Interplay of magnon and electron currents in magnetic heterostructure

In magnetic materials, both electrons and magnons are capable of carrying angular momentum currents. An external electric field can efficiently drive a charge and spin current of electrons, but it is unable to directly produce a chargeless magnon current. The generation of the magnon current is conventionally achieved via thermal gradients or the electron spin injection from interfaces. Here, we investigate the magnon current induced by the momentum and angular momentum transfer from conduction electrons in magnetic layered systems. By using the generic exchange interaction between electrons and magnons, we derive the coupled diffusion equations for electron spins and magnons and we find (a) the ratio between the magnon current and the electric charge current is substantial at room temperature for conventional conducting ferromagnets, (b) the spin diffusion length of electrons is significantly modified by the presence of the nonequilibrium magnon density, and (c) the giant magnetoresistance of the magnetic multilayers for the current perpendicular to the plane of layers is reduced compared to the prior theory without taking into account the magnon current.

Figure 1

(a) The ratio of the magnon current to the charge current and (b) the ratio of the spin current to the charge current, as a function of the exchange coupling magnitude for several different magnon momentum relaxation times and temperatures. The insert in (a) shows the temperature dependence at a fixed $J_{sd}/E_F=0.2$, and the insert in (b) shows the ratio of the magnon current to the spin current at a fixed temperature $T=300$ K. Other parameters are $E_F=5\text{eV},T_C=550\text{K},\text{and}{\tau }_e=7\times {10}^{-16}\text{s}$.

Figure 2

(a) The position dependence of the spin and magnon accumulation. (b) The position dependence of the spin current and magnon current. The parameters are the same as used in Fig. 1.

Figure 3

Magnetoresistance of the magnetic bilayer, normalized to the classical value without the spin-magnon coupling, as a function of the exchange coupling for several different temperatures. We have used a temperature-independent relaxation time in order to single out the temperature dependent contribution from the magnon accumulation.