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High-field magnetization and magnetoresistance of the $A$-site ordered perovskite oxide CaCu$_{3}$Ti$_{4-x}$Ru$_{x}$O$_{12}$~($0 \le x \le 4$)

We have measured high-field magnetization and magnetoresistance of polycrystalline samples of the A-site ordered perovskite CaCu3Ti4-xRuxO12 (x=0 - 4) utilizing a non-destructive pulsed magnet. We find that the magnetization for x=0.5, 1.0 and 1.5 is nonlinear, and tends to saturate in high fields. This is highly nontrivial because the magnetization for x=0 and 4 is linear in external field up to the highest one. We have analyzed this field dependence based on the thermodynamics of magnetic materials, and propose that the external fields delocalize the holes on the Cu2+ ions in order to maximize the entropy. This scenario is qualitatively consistent with a large magnetoresistance of -70% observed at 4.2 K at 52 T for x=1.5.