Energy dispersion of tunnel spin polarization extracted from thermal and electrical spin currents versus bias voltage

The creation of spin current (i.e. the flow of spin angular momentum) is a central basis of spintron-ics [1,2], in which digital information is represented by the spin degree of freedom. It has been intriguingly established that the spin current in ferromagnetic tunnel contacts can be created either by electrical means (induced by a bias voltage) [3,4] or by thermal means (driven by a heat flow) [5,6]. The former of electrical spin injection is due to the spin dependence of tunnel conductance whereas the latter of thermal spin injection is due to the spin dependence of Seebeck tunnel coefficient [6]. Since both these parameters are determined by the energy dispersion of spin-dependent electronic states of the ferromagnetic tunnel contact [5,6], it is of importance to evaluate how its tunnel spin polarization (TSP) changes with energy (E) for completely understanding the variation of electrical and thermal spin currents with a bias voltage. At a small bias, only states near the Fermi energy (E_F) are involved in the tunneling process whereas at a large bias, there is a substantial contribution of electrons from the occupied (empty) states below (above) E_F of the ferromagnet. In the present study, TSP as a function of E for ferromagnetic tunnel contacts (Co₇₀Fe₃₀/MgO) to semiconductors (silicon and germanium) has been extracted from thermal and electrical spin currents versus a bias voltage through a free electron tunneling model. By simultaneously describing the bias variation of thermal and electrical spin signals using the same E dispersion of TSP, we correlate the pronounced (moderate) variation of thermal spin current with voltage to the strong (fair) change of TSP with E in a consistent way. Furthermore, it is shown that for thinner MgO barriers, the application of a modest voltage can switch the thermal spin current on/off and can even reverse its sign, indicating a further improvement in terms of the voltage tunability. The result offers an alternative approach to characterize the E dispersion of TSP of ferromagnetic tunnel contacts, paving the way towards engineering their spin-dependent thermoelectric properties.