Landauer theory of ballistic torkances in non-collinear spin valves

We present a theory of voltage-induced spin-transfer torques in ballistic non-collinear spin valves. The torkance on one ferromagnetic layer is expressed in terms of scattering coefficients of the whole spin valve, in analogy to the Landauer conductance formula. The theory is applied to Co/Cu/Ni(001)-based systems where long-range oscillations of the Ni-torkance as a function of Ni thickness are predicted. The oscillations represent a novel quantum size effect due to the non-collinear magnetic structure. The oscillatory behavior of the torkance contrasts a thickness-independent trend of the conductance.