Low‐temperature spin transport in the S = 1 one‐ and two‐dimensional antiferromagnets with Dzyaloshinskii–Moriya interaction

Abstract

We present a study of the spin transport at low‐temperature in the quantum S = 1 one‐ and two‐dimensional Heisenberg antiferromagnet with the Dzyaloshinskii–Moriya interaction (DM). The spin conductivity is calculated using the Schwinger boson representation and the Kubo formalism of transport in the one‐dimensional case and using the self‐consistent harmonic approximation and the Kubo formalism in the two‐dimensional case. The objective is to determine the regular part of the spin conductivity and the Drude weight DS. This determines if the spin transport has a ballistic or diffusive character. We calculate the regular part of the spin conductivity, σreg(ω), as function of the frequency at T = 0 only and the Drude weight at zero and finite temperatures. We obtained that the spin transport is governed by the multimagnon processes in all cases analyzed since the symmetry of the isotropic Heisenberg antiferromagnetic model is broken with the addition of the DM term.

Spin conductivity of the two-dimensional anisotropic frustrated Heisenberg model in the honeycomb lattice

“…Pires and Lima [28][29][30] treated the two-dimensional easy plane Heisenberg antiferromagnetic model. Lima and Pires [31] studied the spin transport in the two-dimensional anisotropic XY model using the SU(3) Schwinger boson theory in the absence of impurities, Lima [32] has studied the case of the Heisenberg antiferromagnetic model in two dimensions with Dzyaloshinskii-Moriya interaction. Chen et al [33] analyzed the effect of spatial and spin anisotropy on spin conductivity for the S ¼1/2 Heisenberg model on a square lattice and more recently, Kubo et al [34] studied the spin conductivity in two-dimensional non-collinear antiferromagnets at T¼ 0 using spin wave theory and Lima et al [35] have studied the spin transport in the site diluted two-dimensional anisotropic Heisenberg model in the easy plane, using the self-consistent harmonic approximation.…”

“…The Heisenberg equation of motion, _ S z n ¼ i½H; S z n , can be used with Eq. (32) to obtain the spin current operator…”

Antiferromagnetic and Ferromagnetic Spintronics: Transport in the Two-dimensional Ferromagnet and the Role of In-chain and Inter-chain Interactions

“…The peak of the spin conductivity can be determined by measuring of magnetization current. [42,48] In Ref. [49], some experimental techniques were proposed and seem to be feasible.…”

Influence of dilution in the spin transport in the quantum anisotropic two-dimensional Heisenberg antiferromagnet

“…Pires and Lima [12][13][14] treated the case of two-dimensional Heisenberg antiferromagnetic model in the easy plane limit. Lima and Pires [15] studied the spin transport in the two-dimensional anisotropic XY model using the SU(3) Schwinger boson theory in the absence of impurities, Lima [16] studied the case of the Heisenberg antiferromagnetic model in two dimensions with DzyaloshinskiiMoriya interaction. Chen et al [17] analyzed the effect of spatial and spin anisotropy in the spin conductivity for the S¼ 1/2 Heisenberg model in the square lattice and more recently, Lima et al [18] studied the spin transport in the site diluted two-dimensional anisotropic Heisenberg model in the easy plane using the selfconsistent harmonic approximation and the spin transport in the two-dimensional biquadratic Heisenberg model using the SU (3) Schwinger boson theory [19] and in the two-dimensional ferroquadrupolar Heisenberg model using the same formalism [20].…”