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 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.