Thermodynamic perturbation theory for non-interacting quantum particles with application to spin-spin interactions in solids

Abstract

The determination of the Landau free energy (the grand thermodynamic potential) by a perturbation theory is advanced to arbitrary order for the specific case of non-interacting fermionic systems perturbed by a one-particle potential. Peculiar features of the formalism are highlighted, and its applicability for bosons is indicated. The results are employed to develop a more explicit approach describing exchange interactions between spins of Anderson's magnetic impurities in metals, semiconductors, and insulators. Within the fourth order our theory provides on the equal footing formulae for the Ruderman-Kittel-Kasuya-Yosida, Bloembergen-Rowland, superexchange, and two-electron exchange integrals at non-zero temperature.

11 pages

References in corpus (5)

• Dilute ferromagnetic semiconductors: Physics and spintronic structures
• Phase diagram and critical behavior of the random ferromagnet $G{a}_{1-x}M{n}_{x}N$
• Theory of spin waves in ferromagnetic (Ga,Mn)As
• Theory of ferromagnetism driven by superexchange in dilute magnetic semiconductors
• Non-Convergent Perturbation Theory and Misleading Inferences about Parameter Relationships: the Case of Superexchange

Cited by in corpus (4)

• Momentum-resolved spin splitting in Mn-doped trivial CdTe and topological HgTe semiconductors
• Superexchange dominates in magnetic topological insulators
• High-resolution Resonance Spin-flip Raman Spectroscopy of Pairs of Manganese Ions in CdTe
• Tight-binding theory of spin-spin interactions, Curie temperatures, and quantum Hall effects in topological (Hg,Cr)Te in comparison to non-topological (Zn,Cr)Te, and (Ga,Mn)N