We study the ternary clathrate Pr3Pd20Si6 in specific heat and ac susceptibility measurements on a high-quality single crystal, distinguishing antiferromagnetic and antiferroquadrupolar ordering, as well as a hitherto unknown magnetic low-temperature transition. The specific heat shows the direct involvement of nuclear spin degrees of freedom in the antiferromagnetic ordering, which is well supported by our calculation of the hyperfine level scheme without adjustable parameters. Pr3Pd20Si6 is, therefore, one of the rare materials where the nuclear moments are involved in the formation of the magnetic ground state.
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