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Hexagonal UNi_4B is magnetically frustrated, yet it orders antiferromagnetically at T_N = 20 K. However, one third of the U-spins remain paramagnetic below this temperature. In order to track these spins to lower temperature, we measured the specific heat C of \unib between 100 mK and 2 K, and in applied fields up to 9 T. For zero field there is a sharp kink in C at 330 mK, which we interpret as an indication of a second phase transition involving paramagnetic U. The rise in between 7 K and 330 mK and the absence of a large entropy liberated at may be due to a combination of Kondo screening effects and frustration that strongly modifies the low T transition.

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