Quantifying phase separation in terms of magnetoresistive hysteresis loops in strongly phase-separated manganite thin films

Abstract

The present work reports the scaling behaviour of thermomagnetic hysteresis in temperature and magnetic field-dependent resistivity [(ρ–T) and (ρ–H)] measured during cooling/warming and H increasing/decreasing cycles in single crystalline La0.21Pr0.42Ca0.37MnO3 thin films. The zero-magnetic field (H = 0) insulator–metal transition temperature (IMT) measured in warming cycle ( $$T_{{{\text{IM}}}}^{{\text{W}}}$$ ~ 163 K) is higher than that in the cooling cycle ( $$T_{{{\text{IM}}}}^{{\text{C}}}$$ ~ 116 K) and the difference between the two IMTs shrinks as H is increased. The magnetic field dependence of the two IMTs is well fitted by the equation $${T_{{\text{IM}}}}=T_{{{\text{IM}}}}^{0}+\beta {H^\alpha }$$ . Here, $$T_{{{\text{IM}}}}^{0}$$ is the H-independent contribution and the constants, pre-factor $$\beta$$ and exponent $$\alpha$$ determine the H-dependent part of the IMT. The ρ–T loop area diminishes with the increasing H and its scaling with H in the regime which is akin to a magnetic liquid and unstable towards external H (H < 30 kOe) is nicely described by $${A_T}={A_{T0}}{e^{ - {\Gamma}H}}$$ . Here, $${A_{T0}}$$ is the zero-field normalized area and Γ is a constant related to the degree of phase separation. The analysis of the isothermal ρ–H loop area, which increases with H shows a scaling behaviour of the type $$A(H)=a{(H - {H_{{\text{IM}}}})^\eta }$$ . Here, the constant HIM corresponds to the induced AFMI–FMM phase transition and decreases with temperature, while the exponent ‘η’ measures the degree of phase separation.