Role of spin-orbit fluctuations in spin decoherence*

We performed a systematic study of the decoherence mechanism in the molecular compound K$_6$[V$^{IV}_{15}$As$^{III}_6$O$_{42}$(D$_2$O)] $\cdot$ 8D$_2$O, in short V$_{15}$\footnote{M. Martens \textit{et. al.}, PRB \textbf{89}, 2014}, utilizing high-field electron spin resonance at 120 GHz, 241 GHz, and 336 GHz. This system has shown important quantum effects such as coherent spin oscillations\footnote{S. Bertaina \textit{et. al.}, Nature (London) \textbf{466}, 2010} as well as interesting out-of-equilibrium spin dynamics due to phonon bottlenecking\footnote{I. Chiorescu \textit{et. al.}, PRL \textbf{84}, 2000}. The spectra of a single V$_{15}$ crystal were measured and linewidths as a function of orientation, temperature, and field were extracted. By analyzing the shape and orientation anisotropy of the linewidths, we study how fluctuations in each term of the spin Hamiltonian contribute to the spin decoherence with much attention given to the spin-orbit coupling that generates $g$-factor anisotropy. Our conclusion is that fluctuations in the spin-orbit coupling can play an important role in the linewidth of a spin resonance.