\frac{\hbar^2}{2 m} \frac{\partial^2}{\partial x^2} \Psi(x)+V(x) \Psi(x)=E \Psi(x)

\frac{\hbar}{2} \mathbf{J}_s^{\text {pump }}(t)=\frac{\hbar}{4 \pi}\left(\Re g_r^{\uparrow \downarrow} \mathbf{m} \times \frac{d \mathbf{m}}{\mathrm{dt}}+\Im g_r^{\uparrow \downarrow} \frac{d \mathbf{m}}{\mathrm{dt}}\right)

\mu

\text{Spin transfer torque $\boldsymbol{J}_{\boldsymbol{s}}$ puts $\boldsymbol{M}$ into motion}

J_z

1

2

3

1

\frac{t}{T}

\mathcal{H}=-\sum_{i \neq j} J_{i j} \boldsymbol{S}_i \cdot \boldsymbol{S}_j-k_u \sum_i\left(\boldsymbol{S}_i \cdot \boldsymbol{e}\right)^2-\sum_i \mu_s \boldsymbol{S}_i \cdot \boldsymbol{H}_{a p p}