Heat-driven spin currents on large scales

1 Introduction Spintronics is concerned with using the spin of the electron in novel electronic devices. The spin property adds a degree of freedom to the electron transport. Recently, it has become evident that a number of studies of spin-dependent transport included also heat transport and the term " spin caloritronics " was coined [1]. While the charge, spin and heat currents were considered by spintronics founders [2, 3], much attraction to the inclusion of heat in spin-dependent transport stems from the discovery of the so-called spin Seebeck effect [4, 5]. The existence of a bulk spin current on large scales at distances orders of magnitude larger than the spin diffusion length may appear surprising [6], since the more familiar GMR vanishes on such scales. From simple thermodynamical considerations, the currents are functions of the gradients of the intensive ther-modynamical variables, i.e. the temperature gradient , T — the chemical potential gradient —μ and the electric potential gradient , V — which vanish at equilibrium. In order to observe a spin polarisation current, the system has to interact with the exterior through a heat current, an electric current or both. In this Letter, we consider the first case, where a spin polarisation current is driven by a heat current in a stationary state. We use the three-current model (spin-up, spin-down and entropy currents) to show that under the boundary conditions used in the spin Seebeck experiments, one can expect a non-vanishing spin current. The result is known in