885 ISSN 1063-7834, Physics of the Solid State, 2020, Vol. 62, No. 5, pp. 885–890. © Pleiades Publishing, Ltd., 2020. Negative Magnetoresistance Phenomenon in Diluted Granular Multilayers Co 80 Fe 20 (t)|Al 2 O 3 A. El Oujdi a , A. El Kaaouachi b, *, A. Echchelh a , B. Ait Hammou b , R. Tiskatine c , and S. Dlimi c a Laboratory of Energetic Engineering and Materials, Faculty of Sciences Ibn Tofail, Kenitra, Morocco b MPAC Group, Faculty of Sciences, BP 8106, Agadir, 80000 Morocco c Physics Department, Faculty of Sciences, Agadir, 80000 Morocco * e-mail: kaaouachi21@yahoo.fr Received November 6, 2019; revised December 22, 2019; accepted December 27, 2019 Abstract—Several complex theories explaining the phenomenon of negative magnetoresistance (NMR) are discussed, observed in insulating diluted granular multilayers Co 80 Fe 20 (t)|Al 2 O 3 . In fact, this investigation is re-analyzing the experimental measurements of Co 80 Fe 20 with low nominal thickness t = 0.7 nm of granular layers obtained earlier. Two theories such as quantum interference model and localized magnetic moments model are confronted with experimental measurements in order to provide physical explanations to NMR phenomenon. Keywords: Co 80 Fe 20 , negative magnetoresistance, quantum interference, localized magnetic moments model, granular system, magnetic field DOI: 10.1134/S1063783420050212 1. INTRODUCTION The study of magnetoresistance in different mate- rials is the subject of several studies and publications. Indeed, these studies allow to identify the different mechanisms of electrical conduction in these materi- als [1–3]. In previous works [4–9], we have studied transport phenomenon and negative and positive magnetoresistance behaviour on both sides of the metal–insulator transition (MIT) in several 3D and 2D semiconductors, in amorphous alloys, and granu- lar systems [10, 11]. The analysis of magnetoresistance behaviour permits us to highlight different conduction mechanisms in their samples. It is well known that the variable range hopping (VRH) conductivity of the insulating disordered systems was shown by Mott [12, 13] to behave like ln(σ) ∝ . This dependence was obtained by optimising the hopping probability and assuming a slowly varying density of states (DOS) in the vicinity of the Fermi level. On the contrary, Efros and Shklovskii (ES) [15, 16] have predicted that long-range electron–electron interaction reduces the DOS at the Fermi level and creates a soft Coulomb gap (CG), which takes the form N(E) ∝ (E –E F with = 2.The existence of the CG leads to the ES VRH regime of the conductivity, which is written as (1) with p = . Equation (1) remains quite universal, since when = 0, the DOS is constant and p = 0.25, correspond- ing to the Mott regime. But when = 2, the DOS var- ies in the vicinity of the Fermi level and p = 0.5 corre- sponding to ES VRH regime. The experimental situa- tion has been confusing for some time, with both values of p being observed. Mott VRH and ES VRH regimes have been widely observed in many types of disordered materials [17, 18]. In this work, we re-analysed the experimental val- ues of negative magnetoresistance (NMR) in insulat- ing Co 80 Fe 20 with low nominal thickness t = 0.7 nm granular layers measured by Silva et al. [19]. The mea- surements were carried out at three temperatures T = 100, 200, and 300 K and in the range of magnetic field 0 to 9.33 kOe. The experimental magnetoresistance (MR) [19] has been plotted as a function of magnetic field in Fig. 1. A negative MR is observed below 300 K, with an unusual magnitude of about 2% at the lowest tem- peratures (100 K) comparing with NMR obtained at T = 300 K.   σ   ρ   1       0 T T v ) v     σ=σ -         0 0 exp p T T + + v v 1 4 v v SEMICONDUCTORS