Electronic structure of the N-V center in diamond: Experiments A. Lenef, S. W. Brown, D. A. Redman, and S. C. Rand Division of Applied Physics, 1049 Randall Laboratory, University of Michigan, Ann Arbor, Michigan 48109-1120 J. Shigley and E. Fritsch Gemological Institute of America, 1630 Stewart Street, Santa Monica, California 90404-4088 Received 4 August 1995 Quantum-beat spectroscopy has been used to observe excited states of the N-V center in diamond. For the 1.945-eV optical transition, direct evidence is presented for the existence of GHz-scale fine structure, together with a much larger 46-cm -1 level splitting in the E state. An interference effect observed in transient four- wave-mixing response is explained with a polarization selection rule involving Zeeman coherence among magnetic sublevels. Also, detailed dephasing measurements versus temperature and wavelength have identified the decay mechanisms operative among the various states. A comparison of these results with ab initio calculations of excited electronic structure and interactions based on several multielectron models supports the conclusion that the N-V center is a neutral, two-electron center governed by a strong Jahn-Teller effect and weak spin-spin interactions. I. INTRODUCTION The center responsible for pink coloration in diamond, a rare tint in natural diamond, 1 but one easily induced in syn- thetic diamond containing substitutional nitrogen atoms, 2 is the N-V center. It consists of a nitrogen atom and a vacancy on neighboring sites in the carbon lattice and may be formed through a simple process of irradiation and annealing. While its optical 3 and spin-resonance 4 signatures, as well as its C 3 v symmetry, 5 have been known for a long time, the ground- state electronic structure for the center was reassigned only recently, following the observation of unexpected satellite peaks in the persistent hole-burning spectrum. 6 Recent hole-burning 7–9 and electron-paramagnetic- resonance EPR experiments 10 have provided firm evidence that the ground state is a spin triplet, rather than a spin sin- glet as previously thought. The number of active electrons in the center must, therefore, necessarily be even. However, if all unsatisfied bonding electrons in the center are counted two from nitrogen and three from carbons adjacent to the vacancy, the total is five, which is not even. The existence of triplet levels originally prompted Loubser and van Wyk to suggest 4 that the center captures an extra electron to form a six-electron center, which is then negatively charged. How- ever, this conclusion runs counter to the stability of the N-V center of temperatures that permit even the heavy nitrogen impurity atoms to become mobile. 11 Studies of excess elec- tron centers in alkali halide crystals 12 indicate that they ion- ize thermally at temperatures well below those necessary to initiate atomic diffusion. A six-electron model would seem unlikely on this basis, and the charge state and physical and electronic structure of the N-V center are called into ques- tion. We believe this puzzling situation is resolved in the present work. Here, we present direct measurements of excited-state energy-level splittings and dynamics, obtained using photon echo spectroscopy, to complement earlier in- formation on magnetic interactions in the ground state. 13 In a very direct manner, these measurements permit a determina- tion of electronic excited states and dynamics of the N-V center in the vicinity of the 637-nm zero-phonon transition. The experimental term diagram can then be compared with calculations for centers containing two, four, or six active electrons. Splitting patterns for these three models have been predicted 14 after considering the following electron interac- tions: spin-orbit, spin-spin, strain, and the Jahn-Teller effect. Consistency between theory and experiment is obtained in the case of two electrons experiencing a Jahn-Teller effect strong enough to quench the spin-orbit interaction, 15 with finer splittings arising from spin-spin interactions. An important finding is that only two active electrons as- sociated with the nitrogen atom are necessary for understand- ing the origin of the observed optical transitions of the cen- ter. In particular, the dangling bonds on carbons adjacent to the vacancy do not appear to contribute to optical interac- tions. We are thus led to conclude that the N-V center is a neutral rather than a negatively charged nitrogen-vacancy center, with properties determined by the two active nitrogen electrons. II. THEORETICAL The theory of a two- and three-pulse stimulated photon echoes has been discussed previously by many authors. 16 In this section, we merely outline the main results and provide extensions of earlier transient four-wave-mixing calculations necessary to understand and analyze our experimental results in a multilevel system with magnetic degeneracy. Of main interest are expressions for photon echo signal intensities versus interpulse delay times for ultrashort pulses, which generate quantum beats and Zeeman coherence described in Sec. II A. When oscillations in the coherence decay are ob- served as a function of delay between the forward beams quantum and polarization beats, relatively fine energy-level splittings may be deduced for ground and excited states of the center. When the center wavelength of the incident laser PHYSICAL REVIEW B 15 MAY 1996-II VOLUME 53, NUMBER 20 53 0163-1829/96/5320/1342714/$10.00 13 427 © 1996 The American Physical Society