  The interplay between spin transport and thermoelectricity offers several
novel ways of generating, manipulating, and detecting nonequilibrium spin in a
wide range of materials. Here we formulate a phenomenological model in the
spirit of the standard model of electrical spin injection to describe the
electronic mechanism coupling charge, spin, and heat transport and employ the
model to analyze several different geometries containing ferromagnetic (F) and
nonmagnetic (N) regions: F, F/N, and F/N/F junctions which are subject to
thermal gradients. We present analytical formulas for the spin accumulation and
spin current profiles in those junctions that are valid for both tunnel and
transparent (as well as intermediate) contacts. For F/N junctions we calculate
the thermal spin injection efficiency and the spin accumulation induced
nonequilibrium thermopower. We find conditions for countering thermal spin
effects in the N region with electrical spin injection. This compensating
effect should be particularly useful for distinguishing electronic from other
mechanisms of spin injection by thermal gradients. For F/N/F junctions we
analyze the differences in the nonequilibrium thermopower (and chemical
potentials) for parallel and antiparallel orientations of the F magnetizations,
as evidence and a quantitative measure of the spin accumulation in N.
Furthermore, we study the Peltier and spin Peltier effects in F/N and F/N/F
junctions and present analytical formulas for the heat evolution at the
interfaces of isothermal junctions.
