Dingle temperature

If the p labels refer to lattice sites j, this matrix reduces to 6(k) in the KKR matrix M(k) and Eq. (15) can be shown to reduce to Eq. (14). The evaluation of is hindered by the free-electron poles in the b matrices. This has formed a barrier for electronic structure calculations of interstitial impurities, but in some cases this problem was bypassed by using an extended lattice in which interstitial atoms occupy a lattice site. For the calculation of Dingle temperatures [1.3] and interstitial electromigration [14] the accuracy was just sufficient. Recently this accuracy problem has been solved [15, 16]. 

The Dingle reduction factor, Rd, describes the broadening of the otherwise sharp Landau levels due to scattering of the conduction electrons. The usual parameter which describes this scattering is the relaxation time r averaged over one cyclotron orbit [252]. This effect leads to a reduction factor similar to (3.8) for finite temperatures. As a useful parameter the so-called Dingle temperature... 

Because of the nodes only for AF = 0 the Dingle temperature could be determined from the dHvA amplitude dependence over an larger field range. There, however, the Lifshitz-Kosevich formula might no longer work. 

Fig. 42. Effective Dingle temperature X T) of La. parison to the constant X of pure LaBAn absolute shift of X has been applied for all points to match...

The temperature dependence of the SdH amplitude for H a was used to estimate the cyclotron mass of the orbit by the standard procedure /13/. We find a value of m/m -3.2s which agrees well with previously published data. Using this value, a Dingle temperature of Tj =0.7 K is obtained from the field dependence of the amplitude (type B crystal). 

The amplitude of the oscillations depends exponentially on the factor m%, T + To)IB, where mj is the effective cyclotron mass, T the temperature. To the Dingle temperature which measures the mean scattering probability of the electrons by impurities and lattice imperfections. By measuring the amplitude at a number of temperatures one can determine both the mass and the Dingle temperature. The mass is compared with the band calculation, thus providing an additional check on the theoretical model. 

Thus m /t is expected to be the same for two similar orbits with the same mean free path. When the effective mass m is enhanced by a factor of (1 -i- A) from spin fluctuations, eq. (65) indicates that r should also be enhanced by a factor of (1+A). This occurs because a large mass is translated into a small velocity from eq. (64) so that the scattering lifetime becomes (1 + A) times larger than that obtained by eq. (64) if the mean free path is the same. In terms of the Dingle temperature, eq. (65) becomes... 

The above relation between the cyclotron mass and the Dingle temperature was applied to the heavy electrons in Celna, There are two orbits for branch d which possess the same dHvA frequency and therefore the same cross-sectional area of the Fermi surface but a different cyclotron mass, as mentioned above. Thus, hk is the same for the two orbits. Moreover, the mean free path is considered to be the same because it is approximately equal to the average distance between impurities. 

Experimentally, Dingle temperatures have been reported for two orbits (Taillefer et al. 1987) with values of 30 and 70 mK. These small values are due to the fact that they are extracted using the quasiparticle masses, when in actuality it is the band mass which enters the Dingle expression (Shoenberg 1984). Taking this into account, we extract Dingle temperatures of 0.5 and 1.0 K, which are quite reasonable. The... 

In the presence of impurities the Mahan-Nozieres-de Dominicis singularity is broadened due to scattering of band electrons, as shown by Doniach and Sunjic (1970). This effect gives rise to additional quasi-particle damping and resistivity. One simple way to incorporate the impurity effect in the band calculation is to replace the temperature T by T -F Tp, where is the Dingle temperature which measures impurity scattering. The calculated resistivity curves for various values of are shown in fig. 44. These curves compare well with the data for Ce Lai. Pbj in fig. 7 and for Laj, Ce,Sn3 in fig. 9. 

Fig. 44. The calculated resistivity curves for impure systems. The amount of impurity is represented by the Dingle temperature To, which is measured in units of ly/Icg (Liu 1988). The theoretical results are to be compared with the experimental data in figs. 7 and 9.

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