the tetragonal distortion :
(3)the effects of'higher order terms in the exchange interaction. Through a combination of results from our calculations and from experiment, we eliminate mechanisms (1) and (2). On the other hand, including
(3)higher order exchange, giving a cubic or higher odd order term in magnetization in the molecular field, does provide the I to IA transition with only a small change in the tetragonal distortion.
Thus we see that apparently both enhanced crystal- field distortional effects and higher order, possibly anisotropic, exchange coupling are necessary to understand the unusual anisotropic magnetic struc- tural behavior in CeBi.
References
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