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We present a search for ultra-relativistic magnetic monopoles with the Pierre Auger Observatory. Such particles, possibly a relic of phase transitions in the early universe, would deposit a large amount of energy along their path through the atmosphere, comparable to that of ultrahigh-energy cosmic rays (UHECRs). The air shower profile of a magnetic monopole can be effectively distinguished by the fluorescence detector from that of standard UHECRs. No candidate was found in the data collected between 2004 and 2012, with an expected background of less than 0.1 event from UHECRs. The corresponding 90% confidence level (C.L.) upper limits on the flux of ultra-relativistic magnetic monopoles range from $10^{-19}$ (cm$^{2}$ sr s)$^{-1}$ for a Lorentz factor $��=10^9$ to $2.5 \times10^{-21}$ (cm$^{2}$ sr s)$^{-1}$ for $��=10^{12}$. These results - the first obtained with a UHECR detector - improve previously published limits by up to an order of magnitude. Published version. Corrected title. Added journal reference and DOI. Added Report Number

We search for signals of magnetically-induced effects in the arrival directions of ultra-high-energy cosmic rays detected at the Pierre Auger Observatory. We apply two different methods. One is a search for sets of events that show a correlation between their arrival direction and the inverse of their energy, which would be expected if they come from the same point-like source, they have the same electric charge and their deflection is relatively small and coherent. We refer to these sets of events as "multiplets". The second method, called "thrust", is a principal axis analysis aimed to detect the elongated patterns in a region of interest. We study the sensitivity of both methods using a benchmark simulation and we apply them to data in two different searches. The first search is done assuming as source candidates a list of nearby active galactic nuclei and starburst galaxies. The second is an all-sky blind search. We report the results and we find no statistically significant features. We discuss the compatibility of these results with the indications on the mass composition inferred from data of the Pierre Auger Observatory. Published version; correction of a minor typo