The effect of the 4f-quadrupole charge distribution on the electrical resistivity of TmSb

— The interaction between the conduction electrons and the localized 4f-electrons in TmSb has been investigated by measuring the temperature variation in the electrical resistivity. It is shown that the scattering by the 4f-quadrupole charge distribution in Tm gives a contribution to the resistivity of the same order of magnitude as the usual exchange scattering processes. Good agreement is obtained between theory and experiment when this contribution is taken into account. The interaction between conduction electrons and 4f-electrons has a special significance in metallic rare earth systems, since the dominating interionic couplings are established indirectly via the conduction electrons. In this paper we show from resistivity investigations on TmSb that, in some rare earth ions, the conduction electron interaction with the 4fquadrupole charge distribution is as important as the usual exchange interaction. TmSb is from experimental investigations [1, 2] known to be a crystal field only model system. The same conclusion may be drawn if the de Gennes scaling is applied to the known value of the interionic exchange interaction of the isostructural Tb<:Y1_(.Sb system. Both ions have 7 = 6 and a cubic crystal field which is well described by the fourth order parameter only. The only difference in the crystal field level scheme is a change in the overall energy splitting. With an energy separation between the r x (single t)ground state level and the first excited r 4 (tripletlevel of 25.7 K in TmSb and 14.4 K in T b / V ^ S b , we may conclude that the ratio of interionic exchange to crystal field is the same in TmSb as in Tb0 0 6Y0 94Sb. It has previously been shown that a single-ion model calculation based on the exchange interaction between the conduction electrons and the 4f-electrons may account very well for the resistivity measurements on Tb0 0 6Y0 94Sb [3]. The expression for this resistivity contribution may be expressed in a condensed form as : p~ = cP°jgU 2 t r ( / > e ) . (i) Here p°x is a constant which contains the common properties of the conduction electrons and different rare earth ions, c is the rare earth concentration in diluted alloys, g is the Lande factor and the matrices PtJ and Qij, from which the trace is derived, are denned from the crystal field energies Et and states | i > as : p exp(-£,./£B J ) (Ej-EJ/kyT u £ exp(-£ ; /* B T) 1 -^(-[Ei-EjVkz T) i