Muonium as a probe of point defects in type-Ib diamond

Abstract

Muonium (Mu), a bound state of a positively charged muon and an electron, can diffuse through crystal lattices and interact with defect centers in insulators and semiconductors. We demonstrate that this Mu's diffusive property can be used to probe defects in a diamond crystal lattice; specifically, substitutional nitrogen atoms (N$_\text{s}^0$) and nitrogen-vacancy (NV) centers in type-Ib diamond. Upon interaction with these defects, Mu can exchange its electron's spin or change its charge state, which result in muon spin relaxation. However, muons in diamond (and semiconductors in general) can be in a few distinctive muonium states, with each state contributing to the muon signal. In addition, these states can undergo site and charge exchange interaction, forming a dynamic network. Hence, to study the Mu interaction with point defects, the muon data have to be deconvoluted to isolate signals from the diffusing species. To achieve this goal, we have modeled the Mu state exchange dynamics and numerically simulated the time evolution of muon spin polarization by the density matrix method. With a global curve fit to a set of longitudinal field scan data, one can extract the Mu transition rates that involve interaction with the defect centers. The diffusing tetrahedral interstitial Mu was found to interact with the paramagnetic N$_\text{s}^0$ center via electron spin exchange. In contrast, they are converted to form a diamagnetic center upon interaction with the negatively charged NV center.

Figures (4)

• Figure 1: Schematic diagram of the experimental setup. Muons propagate through the beam snout and irradiate a sample ("S"). Muon spins are fully polarized in a direction antiparallel to their momentum vectors (shown by the arrows). The sample was mounted on a closed cycle refrigerator ("CCR") with a radiation shield. Forward ("FD") and backward ("BD") detector segments surrounding the vacuum chamber (shown in gray) detect high-energy decay positrons. There are a total of 96 detectors in EMU with a count rate of 120 million events per hour. A Helmholtz coil (not shown here) applies a uniform longitudinal field at the sample position along the $\vb*{z}$ axis.
• Figure 2: $\mu$SR time spectra measured on the Pristine [(a) and (b)] and NV [(c) and (d)] sample at 290 and 20 K under five representative LF fields i.e. 0 (black), 200 (yellow), 600 (green), 2000 (blue), and 4000 G (red). Five million muon decay events were averaged for each spectrum. Error bars are due to the random decay of the muons, mean lifetime 2.2 $\mu$s, and the Poisson counting statistics of the decay positrons (hence the shorter error bars in the earlier time bins). The full muon asymmetry in this EMU setup, $\approx$22.0 %, was used to normalize the spectra and get $P(t)$ ( i.e. a full asymmetry gives a unity on the y-axes). Solid lines denote results of the curve fitting (see text). The numbers of fit parameters are six for (a) and (b), and five for (c) and (d) (see TABLE \ref{['table:fit_results']}). Reduced chi-squared values were (a) 1.196, (b) 1.174, (c) 1.483, and (d) 1.279. In high LF, there can be systematic errors associated with decay positrons spiralling around field lines, resulting in a small shift in the offset.
• Figure 3: Repolarization curves ($\overline{P}$vs. LF) for the Pristine and NV sample measured at (a) 290 and (b) 20 K. Solid lines denote the curve fit results (see text). The same set of data are replotted for the (c) Pristine and (d) NV sample for comparing their temperature dependence. For clarity, the plots are color-coded such that: black circles for Pristine at 290 K, red squares for Pristine at 20 K, green triangles for NV at 290 K, and blue diamonds for NV at 20 K. Note that the difference in the offsets ($\approx$0.02) in Fig. (a) and (b) are associated with background signals from the silver materials. Even if the two samples were mounted in the same way, there always is a small difference in muon beam coverage. The Supplemental Material has Fig. (a) and (b) after the offset correction SM. With this adjustment, the decoupling of Mu$_\text{T}^0$ can be more clearly compared between Pristine and NV.
• Figure 4: Model of Mu state exchange in the (a) Pristine and (b) NV sample. A superscript and subscript of $\Lambda$ indicate the charge state and Mu site respectively, with a forward slash between before and after a transition.