Applications of Floquet–Magnus and Fer expansion approaches on rotary-resonance recoupling sequence in solid-state nuclear magnetic resonance

Abstract

In this work, we used the Floquet–Magnus expansion (FME) and the Fer expansion (FE) approaches to investigate the spin dynamics during the rotary-resonance recoupling (R3) radiation experiment in solid-state nuclear magnetic resonance (SSNMR). We reformulated the two approaches and calculated their respective effective Hamiltonians and propagators. We compared the two approaches and found that the FME is more appropriate to describe the spin dynamics in the R3 experiment compared to the FE. The equations governing the spin dynamics of the first three orders of the FME look similar to the equations of the FE. Nevertheless, the FME has two additional parameters making the approach more applicable to various situations. This clearly shows that the FME will be more practical for the modifications of the R3 pulse sequence with the major corrections coming from the terms that include the additional parameters, which are not available in the FE. This work is significant and contributes theoretically and numerically in the field of spin dynamics, magnetic resonance and in particular SSNMR.