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Iron doping induces quantum criticality in $\\alpha$-YbAlB$_4$ and magnetic order in both compounds. We report results of muon spin relaxation ($\\mu$SR) experiments in the intermediate-valent alloys $\\alpha$-YbAl$_{1-x}$Fe$_x$B$_4$, $x = 0.014$ and 0.25. For $x = 0.014$ we find no evidence for magnetic order down to 25 mK\\@. 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