Correlated Small Polaron Transport in Mixed Valence Oxides

The electrical transport properties of mixed fdtes, oxidic superconductors and GMR compounds having ions in mixed valence state are shown to originate fhm the correlated motion of polarons and scattering by the spin disorder. The tramprt e e s of mixed valence compounds exhibit anomalous characteristics. In magnetite, it leads to a orderdisorder transition at 120 K with A-type anomaly in the specific heat, which is well below the curie temperature, T, = 850 K [l]. In oxidic superconductors, like (Lal,Sr&Cu04; and YBa2Cu3@4, the normal state resistivities show remarkable linear-T me,tallic behaviour over a wide temperature range 121. In a negative giant magnetoresistance material like La,,Ca,MnQ, a metallic conductivity is observed below the curie temperature and an activated conductivity at T 2 To [3]. We show that a possible reason for these anomalies arise from the existence of mixed valence states A*, on crystallographic similar sites where A is a cation or an anion. Based on a concept of short-range cooperative charge transfer between mixed valence states arising from electron-phonon coupling an expression for dc conductivity is obtained [4] : o = (21~) n mph a2 e2 $ sech2 ( w 2 ) (1) where n is the number of ions in the mixed valence state;oph is the frequency of the longitudinal optic phonon mode which couples the neighbouring ions separated by a distance a, E, is the stablization energy of the small polaron and P = 1kT. Equation (1) describes satisfactorily the transport in mixed fenites [4] as well as in normal state oxidic superconductors [5]. The Venvey transition in magnetite has been attributed to softening of the phonon mode, consequently o p h in eq.(l) vanishes at T = TV [6]. In magnetite, the expression in eq.(l) applies only in the temperature range TV < T < 250 K. The reason is that .scattering of charges by spin-disorders on the h e a r chain is totally ignored. To incorporate it, we express the time, z, between two collisions of the charge camer in the DNde formula, o = ne2z/m*, in the form, 1 1 1 +Z Zc zs. (2) where z, is the collision time obtained from eq.(l) for the correlated motion and z, is the time due to spin-flip arising from the exchange interaction. We may describe z, quasi-classically as, 1 = ~ [ l m(t)](~,) 7s (3) Here m(t) is the reduced magnetization at t = TTT, a id is the average of the z component of the spin of the electron making the jump. To a first approximation, if we take A as l&, we obtain from eq.'s (1) and (3), b(t) = C p %h2 ($&42)[1{l-m(t)) ] (4) C = (2/n) n m+ a2 e2 This expression fits the experimental data of Miles et al. [l for magnetite over the temperamrange TV I T I T, if we take > To. So a maximum occurs near T. [3]. On application of an external magnetic field the magnetoresistance, Ap(H) = p@) p(0) in the system La~,Ca~Mno~ [0.1 I s I 0.91, is obscrved to be negative. LaMnO3 is a wveak ferromagnet and an insulator. When Ca2+ ions are substituted for ~ a ~ + , the d-holes n~o\.e amongst the equivalent Mn positions. However, for small hole concentrations, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:19971261 Cl-634 JOURNAL DE PHYSIQUE IV correlated polaron motion is not possible and the transport is desc r i i by the independent polaron motion. In this case, the Fnnk-Condon factor, e.up(-E$h&, where E, is the polaron binding energy and o , h is the phonon frequency, appears in the expression for conductivity [g] and e-xplains the maximum in the resistivity versus temperature curve. The scattering of the holes is dominated by the spin-flip term and the magnetoresistance is given by, "H'*O' = -MH, ~I(s.(H)) F@) (5) where the quantities on the right indicate the values based on short rangeordering of the spin systems. Equation (5) explains the negative magnetoresistance of the system. We conclude that the electrical transport properties in mixed valence compounds can be explained satisfactorily on the basis of correlated polaron and spin flip scattering processes. [l] Goodenough J.B., 'Recent Advances in Materials Research' (Osford & IBH, New Delhi, 1982) pp.? [2] Iye Y.,' 'Studies of High Temperature Superconductofs' (Nora Science Publ., 1989) pp. 199 [3] Mahendiran R et al., SoLState Co~nm., 94 (1995) 515 [4] Srinivasan G. and Srivastava C.M., Phys. Stat. Sol., B103 (1981) 665 [S] Srivastava C.M., Physica C, 176 (1991) 481 [6] Srivastava C.M., Phys. k t t . , 98A (1983) 192 [A Miles P.A et al., Revs. Mod. Phys., 29 (1957) 289 [8] Riek H.G., 'Polarons in Ionic Crystals and Polar Semiconductors' (North Holland, Amsterdam, 1972) pp. 679-714