Unusual beats of the perpendicular-current giant magnetoresistance and thermopower of magnetic trilayers.

(received July 1996) Oscillations of the giant magnetoresistance (GMR) and thermo-electric power (TEP) vs. both the thickness of the non-magnetic spacer and also that of the ferromagnetic slabs are studied in the current-perpendicular-to-plane (CPP) geometry of magnetic trilayer systems, in terms of a singleband tight-binding model without impurities. The spin-dependent conductance has been calculated from the Kubo formula by means of a recursion Green’s function method and the semi-infinite ideal-lead wires trick. Additionally the TEP is obtained directly from Mott’s formula. In general, the thickness oscillations of the GMR and the TEP may have just one or two (short and long) oscillations. The long period, related to spectacular beats, is apparently of non-RKKY type. The TEP oscillations are strongly enhanced with respect to those of the GMR, have the same periods, but different phases and a negative bias. The phenomenon of giant magnetoresistance (GMR) in magnetic multilayers has been intensively studied both experimentally [1,2] and theoretically [3–7] for more than five years now. After the paper [5] was published it has become clear that one can expect a large magnetoresistance even in systems which have no impurities and no structural defects. As pointed out in [7], the GMRoscillations have not only RKKY- type components, but may additionally reveal large particular non-RKKY oscillations (see below). For the case of semi-infinite ferromagnetic slabs, a period of those extra oscillations with the spacer thickness in the CPP (current perpendicularto-plane) geometry has been shown in [7] to originate from values of the in-plane wavenumber ~ kk at which at least one spectral density vanishes at the ferromagnetic interface. In the present letter we study the CPP-GMR (currentperpendicular-to-plane) behaviour of layered systems of the type W/F1/S/F2/W, where W stands for a semiinfite ideal lead wire, F1 and F2 for different ferromagnets, generally with different thicknesses, and S for the non-magnetic spacer. Thus, apart from the leads, we are dealing with the usual magnetic trilayer systems. Our aim is to show that very pronounced beats may also, under some circumstances, appear as a function of the thicknesses of the ferromagnetic slabs. Besides the giant magneto-resistance effect, we also calculate the corresponding effect for the thermo-electric power (TEP).