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Muon spin rotation measurements of the temperature dependence of the Knight shift in single crystals of U_{0.965}Th_{0.035}Be_{13} have been used to study the static spin susceptibility below the transition temperatures T_{c1} and T_{c2}. While an abrupt reduction of the susceptibility with decreasing temperature is observed below T_{c1}, the susceptibility does not change below T_{c2} and remains at a value below the normal-state susceptibility. In the normal state we find an anomalous anisotropic temperature dependence of the transferred hyperfine coupling between the muon spin and the U 5f-electrons.

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