Spin transport in Heisenberg antiferromagnets

TL;DR

This paper investigates spin transport properties in insulating antiferromagnets modeled by the XXZ Heisenberg Hamiltonian, highlighting how dimensionality influences spin conductivity behavior at low frequencies.

Contribution

It derives a Kubo formula for spin conductivity in these systems and analyzes the effects of dimensionality and interaction regimes on spin transport.

Findings

In 3D, the spin conductivity vanishes linearly at zero frequency.

In 2D, the spin conductivity approaches a finite value at zero frequency.

The Ising regime results in a spin insulator with no spin current.

Abstract

We analyze spin transport in insulating antiferromagnets described by the XXZ Heisenberg model in two and three dimensions. Spin currents can be generated by a magnetic-field gradient or, in systems with spin-orbit coupling, perpendicular to a time-dependent electric field. The Kubo formula for the longitudinal spin conductivity is derived analogously to the Kubo formula for the optical conductivity of electronic systems. The spin conductivity is calculated within interacting spin-wave theory. In the Ising regime, the XXZ magnet is a spin insulator. For the isotropic Heisenberg model, the dimensionality of the system plays a crucial role: In d=3 the regular part of the spin conductivity vanishes linearly in the zero frequency limit, whereas in d=2 it approaches a finite zero frequency value.