We present comprehensive analytical and numerical studies on the pure dephasing of a single Mn spin in a semiconductor quantum dot due to (i) its sp-d exchange interaction with an electronic environment, and (ii) its hyperfine interaction with the nuclear spin environment. For (i), by modeling the electronic environment by an open two-level system, we provide exact analytical expressions and present detailed analysis for the Mn spin pure dephasing in both the Markovian and non-Markovian regimes. This provides a clear physical picture and a general theoretical framework based on which we estimate the Mn spin pure dephasing due to various fluctuations (such as thermal excitation, optical pumping, tunneling, or electron/hole spin relaxation) of the electronic environment and reveals a series of interesting behaviors, such as thermal, optical, and electrical control of the crossover between the Markov and non-Markov regimes. In particular, we find rapid Mn spin pure dephasing on a nanosecond time scale by the thermal fluctuation and optical pumping, but these mechanisms can be strongly suppressed by shifting the electron envelope function relative to the Mn atom with an external electric field through the quantum-confined Stark effect. The thermal fluctuation mechanism is also exponentially suppressed at low temperature. For (ii), we find that the Mn spin dephasing time is limited by the thermal fluctuation of the nuclear spins to a few microseconds even at low temperature and its value varies from sample to sample, depending on the distribution of spinful isotopes on the nearest-neighbor sites surrounding the substitutional Mn atom. Our findings may be useful to understand and suppress the Mn spin pure dephasing for its applications in quantum information processing.

• Received 19 July 2016
• Revised 4 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075443