Anti-Localisation to Strong Localisation: The Interplay of Magnetic Scattering and Structural Disorder

– We study the effect of magnetic scattering on transport in a system with strong structural disorder, using exact finite size calculation of the low frequency optical conductivity. At weak electron-spin coupling, spin disorder leads to a decrease in resistivity, by weakening the quantum interference precursors to Anderson localisation. However, at strong electron-spin coupling, the ‘double exchange’ limit, magnetic scattering increases the effective disorder, sharply increasing the resistivity. We illustrate the several unusual transport regimes in this strong disorder problem, identify a re-entrant insulator-metal-insulator transition, and map out the phase diagram at a generic electron density. Introduction. – The physics of transport and localisation in the presence of structural disorder has been extensively studied [1]. In three dimension (3d) increasing disorder leads to a monotonic increase in the fraction of localised states, and the resistivity in the extended regime, leading finally to the Anderson metal-insulator transition (MIT). The interplay of scattering from ‘paramagnetic’ moments with scattering from structural disorder leads to several new transport regimes, whose character is poorly understood. The presence of weak magnetic scattering actually weakens the localising effect of disorder, as discovered by Lee [2] and by Hikami et al. [3], while strong magnetic coupling, the ‘double exchange’ limit, enhances the localising effect of structural disorder [4]. There is no understanding of how these two endpoints are connected. This experimentally relevant “middle” is wide, unexplored, and beyond the reach of standard Boltzmann transport theory [5]. In this paper we present essentially exact results on the conductivity and MIT considering the combined effect of structural disorder and magnetic scattering, and illustrate the novel transport regimes in the problem. An understanding of transport properties of disordered magnetic systems is of particular relevance now because of intense experimental activity in diluted magnetic semiconductors [6, 7, 8] (DMS), amorphous magnetic semiconductors [9, 10], e.g GdSi, and the manganites Typeset using EURO-TEX 2 EUROPHYSICS LETTERS [11]. Some of these systems, notably those where the magnetic coupling arises from Hunds rule, as in d electron systems, require an understanding beyond the ‘weak magnetic scattering’ studies in the localisation literature. A quick look at the resistivity in the paramagnetic phase in these materials reveal that they are all ‘poor metals’. The resistivity at 300K in the DMS, Ga1−xMnxAs, at x ∼ 0.08, is ≈ 4 − 6 mΩcm [8]. For a-GdSi, in its ‘metallic regime’ this is ∼ 3 mΩcm [9]. For the manganite La1−xSrxMnO3 (LSMO), at large doping, x > 0.3, where electron-phonon coupling effects are expected to be weak, the room temperature resistivity is > 5 mΩcm [12]. To put these numbers in perspective, let us use the Mott ‘minimum metallic conductivity’ [13] as reference. The Mott ‘minimum’ conductivity is ∼ 0.03(e/h̄a0) and if we use a lattice constant a0 = 3Å then σMott ∼ 2.5×104 (Ωm), i.e, the ‘Mott resistivity’ ρMott is approximately 4 mΩcm. Comparing with the experimental data quoted above, for all the systems concerned, ρ/ρMott ∼ O(1) in the paramagnetic phase. There is no standard theory for analysing the scattering from structural and magnetic disorder in this regime. A complete theory of transport, for example the temperature dependence, in any of these systems would of course have to deal with annealed spin disorder. We will discuss these effects in the future, but focus here on the simpler case of scattering from a combination of quenched structural and magnetic disorder. Our principal results are contained in Fig.1, showing the ‘global’ behaviour of the resistivity, and the phase diagram in Fig.3. Model. – We study transport in the following model: