  The ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junction
exhibits thermal and electrical quantum Hall effects. The generated Hall
voltage and transverse temperature gradient can be controlled by the directions
of magnetizations in the FM leads, which inspires the use of FM-TI-FM junctions
as electrical and as heat switches in spintronic devices. Thermal and
electrical Hall coefficients are calculated as functions of the magnetization
directions in ferromagnets and the spin-relaxation time in TI. Both the Hall
voltage and the transverse temperature gradient decrease but are not completely
suppressed even at very short spin-relaxation times. The Hall coefficients turn
out to be independent of the spin-relaxation time for symmetric configuration
of FM leads.
