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We investigate two closely related subjects: (i) existence of a purepersistent spin current in semiconducting mesoscopic device with a spin-orbitinteraction's (SOI), and (ii) the definition of the spin current in thepresence of SOI. Through physical argument from four physical pictures indifferent aspects, we provide strong evidences that the persistent spin currentdoes exist in a device with SOI in the absence of any magnetic materials. Thispersistent spin current is an analog of the persistent charge current in amesoscopic ring threaded by a magnetic flux, and it describes the real spinmotion and can be measured experimentally. We then investigate the definitionof the spin current. We point out that (i) the non-zero spin current in theequilibrium SOI device is the persistent spin current, (ii) the spin current isin general not conserved, and (iii) the Onsager relation is violated for thespin transport no matter what definition of the spin current is used. Theseissues, the non-zero spin current in the equilibrium case, the non-conservedspin current, and the violation of the Onsager relation, are intrinsicproperties of spin transport. We note that the conventional definition of thespin current has very clear physical intuition and describes the spin motionvery well. Therefore we feel that the conventional definition of the spincurrent makes physical sense and there is no need to modify it. In addition,the relationship between the persistent spin current and transport spincurrent, the persistent linear and angular spin currents in the SOI region ofthe hybrid ring, are discussed. Finally, we show that if the spin-spininteraction is included into the Hamiltonian, the persistent spin current isautomatically conserved using the conventional definition.

Persistent spin current in nano-devices and definition of the spin current