Energy and magnetisation transport in non-equilibrium macrospin systems

We investigate numerically the magnetisation dynamics of an array of nano-disks interacting through the magneto-dipolar coupling. In the presence of a temperature gradient, the chain reaches a non-equilibrium steady state where energy and magnetisation currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schr\"odinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a novel setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model