Compensated metal

Metal-loaded zeolites are expressed in the form M1/M2Z, where Mi = reduced metal, Mz = charge-compensating metal ion, and Z = zeolite type. For example, Pt/KL stands for platinum in the channels of an L-zeolite, with K as the charge-compensating cation. Details of zeolite types with their conventional abbreviations can be found in Zeolite Molecular Sieves (D. W. Breck Robert E. Krieger Publishing Company, Malabar, Florida, 1974). 

In these and in subsequent equations, charge-compensating metal ions in the solid will be omitted for brevity. We are assuming that the catalyst is homogeneously... 

Complexes with charge-compensating metal cations... 

Complexes with Charge-Compensating Metal Cations 393... 

If we count the number of valence electrons in a primitive cell, most of the lanthanide compounds are even in number, meaning that they are compensated metals. In this case the transverse magnetoresistance increases as /f" (I 2) for a general direction of the field. Note that the integer n is not equal to 2 because the high-field condition is not fully satisfied in the real compounds. When the magnetoresistance saturates for a particular field direction, often a symmetrical direction, there exist some open orbits whose directions are parallel to JxH, namely a=Ji/2 in -space. 

Experimentally the current direction is fixed to a crystal symmetry axis of the sample and the sample is slowly rotated under constant magnetic field which is perpendicular to flie current direction. The presence of open orbits is revealed by (a) spikes against a low background for the uncompensated metal and (b) dips against a large background for the compensated metal. 

Figure 15a shows a multiply connected hole Fermi surface in band 27. A closed orbit centered at the M point on the M-X—F plane is denoted 1 branch c. This branch is equivalent to branch e in the paramagnetic state. Figure 15b shows two eUipsoidal electron Fermi surfaces centered at the R point and a multiply connected electron one centered at die r point in band 28. NdBe in the antiferromagnetic state is thus a compensated metal, as opposed to the uncompensated metal LaBe, or NdBe in the paramagnetic state. Here, the electron Fermi surface of NdBe in die paramagnetic state is essentially a sphere witii a hollow in the center. 

As a proper reference for the RIn3 compounds, the electronic structure was investigated for Lalns by various theoretical methods. An analysis of the partial density of states revealed that the Bloch states in the lowest three bands consist dominantly of the In s state, and those in the upper part of the valence band consist mainly of the In p and La d states. The Fermi level lies in the vicinity of a sharp peak in the density of states. The Fermi surface consists of two sheets of bands 6 and 7 (Hasegawa 1982). The band 7 electron Fermi surface is essentially a sphere, which is centered at the R point and bulges slightly toward the M point and contains 0.38 electrons per primitive cell. The band 6 hole Fermi surface looks quite complex and contains the same number of holes as electrons, because Laln3 has an even number of Bloch electrons per primitive cell and thus is a compensated metal. 

The results of magnetoresistances for LaSna and CeSna are consistent with the results of the band calculations mentioned above (Hasegawa and Yamagami 1991, Hasegawa et al. 1990). The multiply connected band 8 Fermi surface in LaSna favors the experimentally observed open orbits. All of the Fermi surfaces in CeSna are closed ones, in good agreement widi the compensated metal of CeSna without open orbits. 

A main spherical branch is due to a band 10 electron Fermi surface which is a sphere centered at the F point but has bumps in the (100) direction, as show in fig. 60. The other branches are ascribed to the multiply connected hole Fermi surface associated with band 9. The latter jungle-gym -Fermi surface favors the (100) and (110) open orbits, consistent with magnetoresistance results (Reichelt and Winzer 1978). LaAh is thus a compensated metal. This is simply understood because the primitive cell contains two molecules of LaAli. The cyclotron mass is in the range of 1.7/ o to 0.2mo, as shown in table 15. 

As mentioned above, LaRu2Si2 is an uncompensated metal, while CeRu2Si2 is expected to be a compensated metal from the results of magnetoresistance. As the primitive cell contains one molecule of LaRu2Si2 or CeRu2Si2, we can conclude that the Ce ion becomes tetravalent, namely implying an itinerant 4f-electron character. Therefore, the situation is similar to the relationship between LaSns and CeSn3. 

Magnetoresistance measurements were done for SmCu2, indicating that it is a compensated metal with open orbits, at least, along the b-axis (Maezawa et al. 1986). Shubnikov-de Haas oscillations were observed in the magnetoresistance. The detected dHvA frequencies are in the range of (0.68-1.25) x 10 Oe. 

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