Quantum diffusion of isotropic muonium, Mu_T, in a ¹³C diamond

This study explores the dynamical behavior of hydrogen in diamond, through the study of the hydrogenic analogue species known as the neutral atomic muonium state (Mu_T ≡ μ ⁺e^-). This can be readily studied by the transverse (longitudinal) field muon spin rotation (relaxation) techniques, briefly known as TF-μSR or LF-μSR respectively. This work focuses on the TF-μSR results for the paramagnetic Mu_T state. The Mu_T forms when an implanted positive muon captures an electron in crystalline solid-state materials. It occupies the tetrahedral interstitial site and diffuses via a pathway of these sites. The small mass of Mu_T is intermediate between the light electron and the heavy hydrogen, and is therefore suitable for studies of quantum diffusion in crystalline materials. In the process of diffusion, the spin polarization of the muon ensemble would be affected by interaction with electrons, via formation of correlated states or with the environment via dissipative processes. Such interactions can be monitored, almost background free and very precisely, in a host of experimental modes. This allows a powerful spectroscopy of the formed states as well as the monitoring of the dynamics of those states. In this work, the observables for both the Mu_T (73 ± 5%) and μ_d⁺ (4.3 ± 0.5%) states were measured in the ¹³C sample at temperatures ranging from 11 mK to 320 K, at an applied field of 5 mT. The measured spin relaxation rate for the Mu_T in the ¹³C sample is interpreted within the framework of quantum diffusion. The data show that quantum diffusion of the Mu_T state occurs up to unusually high temperatures in diamond. No evidence of diffusion could be obtained for the diamagnetic state.