SingletTriplet Formulation for Dilute Magnetic Alloys. I. sd Exchange Model
Abstract
Singlettriplet pair (STP) Green functions are formulated and studied for the sd exchange model of dilute magnetic alloys having a single magnetic impurity. Special poles of these STP Green functions (on the unphysical sheet) represent quasibound pair states commonly assumed responsible for the anomalous lowtemperature properties of these systems. The STP Green functions are evaluated by an approximate decoupling procedure along with additional approximations for the singleparticle averages. For a ferromagnetic interaction, the triplet states show no pole except at zero temperature. A singlettriplet pole is found for finite temperature for an antiferromagnetic interaction, no pure singlet pole being found except for T=0. These results follow from evaluation of the poles which involves conditions on both the real and the imaginary parts of the frequency; the more common but incorrect evaluation on the real frequency axis leads to quite different conclusions. This singlettriplet pole corresponds to a lowtemperature state possessing a magnetic moment. A range of values of polarization of the conduction electrons (μ_{α}) is found to be consistent with the existence of such a quasibound state: 0<μ_{α}<=μ_{crit} The maximum μ_{crit} increases with temperature. A comparison is made with certain conclusions of Schrieffer and Wolff, and some differences appear. The results found differ substantially from a parallel calculation made by some of the authors on the Anderson model.
 Publication:

Physical Review
 Pub Date:
 April 1968
 DOI:
 10.1103/PhysRev.168.495
 Bibcode:
 1968PhRv..168..495H