Quantum diffusion of isotropic muonium (Mu_T) in ¹³C diamond studied by LF-mSR spectroscopy

D. Gxawu ^1,2,*, I. Z. Machi ³, S. H. Connell ², S. F. J. Cox⁴, K. Baruth-Ram⁵, M. J. Sithole³

¹ Physics Department, Durban Institute of Technology, Durban 4001, South Africa

² Schonland Research Institute for Nuclear Sciences, University of the Witwatersrand, PO WITS, Johannesburg 2050, South Africa

³ Physics Department, University of South Africa, Box 392, UNISA, Pretoria 0003, South Africa

⁴ ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX110QX, United Kingdom

⁵School of Pure and Applied Physics, University of KwaZulu Natal, Durban 4041, South Africa

The electronic structure and the dynamics of isolated atomic hydrogen in diamond are of fundamental interest to many scientists, since hydrogen is the simplest and the lightest interstitial impurity. However, it is extremely difficult to obtain direct information on isolated hydrogen in diamond, mainly due to its high mobility and reactivity. Much experimentally related information on hydrogen in diamond has thus far been obtained from Muon Spin Rotation (MSR) experiments, where the muonium (m⁺e^-) atom is considered to be the chemical analogue of hydrogen. It is, however, recognised that muonium and hydrogen are incorporated in two different ways in these samples. Hydrogen is usually introduced during the process of sample preparation and reaches thermal and chemical equilibrium before measurements begin, while muonium is observed within 2.2 microseconds after very dilute implantation of almost 100% spin polarized muons. The defected nature of even the purest diamonds available implies that hydrogen can have formed complexes before the measurement. On the other hand, the short time window of MSR provides a unique opportunity of indirectly exploring hydrogen diffusion during its early presence in the sample. Obvious caveats apply due to the lighter mass of muonium in comparing dynamical information.

Dynamical information of the muonium behaviour is inferred from the depolarization rate of the muon ensemble. In this experiment the diamond sample was an isotopically pure ¹³C diamond and the external field is parallel to the initial muon spin polarization. It is already known that the mobile species is muonium in the tetrahedral interstitial site (Mu_T). As the Mu_T diffuses, it experiences a fluctuating field due to the local moments. The fluctuating field induces transitions between the spin sub states of the Mu_T, thereby depolarizing the muon ensemble, analogous to the T₁ mechanism in NMR. The diffusion rate of the Mu_T modifies the power spectrum of the fluctuating field. A careful interpretation of the relaxation behaviour is therefore related to the Mu_T hop-rate by a model. This technique is known as longitudinal field muon spin relaxation (LF-mSR).

The temperature regime spanned the range between 10K and 400K, and the magnetic field was varied in the range 20mT to 4T leading essentially to a three-dimensional data set. This quality of data was necessary to unambiguously extract the hop-rate from the relaxation rate. The nuclear hyperfine interaction is relatively low (600MHz) and temperature independent at low temperatures, and then starts to increase at higher temperatures. The behaviour of the relaxation rate as a function of both temperature and magnetic field in the temperature range considered (5K – 400K) was consistent with quantum diffusion up to the highest temperature yet observed. Attempts to investigate Mu_T diffusion in the higher temperature regime (T ³ 400K) were inhibited by the onset of the conversion of tetrahedral interstitial muonium to bond centered muonium (Mu_BC). The T₁-minimum indicative of different quantum diffusion regimes could not be observed as a consequence. The extracted hopping rates suggest that in the temperature range covered, Mu_T diffuses extremely fast (t ~10¹¹ Hz). The Mu_BC requires considerable lattice relaxation, and it is known that the conversion of Mu_T to Mu_BC is a one step process. The experiment therefore indicates that the Mu_T to Mu_BC transition occurs at a temperature of about 400K as this is the temperature at which the muonium has slowed down sufficiently.

* Corresponding author : Address ……..