Slow spin relaxation in single endohedral fullerene molecules

Well-protected magnetization, tunable quantum states, and long spin-relaxation time are desired for the use of magnetic molecules in spintronics and quantum information technologies. In this work, endohedral fullerene molecules $\mathrm{M}@{\mathrm{C}}_{28}$ with different transition-metal cores were explored through systematic first-principles calculations and spin dynamics analyses. Many of them have bias-tunable structure, stable magnetization, and sizable magnetic anisotropy energy. Furthermore, some of them may have spin-relaxation time up to several milliseconds for their quantum spin states at high temperature (\ensuremath{\sim}10 K) after full consideration of spin-vibration couplings. Our results suggest that these $\mathrm{M}@{\mathrm{C}}_{28}$ provide a rich pool of single-molecule magnets for diverse applications.