FERMI SURFACES AND EFFECTIVE MASSES IN LnB,, Ln q La, Ce AND Pr*

Abstract The Fermi surface has been compared for the three compounds LnB6 (Ln  La, Ce and Pr) by measurement of the de Haas-van Alphen effect. The major part is observed to be similar in each compound, most likely consisting of X-centred ellipsoids with a total effective volume of about 1 electron per formula unit. Differences occur in the details of the shape of the FS, clearly seen for PrB6. Large effective masses, m ∗ , are observed for CeB6 and PrB6, m ∗ = 6 and about 1.8, respectively. These have to be compared with m ∗ = 6.0 for LaB6.


Introduction
In metallic lanthanide systems many questions arise around the character of the 4f electrons, being localised on the ion core or assuming an itinerant character, through the formation of bands hybridised with the s and d states. From the experiments direct information can be obtained by studying Fermi surfaces (FS), their shape and derived properties, and comparing the FS for several Ln compounds of similar nature. When hybridisation takes place one expects to find large dissimilarities.
One such system has been investigated earlier by Johanson  (dHvA) and band theory agree on an FS having a total volume of one electron per formula unit, consisting of large, X-centred electron ellipsoids. The ellipsoids are interconnected by necks along the X-X directions; orbits around the necks and on the ellipsoids crossing the necks are observed over a limited angular range for directions around [ 1001.

Results and Discussion
Here we report data on the shape of the FS for other LnB, compounds. The experimental procedure has been described elsewhere [ 4,5]. The dHvA oscillations are detected in high magnetic fields, between 10 and 21 T for LaB6 and PrB6, respectively, 25 and 33 T for CeB6, at temperatures between 1.3 and 4.2 K.
CeB, shows several magnetic phases as functions of temperature and field [6, 71; one infers from the magnetisation data that in the region where dHvA is measured, a ferromagnetic ordering is imposed by the magnetic field. For PrB6 the situation is less clear. From neutron scattering it was found [ 81 that two magnetic structures exist in zero field, a commensurate antiferromagnetic for T < 4.2 K and an incommensurate for 4.2 K < T < 6.9 K. The moment at T = 1.74 K is 1.77 pg. We measured the magnetisation on a sample consisting of a large number of single crystals. At a temperature of 4.2 K it varies approximately linearly with magnetic field up to 15 T; at 15 T one finds 0.7 pa per Pr atom.
For LaB6, dHvA frequencies are obtained as given earlier by Arko et al. [2]. Our results for the Ce and Pr compound are given in Fig. 1. For PrB6 the labels are given based on the merging of branches at high symmetry directions, indicating that the corresponding surfaces are connected through symmetry. For CeB, the labels are attributed based on the similarity to PrB,.
In all three compounds dHvA orbits are observed with frequencies ranging from 8 to 10 X lo3 T, labeled "a" in Fig. 1. For LaB, they are the belly orbits on the X-centred ellipsoids, x in the notation of ref. 2. In a comparison of the a-branches in Fig. 1 with the data for LaB, (ref. 2), a striking similarity is seen. For PrB, and LaB6 the frequencies are nearly equal; for CeB6 they are 5 -10% larger. The data for the Ce compound do not extend over the full (110) plane for experimental reasons rather than for the nonexistence of dHvA orbits near [ 1101.
For PrB, two other sets of branches, labeled "b" and "c" are observed. Most of them are detected over the full (110) plane, indicating that the corresponding FS sheets are closed. This is in contrast to the LaB6 case, where the lower frequencies are due to orbits involving the X-X necks. The threefold degeneracy of the b branches for the [ill] orientation may have two causes; it can be due to a non-symmetry position in the BZ of the centre of the corresponding sheets. In addition, it may stem from exchange splitting between the two spin directions. However, no such splitting is unambiguously resolved for the other sheets.
The effective mass, m*, of the a branches has been determined by fitting the temperature dependence of the dHvA amplitude to the Lifshitz-Kosevich [ 91 expression. In PrB, we find m* equal to 1.9 ? 0.2 and 1.8 ? 0.2 for a1,2 and a3, respectively, for the [OOl] orientation, using five temperatures between 1.3 and 4.2 K. No such accuracy is obtained in the case of CeB,, as the signal is only observed for temperatures between 1.3 and 2.2 K. The value obtained is 6 + 2 for the a3 branch along [OOl]. For LaB, the corresponding values are 0.65 and 0.61, respectively [2].
The a-branches shown in Fig. 1. have the highest frequency which varies only 25% over all orientations; they stem from orbits on the major FS sheets. When the a-branches have a common origin, the threefold degeneracy in the (001) plane places the centre of the sheets at the X point in the BZ, or M. The dominant part of the Fermi surfaces then has a strong similarity to the one of LaB6. In this picture the f electrons are localised; they influence mainly the dispersion at EF, increasing the effective masses above the value for LaB,. The b-and c-branches for PrB, may arise from distortions of the LaB, bands near El,. No obvious explanation is available for the a' branch.

Conclusion
A direct interpretation of the FS data in terms of a band structure is not yet possible due to the lack of a sufficiently detailed calculation, allowing for the magnetic structure of the materials. A nonmagnetic calculation has been carried out, treating the 4f electrons as itinerant for CeB6 [lo] and for CeB6 and PrB, [ 111. Both calculations indicate 4f states close to EF and strongly mixed with the boron-derived band that is responsible for the Fermi surface of LaB6. The FS derived for the heavier Ln compounds do not resemble the one for LaB, at all. It is made up of sheets centred at r and R; their size is of the correct order of magnitude when compared with the abranches. In this case the similarity between the three compounds is incidental. A comparison with the refined calculation will provide a better answer.