NMR relaxation and rattling phonons in the type-I Ba${}_8$Ga${}_{16}$Sn${}_{30}$ clathrate

Atomic motion of guest atoms inside semiconducting clathrate cages is considered an important source for glasslike thermal behavior. ${}^{69}$Ga and ${}^{71}$Ga nuclear magnetic resonance studies on type I Ba${}_8$Ga${}_{16}$Sn${}_{30}$ show a clear low-temperature relaxation peak attributed to the influence of Ba rattling dynamics on the framework-atom resonance, with a quadrupolar relaxation mechanism as the leading contribution. Data are analyzed using a two-phonon Raman process, according to a recent theory involving localized anharmonic oscillators. Excellent agreement is obtained using this model, with the parameters corresponding to a uniform array of localized oscillators with very large anharmonicity.

Figure 1

${}^{71}$Ga and ${}^{69}$Ga NMR spin-lattice relaxation rates at the central transition frequency under 8.8 T from 4.2 to 295 K. Inset: ${}^{71}$Ga NMR lineshapes at temperatures of 4.2, 77, and 295 K, scaled proportional to 1/$T$.

Figure 2

Separated $T_1$ relaxation rates for ${}^{71}$Ga and ${}^{69}$Ga: ${}^{69}$Ga, quadrupole (diamonds; as labeled), ${}^{71}$Ga, quadrupole (circles; as labeled), ${}^{71}$Ga, magnetic (squares); ${}^{69}$Ga, magnetic (triangles). Inset: Isotopic ratio of overall rates under 8.8 T, with limits for pure quadrupolar/magnetic relaxation indicated.

Figure 3

Quadrupole NMR relaxation rate for ${}^{71}$Ga compared with the fitted 1D anharmonic model (solid curve) and simplified 2D model (inset; solid curve).

Figure 4

Fitted 1D double-well potential and its energy levels.