Visualizing rattling in PrOs ₄Sb ₁₂ by single crystal neutron diffraction and maximum-entropy analysis

In order to obtain a detailed picture of rattling in PrOs ₄Sb ₁₂, a single crystal neutron diffraction experiment and a maximum-entropy analysis were carried out. At room temperature, a widely distributed anisotropic Pr nuclear density in the Sb icosahedron cage was revealed. An unusual trapezoidal form in the cross-sectional density profile of Pr clearly demonstrates the presence of strong anharmonicity in the Pr potential, in which the (111) direction has the maximum spread. The highest density is found at an off-center position along the same direction. The Pr density distribution becomes isotropic and sharp by cooling down to 8 K. Moreover, the highest density of Pr at 8 K is found at the center of the cage. The obtained nuclear density distribution and its temperature variation indicate that the rattling in PrOs ₄Sb ₁₂ is a strong anharmonic thermal motion without an off-center potential minimum.