Breakdown of linear response theory under low-power excitation in NMR. II. The case of “long-lived” signals in homogeneously broadened dipolar spin systems

Abstract

In this work, the previous linear response theory developed to describe low-power, radiofrequency (RF) excitation in inhomogeneously broadened spin systems [Z. Gong and J. D. Walls, J. Chem. Phys. 145, 164201 (2016)] is applied to the problem of low-power excitation in homogeneously broadened dipolar spin systems when the strength of the RF pulse, νRF, is much less than the homogeneous linewidth, Δν12. Application of a low-power pulse for a time Tp with a nominal flip-angle of Θ generates a broad signal with a “dip” at the RF transmitter frequency that deepens with increasing Θ. When a delay is placed before signal acquisition, only a negative, “long-lived” signal from the narrow “dip” remains. If a πX-pulse is applied after low-power excitation, a “long-lived” signal lasting a time t ≈ Tp after the πX-pulse is generated where dephasing due to B0 inhomogeneity, anisotropic bulk magnetic susceptibility, and chemical shift anisotropy is refocused while dephasing due to nonzero chemical shift differences is only partially refocused. Contrary to previous observations, experiments in powdered hexamethylbenzene demonstrate that these “long-lived” signals can exist even in the absence of nonzero chemical shift differences. Additional experimental demonstrations in powdered and single-crystalline adamantane and ferrocene samples are also presented.