This chapter introduces the concept of exchange spin current, which derives from rewriting the exchange interaction in magnets and formulating a spin-wave spin current. States of matter can be classified into several types in terms of magnetic properties. In paramagnetic and diamagnetic states, matter has no magnetic order and exhibits zero magnetization in the absence of external magnetic fields. In ferromagnetic states, the permanent magnetic moments of atoms or ions align parallel to a certain direction, and the matter exhibits finite magnetization even in the absence of external magnetic fields. In ferrimagnets, the moments align antiparallel but the cancellation is not perfect and net magnetization appears. This interaction that aligns spins is called the exchange interaction.
On the equation of state for the “thermal” part of the spin current: The Pauli principle contribution in the spin wave spectrum in a cold fermion system
