Equivalent Circuit Representation and Thermodynamic Limitations of Non-Adiabatic Spin-Transfer Torque effect

RESUMO

We present an equivalent circuit representation of the Thiele equation for the current-driven domain walls. We show that the non-adiabatic spin-transfer torque (\beta-term) cannot be represented by passive elements alone (such as resistors, inductors, and capacitors) and necessarily requires active elements, corresponding to negative dissipation. Consequently, assuming that the driving current is the only power source for the texture dynamics, directly incorporating the \beta-term introduces a fundamental contradiction with thermodynamic principles. This equivalent circuit theory indicates that the interpretation of experiments solely through the \beta-term does not fully capture the underlying physics, highlighting the need to account for effects distinct from the spin dynamics.