Fig. 2: 2-port formulation of spin conductances.

a Any 2-terminal spin conductor can be formulated in terms of 2-port conductance matrices between its terminals. b The currents and voltages are related to each other by 4 × 4 conductances G_ij and currents and voltages are 4-component vectors. c Unlike charge currents, spin conductors may exhibit non-conservation of currents (I₁ + I₂ ≠ 0) and non-reciprocity (G₁₂ ≠ G₂₁). Here, we show an example of a reciprocal spin conductor (G₁₂ = G₂₁ = G₀). Even with the conservative nature of spin currents, it is possible to obtain a circuit description by introducing shunt conductances from the terminal to the ground to account for losses through spin–relaxation or coherent rotation mechanisms.