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Pyrochlore iridates have attracted growing attention because of a theoreticalprediction of a possible topological semimetal phase originating fromall-in-all-out spin ordering. Related to the topological band structure, recentfindings of the magnetic domain wall conduction have stimulated investigationsof magnetic domain distribution in this system. Here, we investigate the sizeof magnetic domains in Eu$_2$Ir$_2$O$_7$ single crystalline thin films bymagnetoresistance (MR) using microscale Hall bars. Two distinct magneticdomains of the all-in-all-out spin structure are known to exhibit linear MR butwith opposite signs, which enables us to estimate the ratio of the two domainsin the patterned channel. The linear MR for 80 ${\times}$ 60 ${\mu}$m$^2$channel is nearly zero after zero-field cooling, suggesting random distributionof domains smaller than the channel size. In contrast, the wide distribution ofthe value of the linear MR is detected in 2 ${\times}$ 2 ${\mu}$m$^2$ channel,reflecting the detectable domain size depending on each cooling-cycle. Comparedto simulation results, we estimate the average size of a single all-in-all-outmagnetic domain as 1-2 ${\mu}$m.

All-in-all-out magnetic domain size in pyrochlore iridate thin films as probed by local magnetotransport