  We theoretically investigate the motion of a domain wall in type-II
superconductors driven by inhomogeneities of temperature or spin density. The
model consists of the time-dependent Ginzburg-Landau equation and the
thermal/spin diffusion equation whose transport coefficients (the thermal/spin
conductivity and the spin relaxation time) depend on the order parameter,
interpolating the values for the superconducting and the normal states. Both
numerical and analytical calculations suggest that the domain wall moves toward
the higher temperature/spin-density region where the order parameter is
suppressed. Both motions can be understood as dynamical processes minimizing
the loss of the condensation energy. We also clearly define the forces on the
domain wall according to their origins.
