Nonlinearity exponent of ac conductivity in disordered systems

Abstract

We measured the real part of ac conductance Σ(x,f) or Σ(T,f) of iron-doped mixed-valent polycrystalline manganite oxides LaMn(1-x)Fe(x)O(3) as a function of frequency f by varying initial conductance Σ(0) by quenched disorder x at a fixed temperature T (room) and by temperature T at a fixed quenched disorder x. At a fixed temperature T, Σ(x,f) of a sample with fixed x remains almost constant at its zero-frequency dc value Σ(0) at lower frequency. With increase in f, Σ(x,f) increases slowly from Σ(0) and finally increases rapidly following a power law with an exponent s at high frequency. Scaled appropriately, the data for Σ(T,f) and Σ(x,f) fall on the same universal curve, indicating the existence of a general scaling formalism for the ac conductivity in disordered systems. The characteristic frequency f(c) at which Σ(x,f) or Σ(T,f) increases for the first time from Σ(0) scales with initial conductance Σ(0) as f(c) ~ Σ(0)(x(f)), where x(f) is the onset exponent. The value of x(f) is nearly equal to one and is found to be independent of x and T. Further, an inverse relationship between x(f) and s provides a self-consistency check of the systematic description of Σ(x,f) or Σ(T,f). This apparent universal value of x(f) is discussed within the framework of existing theoretical models and scaling theories. The relevance to other similar disordered systems is also highlighted.

Nonlinear alternating current conduction in polycrystalline manganites

“…The temperature dependence of conductance of LFMO obeys Mott's law 42 of variable range hopping with the characteristic temperature T 0 increasing with the increase in Fe concentration. 23,40 This increase is not monotonic rather change in slope occurs at x ¼ 0.70 which is associated with the structural change for x ! 0.70.…”

“…Similar behaviors were also observed for the LYCMO-2 sample. Figure 4 shows the result of making the data in Figure 3 collapse into a single curve following the data collapse method 23,33,34 which is described in detail below. The temperature 160 K at which conductance of LYCMO-1 sample is minimum is considered as appropriate starting temperature as the increase in conductance from Ohmic value R 0 is maximum.…”

“…This scaling approach has been successfully applied to different systems such as composites, 13 porous silicon, 22 polyaniline films, 9 electron conducting polymer systems, 2 poly (3-decylpyrrole), 10 and polycrystalline manganites. 23 For f < f c , the scaling function g(y) % 1 corresponds to the fact a)…”

“…Thus, the frequency f c can be called a crossover (characteristic) frequency such that it separates the linear regime from the non-linear regime along the frequency axis. This crossover frequency f c scales with initial conductance R(P, 0) as 10,13,23 …”

“…x f is known as the nonlinearity exponent characterizing the strength of nonlinearity near the onset of nonlinear conduction and has value of the order of unity. 23 Doping by divalent cations (A ¼ Sr, Ca, and Ba) in the La-site of the parent compound LaMnO 3 results in the formation of perovskite system La 1Àx Ca x MnO 3 (with A ¼ Ca), and the valence state of Mn is partially changed from 3þ to 4þ in order to preserve electrical neutrality. 24 The doubleexchange mechanism (coupling between Mn 3þ and Mn 4þ ions through O 2À orbitals) gives rise to the ferromagnetic ordering of such hole doped manganite systems.…”