Nonlinearity exponent of ac conductivity in disordered systems

We measured the real part of ac conductance Σ(x,f) or Σ(T,f) of iron-doped mixed-valent polycrystalline manganite oxides LaMn1−xFexO3 as a function of frequency f by varying initial conductance Σ0 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 Σ0 at lower frequency. With increase in f, Σ(x,f) increases slowly from Σ0 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 fc at which Σ(x,f) or Σ(T,f) increases for the first time from Σ0 scales with initial conductance Σ0 as , where xf is the onset exponent. The value of xf is nearly equal to one and is found to be independent of x and T. Further, an inverse relationship between xf and s provides a self-consistency check of the systematic description of Σ(x,f) or Σ(T,f). This apparent universal value of xf is discussed within the framework of existing theoretical models and scaling theories. The relevance to other similar disordered systems is also highlighted.