Generalized density-of-states and anharmonicity of the low-energy phonon bands from coherent inelastic neutron scattering response in the pyrochlore osmates AOs2O6 (A=K, Rb, Cs)

Inelastic neutron scattering on powder samples has been employed to investigate the lattice dynamics of alkali-metal osmates. We have obtained the neutron weighted generalized phonon density-of-states from momentum-transfer averaged coherent inelastic response. We have paid special attention to the low-energy modes that have been assigned to the Einstein term of the lattice specific heat and from which a rattling behavior of the alkali atoms has been inferred. In all of the three compounds our results reveal a split band with two prominent peaks in the low-energy range associated with the vibrational modes of A atoms. The temperature dependence of these bands has been followed in the range from 1.5 K<300 K. The strongest temperature effect is visible in the case of KOs(2)O(6), the split band peaking at h omega approximate to 5.5 meV, and 6.8 meV at T=300 K softens on cooling resulting in a main band at about h omega approximate to 3.4 meV at T less than or similar to 50 K, while a smaller softening of Delta(h omega)<1 meV is seen in the other two compounds. In agreement with earlier work the temperature dependent modifications of the phonon spectrum can be attributed to the weak potential felt by the A atom in the oversized cage where it is located. At low T the characteristic energies for each of the compounds are well correlated with the specific-heat observations published earlier. The powder averaged phonon response shows Q dependence indicating coherent coupling of the alkali atom vibrations with the rest of the lattice.