Simulation of resonant muon repolarisation in weakly coupled muonium states

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The density matrix method can be used to simulate the evolution of the muon spin polarisation as it interacts with other spins such as electrons or nuclei, which are initially unpolarised. Nuclear dipolar, quadrupolar and hyperfine interactions can be modelled, in addition to external magnetic fields. The polarisation P( t) can then be integrated or fitted in the same way as experimental data. We have extended this method to include periodic effects such as RF magnetic fields which can be of any strength. We have used this method to model electron spin resonance of the shallow donor muonium states found in ZnO and some other II–VI semiconductors, where the hyperfine coupling is at most A=0.5 MHz . The RF magnetic field is applied at the electron's Larmor frequency and, at low power, spin flips of the electron should cause depolarisation of the muon in longitudinal field and splitting of the transverse precession spectrum. For low power a sharp line is predicted, split by the hyperfine interaction with the muon. Hyperfine coupling with Zn nuclear spins broadens this resonance such that it is not observable. Application of high RF power ( γ e B 1> A) is predicted to decouple the electron from the muon leading to narrowing of the transverse precession spectrum and an increase of polarisation in longitudinal field. Both resonance effects have been observed experimentally.