Open Quantum System Theory of Muon Spin Relaxation in Materials

Abstract

We present a non-Markovian theory of muon spin relaxation that treats the implanted muon as an open quantum spin coupled to a temporally correlated local magnetic environment. Using a Schwinger-Keldysh influence-functional formulation, we derive a stochastic equation of motion for the muon spin, in which the fluctuation kernel is fixed by the local-field correlation tensor, while the retarded memory torque is introduced through an effective phenomenological backaction kernel. In the appropriate limits, the theory reduces to standard Kubo-Toyabe descriptions. This enables quantitative, global analysis of zero-field (ZF) and weak longitudinal-field (LF) $\mu$SR spectra beyond the strong-collision approximation. Applied to $\mathrm{Li}_{0.73}\mathrm{CoO}_2$, the model supports a decomposition into a quenched width and a Li-driven dynamical component within the adopted parametrization, and yields fluctuation rates approximately consistent with activated behavior over the intermediate-temperature window. The fitted memory parameter is most visible in the crossover between quasi-static and fast-fluctuation limits.