Spin-anisotropic magnetic impurity in a Fermi gas: poor man's scaling equation integration

Abstract

We consider a single magnetic impurity described by the spin--anisotropic s-d(f) exchange (Kondo) model and formulate scaling equation for the spin-anisotropic model when the density of states (DOS) of electrons is a power law function of energy (measured relative to the Fermi energy). We solve this equation containing terms up to the second order in coupling constants in terms of elliptic functions. From the obtained solution we find the phases corresponding to the infinite isotropic antiferromagnetic Heisenberg exchange, to the impurity spin decoupled from the electron environment (only for the pseudogap DOS), and to the infinite Ising exchange (only for the diverging DOS). We analyze the critical surfaces, corresponding to the finite isotropic antiferromagnetic Heisenberg exchange for the pseudogap DOS.

LaTeX, 9 pages, 5 Figures. As accepted for publication in PRB

References in corpus (7)

• Kondo Quantum Criticality of Magnetic Adatoms in Graphene
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Cited by in corpus (9)

• Poor man's scaling: anisotropic Kondo and Coqblin--Schrieffer models
• Phase boundaries of the pseudogap Anderson and Kondo models
• Kondo effect due to a hydrogen impurity in graphene: a multichannel Kondo problem with diverging hybridization
• From Kondo to local singlet state in graphene nanoribbons with magnetic impurities
• The Kondo effect in the quantum $XX$ spin chain
• Poor man's scaling and Lie algebras
• Anisotropic Kondo screening induced by spin-orbit coupling in quantum wires
• RKKY interaction in graphene at finite temperature
• Poor man's scaling: $XYZ$ Coqblin--Schrieffer model revisited