Fig. 5
Nonlinear increase of MR response in LPCMO-OSV as a function of FMM ratio and phase boundary length per FMM area at different temperatures. a Obtained MR response as a function of FMM ratio controlled by applying different pre-set magnetic field (Bpre). The inset shows the change of MR response as a function of the total length of phase boundary per FMM area (i.e., L/A ratio). The L/A ratios are calculated from the MFM images in Fig. 4 (i.e., FMM-fraction of red area; the total length of phase boundary per unit- fraction of white area per 10 μm×10 μm) at 10 K, 25 K, 50 K, 75 K, and 100 K after applying the pre-set magnetic field, Bpre = 1 T, 3 T, and 7 T, respectively. b Calculated \(\frac{{{\mathrm\it{MR}} + 1}}{{{\mathrm\it{MR}}_{{\mathrm{max}}} + 1}}\) using the Eq. (2) as a function of L/A ratio, consistent with the experimental results in the inset of panel a. MR measurements were taken at V = 0.2 V. The vertical error bars in MR represent the nondeterminacy of the MR measurements and the fitting value of MRmax, the lateral error bars in L/A represent the statistical uncertainty of the MFM measurements of L and A
