  The temperature dependence of spin currents in insulators at the finite
temperature near zero Kelvin is theoretically studied. The spin currents are
carried by Jordan-Wigner fermions and magnons in one- and three- dimensional
insulators. The quasiparticle description of one-dimensional spin systems is
valid only in the finite temperature near zero Kelvin. These spin currents are
generated by the external magnetic field gradient along the quantization axis
and also by the two-particle interaction gradient. In one-dimensional
insulators, quantum fluctuations are strong and the spin current carried by
Jordan-Wigner fermions shows the stronger dependence on temperatures than the
one by magnons.
