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

Abstract

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][4][5][6][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 k 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/F 1 /S/F 2 /W , where W stands for a semiinfite ideal lead wire, F 1 and F 2 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).The calculation technique, we have developed, is based on the Green's function recursion method [8,6]; it is close to that of [6] with one essential exception, namely instead of working with finite systems in the in-plane space (x, y directions), we have reduced the whole problem to one dimension by performing the Fourier transform in the infinite x-y plane. Hence, our Green's functions fulfil the following equation:where for the simple cubic lattice t z,z ′ = t δ z ′ ,z±1 andIn eqn. (2), E F is the Fermi energy; t (< 0) is the nearest-neighbour hopping integral; a is the lattice constant, and V σ (z) is the spin-dependent atomic potential, which we assume to be c...

Perpendicular transport and magnetization processes in magnetic multilayers with strongly and weakly coupled magnetic layers

“…In agreement with the findings of Ref. [10], the oscillations are quite pronounced and have the same period as GMR but exhibit negative bias. Asymptotically they seem to have roughly the same phase as GMR.…”

“…We define, as in Ref. [10], the "giant magneto-TEP-effect" GMTEP analogously to Eq. (1) (with Γ replaced by S).…”

“…where the first three terms describe bilinear exchange coupling between magnetic layers, the next three are Zeeman energy terms (t i being i-th layer thickness and t the overall thickness of all the magnetic layers) and E A (Θ i ) is the crystalline anisotropy, that is t i K sin 2 (2Θ i )/4t and −t i D cos 2 Θ i /t for cubic and uniaxial case respectively. We assume that external magnetic field is applied along the [10] in-plane crystallographic axis, which can be either easy or hard axis depending on the sign of the anisotropy constants. The magnetic moments are confined to the layers plane which corresponds to the strong shape anisotropy.…”

Exchange coupling and ballistic current-perpendicular-to-plane giant magnetoresistance in magnetic trilayers: mutual intercorrelations

“…This quantum contribution has been studied and shown to be quite substantial both by first principles computations 11 and model calculations 12,13 . The aim of the present paper is to confront the GMR oscillations in the ballistic regime 14,12,13 , where only the quantum contribution appears, with those of the exchange coupling. Both quantities are treated on equal footing without any approximations, by precise numerical computations.It is interesting that in spite of plenty of publications on GMR and J, there has been, to our knowledge, only one theoretical attempt 7 devoted to a detailed comparison of both quantities.…”

Ab-initio calculations of the GMR-effect in Fe/V multilayers

“…Due to these simplifications, Asano et al could use a recursive technique, where planes with 12×12 atoms could be treated, and 'perfect leads' could be attached to the sample in the current direction. Although within our group this powerful technique has already been extended to extremely accurate model calculations of the CPP-GMR and of a corresponding Giant Magneto-Thermopower in pure s-band tightbinding samples with infinite planes, [7], the method is not applicable to the present system, since s-, p-, and d-bands, self-consistency, and interactions up to third-nearest neighbours, are needed. However at the end we will discuss our results in the light of [13].…”