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Nanometer-scale movements of domain walls in uniaxial garnet films have been studied by means of micromagnetization measurements using miniature gold and semiconductor Hall probes. The high spatial resolution is achieved due to low intrinsic noise of semiconductor ballistic Hall microprobes. At low (helium) temperatures, the domain walls are found to move by discrete jumps, which we attribute to pinning on isolated defects, and we were able to measure local hysteresis loops associated with pinning on individual pinning centers. The temperature dependence of the coercive field of a single pinning center allowed us to evaluate the characteristic energy and characteristic volume of the pinning center. At higher temperatures, the character of domain wall propagation changed, and walls were found to move not only by jumps between pinning centers but also via elastic bending.