Critical behavior of La0.7Ca0.3MnO3 nanoparticles
We used the modified Arrott plot method to analyze magnetic-field dependences of magnetization, M(H), around the ferromagneticparamagnetic (FM-PM) phase-transition temperature (TC) of three nanocrystalline La0.7Ca0.3MnO3 samples with average crystallite sizes d = 40, 23, and 16 nm.
The analyses obtained the values of critical parameters to be TC ≈ 261 K, β = 0.485 ± 0.005, γ = 1.051 ± 0.094 and δ = 3.1 ± 0.1 for the sample with d = 40 nm, TC ≈ 252 K, β = 0.525 ± 0.010, γ = 0.893 ± 0.139 and δ = 2.7 ± 0.1 for d = 23 nm, and TC ≈ 236 K, β = 0.621 ± 0.008, γ = 0.825 ± 0.007 and δ = 2.2 ± 0.2 for d = 16 nm. With these critical values, the M(H) data points around TC of the samples fall into two universal branches of a scaling function M(H, ε) = |ε|βf±(H/|ε|β+γ), with ε = (T - TC)/TC, f+ for T > TC and f- for T < TC.
The results reveal that the crystallite-size reduction of nanoparticles decreases the TC value. This is ascribed to the decrease of FM doubleexchange interactions between Mn3+ and Mn4+ ions, which is related to the β change from 0.485 for d = 40 nm to 0.621 for d = 16 nm, corresponding to the change in FM order from the long-range type to the short-range one