Exact high- and low-temperature results for the Coqblin-Schreiffer model with applications to YbCuAl

The authors give numerical results for the asymptotic form of the magnetic isotherm M(H) at T=0 for weak and strong fields for the j= 3 / 2 , 5 / 2 and 7 / 2 Coqblin-Schrieffer model (1969). These are derived from integral equations based on the exact diagonalisation of the model. The low-field results indicate a clear change in qualitative behaviour of the model with j. They all show a positive initial curvature which increases with j and contrasts sharply with the behaviour of the standard Kondo model j= 1 / 2 . In high fields the leading terms in an asymptotic expansion in log (g mu H/T 1 ) have been calculated. From these results the Wilson numbers, which relate the zero-temperature susceptibility to Kondo temperature T K , as defined by the high-temperature series expansion in log T/T K , have to be calculated for the j= 3 / 2 , 5 / 2 and 7 / 2 models. The j= 7 / 2 results are applied to the compound YbCuAl. Using the single parameter determined from an earlier fit to the T=4.2K magnetic isotherm the authors find excellent agreement with the high-temperature susceptibility over a temperature range from 140 to 1000K. The results explain the apparent reduction of the moments of the Yb ions from their free-ion values.