Electron-paramagnetic-resonance measurements on the divacancy defect center $R4/W6\mathrm{}$ in diamond

Electron-paramagnetic-resonance (EPR) studies in radiation damaged diamond enriched to 5% ${}^{13}\mathrm{C}$ have resulted in the identification of the nearest-neighbor divacancy center. It is the isotopic enrichment, and consequent observation of ${}^{13}\mathrm{C}$ hyperfine lines, that has permitted the structure to be determined more than 30 years after the discovery of the center, known as $R4\mathrm{}$ or $W6.\mathrm{}$ The center is produced by annealing radiation damaged diamonds to temperatures at which the vacancy is mobile (above about 900 K), and in pure diamond it is the dominant vacancy related product of irradiation and 900 K annealing. The divacancy anneals out upon prolonged annealing to temperatures above about 1100 K. Low-temperature EPR measurements determine the absolute sign of the largest principal value of the Ḏ matrix, $D_3$ to be negative; and measurements at temperatures between 4.2 and 300 K indicate that the Ḏ matrix is temperature dependent in this interval. The center has $C_{2h}$ symmetry at low temperatures (30 K), and appears to change to axial symmetry about $〈111〉$ at high temperatures $(>\mathrm{}400\mathrm{}\hspace{0.5em}\mathrm{K}).\mathrm{}$ Analysis of the ${}^{13}\mathrm{C}$ hyperfine-coupling data using a simple molecular-orbital model shows that at low temperature the unpaired electron probability density is primarily located on four equivalent carbon atoms that are not in the $\{110\}$ plane of reflection symmetry containing the two vacancies. These four carbon atoms show an outward relaxation around the divacancy. The low-temperature symmetry and localization of the unpaired electron probability density is surprising, the former in the light of theoretical predictions of a ${}^3{A}_{2g}$ ground state in the undistorted $D_{3d}$ symmetry and the latter in comparison with divacancies in silicon. A simple defect molecule calculation suggests that the divacancy has a ${}^3{B}_u$ ground state at low temperatures with $C_{2h}$ symmetry. The large linewidth leaves it unclear whether the symmetry changes at high temperatures to $D_{3d}.$ The broadening of the EPR linewidth with increasing temperature does not originate from thermally activated reorientation between sites with $C_{2h}$ symmetry. It appears to be due to rapid spin- lattice relaxation (via the Orbach mechanism) at temperatures above 50 K, and simple analysis suggests that there is an excited state 20(1) meV above the ground state.