FIG. 14.

Breakdown of the S_ν matrices when in-plane spin/charge currents drive transport at interfaces. As in Fig. 13, the matrix S_t determines the spin/charge accumulation μ at the interface (see Eq. 28), the symmetric response $\overline{S}=S_{\text{i}-\text{r}}+S_{\text{t}}$ determines the average spin current ${\overline{\text{j}}}_z$ at the interface (see Eq. 29), and the antisymmetric response ΔS = S_i-r −S_t determines the difference in spin current Δj_z across the interface (see Eq. 30). The column specifies the in-plane spin/charge currents at z = 0^± while the row gives the components of μ, ${\overline{\text{j}}}_z$, or Δj_z, depending on whether Eq. 28, Eq. 29, or Eq. 30 is used. The images depict both the in-plane and out-of-plane spin currents at z = 0^± using block arrows for flow direction and tubular arrows for spin direction.