Superzones

The resistivities of the magnetic borides DyB, H0B12, ErB, and TmB, have been carefully measured by Gabani et al. (1999) for good quality crystals with low room temperature resistivities (10-30 p 2 cm) compared to the early work. Near the antiferromagnetic transition temperatures Tn, the resistivities all show small increases in the form of humps and then rapid drops as the temperature is lowered. This behavior can be explained as an initial increase in the resistivity attributed to the appearance of superzone boundaries within the Brillouin zone, followed by a decrease due to a reduction in spin scattering (Taylor and Darby, 1972 Fournier and Gratz, 1993). 

Fig. 7. Electrical resistivity (residual subtracted) versus temperature for the a- and c-axis of Tb. The dashed curves give the spin disorder component after subtraction of the phonon contribution from the total resistivity. The inset shows the anomalous rise in c-axis resistivity below I m accompanying the opening of the superzone gaps in the Fermi surface. The peak is quenched by applied magnetic fields which destroy the helical order and thereby remove the superzone gaps. (After Hegland et al. 1963.)...

The temperature dependence of the magnetic propagation vector (fig. 3) has been ascribed (Elliott and Wedgewood 1963) to the effects of the superzone gaps in modifying the stable Q. It is also suggested (Evenson and Liu 1969) that the magnetostriction may modify the wave vector. 

Since the wavevector describing the magnetic periodicity of the antiferromagnetic phases of the elements Tb-Tm is parallel to the c-axis, it transpires that the superzone energy gaps effectively remove a considerable fraction of the Fermi surface area projected normal to the c-axis, which thus produces a sharp increase in the c-axis resistivity below Tn (see fig. 6.39). The only portions of the calculated (hole) Fermi surface which have significant velocity components parallel to the c-axis are found in the network of arms located near the hexagonal faces of the Brillouin zone (see ch. 3 section 2.3.1). 

Fig. 14.36. Schematic repiesentation of the evaluation of the spin disorder resistivity (a) Usual extrapolation scheme valid from temperatures above the Debye temperature, (b) The case of dysprosium which has an antiferromagnetic temperature range where superzone boundaries raise the resistivity, (c) The case of an antiferromagnet which does not become ferromagnetic at low temperatures Superzone boundaries may distort results in the whole ordered range (Gratz and Poldy, 1977).

Electrical resistivity measurements on single crystals in the [001] direction by Stalinski et al. (1973) showed that the spin disorder resistivity of RSns compounds was not proportional to the de Gennes factor. Since these materials are antiferromagnetic superzone boundary effects might render impossible the estimation of the spin disorder resistivity as described in subsection 2.1. On the other hand, since the shape of the dp/dT curve of NdSns around the N6el temperature was qualitatively similar to that expected by the theory of... 

De Gennes and Saint James (1963) explained the temperature variation of the spin periodicity in the HAFM structure near by the effects of conduction electrons scattering by the 4f spin disorder. EUiott and Wedgewood (1964) considered the influence of superzone boundaries introduced by the helical structure into the energy spectrum of the conduction free electrons. They showed that with an increase of the 4f spin order the value of Q should decrease and the first-order HAFM-FM transition should occur. Miwa (1965) in his model took into account both these factors. On the base of Miwa s model Umebayashi et al. (1968) obtained the following ejqiression for the pressure dependence of (p... 

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