Fermi surface earths

The nuclear spins and moments of the strongly deformed rare-earth nuclides have been discussed in detail previously within die Nilsson model in connection with the ABMR experiments mentioned above [79]. The addition of the data fiom coUinear fast-beam laser spectroscopy [48, 50, 71], the new reference values on spectroscopic quadrupole moments from muonic and pionic hfs [1], and the refined calculations within the partice-rotor model, including a number of orbitals close to the Fermi surface, have however resulted in a more complete picture and a better understanding of tiie nuclear single-particle stmcture in this region. 

De Haas-van Alphen (dHvA)-type quantum oscillations as observed in the sound velocity and sound attenuation provide important information about the Fermi surface and the electron-phonon interaction (Roberts 1968, Fawcett et al. 1980). This technique has been successfully applied to intermetallic rare-earth compounds as discussed below. Recent progress in dHvA techniques for heavy-fermion materials (Taillefer et al. 1987, Reinders et al. 1986) should make similar MAQO experiments also possible. Compounds studied so far are LaAg, LaB5, LaAlj, RBj, CeSn3, CeB, CeCu and CePbj. 

Experimental knowledge on the Fermi surface of rare earth metals... 

There are two exhaustive reviews of the band structure of rare earth metals by Dimmock (1971) and Freeman (1972). The first article gives a complete discussion of the band calculation results and the second article enlphasizes the magnetic properties as delineated by the electronic properties. Earlier calculations on the energy bands and Fermi surface of rare-earth-like metals Sc and Y by the cellular method have been reviewed by Cracknell (1971). Whenever feasible we will avoid duplicating the materials contained in these articles. 

Fig. 3.7. The webbing feature on the Fermi surface of hexagonal heavy rare earths (Keeton and Loucks, 1968).

It is difficult to visualize the Fermi surface of these metals because there re too many pieces. The bands are relativistic, so it is not possible to fold them out into the extended zone as was done for heavy rare earths. This makes the graphical representation of the Fermi surface rather difficult. In flg. 3.11 we show the cross sections of the various pieces of Fermi surface with the high symmetry planes of the Brillouin zone. A detailed description of the Fermi surface structure is given in the original article. 

One important difference between this Fermi surface and that of heavy rare earths is the lack of large, flat, and nearly parallel webbing pieces perpendicular to the c axis. The authors pointed out a possible relation between the lack of webbing and the occurrence of the dhcp crystal structure. If in the hep phase of these metals the thickness of the webbing is nearly one-half the distance from... 

The Yb metal was the first rare earth metal studied with the de Haas-van Alphen measurement. Tanuma et al. (1967) purified a piece of raw metal by the vacuum distillation method. A single crystal specimen was obtained by spark cutting a large grain in a vapor condensed ingot. The resistivity ratio of the specimen was not reported. The crystal structure was determined to be fee by X-ray analysis at room temperature. Two de Haas-van Alphen frequencies were observed, and the authors suggested that they came from two separate pieces of Fermi surface. Datars and Tanuma (1968) deduced from magnetoresistance measurements at 1.3 K with fields up to 20 KG that there were no open orbits in Yb. Therefore, they concluded that Yb is semimetallic with two small, closed pieces of Fermi surface. ... 

Inspite of all the theoretical predictions about the Fermi surface geometry of rare earth metals, there was scanty experimental confirmation until recently. The difficulty in carrying out the measurements was due to the unavailability of crystals of high purity. Early experiments used the method of positron annihilation, which did not require high purity crystals. Unfortunately, the information obtained this way is not sufficient to map out the Fermi surface. With the development of the electrotransport method of sample purification, see ch. 2 sections 2.3 and 5.7, it is now possible to grow high quality crystals of a number of rare earth metals for de Haas-van Alphen experiments. We will review these results with emphasis on the latest findings. 

The common deficiency of both the Lu and the Y experiments is that only the small orbits were observed. These orbits are most difficult to predict with accuracy, and this makes the interpretation prone to uncertainties. It requires the observation of many more orbits, especially the large ones, to verify the complicated Fermi surface of rare earth metals. 

Investigations on other hexagonal heavy rare earths are summarized in table 3.4. Just like their band structures the optical properties of these metals are very much alike. Optical measurements on polycrystal samples can not detect the differences in the Fermi surface geometry of these metals. The optical conductivities of Gd, Tb, Dy, Ho, and Er obtained by Krizek and Taylor are shown in fig. 3.36. The same kind of similarity in optical properties of different metals is seen in SchOler s results on Gd, Dy and Lu, the data of Knyazev and Noskov (1970) on Gd and Dy, those of Miller et al. on Gd and Tb, those of Erskine et al. on Gd, Tb and Dy, and in those of P6trakian on Gd and Tm. There is also the same kind of inconsistency among the results of different investigators as in Gd. 

Fig. 3.72. The Fermi surface of hep rare earths according to the nearly free electron model (Kasuya, 1966).

X-ray photoemission spectroscopy (XPS) of a number of rare earth metals, including y-Ce, has been carried out by Baer and Busch (1973 and 1974) in order to determine the position of the 4f level relative to the Fermi energy. Although Baer and Busch (1974) found the observed spectrum of y-Ce to change as evaporation conditions were varied, they felt that the peak at 0.9 eV, which was observed in all the samples, was due to the 4f electron. This is in variance with the infrared studies noted above, which suggested a 4f level is just 0.076 eV below the Fermi surface. A close examination of the data of Baer and Busch (1974) indicates that if the 4f level lay within 0.2 eV of the Fermi surface it would almost be impossible to detect due to the steep rise in the XPS spectrum at the Fermi surface. Furthermore it should be noted that the 5d band in lanthanum exhibits a peak at —0.8 eV (Baer and Busch, 1973). More careful studies are needed to see if the 4f level lies at —0.1 eV below the Fermi surface. 

The strong d-like character of large sections of the Fermi surface of the rare earths (Harmon and Freeman 1974) results in a relatively low conduction electron mobility. Furthermore, even in the purest material available, presiduai-describing the temperature independent scattering by non-magnetic impurities and lattice defects-is some 3x 10 flm (Jordan et al. 1974). Thus the electron mean free path is presently limited to a value several orders of magnitude lower than has been achieved for other metals. 

Besides YBa2Cu307, 2D-ACAR has been measured in compounds of the same structure but with different rare earths R=Dy, Ho and Pr (Hoffmann et al. 1993a, 1995). It has been concluded that the electronic structure of these compounds is similar to that of YBa2Cu307, as suggested by band-structure calculations. The ridge, i.e. the Fermi surface sheet originating from the Cu-O chains, is almost unchanged, as probably are the other sheets of the Fermi surface. 

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