Mapping the phase boundaries in thin-film manganites using scale-invariant dielectric response

Magnetocapacitance techniques[1] have been used in a study of (La$_{1-y}$Pr$_{y})_{1-x}$Ca$_{x}$MnO$_{3}$ (LPCMO) thin films to determine the range of phase space, described by frequency ($\omega )$, temperature ($T)$ and field ($H)$, over which a dielectric response of the form, C"($\omega $,T,H) = [C'($\omega $,T,H) - C$_{\infty }$]$^{\gamma }$ , is found to hold. This power-law scaling collapse (PLSC) of the complex capacitance (C', C"), expressed in a Cole-Cole formulation, differs from the well-known ``universal'' dielectric response (UDR) [2], where the exponent $\gamma $ = 1. The influence of film thickness and stoichiometry on the extent of the PLSC region is investigated with the implementation of a new phase-space mapping technique. The mappings clearly illustrate the onset of phase competition in LPCMO, delineating boundaries which correspond to capacitive minima at low temperatures, where the first-order insulator-metal transition occurs, and to the second-order paramagnetic-insulator/charge-ordered-insulator transition at higher temperatures, where a resistive transport signature exists in bulk but not in thin films. Modeling with distributions of UDR elements corresponding to the different manganite phases gives a good qualitative account of the observed behavior, and can lead to the determination of individual phase fractions [1] R. Rairigh, Nature Physics 3, 551 - 555 (2007) [2] Jonscher - J. Phys. D: Appl. Phys. 32* *(1999)