Spin Current Noise of the Spin Seebeck Effect and Spin Pumping

We theoretically investigate the fluctuation of a pure spin current induced by the spin Seebeck effect and spin pumping in a normal-metal–(NM-)ferromagnet(FM) bilayer system. Starting with a simple ferromagnet-insulator–(FI-)NM interface model with both spin-conserving and non-spin-conserving processes, we derive general expressions of the spin current and the spin-current noise at the interface within second-order perturbation of the FI-NM coupling strength, and estimate them for a yttrium-iron-garnet–platinum interface. We show that the spin-current noise can be used to determine the effective spin carried by a magnon modified by the non-spin-conserving process at the interface. In addition, we show that it provides information on the effective spin of a magnon, heating at the interface under spin pumping, and spin Hall angle of the NM.

Figure 1

Two mechanisms for spin-current generation at the interface between a normal metal and a ferromagnetic insulator. (a) Spin Seebeck effect driven by temperature biases ($T_N\ne T_F$) and (b) spin pumping generated by ferromagnetic resonance (i.e., irradiation with microwaves).

Figure 2

Two types of spin conversion at interface. (a) The spin-conserving process is described by $H_1$, and (b) the non-spin-conserving process is described by $H_2$.

Figure 3

Temperature dependence of (a) spin currents, (b) nonequilibrium spin-current shot noises, and (c) their ratios. The solid and dot-dashed lines indicate the result of the spin Seebeck effect for the temperature bias $\mathrm{\Delta }T=1\mathrm{K}$ and the spin pumping, respectively. In (b), thermal noise is denoted by the dashed line.