  In this paper, we present the theoretical predication of a thermospin Hall
effect, in which a transverse spin current can be generated in semiconductors
in the presence of spin-orbit coupling by a frequency-dependent longitudinal
temperature gradient. Because of the thermoelectric effect, there is no net
charge current but there is a heat flow from the hot side to the cold side. We
perform the theoretical calculation of dynamical thermospin Hall conductivity
in a two-dimensional Rashba spintronic system. It has been shown that the
direct interband optical transition dominates the ordering and manipulation of
spin in the generation of a transverse intrinsic spin current. In view of the
role of the thermoelectric effect, the contributions to the thermospin Hall
effect are classified as that originating from a direct contribution of thermal
electronic diffusion and that from the compensatory electron flow in balance
with the thermal diffusion. For a finite system, the analysis yields evidence
that the spin accumulation around the edges of a plate determines the
magnetization. In equilibrium, a field created by a magnetization gradient
emerges in the direction perpendicular to the temperature gradient. The
experimental observation of the thermospin Hall effect is proposed by measuring
the longitudinal temperature difference with the injection of a transverse spin
current and by analyzing the Hall angle. In addition, in order to achieve pure
spin accumulation in the spin Hall effect, an extension of the thermospin Hall
effect for exciting electron-hole pairs in semiconductors is proposed.
