Longitudinal continuum spin conductivity by Kubo formula in the Heisenberg model with bilinear and biquadratic exchange interactions

Abstract

In this work, we investigate the longitudinal continuum spin conductivity of the spin-1 Heisenberg model with biquadratic interaction (the θ parameter controls the ratio of the biquadratic and exchange couplings). The calculations were performed for the model on square lattice in the Néel and ferroquadrupolar phases using spin wave theory and Schwinger boson formalism. In the antiferromagnetic phase that corresponds to range: -π<θ<0 or (sinθ<0), we use the Dyson-Maleev representation to calculate the spin conductivity at T=0 finding the AC spin conductivity diverging at DC limit, ω=0. Evidencing so, that the system is an ideal spin conductor in this limit. In the ferroquadrupolar phase (sinθ>0), we find a different behavior for the spin conductivity which changes abruptly from a scalar to a tensor in the Green-Kubo formula: 〈J〉=σ∇h, where σ is the conductivity, and also, in this case, a superconductor behavior for spin current at DC limit.