Dynamical magnetic susceptibility in the spin-fermion model for cuprate superconductors

Abstract

Using the method of diagram techniques for the spin and Fermi operators in the framework of the SU(2)-invariant spin-fermion model of the electron structure of the CuO₂plane of copper oxides, we obtain an exact representation of the Matsubara Green’s function D_⊥(k, iω_m) of the subsystem of localized spins. This representation includes the Larkin mass operator Σ_L(k, iω_m) and the strength and polarization operators P(k, iω_m) and Π(k, iω_m). The calculation in the one-loop approximation of the mass and strength operators for the Heisenberg spin system in the quantum spin-liquid state allows writing the Green’s function D_⊥(k, iω_m) explicitly and establishing a relation to the result of Shimahara and Takada. An essential point in the developed approach is taking the spin-polaron nature of the Fermi quasiparticles in the spin-fermion model into account in finding the contribution of oxygen holes to the spin response in terms of the polarization operator Π(k, iω_m).