Energy-momentum tensor of a ferromagnet

The energy-momentum tensor provides valuable information about a physical system. Deriving this quantity for a ferromagnet runs into a conceptual difficulty associated with the presence of gyroscopic forces, which are represented by spin Berry-phase terms in the Lagrangian. Their gauge dependence and lack of rotational symmetry lead to paradoxes. E.g., the adiabatic spin torque exerted on a domain wall by a spin-polarized current is either missing or contains unphysical glitches, depending on the gauge choice. It is therefore desirable to derive a gauge-invariant and rotationally symmetric version of the energy-momentum tensor. We achieve this by using the gauge-invariant and symmetric Wess-Zumino action for spins at the expense of introducing an extra dimension, with the ferromagnet living on its boundary. The energy-momentum tensor defined in this (d+2)-dimensional spacetime yields correct physical answers.