Effects of Si substitution on ferromagnetic order and off-center rattling of Eu ions in the type-I clathrate Eu8Ga16Ge30

In the ferromagnetic type-I clathrate Eu ₈Ga ₁₆Ge ₃₀, the divalent Eu ions are known to rattle among off-center positions in the tetrakaidecahedral cage. We have studied effects of Si substitution on the ferromagnetic state and the rattling motion of the Eu ions in Eu ₈Ga ₁₆Ge ₃₀ by measuring the magnetization M , electrical resistivity ρ , thermopower, specific heat C , and Eu partial phonon density of states (Eu pDOS) of Eu ₈Ga 16 − x Ge 30 + x − y − z Si y □ z ( □ = vacancy, 0 ≤ y ≤ 7.3). Upon increasing y from 0 to 7.3, the lattice parameter decreases by 0.7%, which has no effect on the divalent state of Eu. The Curie temperature T C decreases from 36.2 K to 32.6 K, whereas the specific heat jump at T C , Δ C , increases twofold. For y = 0, both ρ ( T ) and d M ( T ) /d T exhibit anomalies below T C at T ∗ ∼ 24 K, which are suppressed by applying magnetic field of 1 T. The anomalies at T ∗ disappear by Si substitution at a low level, y = 3.7. The measured Eu pDOS indicates that the low-lying phonon energy of the Eu ions decreases with Si substitution. This softening means that the off-center rattling is changed to on-center one with large amplitude in an anharmonic potential. Based on these findings, we discuss relationship between the off-center Eu rattling and their collective magnetic behavior.