Chromium Fermi surface

It is immediately apparent from Fig. 20-1 that along the one symmetry line in the Brillouin Zone shown, there are two or three bands crossing the Fermi energy for each metal and therefore quite a complex set of Fermi surfaces. These have been thoroughly studied, using the techniques discussed in connection with simple metals. It would, however, be quite inappropriate here to attempt any complete discussion of this problem, Instead, the Fermi surface of a single system, chromium, will be discussed. It is perhaps the most interesting case, and it illustrates the principal effects that enter considerations of the other systems. We shall then turn to the density of states, which dominates many of the electronic properties. 

The Fermi surface of chromium has been studied by Rath and Callaway (1973), who used an LCAO approach, They obtained bands looking very much like those shown for chromium in Figs. 20-1 and 20-3, and also obtained some cross-sections of the Fermi surfaces. In Fig. 20-5 we give the sections for a (001) plane through the center of the Brillouin Zone containing the [100] line. We may... 

A (001) section of the body-ccnlercd cubic Brillouin Zone showing the Fermi surface cross-sections for chromium, as determined by Rath and Callaway (1973). The energy bands from F at the center to H at the right are shown for comparison they are taken from Fig. 20-1. The surfaces separated by q produce antiferromagnetic order. [After Rath and Callaway, 1973.]... 

A treatment of transport properties in terms of this surface is no more complicated in principle than that in the polyvalent metals, but there is not the simple free-clectron extended-zone scheme that made that case tractable. Friedel oscillations arise from the discontinuity in state occupation at each of these surfaces, just as they did from the Fermi sphere. When in fact there arc rather flat surfaces, as on the octahedra in Fig. 20-6, these oscillations become quite strong and directional. A related effect can occur when two rather flat surfaces are parallel, as in the electron and hole octahedra, in which the system spontaneously develops an oscillatory spin density with a wave number determined by the difference in wave number between the two surfaces, the vector q indicated in Fig. 20-5. This generally accepted explanation of the antiferromagnetism of chromium, based upon nesting of the Fermi surfaces, was first proposed by Lomer (1962). 

Figure 7 Normalized chromium La.a level AEAPS spectra for the CrN films and elemental chromium. The emission current was 2 mA and the modulation voltage was 1 Vp p. The strength of the signal (i.e., the density of unoccupied states at the Fermi level) is more for the films. (Reproduced with permission from Chourasia AR and Hood SJ (2001) Auger electron appearance potential spectroscopy. Surface and Interface Analysis 31 291-296 John Wiley and Sons Ltd.)...

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