Scalar order in PrFe ₄P ₁₂ studied by thermal expansion and magnetostriction

We present the results of high-resolution measurements of the thermal expansion and magnetostriction of the cubic filled skutterudite compound PrFe ₄P ₁₂. The temperature dependence of the thermal expansion δL(T)/L for the three main symmetry directions are nearly identical below T _A, in accordance with a recently proposed scalar order parameter for the A-phase. In the field-angle dependence of the transverse thermal expansion δL(θ)/L along the [001] direction (θ is the angle between the [100] direction and the orientation of a magnetic field within the (001) plane), we find clear twofold oscillation. On the basis of mean-field analyses, we show that the observed twofold oscillation can be interpreted as the the crystal field effect for the cubic T _h symmetry. Our results suggest that the crystal field scheme consists of a Γ ₁ ground state and a Γ ⁽¹⁾ ₄ first-excited state, in both the non-ordered and A-phases.