Observation of a four-spin solid effect

The two-spin solid effect (2SSE) is one of the established continuous wave dynamic nuclear polarization mechanisms that enables enhancement of nuclear magnetic resonance signals. It functions via a state-mixing mechanism that mediates the excitation of forbidden transitions in an electron–nuclear spin system. Specifically, microwave irradiation at frequencies ω(μw) ∼ ω(0S) ± ω(0I), where ω(0S) and ω(0I) are electron and nuclear Larmor frequencies, respectively, yields enhanced nuclear spin polarization. Following the recent rediscovery of the three-spin solid effect (3SSE) [Tan et al., Sci. Adv. 5, eaax2743 (2019)], where the matching condition is given by ω(μw) = ω(0S) ± 2ω(0I), we report here the first direct observation of the four-spin solid effect (4SSE) at ω(μw) = ω(0S) ± 3ω(0I). The forbidden double- and quadruple-quantum transitions were observed in samples containing trityl radicals dispersed in a glycerol–water mixture at 0.35 T/15 MHz/9.8 GHz and 80 K. We present a derivation of the 4SSE effective Hamiltonian, matching conditions, and transition probabilities. Finally, we show that the experimental observations agree with the results from numerical simulations and analytical theory.