Spin current without power reduction

[hokhani]

Spin current is defined as ##I_s=I_\uparrow -I_\downarrow## in which ##I_\uparrow## and ##I_\downarrow##are the currents of spin up and down electrons respectively. One of the advantages of the spin current is that if ##I_\uparrow =-I_\downarrow##, then the charge current ##I_C=I_\uparrow +I_\downarrow=0## while the spin current is not zero. Therefore, the spin is transferred without charge transfer (and so without power reduction as referred in some papers). Now, the question is raised that how the power reduction is zero while the two currents ##I_\uparrow## and ##I_\downarrow## independently waste the power?

 

[BigJDubs]

It is true that both ##I_\uparrow## and ##I_\downarrow## will waste the power, but since they are of equal magnitude and opposite direction, the total power consumed by them will be zero. The spin current can thus transfer spin without consuming power as the charges do not move.