Quantum oscillation of magnetoresistance in tunneling junctions with a nonmagnetic spacer

Abstract

We make a theoretical study of the quantum oscillations of the tunneling magnetoresistance (TMR) as a function of the spacer layer thickness. Such oscillations were recently observed in tunneling junctions with a nonmagnetic metallic spacer at the barrier-electrode interface. It is shown that momentum selection due to the insulating barrier and conduction via quantum well states in the spacer, mediated by diffusive scattering caused by disorder, are essential features required to explain the observed period of oscillation in the TMR ratio and its asymptotic value for thick nonmagnetic spacer.PACS numbers: 75.70.Pa, 73.40.Gk Large magnetoresistance [1,2] observed in ferromagnetic tunneling junctions such as Fe/Al 2 O 3 /Fe and Co/Al 2 O 3 /CoFe currently attracts much interest due to the possibility of its application to magnetic sensors and MRAM elements. Because the tunneling magnetoresistance (TMR) ratio is related to the spin polarization of the ferromagnetic leads [3,4], attempts have been made to fabricate junctions with more highly spin-polarized ferromagnets [5,6]. Realistic calculations [7,8], on the other hand, have given much higher TMR ratios than the observed values, which is probably due to their assumption of epitaxial structures. Recent experiments on TMR using epitaxial junctions [9,10,11], however, were unsuccessful in producing TMR ratios as high as expected. Thus, our understanding of the relationship between the electronic structure of the ferromagnets and the TMR ratio is far from complete.The most important factor governing the TMR ratio may be the electronic structure at junction interfaces [12,13]. In order to clarify its role, several experiments have been performed to measure the dependence of TMR ratio on the thickness of a nonmagnetic metal layer inserted at the interface [14,15,16]. The observed TMR ratios show almost monotonic decrease with increasing thicknesses of inserted layers of Au, Cu, or Cr, contrary to a theoretical study for clean junctions [17] which shows clear oscillations of the TMR ratio as a function of the nonmagnetic layer thickness. Zhang and Levy [18] have successfully explained this decrease in TMR ratio in terms of the decoherence of electron propagation across a nonmagnetic layer. However, recent experiments by Yuasa et al. show clear oscillations of the TMR ratio as a function of Cu layer thickness for high quality NiFe/Al 2 O 3 /Cu/Co junctions in which the Co/Cu electrode is a single crystal [19]. In their experiments, two characteristic features of the oscillations have been observed: (i) the average TMR ratio decays to zero with increasing nonmagnetic layer thickness; (ii) the period of the oscillations is determined solely by the belly or long period Fermi wave vector k F of Cu. The observed period agrees quite well with that of the oscillations of photoemission spectra caused by quantum well states in Co/Cu multilayers [20]. From the theoretical point of view this is confusing, since in addition to the Fermi wave vector [21], another wave vector, i....

Charge pumping by magnetization dynamics in magnetic and semimagnetic tunnel junctions with interfacial Rashba or bulk extrinsic spin-orbit coupling

“…To account for the properties of amorphous AlO x tunnel barrier in MTJs and semi-MTJs employed in the recent spin pumping experiments, 12,19 the on-site potential on I monolayers is chosen as ε I i = U b ± δU b where random fluctuations δU b mimic binary alloy disorder. 42 The impurity potential in the F layers also generates extrinsic SOC, as described by the third sum in Eq. (1).…”

“…Since both of these resistances are dominated by the tunnel barrier potential, they are computed for clean junctions. 42 To model AlO x tunnel barrier, we use binary alloy disorder characterized 42 by δU b = 0.5γ.…”

Non-collinear magnetoelectronics

“…By selecting essentially a single wave vector state by hot-electron injection [111] or tunneling barriers [112], the single standing wave pattern may dominate transport, even reversing the sign of the magnetoresistance. The most suitable theoretical approach for these rather exceptional cases is a numerical computation of the transport coefficients [113], that may be used in the present circuit theory if embedded as a resistive element in a larger environment (see Section VII). For completeness, we would like to add that spin injection into high-mobility semiconductor structures might become possible allowing to realize the coherent precession of the spin accumulation in a ballistic one-dimensional channel by spin-orbit interaction as envisaged by Datta [10].…”

Theory of Tunnel Magnetoresistance

“…18,[68][69][70] In particular, we will demonstrate that i) increasing barrier thickness increases the amplitude of the k F oscillation period relative to the k cp oscillation period, ii) randomness introduced in the barrier also weakens the amplitude of the k cp oscillation period, and iii) the randomness decreases the asymptotic value of the MR ratio. These results are interpreted in terms of the momentum selection of electrons incident on the barrier interface and in terms of the diffusive scattering due to randomness which opens additional conduction channels via quantum well states.…”

“…As a demonstration, we present an analysis of the quantum oscillation of TMR in MTJs with a nonmagnetic spacer. 18) Section 5 is devoted to TMR in realistic MTJs, Fe/MgO/Fe junctions, for which realistic TB model is adopted in the numerical calculation. In sections 6 and 7, specific examples of MTJs, semimetal junctions 19) and manganite junctions, 20,21) respectively, will be dealt with.…”